Subgroups — C₁₃×#62846 #15749185

Order 3328.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3521	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3519	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3514	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3513	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3506	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3505	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3493	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3490	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3484	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3460	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3459	C₂	1	4	yes	maximal, complemented
14	C₁₃×#3455	C₂	1	2	yes	maximal, complemented
15	C₂×C₁₃×#538	C₂	1	4	yes	maximal, complemented
16	C₄×C₁₃×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
17	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#559	C₂²	1	8	yes	complemented
21	C₁₃×#556	C₂²	1	8	yes	complemented
22	C₁₃×#556	C₂²	1	4	yes	complemented
23	C₁₃×#555	C₂²	1	8	yes	complemented
24	C₁₃×#555	C₂²	1	4	yes	complemented
25	C₁₃×#554	C₂²	1	8	yes	complemented
26	C₁₃×#554	C₂²	1	4	yes	complemented
27	C₁₃×#553	C₂²	1	8	yes	complemented
28	C₁₃×#553	C₂²	1	16	yes	complemented
29	C₁₃×#553	C₂²	1	8	yes	complemented
30	C₁₃×#553	C₂²	1	8	yes	complemented
31	C₁₃×#552	C₂²	1	8	yes	complemented
32	C₁₃×#552	C₂²	1	8	yes	complemented
33	C₁₃×#551	C₂²	1	16	yes	complemented
34	C₁₃×#551	C₂²	1	16	yes	complemented
35	C₁₃×#551	C₂²	1	16	yes	complemented
36	C₁₃×#550	C₂²	1	4	yes	complemented
37	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
38	C₁₃×#548	C₂²	1	8	yes	complemented
39	C₁₃×#547	C₂²	1	4	yes	complemented
40	C₁₃×#547	C₂²	1	4	yes	complemented
41	C₁₃×#546	C₂²	1	8	yes	complemented
42	C₁₃×#546	C₂²	1	8	yes	complemented
43	C₁₃×#546	C₂²	1	16	yes	complemented
44	C₁₃×#546	C₂²	1	16	yes	complemented
45	C₁₃×#546	C₂²	1	8	yes	complemented
46	C₁₃×#546	C₂²	1	8	yes	complemented
47	D₄²×C₁₃	C₂²	1	8	yes	complemented
48	D₄²×C₁₃	C₂²	1	8	yes	complemented
49	D₄²×C₁₃	C₂²	1	4	yes	complemented
50	C₁₃×#544	C₂²	1	2	yes	complemented
51	C₁₃×#543	C₂²	1	4	yes	complemented
52	C₁₃×#542	C₂²	1	4	yes	complemented
53	C₁₃×#542	C₂²	1	4	yes	complemented
54	C₁₃×#542	C₂²	1	8	yes	complemented
55	C₁₃×#541	C₂²	1	4	yes	complemented
56	C₁₃×#540	C₂²	1	4	yes	complemented
57	C₁₃×#540	C₂²	1	8	yes	complemented
58	C₁₃×#539	C₂²	1	4	yes	complemented
59	C₁₃×#539	C₂²	1	4	yes	complemented
60	C₁₃×#539	C₂²	1	16	yes	complemented
61	C₁₃×#538	C₂²	1	4	yes	complemented
62	C₁₃×#538	C₂²	1	8	yes	complemented
63	C₁₃×#538	C₂²	1	4	yes	complemented
64	C₁₃×#538	C₂²	1	8	yes	complemented
65	C₁₃×#538	C₂²	1	8	yes	complemented
66	C₁₃×#538	C₂²	1	16	yes	complemented
67	C₁₃×#538	C₂²	1	16	yes	complemented
68	C₁₃×#538	C₂²	1	16	yes	complemented
69	C₁₃×#537	C₂²	1	2	yes	complemented
70	C₁₃×#535	C₂²	1	4	yes	complemented
71	C₁₃×#534	C₂²	1	8	yes	complemented
72	C₁₃×#534	C₂²	1	4	yes	complemented
73	C₁₃×#533	C₂²	1	2	yes	complemented
74	C₁₃×#532	C₂²	1	2	yes	complemented
75	C₁₃×#532	C₂²	1	8	yes	complemented
76	C₁₃×#529	C₂²	1	8	yes	complemented
77	C₁₃×#529	C₂²	1	8	yes	complemented
78	C₁₃×#529	C₂²	1	8	yes	complemented
79	C₁₃×#529	C₂²	1	16	yes	complemented
80	C₁₃×#529	C₂²	1	8	yes	complemented
81	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
82	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
83	C₁₃×#525	C₂²	1	4	yes	complemented
84	C₁₃×#525	C₂²	1	8	yes	complemented
85	C₁₃×#525	C₂²	1	8	yes	complemented
86	C₁₃×#525	C₂²	1	16	yes	complemented
87	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
88	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
89	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
90	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
91	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
92	C₁₃×#520	C₂²	1	4	yes	complemented
93	C₁₃×#520	C₂²	1	8	yes	complemented
94	C₁₃×#518	C₂²	1	2	yes	—
95	C₁₃×#518	C₂²	1	8	yes	complemented
96	C₁₃×#518	C₂²	1	8	yes	complemented
97	C₁₃×#518	C₂²	1	8	yes	complemented
98	C₁₃×#518	C₂²	1	8	yes	complemented
99	C₄×C₁₃×#41	C₂²	1	4	yes	complemented
100	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
101	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
102	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
103	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
104	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
106	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
108	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
109	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
111	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
112	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	C₂⁵×C₁₃	C₂³	1	2	yes	—
114	C₁₃×H(5,𝔽₂)	—	2	16	no	—
115	C₂×C₁₃×#41	C₂³	1	4	yes	—
116	C₂×C₁₃×#41	C₂³	1	8	yes	—
117	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
118	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
119	C₂²×Q₈×C₁₃	C₂³	1	4	yes	complemented
120	C₂²×D₄×C₁₃	—	2	8	no	—
121	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
124	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
126	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
127	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
128	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
130	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
137	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
139	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
140	C₁₃×#127	C₂³	1	8	yes	—
141	C₁₃×#127	C₂³	1	2	yes	complemented
142	C₁₃×#126	C₂³	1	8	yes	—
143	C₁₃×#126	C₂³	1	16	yes	—
144	C₁₃×#126	C₂³	1	8	yes	—
145	C₁₃×#126	C₂³	1	16	yes	complemented
146	C₁₃×#126	C₂³	1	16	yes	complemented
147	C₁₃×#126	C₂³	1	8	yes	complemented
148	C₁₃×#126	C₂³	1	16	yes	complemented
149	C₁₃×#126	C₂³	1	8	yes	complemented
150	C₁₃×#125	C₂³	1	8	yes	complemented
151	C₁₃×#125	C₂³	1	8	yes	complemented
152	C₁₃×#125	C₂³	1	8	yes	complemented
153	C₁₃×#125	C₂³	1	8	yes	complemented
154	C₁₃×#125	C₂³	1	4	yes	complemented
155	C₁₃×#124	C₂³	1	8	yes	—
156	C₁₃×#124	C₂³	1	16	yes	—
157	C₁₃×#124	C₂³	1	8	yes	—
158	C₁₃×#124	C₂³	1	8	yes	—
159	C₁₃×#124	C₂³	1	16	yes	complemented
160	C₁₃×#124	C₂³	1	16	yes	complemented
161	C₁₃×#124	C₂³	1	8	yes	complemented
162	C₁₃×#124	C₂³	1	4	yes	complemented
163	C₁₃×#123	C₂³	1	8	yes	—
164	C₁₃×#123	C₂³	1	16	yes	—
165	C₁₃×#123	C₂³	1	8	yes	—
166	C₁₃×#123	C₂³	1	16	yes	—
167	C₁₃×#123	C₂³	1	8	yes	—
168	C₁₃×#123	C₂³	1	16	yes	complemented
169	C₁₃×#123	C₂³	1	16	yes	complemented
170	C₁₃×#123	C₂³	1	8	yes	complemented
171	C₁₃×#123	C₂³	1	16	yes	complemented
172	C₁₃×#123	C₂³	1	16	yes	complemented
173	C₁₃×#123	C₂³	1	16	yes	complemented
174	C₁₃×#123	C₂³	1	8	yes	complemented
175	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
181	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
182	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
183	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
184	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
185	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
186	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
187	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
188	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
189	C₁₃×#121	C₂³	1	8	yes	—
190	C₁₃×#121	C₂³	1	4	yes	—
191	C₁₃×#121	C₂³	1	8	yes	—
192	C₁₃×#121	C₂³	1	16	yes	—
193	C₁₃×#121	C₂³	1	4	yes	—
194	C₁₃×#121	C₂³	1	16	yes	—
195	C₁₃×#121	C₂³	1	4	yes	—
196	C₁₃×#121	C₂³	1	4	yes	—
197	C₁₃×#121	C₂³	1	16	yes	—
198	C₁₃×#121	C₂³	1	8	yes	—
199	C₁₃×#121	C₂³	1	8	yes	—
200	C₁₃×#121	C₂³	1	8	yes	—
201	C₁₃×#121	C₂³	1	16	yes	complemented
202	C₁₃×#121	C₂³	1	8	yes	complemented
203	C₁₃×#121	C₂³	1	8	yes	complemented
204	C₁₃×#121	C₂³	1	16	yes	complemented
205	C₁₃×#121	C₂³	1	8	yes	complemented
206	C₁₃×#121	C₂³	1	8	yes	complemented
207	C₁₃×#121	C₂³	1	8	yes	complemented
208	C₁₃×#120	C₂³	1	8	yes	—
209	C₁₃×#120	C₂³	1	16	yes	—
210	C₁₃×#120	C₂³	1	16	yes	—
211	C₁₃×#120	C₂³	1	16	yes	—
212	C₁₃×#120	C₂³	1	16	yes	—
213	C₁₃×#120	C₂³	1	16	yes	complemented
214	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
215	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
216	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
217	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
218	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
219	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
220	C₄×D₄×C₁₃	C₂³	1	8	yes	—
221	C₄×D₄×C₁₃	C₂³	1	4	yes	—
222	C₄×D₄×C₁₃	C₂³	1	4	yes	—
223	C₄×D₄×C₁₃	C₂³	1	8	yes	—
224	C₄×D₄×C₁₃	C₂³	1	8	yes	—
225	C₄×D₄×C₁₃	C₂³	1	16	yes	—
226	C₄×D₄×C₁₃	C₂³	1	8	yes	—
227	C₄×D₄×C₁₃	C₂³	1	8	yes	—
228	C₄×D₄×C₁₃	C₂³	1	4	yes	—
229	C₄×D₄×C₁₃	C₂³	1	8	yes	—
230	C₄×D₄×C₁₃	C₂³	1	4	yes	—
231	C₄×D₄×C₁₃	C₂³	1	16	yes	—
232	C₄×D₄×C₁₃	C₂³	1	8	yes	—
233	C₄×D₄×C₁₃	C₂³	1	8	yes	—
234	C₄×D₄×C₁₃	C₂³	1	8	yes	—
235	C₄×D₄×C₁₃	C₂³	1	8	yes	—
236	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
237	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
238	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
239	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
240	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
241	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
242	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
243	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
244	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
245	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
246	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
247	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
248	C₁₃×#117	C₂³	1	4	yes	—
249	C₁₃×#117	C₂³	1	4	yes	—
250	C₁₃×#117	C₂³	1	8	yes	—
251	C₁₃×#117	C₂³	1	4	yes	—
252	C₁₃×#117	C₂³	1	8	yes	complemented
253	C₁₃×#117	C₂³	1	16	yes	complemented
254	C₁₃×#117	C₂³	1	8	yes	complemented
255	C₁₃×#117	C₂³	1	8	yes	complemented
256	C₁₃×#117	C₂³	1	8	yes	complemented
257	C₁₃×#117	C₂³	1	16	yes	complemented
258	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
264	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
265	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
266	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
267	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
269	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
271	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
272	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
273	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
274	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
275	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
276	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
277	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
278	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
279	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
280	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
281	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
282	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
283	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
284	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
285	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
286	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
287	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
288	#62846	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂⁴×C₁₃	—	2	8	no	—
290	C₂⁴×C₁₃	—	8	2	no	—
291	C₂⁴×C₁₃	—	8	2	no	—
292	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
293	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
295	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
296	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
297	C₁₃×#41	—	2	32	no	—
298	C₁₃×#41	—	2	16	no	—
299	C₁₃×#41	—	8	8	no	—
300	C₁₃×#41	—	8	8	no	—
301	C₂×Q₈×C₁₃	—	8	4	no	—
302	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
303	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
304	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
305	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
306	C₂×D₄×C₁₃	—	2	8	no	—
307	C₂×D₄×C₁₃	—	2	32	no	—
308	C₂×D₄×C₁₃	—	2	32	no	—
309	C₂×D₄×C₁₃	—	2	32	no	—
310	C₂×D₄×C₁₃	—	2	4	no	—
311	C₂×D₄×C₁₃	—	8	8	no	—
312	C₂×D₄×C₁₃	—	8	8	no	—
313	C₂×D₄×C₁₃	—	8	4	no	—
314	C₂×D₄×C₁₃	#41	1	8	yes	complemented
315	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
316	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
317	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
318	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
319	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
320	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
321	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
322	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
323	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
324	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
325	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
326	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
327	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
328	C₂²×C₄×C₁₃	—	2	4	no	—
329	C₂²×C₄×C₁₃	—	8	2	no	—
330	C₂²×C₄×C₁₃	—	8	2	no	—
331	C₂²×C₄×C₁₃	—	8	2	no	—
332	C₂²×C₄×C₁₃	—	8	2	no	—
333	C₂²×C₄×C₁₃	—	8	8	no	—
334	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
336	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
337	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
338	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
346	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
347	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
348	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
349	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
350	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
351	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
352	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
353	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
354	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
356	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
357	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
358	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
359	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
360	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
362	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
366	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
369	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
370	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
371	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
372	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
373	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
374	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
375	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
376	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
377	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
378	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
379	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
380	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
381	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
382	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
383	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
384	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
385	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
386	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
387	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
388	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
389	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
390	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
391	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
392	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
393	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
394	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
395	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
396	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
397	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
398	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
399	C₄²×C₁₃	C₂⁴	1	4	yes	—
400	C₄²×C₁₃	C₂⁴	1	8	yes	—
401	C₄²×C₁₃	C₂⁴	1	2	yes	—
402	C₄²×C₁₃	C₂⁴	1	2	yes	—
403	C₄²×C₁₃	C₂⁴	1	8	yes	—
404	C₄²×C₁₃	C₂⁴	1	8	yes	—
405	C₄²×C₁₃	C₂⁴	1	8	yes	—
406	C₄²×C₁₃	C₂⁴	1	16	yes	—
407	#3521	C₂×C₁₃	1	8	yes	complemented
408	#3519	C₂×C₁₃	1	8	yes	complemented
409	#3514	C₂×C₁₃	1	8	yes	complemented
410	#3513	C₂×C₁₃	1	8	yes	complemented
411	#3506	C₂×C₁₃	1	2	yes	complemented
412	#3505	C₂×C₁₃	1	4	yes	complemented
413	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
414	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
415	#3493	C₂×C₁₃	1	2	yes	complemented
416	#3490	C₂×C₁₃	1	4	yes	complemented
417	#3484	C₂×C₁₃	1	2	yes	complemented
418	#3460	C₂×C₁₃	1	2	yes	complemented
419	#3459	C₂×C₁₃	1	4	yes	complemented
420	#3455	C₂×C₁₃	1	2	yes	complemented
421	C₂×#538	C₂×C₁₃	1	4	yes	complemented
422	C₄×H(5,𝔽₂)	C₂×C₁₃	1	2	yes	complemented
423	C₂×#518	C₂×C₁₃	1	1	yes	characteristic, complemented
424	C₂³×C₁₃	—	2	2	no	—
425	C₂³×C₁₃	—	2	4	no	—
426	C₂³×C₁₃	—	2	16	no	—
427	C₂³×C₁₃	—	2	16	no	—
428	C₂³×C₁₃	—	4	2	no	—
429	C₂³×C₁₃	—	4	2	no	—
430	C₂³×C₁₃	—	4	2	no	—
431	C₂³×C₁₃	—	4	2	no	—
432	C₂³×C₁₃	—	4	1	no	—
433	C₂³×C₁₃	—	4	1	no	—
434	C₂³×C₁₃	—	4	8	no	—
435	C₂³×C₁₃	—	4	8	no	—
436	C₂³×C₁₃	—	4	8	no	—
437	C₂³×C₁₃	—	4	8	no	—
438	C₂³×C₁₃	—	8	16	no	—
439	C₂³×C₁₃	C₂×#41	1	8	yes	—
440	C₂³×C₁₃	C₂⁵	1	2	yes	—
441	C₂³×C₁₃	C₂⁵	1	4	yes	—
442	C₂³×C₁₃	C₂⁵	1	8	yes	—
443	C₂³×C₁₃	C₂⁵	1	4	yes	—
444	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
445	Q₈×C₁₃	—	2	8	no	—
446	Q₈×C₁₃	—	4	4	no	—
447	Q₈×C₁₃	—	4	8	no	—
448	Q₈×C₁₃	—	4	4	no	—
449	D₄×C₁₃	—	2	16	no	—
450	D₄×C₁₃	—	2	32	no	—
451	D₄×C₁₃	—	2	16	no	—
452	D₄×C₁₃	—	2	8	no	—
453	D₄×C₁₃	—	2	8	no	—
454	D₄×C₁₃	—	4	4	no	—
455	D₄×C₁₃	—	4	8	no	—
456	D₄×C₁₃	—	4	8	no	—
457	D₄×C₁₃	—	4	16	no	—
458	D₄×C₁₃	—	4	8	no	—
459	D₄×C₁₃	—	4	16	no	—
460	D₄×C₁₃	—	4	4	no	—
461	D₄×C₁₃	C₂×#41	1	16	yes	—
462	C₂×C₄×C₁₃	—	2	2	no	—
463	C₂×C₄×C₁₃	—	2	16	no	—
464	C₂×C₄×C₁₃	—	2	8	no	—
465	C₂×C₄×C₁₃	—	2	16	no	—
466	C₂×C₄×C₁₃	—	4	1	no	—
467	C₂×C₄×C₁₃	—	4	2	no	—
468	C₂×C₄×C₁₃	—	4	1	no	—
469	C₂×C₄×C₁₃	—	4	8	no	—
470	C₂×C₄×C₁₃	—	4	8	no	—
471	C₂×C₄×C₁₃	—	4	1	no	—
472	C₂×C₄×C₁₃	—	4	2	no	—
473	C₂×C₄×C₁₃	—	4	1	no	—
474	C₂×C₄×C₁₃	—	4	4	no	—
475	C₂×C₄×C₁₃	—	4	8	no	—
476	C₂×C₄×C₁₃	—	4	4	no	—
477	C₂×C₄×C₁₃	—	4	16	no	—
478	C₂×C₄×C₁₃	—	4	8	no	—
479	C₂×C₄×C₁₃	—	4	8	no	—
480	C₂×C₄×C₁₃	—	4	8	no	—
481	C₂×C₄×C₁₃	—	4	8	no	—
482	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
483	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
484	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
485	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
486	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
487	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
488	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
489	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
490	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
491	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
492	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
493	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
494	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
495	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
496	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
497	#559	C₂²×C₁₃	1	8	yes	complemented
498	#556	C₂²×C₁₃	1	8	yes	complemented
499	#556	C₂²×C₁₃	1	4	yes	complemented
500	#555	C₂²×C₁₃	1	8	yes	complemented
501	#555	C₂²×C₁₃	1	4	yes	complemented
502	#554	C₂²×C₁₃	1	4	yes	complemented
503	#554	C₂²×C₁₃	1	8	yes	complemented
504	#553	C₂²×C₁₃	1	8	yes	complemented
505	#553	C₂²×C₁₃	1	8	yes	complemented
506	#553	C₂²×C₁₃	1	16	yes	complemented
507	#553	C₂²×C₁₃	1	8	yes	complemented
508	#552	C₂²×C₁₃	1	8	yes	complemented
509	#552	C₂²×C₁₃	1	8	yes	complemented
510	#551	C₂²×C₁₃	1	16	yes	complemented
511	#551	C₂²×C₁₃	1	16	yes	complemented
512	#551	C₂²×C₁₃	1	16	yes	complemented
513	#550	C₂²×C₁₃	1	4	yes	complemented
514	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
515	#548	C₂²×C₁₃	1	8	yes	complemented
516	#547	C₂²×C₁₃	1	4	yes	complemented
517	#547	C₂²×C₁₃	1	4	yes	complemented
518	#546	C₂²×C₁₃	1	8	yes	complemented
519	#546	C₂²×C₁₃	1	8	yes	complemented
520	#546	C₂²×C₁₃	1	16	yes	complemented
521	#546	C₂²×C₁₃	1	16	yes	complemented
522	#546	C₂²×C₁₃	1	8	yes	complemented
523	#546	C₂²×C₁₃	1	8	yes	complemented
524	D₄²	C₂²×C₁₃	1	8	yes	complemented
525	D₄²	C₂²×C₁₃	1	8	yes	complemented
526	D₄²	C₂²×C₁₃	1	4	yes	complemented
527	#544	C₂²×C₁₃	1	2	yes	complemented
528	#543	C₂²×C₁₃	1	4	yes	complemented
529	#542	C₂²×C₁₃	1	4	yes	complemented
530	#542	C₂²×C₁₃	1	4	yes	complemented
531	#542	C₂²×C₁₃	1	8	yes	complemented
532	#541	C₂²×C₁₃	1	4	yes	complemented
533	#540	C₂²×C₁₃	1	4	yes	complemented
534	#540	C₂²×C₁₃	1	8	yes	complemented
535	#539	C₂²×C₁₃	1	4	yes	complemented
536	#539	C₂²×C₁₃	1	4	yes	complemented
537	#539	C₂²×C₁₃	1	16	yes	complemented
538	#538	C₂²×C₁₃	1	4	yes	complemented
539	#538	C₂²×C₁₃	1	8	yes	complemented
540	#538	C₂²×C₁₃	1	4	yes	complemented
541	#538	C₂²×C₁₃	1	8	yes	complemented
542	#538	C₂²×C₁₃	1	8	yes	complemented
543	#538	C₂²×C₁₃	1	16	yes	complemented
544	#538	C₂²×C₁₃	1	16	yes	complemented
545	#538	C₂²×C₁₃	1	16	yes	complemented
546	#537	C₂²×C₁₃	1	2	yes	complemented
547	#535	C₂²×C₁₃	1	4	yes	complemented
548	#534	C₂²×C₁₃	1	8	yes	complemented
549	#534	C₂²×C₁₃	1	4	yes	complemented
550	#533	C₂²×C₁₃	1	2	yes	complemented
551	#532	C₂²×C₁₃	1	2	yes	complemented
552	#532	C₂²×C₁₃	1	8	yes	complemented
553	#529	C₂²×C₁₃	1	8	yes	complemented
554	#529	C₂²×C₁₃	1	8	yes	complemented
555	#529	C₂²×C₁₃	1	8	yes	complemented
556	#529	C₂²×C₁₃	1	16	yes	complemented
557	#529	C₂²×C₁₃	1	8	yes	complemented
558	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
559	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
560	#525	C₂²×C₁₃	1	4	yes	complemented
561	#525	C₂²×C₁₃	1	8	yes	complemented
562	#525	C₂²×C₁₃	1	8	yes	complemented
563	#525	C₂²×C₁₃	1	16	yes	complemented
564	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
565	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
566	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
567	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
568	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
569	#520	C₂²×C₁₃	1	4	yes	complemented
570	#520	C₂²×C₁₃	1	8	yes	complemented
571	#518	C₂²×C₁₃	1	2	yes	—
572	#518	C₂²×C₁₃	1	8	yes	complemented
573	#518	C₂²×C₁₃	1	8	yes	complemented
574	#518	C₂²×C₁₃	1	8	yes	complemented
575	#518	C₂²×C₁₃	1	8	yes	complemented
576	C₄×#41	C₂²×C₁₃	1	4	yes	complemented
577	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
578	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
579	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
580	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
581	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
582	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
583	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
584	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
585	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
586	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
587	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
588	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
589	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
590	C₂²×C₁₃	—	2	1	no	—
591	C₂²×C₁₃	—	2	1	no	—
592	C₂²×C₁₃	—	2	4	no	—
593	C₂²×C₁₃	—	2	4	no	—
594	C₂²×C₁₃	—	2	2	no	—
595	C₂²×C₁₃	—	2	8	no	—
596	C₂²×C₁₃	—	2	4	no	—
597	C₂²×C₁₃	—	2	8	no	—
598	C₂²×C₁₃	—	2	4	no	—
599	C₂²×C₁₃	—	2	4	no	—
600	C₂²×C₁₃	—	2	8	no	—
601	C₂²×C₁₃	—	2	2	no	—
602	C₂²×C₁₃	—	2	2	no	—
603	C₂²×C₁₃	—	4	8	no	—
604	C₂²×C₁₃	—	4	8	no	—
605	C₂²×C₁₃	—	4	4	no	—
606	C₂²×C₁₃	—	8	16	no	—
607	C₂²×C₁₃	—	8	16	no	—
608	C₂²×C₁₃	C₂²×#41	1	8	yes	—
609	C₂²×C₁₃	C₂²×#41	1	2	yes	—
610	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
611	C₄×C₁₃	—	2	2	no	—
612	C₄×C₁₃	—	2	8	no	—
613	C₄×C₁₃	—	2	2	no	—
614	C₄×C₁₃	—	2	4	no	—
615	C₄×C₁₃	—	2	2	no	—
616	C₄×C₁₃	—	2	1	no	—
617	C₄×C₁₃	—	2	8	no	—
618	C₄×C₁₃	—	2	4	no	—
619	C₄×C₁₃	—	2	2	no	—
620	C₄×C₁₃	—	2	1	no	—
621	C₄×C₁₃	—	2	8	no	—
622	C₄×C₁₃	C₂²×#41	1	4	yes	—
623	C₂⁵	C₂³×C₁₃	1	2	yes	—
624	H(5,𝔽₂)	—	2	16	no	—
625	C₂×#41	C₂³×C₁₃	1	4	yes	—
626	C₂×#41	C₂³×C₁₃	1	8	yes	—
627	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
628	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
629	C₂²×Q₈	C₂³×C₁₃	1	4	yes	complemented
630	C₂²×D₄	—	2	8	no	—
631	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
632	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
633	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
634	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
635	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
636	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
637	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
638	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
639	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
640	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
641	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
642	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
643	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
644	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
645	C₂³×C₄	C₂³×C₁₃	1	8	yes	complemented
646	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
647	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
648	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
649	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
650	#127	C₂³×C₁₃	1	8	yes	—
651	#127	C₂³×C₁₃	1	2	yes	complemented
652	#126	C₂³×C₁₃	1	8	yes	—
653	#126	C₂³×C₁₃	1	16	yes	—
654	#126	C₂³×C₁₃	1	8	yes	—
655	#126	C₂³×C₁₃	1	16	yes	complemented
656	#126	C₂³×C₁₃	1	16	yes	complemented
657	#126	C₂³×C₁₃	1	8	yes	complemented
658	#126	C₂³×C₁₃	1	16	yes	complemented
659	#126	C₂³×C₁₃	1	8	yes	complemented
660	#125	C₂³×C₁₃	1	8	yes	complemented
661	#125	C₂³×C₁₃	1	8	yes	complemented
662	#125	C₂³×C₁₃	1	8	yes	complemented
663	#125	C₂³×C₁₃	1	8	yes	complemented
664	#125	C₂³×C₁₃	1	4	yes	complemented
665	#124	C₂³×C₁₃	1	8	yes	—
666	#124	C₂³×C₁₃	1	16	yes	—
667	#124	C₂³×C₁₃	1	8	yes	—
668	#124	C₂³×C₁₃	1	8	yes	—
669	#124	C₂³×C₁₃	1	16	yes	complemented
670	#124	C₂³×C₁₃	1	16	yes	complemented
671	#124	C₂³×C₁₃	1	8	yes	complemented
672	#124	C₂³×C₁₃	1	4	yes	complemented
673	#123	C₂³×C₁₃	1	8	yes	—
674	#123	C₂³×C₁₃	1	16	yes	—
675	#123	C₂³×C₁₃	1	8	yes	—
676	#123	C₂³×C₁₃	1	16	yes	—
677	#123	C₂³×C₁₃	1	8	yes	—
678	#123	C₂³×C₁₃	1	16	yes	complemented
679	#123	C₂³×C₁₃	1	16	yes	complemented
680	#123	C₂³×C₁₃	1	8	yes	complemented
681	#123	C₂³×C₁₃	1	16	yes	complemented
682	#123	C₂³×C₁₃	1	16	yes	complemented
683	#123	C₂³×C₁₃	1	16	yes	complemented
684	#123	C₂³×C₁₃	1	8	yes	complemented
685	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
686	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
687	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
688	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
689	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
690	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
691	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
692	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
693	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
694	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
695	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
696	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
697	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
698	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
699	#121	C₂³×C₁₃	1	8	yes	—
700	#121	C₂³×C₁₃	1	4	yes	—
701	#121	C₂³×C₁₃	1	8	yes	—
702	#121	C₂³×C₁₃	1	16	yes	—
703	#121	C₂³×C₁₃	1	4	yes	—
704	#121	C₂³×C₁₃	1	16	yes	—
705	#121	C₂³×C₁₃	1	4	yes	—
706	#121	C₂³×C₁₃	1	4	yes	—
707	#121	C₂³×C₁₃	1	16	yes	—
708	#121	C₂³×C₁₃	1	8	yes	—
709	#121	C₂³×C₁₃	1	8	yes	—
710	#121	C₂³×C₁₃	1	8	yes	—
711	#121	C₂³×C₁₃	1	16	yes	complemented
712	#121	C₂³×C₁₃	1	8	yes	complemented
713	#121	C₂³×C₁₃	1	8	yes	complemented
714	#121	C₂³×C₁₃	1	16	yes	complemented
715	#121	C₂³×C₁₃	1	8	yes	complemented
716	#121	C₂³×C₁₃	1	8	yes	complemented
717	#121	C₂³×C₁₃	1	8	yes	complemented
718	#120	C₂³×C₁₃	1	8	yes	—
719	#120	C₂³×C₁₃	1	16	yes	—
720	#120	C₂³×C₁₃	1	16	yes	—
721	#120	C₂³×C₁₃	1	16	yes	—
722	#120	C₂³×C₁₃	1	16	yes	—
723	#120	C₂³×C₁₃	1	16	yes	complemented
724	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
725	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
726	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
727	C₄×Q₈	C₂³×C₁₃	1	8	yes	complemented
728	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
729	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
730	C₄×D₄	C₂³×C₁₃	1	8	yes	—
731	C₄×D₄	C₂³×C₁₃	1	4	yes	—
732	C₄×D₄	C₂³×C₁₃	1	4	yes	—
733	C₄×D₄	C₂³×C₁₃	1	8	yes	—
734	C₄×D₄	C₂³×C₁₃	1	8	yes	—
735	C₄×D₄	C₂³×C₁₃	1	16	yes	—
736	C₄×D₄	C₂³×C₁₃	1	8	yes	—
737	C₄×D₄	C₂³×C₁₃	1	8	yes	—
738	C₄×D₄	C₂³×C₁₃	1	4	yes	—
739	C₄×D₄	C₂³×C₁₃	1	8	yes	—
740	C₄×D₄	C₂³×C₁₃	1	4	yes	—
741	C₄×D₄	C₂³×C₁₃	1	16	yes	—
742	C₄×D₄	C₂³×C₁₃	1	8	yes	—
743	C₄×D₄	C₂³×C₁₃	1	8	yes	—
744	C₄×D₄	C₂³×C₁₃	1	8	yes	—
745	C₄×D₄	C₂³×C₁₃	1	8	yes	—
746	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
747	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
748	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
749	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
750	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
751	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
752	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
753	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
754	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
755	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
756	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
757	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
758	#117	C₂³×C₁₃	1	4	yes	—
759	#117	C₂³×C₁₃	1	4	yes	—
760	#117	C₂³×C₁₃	1	8	yes	—
761	#117	C₂³×C₁₃	1	4	yes	—
762	#117	C₂³×C₁₃	1	8	yes	complemented
763	#117	C₂³×C₁₃	1	16	yes	complemented
764	#117	C₂³×C₁₃	1	8	yes	complemented
765	#117	C₂³×C₁₃	1	8	yes	complemented
766	#117	C₂³×C₁₃	1	8	yes	complemented
767	#117	C₂³×C₁₃	1	16	yes	complemented
768	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
769	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
770	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
771	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
772	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
773	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
774	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
775	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
776	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
777	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
778	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
779	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
780	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
781	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
782	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
783	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
784	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
785	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
791	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
792	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
793	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
794	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
795	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
796	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
797	C₂×C₄²	C₂³×C₁₃	1	8	yes	complemented
798	C₂×C₁₃	—	2	2	no	—
799	C₂×C₁₃	—	2	8	no	—
800	C₂×C₁₃	—	4	4	no	—
801	C₂×C₁₃	—	4	2	no	—
802	C₂×C₁₃	—	4	8	no	—
803	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
804	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
805	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
806	C₂⁴	—	2	8	no	—
807	C₂⁴	—	8	2	no	—
808	C₂⁴	—	8	2	no	—
809	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
810	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
812	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
813	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
814	#41	—	2	32	no	—
815	#41	—	2	16	no	—
816	#41	—	8	8	no	—
817	#41	—	8	8	no	—
818	C₂×Q₈	—	8	4	no	—
819	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
820	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
821	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
822	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
823	C₂×D₄	—	2	8	no	—
824	C₂×D₄	—	2	32	no	—
825	C₂×D₄	—	2	32	no	—
826	C₂×D₄	—	2	32	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	8	8	no	—
829	C₂×D₄	—	8	8	no	—
830	C₂×D₄	—	8	4	no	—
831	C₂×D₄	C₁₃×#41	1	8	yes	complemented
832	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
833	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
834	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
835	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
836	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
837	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
838	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
839	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
840	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
841	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
842	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
843	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
844	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
845	C₂²×C₄	—	2	4	no	—
846	C₂²×C₄	—	8	2	no	—
847	C₂²×C₄	—	8	2	no	—
848	C₂²×C₄	—	8	2	no	—
849	C₂²×C₄	—	8	2	no	—
850	C₂²×C₄	—	8	8	no	—
851	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
853	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
854	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
855	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
862	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
863	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
864	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
865	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
866	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
867	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
868	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
869	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
870	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
871	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
872	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
873	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
874	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
876	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
877	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
878	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
879	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
880	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
881	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
882	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
883	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
884	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
885	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
886	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
887	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
888	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
889	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
890	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
891	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
892	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
893	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
894	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
895	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
896	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
897	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
898	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
899	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
900	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
901	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
902	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
903	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
904	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
905	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
906	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
907	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
908	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
909	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
910	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
911	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
912	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
913	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
914	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
915	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
916	C₄²	C₂⁴×C₁₃	1	4	yes	—
917	C₄²	C₂⁴×C₁₃	1	8	yes	—
918	C₄²	C₂⁴×C₁₃	1	2	yes	—
919	C₄²	C₂⁴×C₁₃	1	2	yes	—
920	C₄²	C₂⁴×C₁₃	1	8	yes	—
921	C₄²	C₂⁴×C₁₃	1	8	yes	—
922	C₄²	C₂⁴×C₁₃	1	8	yes	—
923	C₄²	C₂⁴×C₁₃	1	16	yes	—
924	C₁₃	#62846	1	1	yes	characteristic, direct product factor, Sylow
925	C₂³	—	2	2	no	—
926	C₂³	—	2	4	no	—
927	C₂³	—	2	16	no	—
928	C₂³	—	2	16	no	—
929	C₂³	—	4	2	no	—
930	C₂³	—	4	2	no	—
931	C₂³	—	4	2	no	—
932	C₂³	—	4	2	no	—
933	C₂³	—	4	1	no	—
934	C₂³	—	4	1	no	—
935	C₂³	—	4	8	no	—
936	C₂³	—	4	8	no	—
937	C₂³	—	4	8	no	—
938	C₂³	—	4	8	no	—
939	C₂³	—	8	16	no	—
940	C₂³	C₂×C₁₃×#41	1	8	yes	—
941	C₂³	C₂⁵×C₁₃	1	2	yes	—
942	C₂³	C₂⁵×C₁₃	1	4	yes	—
943	C₂³	C₂⁵×C₁₃	1	8	yes	—
944	C₂³	C₂⁵×C₁₃	1	4	yes	—
945	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
946	Q₈	—	2	8	no	—
947	Q₈	—	4	4	no	—
948	Q₈	—	4	8	no	—
949	Q₈	—	4	4	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	32	no	—
952	D₄	—	2	16	no	—
953	D₄	—	2	8	no	—
954	D₄	—	2	8	no	—
955	D₄	—	4	4	no	—
956	D₄	—	4	8	no	—
957	D₄	—	4	8	no	—
958	D₄	—	4	16	no	—
959	D₄	—	4	8	no	—
960	D₄	—	4	16	no	—
961	D₄	—	4	4	no	—
962	D₄	C₂×C₁₃×#41	1	16	yes	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	16	no	—
965	C₂×C₄	—	2	8	no	—
966	C₂×C₄	—	2	16	no	—
967	C₂×C₄	—	4	1	no	—
968	C₂×C₄	—	4	2	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	8	no	—
971	C₂×C₄	—	4	8	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	2	no	—
974	C₂×C₄	—	4	1	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	8	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	4	16	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	4	8	no	—
981	C₂×C₄	—	4	8	no	—
982	C₂×C₄	—	4	8	no	—
983	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
984	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
985	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
986	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
987	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
988	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
989	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
990	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
991	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
992	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
993	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
994	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
995	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	8	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	8	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	4	no	—
1006	C₂²	—	2	8	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	4	8	no	—
1010	C₂²	—	4	8	no	—
1011	C₂²	—	4	4	no	—
1012	C₂²	—	8	16	no	—
1013	C₂²	—	8	16	no	—
1014	C₂²	C₂²×C₁₃×#41	1	8	yes	—
1015	C₂²	C₂²×C₁₃×#41	1	2	yes	—
1016	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	8	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	2	4	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	1	no	—
1023	C₄	—	2	8	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	1	no	—
1027	C₄	—	2	8	no	—
1028	C₄	C₂²×C₁₃×#41	1	4	yes	—
1029	C₂	—	2	2	no	—
1030	C₂	—	2	8	no	—
1031	C₂	—	4	2	no	—
1032	C₂	—	4	4	no	—
1033	C₂	—	4	8	no	—
1034	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
1035	C₂	C₁₃×H(7,𝔽₂)	1	1	yes	characteristic
1036	C₂	C₁₃×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3521	C₂	semidirect
2. C₁₃×#3519	C₂	semidirect
3. C₁₃×#3514	C₂	semidirect
4. C₁₃×#3513	C₂	semidirect
5. C₁₃×#3506	C₂	semidirect
6. C₁₃×#3505	C₂	semidirect
7. C₁₃×#3501	C₂	semidirect
8. C₁₃×#3496	C₂	semidirect
9. C₁₃×#3493	C₂	semidirect
10. C₁₃×#3490	C₂	semidirect
11. C₁₃×#3484	C₂	semidirect
12. C₁₃×#3460	C₂	semidirect
13. C₁₃×#3459	C₂	semidirect
14. C₁₃×#3455	C₂	semidirect
15. C₂×C₁₃×#538	C₂	semidirect
16. C₄×C₁₃×H(5,𝔽₂)	C₂	semidirect
17. C₂×C₁₃×#518	C₂	semidirect
20. C₁₃×#559	C₂²	semidirect
21. C₁₃×#556	C₂²	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#555	C₂²	semidirect
24. C₁₃×#555	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
26. C₁₃×#554	C₂²	semidirect
27. C₁₃×#553	C₂²	semidirect
28. C₁₃×#553	C₂²	semidirect
29. C₁₃×#553	C₂²	semidirect
30. C₁₃×#553	C₂²	semidirect
31. C₁₃×#552	C₂²	semidirect
32. C₁₃×#552	C₂²	semidirect
33. C₁₃×#551	C₂²	semidirect
34. C₁₃×#551	C₂²	semidirect
35. C₁₃×#551	C₂²	semidirect
36. C₁₃×#550	C₂²	semidirect
37. D₄×Q₈×C₁₃	C₂²	semidirect
38. C₁₃×#548	C₂²	semidirect
39. C₁₃×#547	C₂²	semidirect
40. C₁₃×#547	C₂²	semidirect
41. C₁₃×#546	C₂²	semidirect
42. C₁₃×#546	C₂²	semidirect
43. C₁₃×#546	C₂²	semidirect
44. C₁₃×#546	C₂²	semidirect
45. C₁₃×#546	C₂²	semidirect
46. C₁₃×#546	C₂²	semidirect
47. D₄²×C₁₃	C₂²	semidirect
48. D₄²×C₁₃	C₂²	semidirect
49. D₄²×C₁₃	C₂²	semidirect
50. C₁₃×#544	C₂²	semidirect
51. C₁₃×#543	C₂²	semidirect
52. C₁₃×#542	C₂²	semidirect
53. C₁₃×#542	C₂²	semidirect
54. C₁₃×#542	C₂²	semidirect
55. C₁₃×#541	C₂²	semidirect
56. C₁₃×#540	C₂²	semidirect
57. C₁₃×#540	C₂²	semidirect
58. C₁₃×#539	C₂²	semidirect
59. C₁₃×#539	C₂²	semidirect
60. C₁₃×#539	C₂²	semidirect
61. C₁₃×#538	C₂²	semidirect
62. C₁₃×#538	C₂²	semidirect
63. C₁₃×#538	C₂²	semidirect
64. C₁₃×#538	C₂²	semidirect
65. C₁₃×#538	C₂²	semidirect
66. C₁₃×#538	C₂²	semidirect
67. C₁₃×#538	C₂²	semidirect
68. C₁₃×#538	C₂²	semidirect
69. C₁₃×#537	C₂²	semidirect
70. C₁₃×#535	C₂²	semidirect
71. C₁₃×#534	C₂²	semidirect
72. C₁₃×#534	C₂²	semidirect
73. C₁₃×#533	C₂²	semidirect
74. C₁₃×#532	C₂²	semidirect
75. C₁₃×#532	C₂²	semidirect
76. C₁₃×#529	C₂²	semidirect
77. C₁₃×#529	C₂²	semidirect
78. C₁₃×#529	C₂²	semidirect
79. C₁₃×#529	C₂²	semidirect
80. C₁₃×#529	C₂²	semidirect
81. C₂×C₁₃×#126	C₂²	semidirect
82. C₂×C₁₃×#124	C₂²	semidirect
83. C₁₃×#525	C₂²	semidirect
84. C₁₃×#525	C₂²	semidirect
85. C₁₃×#525	C₂²	semidirect
86. C₁₃×#525	C₂²	semidirect
87. C₂×C₁₃×#123	C₂²	semidirect
88. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
89. C₂×C₁₃×#121	C₂²	semidirect
90. C₂×C₁₃×#121	C₂²	semidirect
91. C₂×C₁₃×#120	C₂²	semidirect
92. C₁₃×#520	C₂²	semidirect
93. C₁₃×#520	C₂²	semidirect
95. C₁₃×#518	C₂²	semidirect
96. C₁₃×#518	C₂²	semidirect
97. C₁₃×#518	C₂²	semidirect
98. C₁₃×#518	C₂²	semidirect
99. C₄×C₁₃×#41	C₂²	semidirect
100. C₄×C₁₃×#41	C₂²	semidirect
103. C₂×C₄×D₄×C₁₃	C₂²	semidirect
104. C₂×C₄×D₄×C₁₃	C₂²	semidirect
105. C₂×C₄×D₄×C₁₃	C₂²	semidirect
106. C₂×C₄×D₄×C₁₃	C₂²	semidirect
107. C₂×C₄×D₄×C₁₃	C₂²	semidirect
108. C₂×C₄×D₄×C₁₃	C₂²	semidirect
109. C₂×C₁₃×#117	C₂²	semidirect
110. C₂×C₁₃×#117	C₂²	semidirect
111. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
112. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
117. C₂×C₁₃×#41	C₂³	semidirect
118. C₂×C₁₃×#41	C₂³	semidirect
119. C₂²×Q₈×C₁₃	C₂³	semidirect
129. C₂²×D₄×C₁₃	C₂³	semidirect
135. C₂³×C₄×C₁₃	C₂³	semidirect
136. C₁₃×C₄⋊Q₈	C₂³	semidirect
137. C₁₃×C₄⋊Q₈	C₂³	semidirect
138. C₁₃×C₄⋊Q₈	C₂³	semidirect
139. C₁₃×C₄⋊Q₈	C₂³	semidirect
141. C₁₃×#127	C₂³	semidirect
145. C₁₃×#126	C₂³	semidirect
146. C₁₃×#126	C₂³	semidirect
147. C₁₃×#126	C₂³	semidirect
148. C₁₃×#126	C₂³	semidirect
149. C₁₃×#126	C₂³	semidirect
150. C₁₃×#125	C₂³	semidirect
151. C₁₃×#125	C₂³	semidirect
152. C₁₃×#125	C₂³	semidirect
153. C₁₃×#125	C₂³	semidirect
154. C₁₃×#125	C₂³	semidirect
159. C₁₃×#124	C₂³	semidirect
160. C₁₃×#124	C₂³	semidirect
161. C₁₃×#124	C₂³	semidirect
162. C₁₃×#124	C₂³	semidirect
168. C₁₃×#123	C₂³	semidirect
169. C₁₃×#123	C₂³	semidirect
170. C₁₃×#123	C₂³	semidirect
171. C₁₃×#123	C₂³	semidirect
172. C₁₃×#123	C₂³	semidirect
173. C₁₃×#123	C₂³	semidirect
174. C₁₃×#123	C₂³	semidirect
180. C₁₃×C₂²⋊Q₈	C₂³	semidirect
181. C₁₃×C₂²⋊Q₈	C₂³	semidirect
182. C₁₃×C₂²⋊Q₈	C₂³	semidirect
183. C₁₃×C₂²⋊Q₈	C₂³	semidirect
184. C₁₃×C₂²⋊Q₈	C₂³	semidirect
185. C₁₃×C₂²⋊Q₈	C₂³	semidirect
186. C₁₃×C₂²⋊Q₈	C₂³	semidirect
187. C₁₃×C₂²⋊Q₈	C₂³	semidirect
188. C₁₃×C₂²⋊Q₈	C₂³	semidirect
201. C₁₃×#121	C₂³	semidirect
202. C₁₃×#121	C₂³	semidirect
203. C₁₃×#121	C₂³	semidirect
204. C₁₃×#121	C₂³	semidirect
205. C₁₃×#121	C₂³	semidirect
206. C₁₃×#121	C₂³	semidirect
207. C₁₃×#121	C₂³	semidirect
213. C₁₃×#120	C₂³	semidirect
214. C₄×Q₈×C₁₃	C₂³	semidirect
215. C₄×Q₈×C₁₃	C₂³	semidirect
216. C₄×Q₈×C₁₃	C₂³	semidirect
217. C₄×Q₈×C₁₃	C₂³	semidirect
218. C₄×Q₈×C₁₃	C₂³	semidirect
219. C₄×Q₈×C₁₃	C₂³	semidirect
236. C₄×D₄×C₁₃	C₂³	semidirect
237. C₄×D₄×C₁₃	C₂³	semidirect
238. C₄×D₄×C₁₃	C₂³	semidirect
239. C₄×D₄×C₁₃	C₂³	semidirect
240. C₄×D₄×C₁₃	C₂³	semidirect
241. C₄×D₄×C₁₃	C₂³	semidirect
242. C₄×D₄×C₁₃	C₂³	semidirect
243. C₄×D₄×C₁₃	C₂³	semidirect
244. C₄×D₄×C₁₃	C₂³	semidirect
245. C₄×D₄×C₁₃	C₂³	semidirect
246. C₄×D₄×C₁₃	C₂³	semidirect
247. C₄×D₄×C₁₃	C₂³	semidirect
252. C₁₃×#117	C₂³	semidirect
253. C₁₃×#117	C₂³	semidirect
254. C₁₃×#117	C₂³	semidirect
255. C₁₃×#117	C₂³	semidirect
256. C₁₃×#117	C₂³	semidirect
257. C₁₃×#117	C₂³	semidirect
262. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
263. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
264. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
265. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
266. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
280. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
281. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
282. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
286. C₂×C₄²×C₁₃	C₂³	semidirect
287. C₂×C₄²×C₁₃	C₂³	semidirect
288. #62846	C₁₃	direct (N × H)
314. C₂×D₄×C₁₃	#41	semidirect
407. #3521	C₂×C₁₃	semidirect
408. #3519	C₂×C₁₃	semidirect
409. #3514	C₂×C₁₃	semidirect
410. #3513	C₂×C₁₃	semidirect
411. #3506	C₂×C₁₃	semidirect
412. #3505	C₂×C₁₃	semidirect
413. #3501	C₂×C₁₃	semidirect
414. #3496	C₂×C₁₃	semidirect
415. #3493	C₂×C₁₃	semidirect
416. #3490	C₂×C₁₃	semidirect
417. #3484	C₂×C₁₃	semidirect
418. #3460	C₂×C₁₃	semidirect
419. #3459	C₂×C₁₃	semidirect
420. #3455	C₂×C₁₃	semidirect
421. C₂×#538	C₂×C₁₃	semidirect
422. C₄×H(5,𝔽₂)	C₂×C₁₃	semidirect
423. C₂×#518	C₂×C₁₃	semidirect
497. #559	C₂²×C₁₃	semidirect
498. #556	C₂²×C₁₃	semidirect
499. #556	C₂²×C₁₃	semidirect
500. #555	C₂²×C₁₃	semidirect
501. #555	C₂²×C₁₃	semidirect
502. #554	C₂²×C₁₃	semidirect
503. #554	C₂²×C₁₃	semidirect
504. #553	C₂²×C₁₃	semidirect
505. #553	C₂²×C₁₃	semidirect
506. #553	C₂²×C₁₃	semidirect
507. #553	C₂²×C₁₃	semidirect
508. #552	C₂²×C₁₃	semidirect
509. #552	C₂²×C₁₃	semidirect
510. #551	C₂²×C₁₃	semidirect
511. #551	C₂²×C₁₃	semidirect
512. #551	C₂²×C₁₃	semidirect
513. #550	C₂²×C₁₃	semidirect
514. D₄×Q₈	C₂²×C₁₃	semidirect
515. #548	C₂²×C₁₃	semidirect
516. #547	C₂²×C₁₃	semidirect
517. #547	C₂²×C₁₃	semidirect
518. #546	C₂²×C₁₃	semidirect
519. #546	C₂²×C₁₃	semidirect
520. #546	C₂²×C₁₃	semidirect
521. #546	C₂²×C₁₃	semidirect
522. #546	C₂²×C₁₃	semidirect
523. #546	C₂²×C₁₃	semidirect
524. D₄²	C₂²×C₁₃	semidirect
525. D₄²	C₂²×C₁₃	semidirect
526. D₄²	C₂²×C₁₃	semidirect
527. #544	C₂²×C₁₃	semidirect
528. #543	C₂²×C₁₃	semidirect
529. #542	C₂²×C₁₃	semidirect
530. #542	C₂²×C₁₃	semidirect
531. #542	C₂²×C₁₃	semidirect
532. #541	C₂²×C₁₃	semidirect
533. #540	C₂²×C₁₃	semidirect
534. #540	C₂²×C₁₃	semidirect
535. #539	C₂²×C₁₃	semidirect
536. #539	C₂²×C₁₃	semidirect
537. #539	C₂²×C₁₃	semidirect
538. #538	C₂²×C₁₃	semidirect
539. #538	C₂²×C₁₃	semidirect
540. #538	C₂²×C₁₃	semidirect
541. #538	C₂²×C₁₃	semidirect
542. #538	C₂²×C₁₃	semidirect
543. #538	C₂²×C₁₃	semidirect
544. #538	C₂²×C₁₃	semidirect
545. #538	C₂²×C₁₃	semidirect
546. #537	C₂²×C₁₃	semidirect
547. #535	C₂²×C₁₃	semidirect
548. #534	C₂²×C₁₃	semidirect
549. #534	C₂²×C₁₃	semidirect
550. #533	C₂²×C₁₃	semidirect
551. #532	C₂²×C₁₃	semidirect
552. #532	C₂²×C₁₃	semidirect
553. #529	C₂²×C₁₃	semidirect
554. #529	C₂²×C₁₃	semidirect
555. #529	C₂²×C₁₃	semidirect
556. #529	C₂²×C₁₃	semidirect
557. #529	C₂²×C₁₃	semidirect
558. C₂×#126	C₂²×C₁₃	semidirect
559. C₂×#124	C₂²×C₁₃	semidirect
560. #525	C₂²×C₁₃	semidirect
561. #525	C₂²×C₁₃	semidirect
562. #525	C₂²×C₁₃	semidirect
563. #525	C₂²×C₁₃	semidirect
564. C₂×#123	C₂²×C₁₃	semidirect
565. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
566. C₂×#121	C₂²×C₁₃	semidirect
567. C₂×#121	C₂²×C₁₃	semidirect
568. C₂×#120	C₂²×C₁₃	semidirect
569. #520	C₂²×C₁₃	semidirect
570. #520	C₂²×C₁₃	semidirect
572. #518	C₂²×C₁₃	semidirect
573. #518	C₂²×C₁₃	semidirect
574. #518	C₂²×C₁₃	semidirect
575. #518	C₂²×C₁₃	semidirect
576. C₄×#41	C₂²×C₁₃	semidirect
577. C₄×#41	C₂²×C₁₃	semidirect
580. C₂×C₄×D₄	C₂²×C₁₃	semidirect
581. C₂×C₄×D₄	C₂²×C₁₃	semidirect
582. C₂×C₄×D₄	C₂²×C₁₃	semidirect
583. C₂×C₄×D₄	C₂²×C₁₃	semidirect
584. C₂×C₄×D₄	C₂²×C₁₃	semidirect
585. C₂×C₄×D₄	C₂²×C₁₃	semidirect
586. C₂×#117	C₂²×C₁₃	semidirect
587. C₂×#117	C₂²×C₁₃	semidirect
588. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
589. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
627. C₂×#41	C₂³×C₁₃	semidirect
628. C₂×#41	C₂³×C₁₃	semidirect
629. C₂²×Q₈	C₂³×C₁₃	semidirect
639. C₂²×D₄	C₂³×C₁₃	semidirect
645. C₂³×C₄	C₂³×C₁₃	semidirect
646. C₄⋊Q₈	C₂³×C₁₃	semidirect
647. C₄⋊Q₈	C₂³×C₁₃	semidirect
648. C₄⋊Q₈	C₂³×C₁₃	semidirect
649. C₄⋊Q₈	C₂³×C₁₃	semidirect
651. #127	C₂³×C₁₃	semidirect
655. #126	C₂³×C₁₃	semidirect
656. #126	C₂³×C₁₃	semidirect
657. #126	C₂³×C₁₃	semidirect
658. #126	C₂³×C₁₃	semidirect
659. #126	C₂³×C₁₃	semidirect
660. #125	C₂³×C₁₃	semidirect
661. #125	C₂³×C₁₃	semidirect
662. #125	C₂³×C₁₃	semidirect
663. #125	C₂³×C₁₃	semidirect
664. #125	C₂³×C₁₃	semidirect
669. #124	C₂³×C₁₃	semidirect
670. #124	C₂³×C₁₃	semidirect
671. #124	C₂³×C₁₃	semidirect
672. #124	C₂³×C₁₃	semidirect
678. #123	C₂³×C₁₃	semidirect
679. #123	C₂³×C₁₃	semidirect
680. #123	C₂³×C₁₃	semidirect
681. #123	C₂³×C₁₃	semidirect
682. #123	C₂³×C₁₃	semidirect
683. #123	C₂³×C₁₃	semidirect
684. #123	C₂³×C₁₃	semidirect
690. C₂²⋊Q₈	C₂³×C₁₃	semidirect
691. C₂²⋊Q₈	C₂³×C₁₃	semidirect
692. C₂²⋊Q₈	C₂³×C₁₃	semidirect
693. C₂²⋊Q₈	C₂³×C₁₃	semidirect
694. C₂²⋊Q₈	C₂³×C₁₃	semidirect
695. C₂²⋊Q₈	C₂³×C₁₃	semidirect
696. C₂²⋊Q₈	C₂³×C₁₃	semidirect
697. C₂²⋊Q₈	C₂³×C₁₃	semidirect
698. C₂²⋊Q₈	C₂³×C₁₃	semidirect
711. #121	C₂³×C₁₃	semidirect
712. #121	C₂³×C₁₃	semidirect
713. #121	C₂³×C₁₃	semidirect
714. #121	C₂³×C₁₃	semidirect
715. #121	C₂³×C₁₃	semidirect
716. #121	C₂³×C₁₃	semidirect
717. #121	C₂³×C₁₃	semidirect
723. #120	C₂³×C₁₃	semidirect
724. C₄×Q₈	C₂³×C₁₃	semidirect
725. C₄×Q₈	C₂³×C₁₃	semidirect
726. C₄×Q₈	C₂³×C₁₃	semidirect
727. C₄×Q₈	C₂³×C₁₃	semidirect
728. C₄×Q₈	C₂³×C₁₃	semidirect
729. C₄×Q₈	C₂³×C₁₃	semidirect
746. C₄×D₄	C₂³×C₁₃	semidirect
747. C₄×D₄	C₂³×C₁₃	semidirect
748. C₄×D₄	C₂³×C₁₃	semidirect
749. C₄×D₄	C₂³×C₁₃	semidirect
750. C₄×D₄	C₂³×C₁₃	semidirect
751. C₄×D₄	C₂³×C₁₃	semidirect
752. C₄×D₄	C₂³×C₁₃	semidirect
753. C₄×D₄	C₂³×C₁₃	semidirect
754. C₄×D₄	C₂³×C₁₃	semidirect
755. C₄×D₄	C₂³×C₁₃	semidirect
756. C₄×D₄	C₂³×C₁₃	semidirect
757. C₄×D₄	C₂³×C₁₃	semidirect
762. #117	C₂³×C₁₃	semidirect
763. #117	C₂³×C₁₃	semidirect
764. #117	C₂³×C₁₃	semidirect
765. #117	C₂³×C₁₃	semidirect
766. #117	C₂³×C₁₃	semidirect
767. #117	C₂³×C₁₃	semidirect
772. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
773. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
774. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
775. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
776. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
790. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
791. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
792. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
796. C₂×C₄²	C₂³×C₁₃	semidirect
797. C₂×C₄²	C₂³×C₁₃	semidirect
831. C₂×D₄	C₁₃×#41	semidirect
924. C₁₃	#62846	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3521	2
C₁₃×#3519	2
C₁₃×#3514	2
C₁₃×#3513	2
C₁₃×#3506	2
C₁₃×#3505	2
C₁₃×#3501	2
C₁₃×#3496	2
C₁₃×#3493	2
C₁₃×#3490	2
C₁₃×#3484	2
C₁₃×#3460	2
C₁₃×#3459	2
C₁₃×#3455	2
C₂×C₁₃×#538	2
C₄×C₁₃×H(5,𝔽₂)	2
C₂×C₁₃×#518	2
#62846	13

Subgroups — C13×#62846 #15749185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62846 #15749185