Subgroups — C₁₃×#62847 #15749186

Order 3328.

7106 conjugacy classes of subgroups.

The subgroup lattice has 1000 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×#3520	C₂	1	8	yes	maximal, complemented
3	C₁₃×#3515	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3513	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3507	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×#3492	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3491	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3485	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3461	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×#539	C₂	1	4	yes	maximal, complemented
16	C₄×C₁₃×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
17	C₂×C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₁₃×#559	C₂²	1	4	yes	complemented
21	C₁₃×#557	C₂²	1	4	yes	complemented
22	C₁₃×#556	C₂²	1	8	yes	complemented
23	C₁₃×#556	C₂²	1	4	yes	complemented
24	C₁₃×#554	C₂²	1	4	yes	complemented
25	C₁₃×#554	C₂²	1	8	yes	complemented
26	C₁₃×#554	C₂²	1	4	yes	complemented
27	C₁₃×#554	C₂²	1	8	yes	complemented
28	C₁₃×#553	C₂²	1	8	yes	complemented
29	C₁₃×#553	C₂²	1	8	yes	complemented
30	C₁₃×#553	C₂²	1	16	yes	complemented
31	C₁₃×#552	C₂²	1	16	yes	complemented
32	C₁₃×#552	C₂²	1	16	yes	complemented
33	C₁₃×#552	C₂²	1	8	yes	complemented
34	C₁₃×#552	C₂²	1	8	yes	complemented
35	C₁₃×#552	C₂²	1	8	yes	complemented
36	C₁₃×#551	C₂²	1	16	yes	complemented
37	C₁₃×#551	C₂²	1	16	yes	complemented
38	C₁₃×#551	C₂²	1	16	yes	complemented
39	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
40	C₁₃×#548	C₂²	1	8	yes	complemented
41	C₁₃×#547	C₂²	1	8	yes	complemented
42	C₁₃×#547	C₂²	1	8	yes	complemented
43	C₁₃×#547	C₂²	1	8	yes	complemented
44	C₁₃×#547	C₂²	1	4	yes	complemented
45	C₁₃×#546	C₂²	1	8	yes	complemented
46	C₁₃×#546	C₂²	1	8	yes	complemented
47	C₁₃×#546	C₂²	1	8	yes	complemented
48	C₁₃×#546	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	8	yes	complemented
54	C₁₃×#542	C₂²	1	4	yes	complemented
55	C₁₃×#541	C₂²	1	8	yes	complemented
56	C₁₃×#541	C₂²	1	4	yes	complemented
57	C₁₃×#540	C₂²	1	4	yes	complemented
58	C₁₃×#539	C₂²	1	16	yes	complemented
59	C₁₃×#539	C₂²	1	16	yes	complemented
60	C₁₃×#539	C₂²	1	4	yes	complemented
61	C₁₃×#539	C₂²	1	8	yes	complemented
62	C₁₃×#539	C₂²	1	8	yes	complemented
63	C₁₃×#539	C₂²	1	8	yes	complemented
64	C₁₃×#539	C₂²	1	16	yes	complemented
65	C₁₃×#539	C₂²	1	4	yes	complemented
66	C₁₃×#538	C₂²	1	16	yes	complemented
67	C₁₃×#538	C₂²	1	4	yes	complemented
68	C₁₃×#538	C₂²	1	4	yes	complemented
69	C₁₃×#537	C₂²	1	2	yes	—
70	C₁₃×#536	C₂²	1	4	yes	complemented
71	C₁₃×#534	C₂²	1	4	yes	—
72	C₁₃×#534	C₂²	1	8	yes	complemented
73	C₁₃×#533	C₂²	1	8	yes	complemented
74	C₁₃×#533	C₂²	1	2	yes	complemented
75	C₁₃×#532	C₂²	1	2	yes	—
76	C₁₃×#529	C₂²	1	8	yes	complemented
77	C₁₃×#529	C₂²	1	16	yes	complemented
78	C₁₃×#529	C₂²	1	8	yes	complemented
79	C₁₃×#529	C₂²	1	8	yes	complemented
80	C₁₃×#529	C₂²	1	8	yes	complemented
81	C₁₃×#529	C₂²	1	8	yes	complemented
82	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
83	C₂×C₁₃×#125	C₂²	1	8	yes	complemented
84	C₁₃×#525	C₂²	1	16	yes	complemented
85	C₁₃×#525	C₂²	1	4	yes	complemented
86	C₁₃×#525	C₂²	1	8	yes	complemented
87	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
88	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
89	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
90	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
91	C₂×C₁₃×#121	C₂²	1	4	yes	—
92	C₁₃×#520	C₂²	1	8	yes	complemented
93	C₁₃×#520	C₂²	1	8	yes	complemented
94	C₁₃×#520	C₂²	1	8	yes	complemented
95	C₁₃×#520	C₂²	1	4	yes	complemented
96	C₁₃×#518	C₂²	1	2	yes	—
97	C₁₃×#518	C₂²	1	8	yes	complemented
98	C₁₃×#518	C₂²	1	8	yes	complemented
99	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
100	C₄×C₁₃×#41	C₂²	1	4	yes	complemented
101	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
103	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
104	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
105	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
106	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
107	C₂×C₄×D₄×C₁₃	C₂²	1	2	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	2	yes	complemented
111	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
112	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
113	C₁₃×H(5,𝔽₂)	—	2	16	no	—
114	C₂×C₁₃×#41	—	2	8	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	—
118	C₂×C₁₃×#41	C₂³	1	8	yes	—
119	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
121	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
122	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
123	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
124	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
125	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
132	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
137	C₁₃×#127	C₂³	1	2	yes	—
138	C₁₃×#126	C₂³	1	8	yes	—
139	C₁₃×#126	C₂³	1	16	yes	—
140	C₁₃×#126	C₂³	1	16	yes	—
141	C₁₃×#126	C₂³	1	16	yes	—
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	8	yes	—
146	C₁₃×#126	C₂³	1	16	yes	—
147	C₁₃×#125	C₂³	1	8	yes	—
148	C₁₃×#125	C₂³	1	16	yes	—
149	C₁₃×#125	C₂³	1	16	yes	—
150	C₁₃×#125	C₂³	1	16	yes	—
151	C₁₃×#125	C₂³	1	8	yes	—
152	C₁₃×#125	C₂³	1	8	yes	—
153	C₁₃×#125	C₂³	1	8	yes	—
154	C₁₃×#125	C₂³	1	8	yes	—
155	C₁₃×#125	C₂³	1	4	yes	—
156	C₁₃×#124	C₂³	1	8	yes	—
157	C₁₃×#124	C₂³	1	8	yes	—
158	C₁₃×#124	C₂³	1	8	yes	—
159	C₁₃×#124	C₂³	1	8	yes	—
160	C₁₃×#124	C₂³	1	8	yes	—
161	C₁₃×#124	C₂³	1	4	yes	—
162	C₁₃×#123	C₂³	1	8	yes	—
163	C₁₃×#123	C₂³	1	8	yes	—
164	C₁₃×#123	C₂³	1	16	yes	—
165	C₁₃×#123	C₂³	1	16	yes	—
166	C₁₃×#123	C₂³	1	16	yes	—
167	C₁₃×#123	C₂³	1	16	yes	—
168	C₁₃×#123	C₂³	1	16	yes	—
169	C₁₃×#123	C₂³	1	16	yes	—
170	C₁₃×#123	C₂³	1	8	yes	—
171	C₁₃×#123	C₂³	1	16	yes	—
172	C₁₃×#123	C₂³	1	16	yes	—
173	C₁₃×#123	C₂³	1	16	yes	—
174	C₁₃×#123	C₂³	1	8	yes	—
175	C₁₃×#123	C₂³	1	8	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
181	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
182	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
183	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
184	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
185	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
188	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
190	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
191	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
194	C₁₃×#121	C₂³	1	4	yes	—
195	C₁₃×#121	C₂³	1	8	yes	—
196	C₁₃×#121	C₂³	1	8	yes	—
197	C₁₃×#121	C₂³	1	8	yes	—
198	C₁₃×#121	C₂³	1	8	yes	—
199	C₁₃×#121	C₂³	1	16	yes	—
200	C₁₃×#121	C₂³	1	8	yes	—
201	C₁₃×#121	C₂³	1	4	yes	—
202	C₁₃×#121	C₂³	1	4	yes	—
203	C₁₃×#121	C₂³	1	4	yes	—
204	C₁₃×#121	C₂³	1	16	yes	—
205	C₁₃×#121	C₂³	1	8	yes	—
206	C₁₃×#121	C₂³	1	8	yes	—
207	C₁₃×#120	C₂³	1	8	yes	—
208	C₁₃×#120	C₂³	1	16	yes	—
209	C₁₃×#120	C₂³	1	16	yes	—
210	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
211	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
214	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
216	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
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	16	yes	—
224	C₄×D₄×C₁₃	C₂³	1	8	yes	—
225	C₄×D₄×C₁₃	C₂³	1	4	yes	—
226	C₄×D₄×C₁₃	C₂³	1	8	yes	—
227	C₄×D₄×C₁₃	C₂³	1	16	yes	—
228	C₄×D₄×C₁₃	C₂³	1	16	yes	—
229	C₄×D₄×C₁₃	C₂³	1	8	yes	—
230	C₄×D₄×C₁₃	C₂³	1	16	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	4	yes	—
237	C₄×D₄×C₁₃	C₂³	1	16	yes	—
238	C₄×D₄×C₁₃	C₂³	1	8	yes	—
239	C₄×D₄×C₁₃	C₂³	1	16	yes	—
240	C₄×D₄×C₁₃	C₂³	1	8	yes	—
241	C₄×D₄×C₁₃	C₂³	1	8	yes	—
242	C₄×D₄×C₁₃	C₂³	1	8	yes	—
243	C₄×D₄×C₁₃	C₂³	1	4	yes	—
244	C₄×D₄×C₁₃	C₂³	1	4	yes	—
245	C₁₃×#117	C₂³	1	4	yes	—
246	C₁₃×#117	C₂³	1	4	yes	—
247	C₁₃×#117	C₂³	1	16	yes	—
248	C₁₃×#117	C₂³	1	4	yes	—
249	C₁₃×#117	C₂³	1	8	yes	—
250	C₁₃×#117	C₂³	1	16	yes	—
251	C₁₃×#117	C₂³	1	8	yes	—
252	C₁₃×#117	C₂³	1	16	yes	—
253	C₁₃×#117	C₂³	1	8	yes	—
254	C₁₃×#117	C₂³	1	16	yes	—
255	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
260	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
264	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
266	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
267	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
268	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
269	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
270	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
271	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	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	1	yes	characteristic
275	C₂×C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
277	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
278	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
279	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
280	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
281	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
282	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
283	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
284	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
285	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
286	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
287	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
288	#62847	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
290	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
291	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
292	C₁₃×#41	—	2	32	no	—
293	C₁₃×#41	—	2	32	no	—
294	C₁₃×#41	—	2	16	no	—
295	C₁₃×#41	—	8	8	no	—
296	C₂×Q₈×C₁₃	—	2	4	no	—
297	C₂×Q₈×C₁₃	—	8	4	no	—
298	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
299	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
300	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
301	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
302	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
303	C₂×D₄×C₁₃	—	2	8	no	—
304	C₂×D₄×C₁₃	—	2	32	no	—
305	C₂×D₄×C₁₃	—	2	32	no	—
306	C₂×D₄×C₁₃	—	8	4	no	—
307	C₂×D₄×C₁₃	#41	1	8	yes	complemented
308	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
309	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
310	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
311	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
312	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
313	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
314	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
315	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
316	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
317	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
318	C₂²×C₄×C₁₃	—	2	8	no	—
319	C₂²×C₄×C₁₃	—	2	4	no	—
320	C₂²×C₄×C₁₃	—	8	2	no	—
321	C₂²×C₄×C₁₃	—	8	8	no	—
322	C₂²×C₄×C₁₃	—	8	2	no	—
323	C₂²×C₄×C₁₃	—	8	2	no	—
324	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
326	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
327	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
328	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
330	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
333	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
334	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
337	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
340	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
341	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
342	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
343	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
344	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
346	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
347	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
348	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
349	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
350	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
351	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
352	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
353	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
354	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
355	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
356	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
357	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
358	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
359	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
360	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
362	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
366	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
369	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
370	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
371	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
372	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
373	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
374	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
375	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
376	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
377	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
378	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
379	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
380	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
381	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
382	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
383	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
384	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
385	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
386	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
387	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
388	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
389	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
390	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
391	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
392	C₄²×C₁₃	C₂⁴	1	4	yes	—
393	C₄²×C₁₃	C₂⁴	1	8	yes	—
394	C₄²×C₁₃	C₂⁴	1	16	yes	—
395	C₄²×C₁₃	C₂⁴	1	8	yes	—
396	C₄²×C₁₃	C₂⁴	1	8	yes	—
397	C₄²×C₁₃	C₂⁴	1	8	yes	—
398	C₄²×C₁₃	C₂⁴	1	8	yes	—
399	C₄²×C₁₃	C₂⁴	1	2	yes	—
400	C₄²×C₁₃	C₂⁴	1	2	yes	—
401	#3521	C₂×C₁₃	1	8	yes	complemented
402	#3520	C₂×C₁₃	1	8	yes	complemented
403	#3515	C₂×C₁₃	1	8	yes	complemented
404	#3513	C₂×C₁₃	1	8	yes	complemented
405	#3507	C₂×C₁₃	1	2	yes	complemented
406	#3505	C₂×C₁₃	1	4	yes	complemented
407	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
408	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
409	#3492	C₂×C₁₃	1	2	yes	complemented
410	#3491	C₂×C₁₃	1	4	yes	complemented
411	#3485	C₂×C₁₃	1	2	yes	complemented
412	#3461	C₂×C₁₃	1	2	yes	complemented
413	#3459	C₂×C₁₃	1	4	yes	complemented
414	#3455	C₂×C₁₃	1	2	yes	complemented
415	C₂×#539	C₂×C₁₃	1	4	yes	complemented
416	C₄×H(5,𝔽₂)	C₂×C₁₃	1	2	yes	complemented
417	C₂×#520	C₂×C₁₃	1	1	yes	characteristic, complemented
418	C₂³×C₁₃	—	2	2	no	—
419	C₂³×C₁₃	—	2	16	no	—
420	C₂³×C₁₃	—	4	2	no	—
421	C₂³×C₁₃	—	4	1	no	—
422	C₂³×C₁₃	—	4	2	no	—
423	C₂³×C₁₃	—	4	1	no	—
424	C₂³×C₁₃	—	4	8	no	—
425	C₂³×C₁₃	—	4	8	no	—
426	C₂³×C₁₃	C₂×#41	1	8	yes	—
427	C₂³×C₁₃	C₂⁵	1	8	yes	—
428	C₂³×C₁₃	C₂⁵	1	2	yes	—
429	C₂³×C₁₃	C₂⁵	1	4	yes	—
430	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
431	Q₈×C₁₃	—	2	8	no	—
432	Q₈×C₁₃	—	2	8	no	—
433	Q₈×C₁₃	—	4	4	no	—
434	Q₈×C₁₃	—	4	8	no	—
435	Q₈×C₁₃	—	4	4	no	—
436	D₄×C₁₃	—	2	32	no	—
437	D₄×C₁₃	—	2	16	no	—
438	D₄×C₁₃	—	2	16	no	—
439	D₄×C₁₃	—	2	8	no	—
440	D₄×C₁₃	—	4	4	no	—
441	D₄×C₁₃	—	4	8	no	—
442	D₄×C₁₃	—	4	8	no	—
443	D₄×C₁₃	—	4	4	no	—
444	D₄×C₁₃	—	4	8	no	—
445	D₄×C₁₃	C₂×#41	1	16	yes	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	4	no	—
448	C₂×C₄×C₁₃	—	2	16	no	—
449	C₂×C₄×C₁₃	—	2	16	no	—
450	C₂×C₄×C₁₃	—	2	8	no	—
451	C₂×C₄×C₁₃	—	2	16	no	—
452	C₂×C₄×C₁₃	—	4	1	no	—
453	C₂×C₄×C₁₃	—	4	8	no	—
454	C₂×C₄×C₁₃	—	4	2	no	—
455	C₂×C₄×C₁₃	—	4	8	no	—
456	C₂×C₄×C₁₃	—	4	1	no	—
457	C₂×C₄×C₁₃	—	4	2	no	—
458	C₂×C₄×C₁₃	—	4	4	no	—
459	C₂×C₄×C₁₃	—	4	4	no	—
460	C₂×C₄×C₁₃	—	4	8	no	—
461	C₂×C₄×C₁₃	—	4	8	no	—
462	C₂×C₄×C₁₃	—	4	16	no	—
463	C₂×C₄×C₁₃	—	4	1	no	—
464	C₂×C₄×C₁₃	—	4	8	no	—
465	C₂×C₄×C₁₃	—	4	8	no	—
466	C₂×C₄×C₁₃	—	4	1	no	—
467	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
468	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
469	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
470	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
471	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
472	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
473	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
474	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
475	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
476	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
477	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
478	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
479	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
480	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
481	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
482	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
483	#559	C₂²×C₁₃	1	4	yes	complemented
484	#557	C₂²×C₁₃	1	4	yes	complemented
485	#556	C₂²×C₁₃	1	8	yes	complemented
486	#556	C₂²×C₁₃	1	4	yes	complemented
487	#554	C₂²×C₁₃	1	8	yes	complemented
488	#554	C₂²×C₁₃	1	8	yes	complemented
489	#554	C₂²×C₁₃	1	4	yes	complemented
490	#554	C₂²×C₁₃	1	4	yes	complemented
491	#553	C₂²×C₁₃	1	8	yes	complemented
492	#553	C₂²×C₁₃	1	16	yes	complemented
493	#553	C₂²×C₁₃	1	8	yes	complemented
494	#552	C₂²×C₁₃	1	16	yes	complemented
495	#552	C₂²×C₁₃	1	16	yes	complemented
496	#552	C₂²×C₁₃	1	8	yes	complemented
497	#552	C₂²×C₁₃	1	8	yes	complemented
498	#552	C₂²×C₁₃	1	8	yes	complemented
499	#551	C₂²×C₁₃	1	16	yes	complemented
500	#551	C₂²×C₁₃	1	16	yes	complemented
501	#551	C₂²×C₁₃	1	16	yes	complemented
502	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
503	#548	C₂²×C₁₃	1	8	yes	complemented
504	#547	C₂²×C₁₃	1	8	yes	complemented
505	#547	C₂²×C₁₃	1	8	yes	complemented
506	#547	C₂²×C₁₃	1	8	yes	complemented
507	#547	C₂²×C₁₃	1	4	yes	complemented
508	#546	C₂²×C₁₃	1	8	yes	complemented
509	#546	C₂²×C₁₃	1	8	yes	complemented
510	#546	C₂²×C₁₃	1	8	yes	complemented
511	#546	C₂²×C₁₃	1	8	yes	complemented
512	D₄²	C₂²×C₁₃	1	4	yes	complemented
513	#544	C₂²×C₁₃	1	2	yes	complemented
514	#543	C₂²×C₁₃	1	4	yes	complemented
515	#542	C₂²×C₁₃	1	4	yes	complemented
516	#542	C₂²×C₁₃	1	4	yes	complemented
517	#542	C₂²×C₁₃	1	8	yes	complemented
518	#541	C₂²×C₁₃	1	4	yes	complemented
519	#541	C₂²×C₁₃	1	8	yes	complemented
520	#540	C₂²×C₁₃	1	4	yes	complemented
521	#539	C₂²×C₁₃	1	4	yes	complemented
522	#539	C₂²×C₁₃	1	8	yes	complemented
523	#539	C₂²×C₁₃	1	8	yes	complemented
524	#539	C₂²×C₁₃	1	8	yes	complemented
525	#539	C₂²×C₁₃	1	16	yes	complemented
526	#539	C₂²×C₁₃	1	16	yes	complemented
527	#539	C₂²×C₁₃	1	4	yes	complemented
528	#539	C₂²×C₁₃	1	16	yes	complemented
529	#538	C₂²×C₁₃	1	4	yes	complemented
530	#538	C₂²×C₁₃	1	4	yes	complemented
531	#538	C₂²×C₁₃	1	16	yes	complemented
532	#537	C₂²×C₁₃	1	2	yes	—
533	#536	C₂²×C₁₃	1	4	yes	complemented
534	#534	C₂²×C₁₃	1	4	yes	—
535	#534	C₂²×C₁₃	1	8	yes	complemented
536	#533	C₂²×C₁₃	1	2	yes	complemented
537	#533	C₂²×C₁₃	1	8	yes	complemented
538	#532	C₂²×C₁₃	1	2	yes	—
539	#529	C₂²×C₁₃	1	8	yes	complemented
540	#529	C₂²×C₁₃	1	8	yes	complemented
541	#529	C₂²×C₁₃	1	8	yes	complemented
542	#529	C₂²×C₁₃	1	16	yes	complemented
543	#529	C₂²×C₁₃	1	8	yes	complemented
544	#529	C₂²×C₁₃	1	8	yes	complemented
545	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
546	C₂×#125	C₂²×C₁₃	1	8	yes	complemented
547	#525	C₂²×C₁₃	1	4	yes	complemented
548	#525	C₂²×C₁₃	1	8	yes	complemented
549	#525	C₂²×C₁₃	1	16	yes	complemented
550	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
551	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
552	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
553	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
554	C₂×#121	C₂²×C₁₃	1	4	yes	—
555	#520	C₂²×C₁₃	1	8	yes	complemented
556	#520	C₂²×C₁₃	1	8	yes	complemented
557	#520	C₂²×C₁₃	1	4	yes	complemented
558	#520	C₂²×C₁₃	1	8	yes	complemented
559	#518	C₂²×C₁₃	1	2	yes	—
560	#518	C₂²×C₁₃	1	8	yes	complemented
561	#518	C₂²×C₁₃	1	8	yes	complemented
562	C₄×#41	C₂²×C₁₃	1	4	yes	complemented
563	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
564	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
565	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
566	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
567	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
568	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
569	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
570	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
571	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
572	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
573	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
574	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
575	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
576	C₂²×C₁₃	—	2	1	no	—
577	C₂²×C₁₃	—	2	4	no	—
578	C₂²×C₁₃	—	2	1	no	—
579	C₂²×C₁₃	—	2	4	no	—
580	C₂²×C₁₃	—	2	2	no	—
581	C₂²×C₁₃	—	2	8	no	—
582	C₂²×C₁₃	—	2	2	no	—
583	C₂²×C₁₃	—	2	8	no	—
584	C₂²×C₁₃	—	2	8	no	—
585	C₂²×C₁₃	—	2	2	no	—
586	C₂²×C₁₃	—	4	8	no	—
587	C₂²×C₁₃	—	4	4	no	—
588	C₂²×C₁₃	—	8	16	no	—
589	C₂²×C₁₃	C₂²×#41	1	8	yes	—
590	C₂²×C₁₃	C₂²×#41	1	2	yes	—
591	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
592	C₄×C₁₃	—	2	2	no	—
593	C₄×C₁₃	—	2	8	no	—
594	C₄×C₁₃	—	2	4	no	—
595	C₄×C₁₃	—	2	2	no	—
596	C₄×C₁₃	—	2	4	no	—
597	C₄×C₁₃	—	2	1	no	—
598	C₄×C₁₃	—	2	4	no	—
599	C₄×C₁₃	—	2	8	no	—
600	C₄×C₁₃	—	2	1	no	—
601	C₄×C₁₃	—	2	2	no	—
602	C₄×C₁₃	—	2	8	no	—
603	C₄×C₁₃	—	2	2	no	—
604	C₄×C₁₃	C₂²×#41	1	4	yes	—
605	H(5,𝔽₂)	—	2	16	no	—
606	C₂×#41	—	2	8	no	—
607	C₂×#41	C₂³×C₁₃	1	4	yes	—
608	C₂×#41	C₂³×C₁₃	1	8	yes	—
609	C₂×#41	C₂³×C₁₃	1	8	yes	—
610	C₂×#41	C₂³×C₁₃	1	8	yes	—
611	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
612	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
613	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
614	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
615	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
616	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
617	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
619	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
621	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
622	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
623	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
624	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
625	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
626	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
627	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
628	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
629	#127	C₂³×C₁₃	1	2	yes	—
630	#126	C₂³×C₁₃	1	8	yes	—
631	#126	C₂³×C₁₃	1	16	yes	—
632	#126	C₂³×C₁₃	1	16	yes	—
633	#126	C₂³×C₁₃	1	16	yes	—
634	#126	C₂³×C₁₃	1	8	yes	—
635	#126	C₂³×C₁₃	1	16	yes	—
636	#126	C₂³×C₁₃	1	8	yes	—
637	#126	C₂³×C₁₃	1	8	yes	—
638	#126	C₂³×C₁₃	1	16	yes	—
639	#125	C₂³×C₁₃	1	8	yes	—
640	#125	C₂³×C₁₃	1	16	yes	—
641	#125	C₂³×C₁₃	1	16	yes	—
642	#125	C₂³×C₁₃	1	16	yes	—
643	#125	C₂³×C₁₃	1	8	yes	—
644	#125	C₂³×C₁₃	1	8	yes	—
645	#125	C₂³×C₁₃	1	8	yes	—
646	#125	C₂³×C₁₃	1	8	yes	—
647	#125	C₂³×C₁₃	1	4	yes	—
648	#124	C₂³×C₁₃	1	8	yes	—
649	#124	C₂³×C₁₃	1	8	yes	—
650	#124	C₂³×C₁₃	1	8	yes	—
651	#124	C₂³×C₁₃	1	8	yes	—
652	#124	C₂³×C₁₃	1	8	yes	—
653	#124	C₂³×C₁₃	1	4	yes	—
654	#123	C₂³×C₁₃	1	8	yes	—
655	#123	C₂³×C₁₃	1	8	yes	—
656	#123	C₂³×C₁₃	1	16	yes	—
657	#123	C₂³×C₁₃	1	16	yes	—
658	#123	C₂³×C₁₃	1	16	yes	—
659	#123	C₂³×C₁₃	1	16	yes	—
660	#123	C₂³×C₁₃	1	16	yes	—
661	#123	C₂³×C₁₃	1	16	yes	—
662	#123	C₂³×C₁₃	1	8	yes	—
663	#123	C₂³×C₁₃	1	16	yes	—
664	#123	C₂³×C₁₃	1	16	yes	—
665	#123	C₂³×C₁₃	1	16	yes	—
666	#123	C₂³×C₁₃	1	8	yes	—
667	#123	C₂³×C₁₃	1	8	yes	—
668	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
669	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
670	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
671	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
672	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
673	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
674	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
675	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
676	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
677	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
678	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
679	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
680	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
681	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
682	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
683	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
684	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
685	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
686	#121	C₂³×C₁₃	1	4	yes	—
687	#121	C₂³×C₁₃	1	8	yes	—
688	#121	C₂³×C₁₃	1	8	yes	—
689	#121	C₂³×C₁₃	1	8	yes	—
690	#121	C₂³×C₁₃	1	8	yes	—
691	#121	C₂³×C₁₃	1	16	yes	—
692	#121	C₂³×C₁₃	1	8	yes	—
693	#121	C₂³×C₁₃	1	4	yes	—
694	#121	C₂³×C₁₃	1	4	yes	—
695	#121	C₂³×C₁₃	1	4	yes	—
696	#121	C₂³×C₁₃	1	16	yes	—
697	#121	C₂³×C₁₃	1	8	yes	—
698	#121	C₂³×C₁₃	1	8	yes	—
699	#120	C₂³×C₁₃	1	8	yes	—
700	#120	C₂³×C₁₃	1	16	yes	—
701	#120	C₂³×C₁₃	1	16	yes	—
702	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
703	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
704	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
705	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
706	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
707	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
708	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
709	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
710	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
711	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
712	C₄×D₄	C₂³×C₁₃	1	8	yes	—
713	C₄×D₄	C₂³×C₁₃	1	4	yes	—
714	C₄×D₄	C₂³×C₁₃	1	4	yes	—
715	C₄×D₄	C₂³×C₁₃	1	8	yes	—
716	C₄×D₄	C₂³×C₁₃	1	16	yes	—
717	C₄×D₄	C₂³×C₁₃	1	4	yes	—
718	C₄×D₄	C₂³×C₁₃	1	8	yes	—
719	C₄×D₄	C₂³×C₁₃	1	16	yes	—
720	C₄×D₄	C₂³×C₁₃	1	16	yes	—
721	C₄×D₄	C₂³×C₁₃	1	8	yes	—
722	C₄×D₄	C₂³×C₁₃	1	16	yes	—
723	C₄×D₄	C₂³×C₁₃	1	16	yes	—
724	C₄×D₄	C₂³×C₁₃	1	8	yes	—
725	C₄×D₄	C₂³×C₁₃	1	8	yes	—
726	C₄×D₄	C₂³×C₁₃	1	8	yes	—
727	C₄×D₄	C₂³×C₁₃	1	8	yes	—
728	C₄×D₄	C₂³×C₁₃	1	4	yes	—
729	C₄×D₄	C₂³×C₁₃	1	16	yes	—
730	C₄×D₄	C₂³×C₁₃	1	8	yes	—
731	C₄×D₄	C₂³×C₁₃	1	16	yes	—
732	C₄×D₄	C₂³×C₁₃	1	8	yes	—
733	C₄×D₄	C₂³×C₁₃	1	8	yes	—
734	C₄×D₄	C₂³×C₁₃	1	8	yes	—
735	C₄×D₄	C₂³×C₁₃	1	4	yes	—
736	C₄×D₄	C₂³×C₁₃	1	4	yes	—
737	#117	C₂³×C₁₃	1	4	yes	—
738	#117	C₂³×C₁₃	1	4	yes	—
739	#117	C₂³×C₁₃	1	16	yes	—
740	#117	C₂³×C₁₃	1	4	yes	—
741	#117	C₂³×C₁₃	1	8	yes	—
742	#117	C₂³×C₁₃	1	16	yes	—
743	#117	C₂³×C₁₃	1	8	yes	—
744	#117	C₂³×C₁₃	1	16	yes	—
745	#117	C₂³×C₁₃	1	8	yes	—
746	#117	C₂³×C₁₃	1	16	yes	—
747	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
749	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
753	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
754	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
755	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
756	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
758	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
759	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
760	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
761	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
762	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
763	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
767	C₂×C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
768	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
774	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
775	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
776	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
777	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
778	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
779	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
780	C₂×C₁₃	—	2	2	no	—
781	C₂×C₁₃	—	2	8	no	—
782	C₂×C₁₃	—	4	2	no	—
783	C₂×C₁₃	—	4	8	no	—
784	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
785	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
786	C₂×C₁₃	2₋¹⁺⁶	1	1	yes	characteristic
787	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
788	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
789	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
790	#41	—	2	32	no	—
791	#41	—	2	32	no	—
792	#41	—	2	16	no	—
793	#41	—	8	8	no	—
794	C₂×Q₈	—	2	4	no	—
795	C₂×Q₈	—	8	4	no	—
796	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
797	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
798	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
799	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
800	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
801	C₂×D₄	—	2	8	no	—
802	C₂×D₄	—	2	32	no	—
803	C₂×D₄	—	2	32	no	—
804	C₂×D₄	—	8	4	no	—
805	C₂×D₄	C₁₃×#41	1	8	yes	complemented
806	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
807	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
808	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
809	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
810	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
811	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
812	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
813	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
814	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
815	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
816	C₂²×C₄	—	2	8	no	—
817	C₂²×C₄	—	2	4	no	—
818	C₂²×C₄	—	8	2	no	—
819	C₂²×C₄	—	8	8	no	—
820	C₂²×C₄	—	8	2	no	—
821	C₂²×C₄	—	8	2	no	—
822	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
824	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
825	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
826	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
828	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
831	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
832	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
835	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
838	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
839	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
840	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
841	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
842	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
843	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
844	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
845	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
846	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
847	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
848	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
849	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
850	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
851	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
852	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
853	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
854	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
855	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
856	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
857	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
858	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
859	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
860	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
861	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
862	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
863	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
864	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
865	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
866	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
867	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
868	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
869	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
870	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
871	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
872	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
873	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
874	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
875	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
876	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
877	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
878	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
879	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
880	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
881	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
882	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
883	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
884	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
885	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
886	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
887	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
888	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
889	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
890	C₄²	C₂⁴×C₁₃	1	4	yes	—
891	C₄²	C₂⁴×C₁₃	1	8	yes	—
892	C₄²	C₂⁴×C₁₃	1	16	yes	—
893	C₄²	C₂⁴×C₁₃	1	8	yes	—
894	C₄²	C₂⁴×C₁₃	1	8	yes	—
895	C₄²	C₂⁴×C₁₃	1	8	yes	—
896	C₄²	C₂⁴×C₁₃	1	8	yes	—
897	C₄²	C₂⁴×C₁₃	1	2	yes	—
898	C₄²	C₂⁴×C₁₃	1	2	yes	—
899	C₁₃	#62847	1	1	yes	characteristic, direct product factor, Sylow
900	C₂³	—	2	2	no	—
901	C₂³	—	2	16	no	—
902	C₂³	—	4	2	no	—
903	C₂³	—	4	1	no	—
904	C₂³	—	4	2	no	—
905	C₂³	—	4	1	no	—
906	C₂³	—	4	8	no	—
907	C₂³	—	4	8	no	—
908	C₂³	C₂×C₁₃×#41	1	8	yes	—
909	C₂³	C₂⁵×C₁₃	1	8	yes	—
910	C₂³	C₂⁵×C₁₃	1	2	yes	—
911	C₂³	C₂⁵×C₁₃	1	4	yes	—
912	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
913	Q₈	—	2	8	no	—
914	Q₈	—	2	8	no	—
915	Q₈	—	4	4	no	—
916	Q₈	—	4	8	no	—
917	Q₈	—	4	4	no	—
918	D₄	—	2	32	no	—
919	D₄	—	2	16	no	—
920	D₄	—	2	16	no	—
921	D₄	—	2	8	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	8	no	—
924	D₄	—	4	8	no	—
925	D₄	—	4	4	no	—
926	D₄	—	4	8	no	—
927	D₄	C₂×C₁₃×#41	1	16	yes	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	4	no	—
930	C₂×C₄	—	2	16	no	—
931	C₂×C₄	—	2	16	no	—
932	C₂×C₄	—	2	8	no	—
933	C₂×C₄	—	2	16	no	—
934	C₂×C₄	—	4	1	no	—
935	C₂×C₄	—	4	8	no	—
936	C₂×C₄	—	4	2	no	—
937	C₂×C₄	—	4	8	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	8	no	—
943	C₂×C₄	—	4	8	no	—
944	C₂×C₄	—	4	16	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	8	no	—
947	C₂×C₄	—	4	8	no	—
948	C₂×C₄	—	4	1	no	—
949	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
950	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
951	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
952	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
953	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
954	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
955	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
956	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
957	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
958	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
959	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
960	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
961	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
962	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	4	no	—
965	C₂²	—	2	1	no	—
966	C₂²	—	2	4	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	8	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	8	no	—
971	C₂²	—	2	8	no	—
972	C₂²	—	2	2	no	—
973	C₂²	—	4	8	no	—
974	C₂²	—	4	4	no	—
975	C₂²	—	8	16	no	—
976	C₂²	C₂²×C₁₃×#41	1	8	yes	—
977	C₂²	C₂²×C₁₃×#41	1	2	yes	—
978	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
979	C₄	—	2	2	no	—
980	C₄	—	2	8	no	—
981	C₄	—	2	4	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	4	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	4	no	—
986	C₄	—	2	8	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	8	no	—
990	C₄	—	2	2	no	—
991	C₄	C₂²×C₁₃×#41	1	4	yes	—
992	C₂	—	2	2	no	—
993	C₂	—	2	8	no	—
994	C₂	—	4	2	no	—
995	C₂	—	4	8	no	—
996	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
997	C₂	C₁₃×H(7,𝔽₂)	1	1	yes	characteristic
998	C₂	C₁₃×2₋¹⁺⁶	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×#3520	C₂	semidirect
3. C₁₃×#3515	C₂	semidirect
4. C₁₃×#3513	C₂	semidirect
5. C₁₃×#3507	C₂	semidirect
6. C₁₃×#3505	C₂	semidirect
7. C₁₃×#3501	C₂	semidirect
8. C₁₃×#3496	C₂	semidirect
9. C₁₃×#3492	C₂	semidirect
10. C₁₃×#3491	C₂	semidirect
11. C₁₃×#3485	C₂	semidirect
12. C₁₃×#3461	C₂	semidirect
13. C₁₃×#3459	C₂	semidirect
14. C₁₃×#3455	C₂	semidirect
15. C₂×C₁₃×#539	C₂	semidirect
16. C₄×C₁₃×H(5,𝔽₂)	C₂	semidirect
17. C₂×C₁₃×#520	C₂	semidirect
20. C₁₃×#559	C₂²	semidirect
21. C₁₃×#557	C₂²	semidirect
22. C₁₃×#556	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#554	C₂²	semidirect
25. C₁₃×#554	C₂²	semidirect
26. C₁₃×#554	C₂²	semidirect
27. C₁₃×#554	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×#552	C₂²	semidirect
34. C₁₃×#552	C₂²	semidirect
35. C₁₃×#552	C₂²	semidirect
36. C₁₃×#551	C₂²	semidirect
37. C₁₃×#551	C₂²	semidirect
38. C₁₃×#551	C₂²	semidirect
39. D₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#548	C₂²	semidirect
41. C₁₃×#547	C₂²	semidirect
42. C₁₃×#547	C₂²	semidirect
43. C₁₃×#547	C₂²	semidirect
44. C₁₃×#547	C₂²	semidirect
45. C₁₃×#546	C₂²	semidirect
46. C₁₃×#546	C₂²	semidirect
47. C₁₃×#546	C₂²	semidirect
48. C₁₃×#546	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×#541	C₂²	semidirect
57. C₁₃×#540	C₂²	semidirect
58. C₁₃×#539	C₂²	semidirect
59. C₁₃×#539	C₂²	semidirect
60. C₁₃×#539	C₂²	semidirect
61. C₁₃×#539	C₂²	semidirect
62. C₁₃×#539	C₂²	semidirect
63. C₁₃×#539	C₂²	semidirect
64. C₁₃×#539	C₂²	semidirect
65. C₁₃×#539	C₂²	semidirect
66. C₁₃×#538	C₂²	semidirect
67. C₁₃×#538	C₂²	semidirect
68. C₁₃×#538	C₂²	semidirect
70. C₁₃×#536	C₂²	semidirect
72. C₁₃×#534	C₂²	semidirect
73. C₁₃×#533	C₂²	semidirect
74. C₁₃×#533	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. C₁₃×#529	C₂²	semidirect
82. C₂×C₁₃×#126	C₂²	semidirect
83. C₂×C₁₃×#125	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×#123	C₂²	semidirect
89. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
90. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
92. C₁₃×#520	C₂²	semidirect
93. C₁₃×#520	C₂²	semidirect
94. C₁₃×#520	C₂²	semidirect
95. C₁₃×#520	C₂²	semidirect
97. C₁₃×#518	C₂²	semidirect
98. C₁₃×#518	C₂²	semidirect
99. C₄×C₁₃×#41	C₂²	semidirect
100. C₄×C₁₃×#41	C₂²	semidirect
101. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
102. C₂×C₄×Q₈×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×C₄⋊C₄	C₂²	semidirect
112. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
288. #62847	C₁₃	direct (N × H)
307. C₂×D₄×C₁₃	#41	semidirect
401. #3521	C₂×C₁₃	semidirect
402. #3520	C₂×C₁₃	semidirect
403. #3515	C₂×C₁₃	semidirect
404. #3513	C₂×C₁₃	semidirect
405. #3507	C₂×C₁₃	semidirect
406. #3505	C₂×C₁₃	semidirect
407. #3501	C₂×C₁₃	semidirect
408. #3496	C₂×C₁₃	semidirect
409. #3492	C₂×C₁₃	semidirect
410. #3491	C₂×C₁₃	semidirect
411. #3485	C₂×C₁₃	semidirect
412. #3461	C₂×C₁₃	semidirect
413. #3459	C₂×C₁₃	semidirect
414. #3455	C₂×C₁₃	semidirect
415. C₂×#539	C₂×C₁₃	semidirect
416. C₄×H(5,𝔽₂)	C₂×C₁₃	semidirect
417. C₂×#520	C₂×C₁₃	semidirect
483. #559	C₂²×C₁₃	semidirect
484. #557	C₂²×C₁₃	semidirect
485. #556	C₂²×C₁₃	semidirect
486. #556	C₂²×C₁₃	semidirect
487. #554	C₂²×C₁₃	semidirect
488. #554	C₂²×C₁₃	semidirect
489. #554	C₂²×C₁₃	semidirect
490. #554	C₂²×C₁₃	semidirect
491. #553	C₂²×C₁₃	semidirect
492. #553	C₂²×C₁₃	semidirect
493. #553	C₂²×C₁₃	semidirect
494. #552	C₂²×C₁₃	semidirect
495. #552	C₂²×C₁₃	semidirect
496. #552	C₂²×C₁₃	semidirect
497. #552	C₂²×C₁₃	semidirect
498. #552	C₂²×C₁₃	semidirect
499. #551	C₂²×C₁₃	semidirect
500. #551	C₂²×C₁₃	semidirect
501. #551	C₂²×C₁₃	semidirect
502. D₄×Q₈	C₂²×C₁₃	semidirect
503. #548	C₂²×C₁₃	semidirect
504. #547	C₂²×C₁₃	semidirect
505. #547	C₂²×C₁₃	semidirect
506. #547	C₂²×C₁₃	semidirect
507. #547	C₂²×C₁₃	semidirect
508. #546	C₂²×C₁₃	semidirect
509. #546	C₂²×C₁₃	semidirect
510. #546	C₂²×C₁₃	semidirect
511. #546	C₂²×C₁₃	semidirect
512. D₄²	C₂²×C₁₃	semidirect
513. #544	C₂²×C₁₃	semidirect
514. #543	C₂²×C₁₃	semidirect
515. #542	C₂²×C₁₃	semidirect
516. #542	C₂²×C₁₃	semidirect
517. #542	C₂²×C₁₃	semidirect
518. #541	C₂²×C₁₃	semidirect
519. #541	C₂²×C₁₃	semidirect
520. #540	C₂²×C₁₃	semidirect
521. #539	C₂²×C₁₃	semidirect
522. #539	C₂²×C₁₃	semidirect
523. #539	C₂²×C₁₃	semidirect
524. #539	C₂²×C₁₃	semidirect
525. #539	C₂²×C₁₃	semidirect
526. #539	C₂²×C₁₃	semidirect
527. #539	C₂²×C₁₃	semidirect
528. #539	C₂²×C₁₃	semidirect
529. #538	C₂²×C₁₃	semidirect
530. #538	C₂²×C₁₃	semidirect
531. #538	C₂²×C₁₃	semidirect
533. #536	C₂²×C₁₃	semidirect
535. #534	C₂²×C₁₃	semidirect
536. #533	C₂²×C₁₃	semidirect
537. #533	C₂²×C₁₃	semidirect
539. #529	C₂²×C₁₃	semidirect
540. #529	C₂²×C₁₃	semidirect
541. #529	C₂²×C₁₃	semidirect
542. #529	C₂²×C₁₃	semidirect
543. #529	C₂²×C₁₃	semidirect
544. #529	C₂²×C₁₃	semidirect
545. C₂×#126	C₂²×C₁₃	semidirect
546. C₂×#125	C₂²×C₁₃	semidirect
547. #525	C₂²×C₁₃	semidirect
548. #525	C₂²×C₁₃	semidirect
549. #525	C₂²×C₁₃	semidirect
550. C₂×#123	C₂²×C₁₃	semidirect
551. C₂×#123	C₂²×C₁₃	semidirect
552. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
553. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
555. #520	C₂²×C₁₃	semidirect
556. #520	C₂²×C₁₃	semidirect
557. #520	C₂²×C₁₃	semidirect
558. #520	C₂²×C₁₃	semidirect
560. #518	C₂²×C₁₃	semidirect
561. #518	C₂²×C₁₃	semidirect
562. C₄×#41	C₂²×C₁₃	semidirect
563. C₄×#41	C₂²×C₁₃	semidirect
564. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
565. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
568. C₂×C₄×D₄	C₂²×C₁₃	semidirect
569. C₂×C₄×D₄	C₂²×C₁₃	semidirect
570. C₂×C₄×D₄	C₂²×C₁₃	semidirect
571. C₂×C₄×D₄	C₂²×C₁₃	semidirect
572. C₂×#117	C₂²×C₁₃	semidirect
573. C₂×#117	C₂²×C₁₃	semidirect
574. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
575. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
805. C₂×D₄	C₁₃×#41	semidirect
899. C₁₃	#62847	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×#3520	2
C₁₃×#3515	2
C₁₃×#3513	2
C₁₃×#3507	2
C₁₃×#3505	2
C₁₃×#3501	2
C₁₃×#3496	2
C₁₃×#3492	2
C₁₃×#3491	2
C₁₃×#3485	2
C₁₃×#3461	2
C₁₃×#3459	2
C₁₃×#3455	2
C₂×C₁₃×#539	2
C₄×C₁₃×H(5,𝔽₂)	2
C₂×C₁₃×#520	2
#62847	13

Subgroups — C13×#62847 #15749186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62847 #15749186