Subgroups — C₁₃×#62930 #15749269

Order 3328.

7318 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3558	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3549	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3547	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3542	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3540	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3537	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3519	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3511	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3506	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3494	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3493	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3488	C₂	1	4	yes	maximal, complemented
14	C₂×C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×C₁₃×#41	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3449	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
19	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
20	C₁₃×#562	C₂²	1	16	yes	complemented
21	C₁₃×H(3,𝔽₄)	C₂²	1	16	yes	complemented
22	C₁₃×#560	C₂²	1	16	yes	complemented
23	C₁₃×#559	C₂²	1	16	yes	complemented
24	C₁₃×#556	C₂²	1	4	yes	complemented
25	C₁₃×#556	C₂²	1	8	yes	complemented
26	C₁₃×#555	C₂²	1	4	yes	complemented
27	C₁₃×#555	C₂²	1	8	yes	complemented
28	C₁₃×#555	C₂²	1	8	yes	complemented
29	C₁₃×#555	C₂²	1	4	yes	complemented
30	C₁₃×#555	C₂²	1	8	yes	complemented
31	C₁₃×#555	C₂²	1	4	yes	complemented
32	C₁₃×#554	C₂²	1	4	yes	complemented
33	C₁₃×#553	C₂²	1	8	yes	complemented
34	C₁₃×#553	C₂²	1	8	yes	complemented
35	C₁₃×#553	C₂²	1	8	yes	complemented
36	C₁₃×#553	C₂²	1	8	yes	complemented
37	C₁₃×#552	C₂²	1	8	yes	complemented
38	C₁₃×#551	C₂²	1	16	yes	complemented
39	C₁₃×#550	C₂²	1	2	yes	complemented
40	C₁₃×#550	C₂²	1	8	yes	complemented
41	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
42	C₁₃×#548	C₂²	1	4	yes	complemented
43	C₁₃×#548	C₂²	1	8	yes	complemented
44	C₁₃×#548	C₂²	1	8	yes	complemented
45	C₁₃×#547	C₂²	1	4	yes	complemented
46	C₁₃×#547	C₂²	1	4	yes	complemented
47	C₁₃×#547	C₂²	1	4	yes	complemented
48	C₁₃×#547	C₂²	1	2	yes	complemented
49	C₁₃×#546	C₂²	1	8	yes	complemented
50	C₁₃×#546	C₂²	1	16	yes	complemented
51	C₁₃×#546	C₂²	1	8	yes	complemented
52	C₁₃×#546	C₂²	1	4	yes	complemented
53	C₁₃×#546	C₂²	1	8	yes	complemented
54	C₁₃×#546	C₂²	1	16	yes	complemented
55	D₄²×C₁₃	C₂²	1	8	yes	complemented
56	D₄²×C₁₃	C₂²	1	4	yes	complemented
57	D₄²×C₁₃	C₂²	1	4	yes	complemented
58	D₄²×C₁₃	C₂²	1	16	yes	complemented
59	D₄²×C₁₃	C₂²	1	8	yes	complemented
60	D₄²×C₁₃	C₂²	1	2	yes	complemented
61	C₁₃×#544	C₂²	1	4	yes	complemented
62	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#542	C₂²	1	4	yes	complemented
64	C₁₃×#542	C₂²	1	8	yes	complemented
65	C₁₃×#542	C₂²	1	8	yes	complemented
66	C₁₃×#542	C₂²	1	16	yes	complemented
67	C₁₃×#540	C₂²	1	8	yes	complemented
68	C₁₃×#540	C₂²	1	4	yes	complemented
69	C₁₃×#540	C₂²	1	8	yes	complemented
70	C₁₃×#538	C₂²	1	16	yes	complemented
71	C₁₃×#538	C₂²	1	8	yes	complemented
72	C₁₃×#538	C₂²	1	8	yes	complemented
73	C₁₃×#538	C₂²	1	16	yes	complemented
74	C₁₃×#538	C₂²	1	4	yes	complemented
75	C₁₃×#537	C₂²	1	8	yes	complemented
76	C₁₃×#537	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#537	C₂²	1	4	yes	complemented
78	C₁₃×#537	C₂²	1	2	yes	complemented
79	C₁₃×#536	C₂²	1	8	yes	complemented
80	C₁₃×#535	C₂²	1	8	yes	complemented
81	C₁₃×#535	C₂²	1	8	yes	complemented
82	C₁₃×#535	C₂²	1	16	yes	complemented
83	C₁₃×#535	C₂²	1	8	yes	complemented
84	C₁₃×#535	C₂²	1	4	yes	complemented
85	C₁₃×#535	C₂²	1	2	yes	complemented
86	C₁₃×#534	C₂²	1	8	yes	complemented
87	C₁₃×#534	C₂²	1	8	yes	complemented
88	C₁₃×#534	C₂²	1	4	yes	complemented
89	C₁₃×#533	C₂²	1	4	yes	complemented
90	C₁₃×#532	C₂²	1	4	yes	complemented
91	C₁₃×#532	C₂²	1	4	yes	complemented
92	C₁₃×#532	C₂²	1	4	yes	complemented
93	C₁₃×#532	C₂²	1	8	yes	complemented
94	C₁₃×#532	C₂²	1	2	yes	complemented
95	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
96	C₁₃×#529	C₂²	1	4	yes	complemented
97	C₁₃×#529	C₂²	1	8	yes	complemented
98	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
99	C₁₃×#525	C₂²	1	8	yes	complemented
100	C₁₃×#525	C₂²	1	4	yes	complemented
101	C₁₃×#525	C₂²	1	8	yes	complemented
102	C₁₃×#525	C₂²	1	8	yes	complemented
103	C₁₃×#525	C₂²	1	8	yes	complemented
104	C₁₃×#525	C₂²	1	4	yes	complemented
105	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
106	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
107	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
108	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
109	C₁₃×#520	C₂²	1	4	yes	complemented
110	C₁₃×#520	C₂²	1	4	yes	complemented
111	C₁₃×#518	C₂²	1	4	yes	complemented
112	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
113	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
114	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
117	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
118	C₁₃×H(5,𝔽₂)	—	4	8	no	—
119	C₂×C₁₃×#41	—	4	16	no	—
120	C₂×C₁₃×#41	C₂³	1	2	yes	—
121	C₂×C₁₃×#41	C₂³	1	4	yes	—
122	C₂×C₁₃×#41	C₂³	1	4	yes	—
123	C₂×C₁₃×#41	C₂³	1	4	yes	—
124	C₂×C₁₃×#41	C₂³	1	4	yes	—
125	C₂×C₁₃×#41	C₂³	1	8	yes	—
126	C₂×C₁₃×#41	C₂³	1	8	yes	—
127	C₂×C₁₃×#41	C₂³	1	8	yes	—
128	C₂×C₁₃×#41	C₂³	1	8	yes	—
129	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
130	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
131	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
134	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
135	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
136	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
137	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
138	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
139	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
140	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
141	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
144	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
145	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
146	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
147	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
148	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
149	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
150	C₁₃×#127	C₂³	1	2	yes	—
151	C₁₃×#127	C₂³	1	8	yes	—
152	C₁₃×#127	C₂³	1	4	yes	—
153	C₁₃×#127	C₂³	1	4	yes	—
154	C₁₃×#127	C₂³	1	16	yes	—
155	C₁₃×#126	C₂³	1	8	yes	—
156	C₁₃×#126	C₂³	1	16	yes	—
157	C₁₃×#126	C₂³	1	16	yes	—
158	C₁₃×#126	C₂³	1	16	yes	—
159	C₁₃×#125	C₂³	1	4	yes	—
160	C₁₃×#125	C₂³	1	8	yes	—
161	C₁₃×#125	C₂³	1	8	yes	—
162	C₁₃×#124	C₂³	1	16	yes	—
163	C₁₃×#124	C₂³	1	16	yes	—
164	C₁₃×#124	C₂³	1	4	yes	—
165	C₁₃×#124	C₂³	1	8	yes	—
166	C₁₃×#124	C₂³	1	16	yes	—
167	C₁₃×#124	C₂³	1	8	yes	—
168	C₁₃×#124	C₂³	1	8	yes	—
169	C₁₃×#124	C₂³	1	4	yes	—
170	C₁₃×#124	C₂³	1	8	yes	—
171	C₁₃×#124	C₂³	1	16	yes	—
172	C₁₃×#124	C₂³	1	16	yes	—
173	C₁₃×#124	C₂³	1	16	yes	—
174	C₁₃×#123	C₂³	1	8	yes	—
175	C₁₃×#123	C₂³	1	16	yes	—
176	C₁₃×#123	C₂³	1	16	yes	—
177	C₁₃×#123	C₂³	1	8	yes	—
178	C₁₃×#123	C₂³	1	16	yes	—
179	C₁₃×#123	C₂³	1	8	yes	—
180	C₁₃×#123	C₂³	1	8	yes	—
181	C₁₃×#123	C₂³	1	8	yes	—
182	C₁₃×#123	C₂³	1	16	yes	—
183	C₁₃×#123	C₂³	1	16	yes	—
184	C₁₃×#123	C₂³	1	16	yes	—
185	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
188	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
190	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
191	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
195	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
198	C₁₃×#121	C₂³	1	4	yes	—
199	C₁₃×#121	C₂³	1	8	yes	—
200	C₁₃×#121	C₂³	1	4	yes	—
201	C₁₃×#121	C₂³	1	4	yes	—
202	C₁₃×#121	C₂³	1	8	yes	—
203	C₁₃×#121	C₂³	1	8	yes	—
204	C₁₃×#121	C₂³	1	8	yes	—
205	C₁₃×#121	C₂³	1	8	yes	—
206	C₁₃×#121	C₂³	1	8	yes	—
207	C₁₃×#121	C₂³	1	8	yes	—
208	C₁₃×#121	C₂³	1	16	yes	—
209	C₁₃×#121	C₂³	1	16	yes	—
210	C₁₃×#121	C₂³	1	8	yes	—
211	C₁₃×#121	C₂³	1	4	yes	—
212	C₁₃×#121	C₂³	1	4	yes	—
213	C₁₃×#121	C₂³	1	4	yes	—
214	C₁₃×#121	C₂³	1	4	yes	—
215	C₁₃×#121	C₂³	1	4	yes	—
216	C₁₃×#121	C₂³	1	8	yes	—
217	C₁₃×#121	C₂³	1	8	yes	—
218	C₁₃×#121	C₂³	1	8	yes	—
219	C₁₃×#121	C₂³	1	8	yes	—
220	C₁₃×#121	C₂³	1	4	yes	—
221	C₁₃×#121	C₂³	1	16	yes	—
222	C₁₃×#121	C₂³	1	8	yes	—
223	C₁₃×#121	C₂³	1	4	yes	—
224	C₁₃×#121	C₂³	1	4	yes	—
225	C₁₃×#121	C₂³	1	8	yes	—
226	C₁₃×#121	C₂³	1	8	yes	—
227	C₁₃×#121	C₂³	1	16	yes	—
228	C₁₃×#121	C₂³	1	16	yes	—
229	C₁₃×#121	C₂³	1	16	yes	—
230	C₁₃×#121	C₂³	1	16	yes	—
231	C₁₃×#120	C₂³	1	16	yes	—
232	C₁₃×#120	C₂³	1	8	yes	—
233	C₁₃×#120	C₂³	1	16	yes	—
234	C₁₃×#120	C₂³	1	8	yes	—
235	C₁₃×#120	C₂³	1	8	yes	—
236	C₁₃×#120	C₂³	1	16	yes	—
237	C₁₃×#120	C₂³	1	8	yes	—
238	C₁₃×#120	C₂³	1	16	yes	—
239	C₁₃×#120	C₂³	1	16	yes	—
240	C₁₃×#120	C₂³	1	16	yes	—
241	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
243	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
244	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
245	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
246	C₄×D₄×C₁₃	C₂³	1	2	yes	—
247	C₄×D₄×C₁₃	C₂³	1	4	yes	—
248	C₄×D₄×C₁₃	C₂³	1	4	yes	—
249	C₄×D₄×C₁₃	C₂³	1	8	yes	—
250	C₄×D₄×C₁₃	C₂³	1	4	yes	—
251	C₄×D₄×C₁₃	C₂³	1	4	yes	—
252	C₄×D₄×C₁₃	C₂³	1	2	yes	—
253	C₄×D₄×C₁₃	C₂³	1	8	yes	—
254	C₄×D₄×C₁₃	C₂³	1	4	yes	—
255	C₄×D₄×C₁₃	C₂³	1	4	yes	—
256	C₄×D₄×C₁₃	C₂³	1	4	yes	—
257	C₄×D₄×C₁₃	C₂³	1	2	yes	—
258	C₄×D₄×C₁₃	C₂³	1	4	yes	—
259	C₄×D₄×C₁₃	C₂³	1	2	yes	—
260	C₄×D₄×C₁₃	C₂³	1	8	yes	—
261	C₄×D₄×C₁₃	C₂³	1	8	yes	—
262	C₄×D₄×C₁₃	C₂³	1	8	yes	—
263	C₄×D₄×C₁₃	C₂³	1	8	yes	—
264	C₄×D₄×C₁₃	C₂³	1	16	yes	—
265	C₄×D₄×C₁₃	C₂³	1	16	yes	—
266	C₄×D₄×C₁₃	C₂³	1	8	yes	—
267	C₄×D₄×C₁₃	C₂³	1	8	yes	—
268	C₄×D₄×C₁₃	C₂³	1	4	yes	—
269	C₄×D₄×C₁₃	C₂³	1	16	yes	—
270	C₄×D₄×C₁₃	C₂³	1	8	yes	—
271	C₄×D₄×C₁₃	C₂³	1	16	yes	—
272	C₁₃×#117	C₂³	1	4	yes	—
273	C₁₃×#117	C₂³	1	8	yes	—
274	C₁₃×#117	C₂³	1	8	yes	—
275	C₁₃×#117	C₂³	1	4	yes	—
276	C₁₃×#117	C₂³	1	8	yes	—
277	C₁₃×#117	C₂³	1	2	yes	—
278	C₁₃×#117	C₂³	1	4	yes	—
279	C₁₃×#117	C₂³	1	4	yes	—
280	C₁₃×#117	C₂³	1	8	yes	—
281	C₁₃×#117	C₂³	1	8	yes	—
282	C₁₃×#117	C₂³	1	16	yes	—
283	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
286	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
287	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
288	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
289	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
290	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
291	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
292	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
293	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
294	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
295	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
296	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
297	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
298	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
300	#62930	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
301	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
302	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
303	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
304	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
305	C₁₃×#41	—	2	8	no	—
306	C₁₃×#41	—	2	16	no	—
307	C₁₃×#41	—	4	16	no	—
308	C₁₃×#41	—	4	8	no	—
309	C₁₃×#41	—	4	16	no	—
310	C₁₃×#41	—	4	8	no	—
311	C₁₃×#41	—	4	8	no	—
312	C₁₃×#41	—	4	16	no	—
313	C₁₃×#41	—	8	8	no	—
314	C₂×Q₈×C₁₃	—	4	8	no	—
315	C₂×Q₈×C₁₃	—	8	2	no	—
316	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
317	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
318	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
319	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
320	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
321	C₂×D₄×C₁₃	—	2	4	no	—
322	C₂×D₄×C₁₃	—	4	2	no	—
323	C₂×D₄×C₁₃	—	4	8	no	—
324	C₂×D₄×C₁₃	—	4	8	no	—
325	C₂×D₄×C₁₃	—	4	8	no	—
326	C₂×D₄×C₁₃	—	4	16	no	—
327	C₂×D₄×C₁₃	—	4	16	no	—
328	C₂×D₄×C₁₃	—	4	16	no	—
329	C₂×D₄×C₁₃	—	8	4	no	—
330	C₂×D₄×C₁₃	—	8	16	no	—
331	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
332	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
333	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
334	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
335	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
336	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
337	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
338	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
339	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
340	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
341	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
342	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
343	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
344	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
345	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
346	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
347	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
348	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
349	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
350	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
351	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
352	C₂²×C₄×C₁₃	—	2	8	no	—
353	C₂²×C₄×C₁₃	—	4	4	no	—
354	C₂²×C₄×C₁₃	—	4	16	no	—
355	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
358	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
361	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
362	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
363	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
366	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
367	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
368	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
369	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
370	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
371	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
372	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
373	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
375	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
376	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
377	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
378	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
379	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
380	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
381	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
382	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
383	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
384	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
385	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
386	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
387	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
388	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
389	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
390	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
391	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
392	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
393	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
394	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
395	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
396	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
397	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
398	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
399	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
400	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
401	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
402	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
403	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
404	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
405	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
406	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
407	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
408	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
409	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
410	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
411	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
412	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
413	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
414	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
415	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
416	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
417	C₄²×C₁₃	C₂⁴	1	2	yes	—
418	C₄²×C₁₃	C₂⁴	1	8	yes	—
419	C₄²×C₁₃	C₂⁴	1	8	yes	—
420	C₄²×C₁₃	C₂⁴	1	2	yes	—
421	C₄²×C₁₃	C₂⁴	1	4	yes	—
422	C₄²×C₁₃	C₂⁴	1	4	yes	—
423	C₄²×C₁₃	C₂⁴	1	4	yes	—
424	C₄²×C₁₃	C₂⁴	1	16	yes	—
425	#3558	C₂×C₁₃	1	8	yes	complemented
426	#3549	C₂×C₁₃	1	4	yes	complemented
427	#3547	C₂×C₁₃	1	4	yes	complemented
428	#3542	C₂×C₁₃	1	8	yes	complemented
429	#3540	C₂×C₁₃	1	8	yes	complemented
430	#3537	C₂×C₁₃	1	4	yes	complemented
431	#3519	C₂×C₁₃	1	4	yes	complemented
432	#3511	C₂×C₁₃	1	2	yes	complemented
433	#3506	C₂×C₁₃	1	4	yes	complemented
434	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
435	#3494	C₂×C₁₃	1	4	yes	complemented
436	#3493	C₂×C₁₃	1	2	yes	complemented
437	#3488	C₂×C₁₃	1	4	yes	complemented
438	C₂×#555	C₂×C₁₃	1	1	yes	characteristic, complemented
439	D₄×#41	C₂×C₁₃	1	2	yes	complemented
440	#3460	C₂×C₁₃	1	1	yes	characteristic, complemented
441	#3449	C₂×C₁₃	1	2	yes	complemented
442	C₂³×C₁₃	—	2	4	no	—
443	C₂³×C₁₃	—	2	4	no	—
444	C₂³×C₁₃	—	4	8	no	—
445	C₂³×C₁₃	—	4	2	no	—
446	C₂³×C₁₃	—	4	2	no	—
447	C₂³×C₁₃	—	4	8	no	—
448	C₂³×C₁₃	—	4	2	no	—
449	C₂³×C₁₃	—	4	2	no	—
450	C₂³×C₁₃	—	4	8	no	—
451	C₂³×C₁₃	—	4	8	no	—
452	C₂³×C₁₃	—	4	8	no	—
453	C₂³×C₁₃	—	4	8	no	—
454	C₂³×C₁₃	C₂⁵	1	4	yes	—
455	C₂³×C₁₃	C₂⁵	1	8	yes	—
456	C₂³×C₁₃	C₂⁵	1	4	yes	—
457	C₂³×C₁₃	C₂⁵	1	4	yes	—
458	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
459	Q₈×C₁₃	—	2	4	no	—
460	Q₈×C₁₃	—	2	8	no	—
461	Q₈×C₁₃	—	4	8	no	—
462	Q₈×C₁₃	—	4	8	no	—
463	Q₈×C₁₃	—	4	4	no	—
464	D₄×C₁₃	—	2	16	no	—
465	D₄×C₁₃	—	2	8	no	—
466	D₄×C₁₃	—	2	8	no	—
467	D₄×C₁₃	—	2	8	no	—
468	D₄×C₁₃	—	2	4	no	—
469	D₄×C₁₃	—	2	4	no	—
470	D₄×C₁₃	—	2	8	no	—
471	D₄×C₁₃	—	4	16	no	—
472	D₄×C₁₃	—	4	2	no	—
473	D₄×C₁₃	—	4	8	no	—
474	D₄×C₁₃	—	4	8	no	—
475	D₄×C₁₃	—	4	8	no	—
476	D₄×C₁₃	—	4	8	no	—
477	D₄×C₁₃	—	4	8	no	—
478	D₄×C₁₃	—	4	8	no	—
479	D₄×C₁₃	—	4	8	no	—
480	D₄×C₁₃	—	4	16	no	—
481	D₄×C₁₃	—	4	16	no	—
482	D₄×C₁₃	—	4	4	no	—
483	D₄×C₁₃	—	4	8	no	—
484	D₄×C₁₃	—	4	4	no	—
485	C₂×C₄×C₁₃	—	2	4	no	—
486	C₂×C₄×C₁₃	—	2	8	no	—
487	C₂×C₄×C₁₃	—	2	8	no	—
488	C₂×C₄×C₁₃	—	2	8	no	—
489	C₂×C₄×C₁₃	—	2	16	no	—
490	C₂×C₄×C₁₃	—	2	2	no	—
491	C₂×C₄×C₁₃	—	2	8	no	—
492	C₂×C₄×C₁₃	—	2	8	no	—
493	C₂×C₄×C₁₃	—	4	4	no	—
494	C₂×C₄×C₁₃	—	4	2	no	—
495	C₂×C₄×C₁₃	—	4	8	no	—
496	C₂×C₄×C₁₃	—	4	8	no	—
497	C₂×C₄×C₁₃	—	4	8	no	—
498	C₂×C₄×C₁₃	—	4	8	no	—
499	C₂×C₄×C₁₃	—	4	4	no	—
500	C₂×C₄×C₁₃	—	4	16	no	—
501	C₂×C₄×C₁₃	—	4	1	no	—
502	C₂×C₄×C₁₃	—	4	4	no	—
503	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
504	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
505	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
506	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
507	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
508	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
509	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
510	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
511	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
512	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
513	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
514	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
515	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
516	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
517	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
518	#562	C₂²×C₁₃	1	16	yes	complemented
519	H(3,𝔽₄)	C₂²×C₁₃	1	16	yes	complemented
520	#560	C₂²×C₁₃	1	16	yes	complemented
521	#559	C₂²×C₁₃	1	16	yes	complemented
522	#556	C₂²×C₁₃	1	8	yes	complemented
523	#556	C₂²×C₁₃	1	4	yes	complemented
524	#555	C₂²×C₁₃	1	4	yes	complemented
525	#555	C₂²×C₁₃	1	8	yes	complemented
526	#555	C₂²×C₁₃	1	4	yes	complemented
527	#555	C₂²×C₁₃	1	8	yes	complemented
528	#555	C₂²×C₁₃	1	8	yes	complemented
529	#555	C₂²×C₁₃	1	4	yes	complemented
530	#554	C₂²×C₁₃	1	4	yes	complemented
531	#553	C₂²×C₁₃	1	8	yes	complemented
532	#553	C₂²×C₁₃	1	8	yes	complemented
533	#553	C₂²×C₁₃	1	8	yes	complemented
534	#553	C₂²×C₁₃	1	8	yes	complemented
535	#552	C₂²×C₁₃	1	8	yes	complemented
536	#551	C₂²×C₁₃	1	16	yes	complemented
537	#550	C₂²×C₁₃	1	2	yes	complemented
538	#550	C₂²×C₁₃	1	8	yes	complemented
539	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
540	#548	C₂²×C₁₃	1	4	yes	complemented
541	#548	C₂²×C₁₃	1	8	yes	complemented
542	#548	C₂²×C₁₃	1	8	yes	complemented
543	#547	C₂²×C₁₃	1	4	yes	complemented
544	#547	C₂²×C₁₃	1	2	yes	complemented
545	#547	C₂²×C₁₃	1	4	yes	complemented
546	#547	C₂²×C₁₃	1	4	yes	complemented
547	#546	C₂²×C₁₃	1	4	yes	complemented
548	#546	C₂²×C₁₃	1	8	yes	complemented
549	#546	C₂²×C₁₃	1	16	yes	complemented
550	#546	C₂²×C₁₃	1	8	yes	complemented
551	#546	C₂²×C₁₃	1	8	yes	complemented
552	#546	C₂²×C₁₃	1	16	yes	complemented
553	D₄²	C₂²×C₁₃	1	4	yes	complemented
554	D₄²	C₂²×C₁₃	1	2	yes	complemented
555	D₄²	C₂²×C₁₃	1	16	yes	complemented
556	D₄²	C₂²×C₁₃	1	8	yes	complemented
557	D₄²	C₂²×C₁₃	1	4	yes	complemented
558	D₄²	C₂²×C₁₃	1	8	yes	complemented
559	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
560	#544	C₂²×C₁₃	1	4	yes	complemented
561	#542	C₂²×C₁₃	1	4	yes	complemented
562	#542	C₂²×C₁₃	1	8	yes	complemented
563	#542	C₂²×C₁₃	1	8	yes	complemented
564	#542	C₂²×C₁₃	1	16	yes	complemented
565	#540	C₂²×C₁₃	1	4	yes	complemented
566	#540	C₂²×C₁₃	1	8	yes	complemented
567	#540	C₂²×C₁₃	1	8	yes	complemented
568	#538	C₂²×C₁₃	1	4	yes	complemented
569	#538	C₂²×C₁₃	1	8	yes	complemented
570	#538	C₂²×C₁₃	1	16	yes	complemented
571	#538	C₂²×C₁₃	1	16	yes	complemented
572	#538	C₂²×C₁₃	1	8	yes	complemented
573	#537	C₂²×C₁₃	1	1	yes	characteristic, complemented
574	#537	C₂²×C₁₃	1	4	yes	complemented
575	#537	C₂²×C₁₃	1	2	yes	complemented
576	#537	C₂²×C₁₃	1	8	yes	complemented
577	#536	C₂²×C₁₃	1	8	yes	complemented
578	#535	C₂²×C₁₃	1	8	yes	complemented
579	#535	C₂²×C₁₃	1	2	yes	complemented
580	#535	C₂²×C₁₃	1	8	yes	complemented
581	#535	C₂²×C₁₃	1	4	yes	complemented
582	#535	C₂²×C₁₃	1	8	yes	complemented
583	#535	C₂²×C₁₃	1	16	yes	complemented
584	#534	C₂²×C₁₃	1	8	yes	complemented
585	#534	C₂²×C₁₃	1	4	yes	complemented
586	#534	C₂²×C₁₃	1	8	yes	complemented
587	#533	C₂²×C₁₃	1	4	yes	complemented
588	#532	C₂²×C₁₃	1	8	yes	complemented
589	#532	C₂²×C₁₃	1	4	yes	complemented
590	#532	C₂²×C₁₃	1	2	yes	complemented
591	#532	C₂²×C₁₃	1	4	yes	complemented
592	#532	C₂²×C₁₃	1	4	yes	complemented
593	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
594	#529	C₂²×C₁₃	1	4	yes	complemented
595	#529	C₂²×C₁₃	1	8	yes	complemented
596	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
597	#525	C₂²×C₁₃	1	8	yes	complemented
598	#525	C₂²×C₁₃	1	8	yes	complemented
599	#525	C₂²×C₁₃	1	4	yes	complemented
600	#525	C₂²×C₁₃	1	4	yes	complemented
601	#525	C₂²×C₁₃	1	8	yes	complemented
602	#525	C₂²×C₁₃	1	8	yes	complemented
603	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
604	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
605	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
606	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
607	#520	C₂²×C₁₃	1	4	yes	complemented
608	#520	C₂²×C₁₃	1	4	yes	complemented
609	#518	C₂²×C₁₃	1	4	yes	complemented
610	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
611	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
614	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
615	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
616	C₂²×C₁₃	—	2	1	no	—
617	C₂²×C₁₃	—	2	1	no	—
618	C₂²×C₁₃	—	2	4	no	—
619	C₂²×C₁₃	—	2	4	no	—
620	C₂²×C₁₃	—	2	8	no	—
621	C₂²×C₁₃	—	2	4	no	—
622	C₂²×C₁₃	—	2	4	no	—
623	C₂²×C₁₃	—	2	4	no	—
624	C₂²×C₁₃	—	2	4	no	—
625	C₂²×C₁₃	—	2	8	no	—
626	C₂²×C₁₃	—	2	8	no	—
627	C₂²×C₁₃	—	2	4	no	—
628	C₂²×C₁₃	—	2	4	no	—
629	C₂²×C₁₃	—	2	4	no	—
630	C₂²×C₁₃	—	8	4	no	—
631	C₂²×C₁₃	—	8	4	no	—
632	C₂²×C₁₃	—	8	16	no	—
633	C₂²×C₁₃	—	16	8	no	—
634	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
635	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
636	C₄×C₁₃	—	2	2	no	—
637	C₄×C₁₃	—	2	2	no	—
638	C₄×C₁₃	—	2	8	no	—
639	C₄×C₁₃	—	2	4	no	—
640	C₄×C₁₃	—	2	1	no	—
641	C₄×C₁₃	—	2	4	no	—
642	C₄×C₁₃	—	2	4	no	—
643	C₄×C₁₃	—	2	4	no	—
644	C₄×C₁₃	—	2	8	no	—
645	C₄×C₁₃	—	2	2	no	—
646	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
647	C₄×C₁₃	#585	1	2	yes	—
648	H(5,𝔽₂)	—	4	8	no	—
649	C₂×#41	—	4	16	no	—
650	C₂×#41	C₂³×C₁₃	1	2	yes	—
651	C₂×#41	C₂³×C₁₃	1	4	yes	—
652	C₂×#41	C₂³×C₁₃	1	4	yes	—
653	C₂×#41	C₂³×C₁₃	1	4	yes	—
654	C₂×#41	C₂³×C₁₃	1	4	yes	—
655	C₂×#41	C₂³×C₁₃	1	8	yes	—
656	C₂×#41	C₂³×C₁₃	1	8	yes	—
657	C₂×#41	C₂³×C₁₃	1	8	yes	—
658	C₂×#41	C₂³×C₁₃	1	8	yes	—
659	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
660	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
661	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
662	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
663	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
664	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
665	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
666	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
667	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
668	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
669	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
670	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
671	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
672	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
673	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
674	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
675	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
676	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
677	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
678	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
679	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
680	#127	C₂³×C₁₃	1	2	yes	—
681	#127	C₂³×C₁₃	1	8	yes	—
682	#127	C₂³×C₁₃	1	4	yes	—
683	#127	C₂³×C₁₃	1	4	yes	—
684	#127	C₂³×C₁₃	1	16	yes	—
685	#126	C₂³×C₁₃	1	8	yes	—
686	#126	C₂³×C₁₃	1	16	yes	—
687	#126	C₂³×C₁₃	1	16	yes	—
688	#126	C₂³×C₁₃	1	16	yes	—
689	#125	C₂³×C₁₃	1	4	yes	—
690	#125	C₂³×C₁₃	1	8	yes	—
691	#125	C₂³×C₁₃	1	8	yes	—
692	#124	C₂³×C₁₃	1	16	yes	—
693	#124	C₂³×C₁₃	1	16	yes	—
694	#124	C₂³×C₁₃	1	4	yes	—
695	#124	C₂³×C₁₃	1	8	yes	—
696	#124	C₂³×C₁₃	1	16	yes	—
697	#124	C₂³×C₁₃	1	8	yes	—
698	#124	C₂³×C₁₃	1	8	yes	—
699	#124	C₂³×C₁₃	1	4	yes	—
700	#124	C₂³×C₁₃	1	8	yes	—
701	#124	C₂³×C₁₃	1	16	yes	—
702	#124	C₂³×C₁₃	1	16	yes	—
703	#124	C₂³×C₁₃	1	16	yes	—
704	#123	C₂³×C₁₃	1	8	yes	—
705	#123	C₂³×C₁₃	1	16	yes	—
706	#123	C₂³×C₁₃	1	16	yes	—
707	#123	C₂³×C₁₃	1	8	yes	—
708	#123	C₂³×C₁₃	1	16	yes	—
709	#123	C₂³×C₁₃	1	8	yes	—
710	#123	C₂³×C₁₃	1	8	yes	—
711	#123	C₂³×C₁₃	1	8	yes	—
712	#123	C₂³×C₁₃	1	16	yes	—
713	#123	C₂³×C₁₃	1	16	yes	—
714	#123	C₂³×C₁₃	1	16	yes	—
715	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
716	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
717	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
718	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
719	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
720	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
721	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
722	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
723	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
724	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
725	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
726	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
727	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
728	#121	C₂³×C₁₃	1	4	yes	—
729	#121	C₂³×C₁₃	1	8	yes	—
730	#121	C₂³×C₁₃	1	4	yes	—
731	#121	C₂³×C₁₃	1	4	yes	—
732	#121	C₂³×C₁₃	1	8	yes	—
733	#121	C₂³×C₁₃	1	8	yes	—
734	#121	C₂³×C₁₃	1	8	yes	—
735	#121	C₂³×C₁₃	1	8	yes	—
736	#121	C₂³×C₁₃	1	8	yes	—
737	#121	C₂³×C₁₃	1	8	yes	—
738	#121	C₂³×C₁₃	1	16	yes	—
739	#121	C₂³×C₁₃	1	16	yes	—
740	#121	C₂³×C₁₃	1	8	yes	—
741	#121	C₂³×C₁₃	1	4	yes	—
742	#121	C₂³×C₁₃	1	4	yes	—
743	#121	C₂³×C₁₃	1	4	yes	—
744	#121	C₂³×C₁₃	1	4	yes	—
745	#121	C₂³×C₁₃	1	4	yes	—
746	#121	C₂³×C₁₃	1	8	yes	—
747	#121	C₂³×C₁₃	1	8	yes	—
748	#121	C₂³×C₁₃	1	8	yes	—
749	#121	C₂³×C₁₃	1	8	yes	—
750	#121	C₂³×C₁₃	1	4	yes	—
751	#121	C₂³×C₁₃	1	16	yes	—
752	#121	C₂³×C₁₃	1	8	yes	—
753	#121	C₂³×C₁₃	1	4	yes	—
754	#121	C₂³×C₁₃	1	4	yes	—
755	#121	C₂³×C₁₃	1	8	yes	—
756	#121	C₂³×C₁₃	1	8	yes	—
757	#121	C₂³×C₁₃	1	16	yes	—
758	#121	C₂³×C₁₃	1	16	yes	—
759	#121	C₂³×C₁₃	1	16	yes	—
760	#121	C₂³×C₁₃	1	16	yes	—
761	#120	C₂³×C₁₃	1	16	yes	—
762	#120	C₂³×C₁₃	1	8	yes	—
763	#120	C₂³×C₁₃	1	16	yes	—
764	#120	C₂³×C₁₃	1	8	yes	—
765	#120	C₂³×C₁₃	1	8	yes	—
766	#120	C₂³×C₁₃	1	16	yes	—
767	#120	C₂³×C₁₃	1	8	yes	—
768	#120	C₂³×C₁₃	1	16	yes	—
769	#120	C₂³×C₁₃	1	16	yes	—
770	#120	C₂³×C₁₃	1	16	yes	—
771	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
772	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
773	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
774	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
775	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
776	C₄×D₄	C₂³×C₁₃	1	2	yes	—
777	C₄×D₄	C₂³×C₁₃	1	4	yes	—
778	C₄×D₄	C₂³×C₁₃	1	4	yes	—
779	C₄×D₄	C₂³×C₁₃	1	8	yes	—
780	C₄×D₄	C₂³×C₁₃	1	4	yes	—
781	C₄×D₄	C₂³×C₁₃	1	4	yes	—
782	C₄×D₄	C₂³×C₁₃	1	2	yes	—
783	C₄×D₄	C₂³×C₁₃	1	8	yes	—
784	C₄×D₄	C₂³×C₁₃	1	4	yes	—
785	C₄×D₄	C₂³×C₁₃	1	4	yes	—
786	C₄×D₄	C₂³×C₁₃	1	4	yes	—
787	C₄×D₄	C₂³×C₁₃	1	2	yes	—
788	C₄×D₄	C₂³×C₁₃	1	4	yes	—
789	C₄×D₄	C₂³×C₁₃	1	2	yes	—
790	C₄×D₄	C₂³×C₁₃	1	8	yes	—
791	C₄×D₄	C₂³×C₁₃	1	8	yes	—
792	C₄×D₄	C₂³×C₁₃	1	8	yes	—
793	C₄×D₄	C₂³×C₁₃	1	8	yes	—
794	C₄×D₄	C₂³×C₁₃	1	16	yes	—
795	C₄×D₄	C₂³×C₁₃	1	16	yes	—
796	C₄×D₄	C₂³×C₁₃	1	8	yes	—
797	C₄×D₄	C₂³×C₁₃	1	8	yes	—
798	C₄×D₄	C₂³×C₁₃	1	4	yes	—
799	C₄×D₄	C₂³×C₁₃	1	16	yes	—
800	C₄×D₄	C₂³×C₁₃	1	8	yes	—
801	C₄×D₄	C₂³×C₁₃	1	16	yes	—
802	#117	C₂³×C₁₃	1	4	yes	—
803	#117	C₂³×C₁₃	1	8	yes	—
804	#117	C₂³×C₁₃	1	8	yes	—
805	#117	C₂³×C₁₃	1	4	yes	—
806	#117	C₂³×C₁₃	1	8	yes	—
807	#117	C₂³×C₁₃	1	2	yes	—
808	#117	C₂³×C₁₃	1	4	yes	—
809	#117	C₂³×C₁₃	1	4	yes	—
810	#117	C₂³×C₁₃	1	8	yes	—
811	#117	C₂³×C₁₃	1	8	yes	—
812	#117	C₂³×C₁₃	1	16	yes	—
813	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
814	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
815	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
816	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
817	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
818	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
819	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
827	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
828	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
829	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
830	C₂×C₁₃	—	2	2	no	—
831	C₂×C₁₃	—	4	4	no	—
832	C₂×C₁₃	—	4	4	no	—
833	C₂×C₁₃	—	4	8	no	—
834	C₂×C₁₃	—	4	4	no	—
835	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
836	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
837	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
838	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
839	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
840	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
841	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
842	#41	—	2	8	no	—
843	#41	—	2	16	no	—
844	#41	—	4	16	no	—
845	#41	—	4	8	no	—
846	#41	—	4	16	no	—
847	#41	—	4	8	no	—
848	#41	—	4	8	no	—
849	#41	—	4	16	no	—
850	#41	—	8	8	no	—
851	C₂×Q₈	—	4	8	no	—
852	C₂×Q₈	—	8	2	no	—
853	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
854	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
855	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
856	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
857	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
858	C₂×D₄	—	2	4	no	—
859	C₂×D₄	—	4	8	no	—
860	C₂×D₄	—	4	16	no	—
861	C₂×D₄	—	4	2	no	—
862	C₂×D₄	—	4	8	no	—
863	C₂×D₄	—	4	8	no	—
864	C₂×D₄	—	4	16	no	—
865	C₂×D₄	—	4	16	no	—
866	C₂×D₄	—	8	4	no	—
867	C₂×D₄	—	8	16	no	—
868	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
869	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
870	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
871	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
872	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
873	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
874	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
875	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
876	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
877	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
878	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
879	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
880	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
881	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
882	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
883	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
884	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
885	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
886	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
887	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
888	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
889	C₂²×C₄	—	2	8	no	—
890	C₂²×C₄	—	4	16	no	—
891	C₂²×C₄	—	4	4	no	—
892	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
893	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
895	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
896	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
897	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
898	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
899	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
900	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
901	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
902	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
903	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
904	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
905	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
906	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
907	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
908	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
909	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
910	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
911	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
912	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
913	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
914	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
915	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
916	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
917	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
918	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
919	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
920	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
921	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
922	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
923	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
924	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
925	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
926	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
927	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
928	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
929	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
930	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
931	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
932	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
933	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
934	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
935	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
936	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
937	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
938	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
939	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
940	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
941	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
942	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
943	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
944	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
945	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
946	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
947	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
948	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
949	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
950	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
951	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
952	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
953	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
954	C₄²	C₂⁴×C₁₃	1	2	yes	—
955	C₄²	C₂⁴×C₁₃	1	8	yes	—
956	C₄²	C₂⁴×C₁₃	1	8	yes	—
957	C₄²	C₂⁴×C₁₃	1	2	yes	—
958	C₄²	C₂⁴×C₁₃	1	4	yes	—
959	C₄²	C₂⁴×C₁₃	1	4	yes	—
960	C₄²	C₂⁴×C₁₃	1	4	yes	—
961	C₄²	C₂⁴×C₁₃	1	16	yes	—
962	C₁₃	#62930	1	1	yes	characteristic, direct product factor, Sylow
963	C₂³	—	2	4	no	—
964	C₂³	—	2	4	no	—
965	C₂³	—	4	8	no	—
966	C₂³	—	4	2	no	—
967	C₂³	—	4	2	no	—
968	C₂³	—	4	8	no	—
969	C₂³	—	4	2	no	—
970	C₂³	—	4	2	no	—
971	C₂³	—	4	8	no	—
972	C₂³	—	4	8	no	—
973	C₂³	—	4	8	no	—
974	C₂³	—	4	8	no	—
975	C₂³	C₂⁵×C₁₃	1	4	yes	—
976	C₂³	C₂⁵×C₁₃	1	8	yes	—
977	C₂³	C₂⁵×C₁₃	1	4	yes	—
978	C₂³	C₂⁵×C₁₃	1	4	yes	—
979	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
980	Q₈	—	2	4	no	—
981	Q₈	—	2	8	no	—
982	Q₈	—	4	8	no	—
983	Q₈	—	4	8	no	—
984	Q₈	—	4	4	no	—
985	D₄	—	2	16	no	—
986	D₄	—	2	8	no	—
987	D₄	—	2	8	no	—
988	D₄	—	2	8	no	—
989	D₄	—	2	4	no	—
990	D₄	—	2	4	no	—
991	D₄	—	2	8	no	—
992	D₄	—	4	16	no	—
993	D₄	—	4	2	no	—
994	D₄	—	4	8	no	—
995	D₄	—	4	8	no	—
996	D₄	—	4	8	no	—
997	D₄	—	4	8	no	—
998	D₄	—	4	8	no	—
999	D₄	—	4	8	no	—
1000	D₄	—	4	8	no	—
1001	D₄	—	4	16	no	—
1002	D₄	—	4	16	no	—
1003	D₄	—	4	4	no	—
1004	D₄	—	4	8	no	—
1005	D₄	—	4	4	no	—
1006	C₂×C₄	—	2	4	no	—
1007	C₂×C₄	—	2	8	no	—
1008	C₂×C₄	—	2	8	no	—
1009	C₂×C₄	—	2	8	no	—
1010	C₂×C₄	—	2	16	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	8	no	—
1013	C₂×C₄	—	2	8	no	—
1014	C₂×C₄	—	4	8	no	—
1015	C₂×C₄	—	4	4	no	—
1016	C₂×C₄	—	4	2	no	—
1017	C₂×C₄	—	4	8	no	—
1018	C₂×C₄	—	4	8	no	—
1019	C₂×C₄	—	4	8	no	—
1020	C₂×C₄	—	4	4	no	—
1021	C₂×C₄	—	4	16	no	—
1022	C₂×C₄	—	4	1	no	—
1023	C₂×C₄	—	4	4	no	—
1024	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
1025	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1026	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1027	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1028	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
1029	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1030	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1031	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1032	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1033	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
1034	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
1035	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
1036	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	4	no	—
1040	C₂²	—	2	4	no	—
1041	C₂²	—	2	8	no	—
1042	C₂²	—	2	4	no	—
1043	C₂²	—	2	4	no	—
1044	C₂²	—	2	4	no	—
1045	C₂²	—	2	4	no	—
1046	C₂²	—	2	8	no	—
1047	C₂²	—	2	8	no	—
1048	C₂²	—	2	4	no	—
1049	C₂²	—	2	4	no	—
1050	C₂²	—	2	4	no	—
1051	C₂²	—	8	4	no	—
1052	C₂²	—	8	4	no	—
1053	C₂²	—	8	16	no	—
1054	C₂²	—	16	8	no	—
1055	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1056	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	8	no	—
1060	C₄	—	2	4	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	4	no	—
1063	C₄	—	2	4	no	—
1064	C₄	—	2	4	no	—
1065	C₄	—	2	8	no	—
1066	C₄	—	2	2	no	—
1067	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
1068	C₄	C₁₃×#585	1	2	yes	—
1069	C₂	—	2	2	no	—
1070	C₂	—	4	4	no	—
1071	C₂	—	4	4	no	—
1072	C₂	—	4	8	no	—
1073	C₂	—	4	4	no	—
1074	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1075	C₂	C₂×C₁₃×#585	1	1	yes	characteristic
1076	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×#3558	C₂	semidirect
2. C₁₃×#3549	C₂	semidirect
3. C₁₃×#3547	C₂	semidirect
4. C₁₃×#3542	C₂	semidirect
5. C₁₃×#3540	C₂	semidirect
6. C₁₃×#3537	C₂	semidirect
7. C₁₃×#3519	C₂	semidirect
8. C₁₃×#3511	C₂	semidirect
9. C₁₃×#3506	C₂	semidirect
10. C₁₃×#3496	C₂	semidirect
11. C₁₃×#3494	C₂	semidirect
12. C₁₃×#3493	C₂	semidirect
13. C₁₃×#3488	C₂	semidirect
14. C₂×C₁₃×#555	C₂	semidirect
15. D₄×C₁₃×#41	C₂	semidirect
16. C₁₃×#3460	C₂	semidirect
17. C₁₃×#3449	C₂	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
19. C₂²×C₁₃×#41	C₂²	semidirect
20. C₁₃×#562	C₂²	semidirect
21. C₁₃×H(3,𝔽₄)	C₂²	semidirect
22. C₁₃×#560	C₂²	semidirect
23. C₁₃×#559	C₂²	semidirect
24. C₁₃×#556	C₂²	semidirect
25. C₁₃×#556	C₂²	semidirect
26. C₁₃×#555	C₂²	semidirect
27. C₁₃×#555	C₂²	semidirect
28. C₁₃×#555	C₂²	semidirect
29. C₁₃×#555	C₂²	semidirect
30. C₁₃×#555	C₂²	semidirect
31. C₁₃×#555	C₂²	semidirect
32. C₁₃×#554	C₂²	semidirect
33. C₁₃×#553	C₂²	semidirect
34. C₁₃×#553	C₂²	semidirect
35. C₁₃×#553	C₂²	semidirect
36. C₁₃×#553	C₂²	semidirect
37. C₁₃×#552	C₂²	semidirect
38. C₁₃×#551	C₂²	semidirect
39. C₁₃×#550	C₂²	semidirect
40. C₁₃×#550	C₂²	semidirect
41. D₄×Q₈×C₁₃	C₂²	semidirect
42. C₁₃×#548	C₂²	semidirect
43. C₁₃×#548	C₂²	semidirect
44. C₁₃×#548	C₂²	semidirect
45. C₁₃×#547	C₂²	semidirect
46. C₁₃×#547	C₂²	semidirect
47. C₁₃×#547	C₂²	semidirect
48. C₁₃×#547	C₂²	semidirect
49. C₁₃×#546	C₂²	semidirect
50. C₁₃×#546	C₂²	semidirect
51. C₁₃×#546	C₂²	semidirect
52. C₁₃×#546	C₂²	semidirect
53. C₁₃×#546	C₂²	semidirect
54. C₁₃×#546	C₂²	semidirect
55. D₄²×C₁₃	C₂²	semidirect
56. D₄²×C₁₃	C₂²	semidirect
57. D₄²×C₁₃	C₂²	semidirect
58. D₄²×C₁₃	C₂²	semidirect
59. D₄²×C₁₃	C₂²	semidirect
60. D₄²×C₁₃	C₂²	semidirect
61. C₁₃×#544	C₂²	semidirect
62. C₁₃×#544	C₂²	semidirect
63. C₁₃×#542	C₂²	semidirect
64. C₁₃×#542	C₂²	semidirect
65. C₁₃×#542	C₂²	semidirect
66. C₁₃×#542	C₂²	semidirect
67. C₁₃×#540	C₂²	semidirect
68. C₁₃×#540	C₂²	semidirect
69. C₁₃×#540	C₂²	semidirect
70. C₁₃×#538	C₂²	semidirect
71. C₁₃×#538	C₂²	semidirect
72. C₁₃×#538	C₂²	semidirect
73. C₁₃×#538	C₂²	semidirect
74. C₁₃×#538	C₂²	semidirect
75. C₁₃×#537	C₂²	semidirect
76. C₁₃×#537	C₂²	semidirect
77. C₁₃×#537	C₂²	semidirect
78. C₁₃×#537	C₂²	semidirect
79. C₁₃×#536	C₂²	semidirect
80. C₁₃×#535	C₂²	semidirect
81. C₁₃×#535	C₂²	semidirect
82. C₁₃×#535	C₂²	semidirect
83. C₁₃×#535	C₂²	semidirect
84. C₁₃×#535	C₂²	semidirect
85. C₁₃×#535	C₂²	semidirect
86. C₁₃×#534	C₂²	semidirect
87. C₁₃×#534	C₂²	semidirect
88. C₁₃×#534	C₂²	semidirect
89. C₁₃×#533	C₂²	semidirect
90. C₁₃×#532	C₂²	semidirect
91. C₁₃×#532	C₂²	semidirect
92. C₁₃×#532	C₂²	semidirect
93. C₁₃×#532	C₂²	semidirect
94. C₁₃×#532	C₂²	semidirect
95. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
96. C₁₃×#529	C₂²	semidirect
97. C₁₃×#529	C₂²	semidirect
98. C₂×C₁₃×#124	C₂²	semidirect
99. C₁₃×#525	C₂²	semidirect
100. C₁₃×#525	C₂²	semidirect
101. C₁₃×#525	C₂²	semidirect
102. C₁₃×#525	C₂²	semidirect
103. C₁₃×#525	C₂²	semidirect
104. C₁₃×#525	C₂²	semidirect
105. C₂×C₁₃×#121	C₂²	semidirect
106. C₂×C₁₃×#121	C₂²	semidirect
107. C₂×C₁₃×#121	C₂²	semidirect
108. C₂×C₁₃×#121	C₂²	semidirect
109. C₁₃×#520	C₂²	semidirect
110. C₁₃×#520	C₂²	semidirect
111. C₁₃×#518	C₂²	semidirect
112. C₄×C₁₃×#41	C₂²	semidirect
113. C₂×C₄×D₄×C₁₃	C₂²	semidirect
114. C₂×C₄×D₄×C₁₃	C₂²	semidirect
115. C₂×C₄×D₄×C₁₃	C₂²	semidirect
116. C₂×C₁₃×#117	C₂²	semidirect
117. C₂×C₁₃×#117	C₂²	semidirect
300. #62930	C₁₃	direct (N × H)
425. #3558	C₂×C₁₃	semidirect
426. #3549	C₂×C₁₃	semidirect
427. #3547	C₂×C₁₃	semidirect
428. #3542	C₂×C₁₃	semidirect
429. #3540	C₂×C₁₃	semidirect
430. #3537	C₂×C₁₃	semidirect
431. #3519	C₂×C₁₃	semidirect
432. #3511	C₂×C₁₃	semidirect
433. #3506	C₂×C₁₃	semidirect
434. #3496	C₂×C₁₃	semidirect
435. #3494	C₂×C₁₃	semidirect
436. #3493	C₂×C₁₃	semidirect
437. #3488	C₂×C₁₃	semidirect
438. C₂×#555	C₂×C₁₃	semidirect
439. D₄×#41	C₂×C₁₃	semidirect
440. #3460	C₂×C₁₃	semidirect
441. #3449	C₂×C₁₃	semidirect
516. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
517. C₂²×#41	C₂²×C₁₃	semidirect
518. #562	C₂²×C₁₃	semidirect
519. H(3,𝔽₄)	C₂²×C₁₃	semidirect
520. #560	C₂²×C₁₃	semidirect
521. #559	C₂²×C₁₃	semidirect
522. #556	C₂²×C₁₃	semidirect
523. #556	C₂²×C₁₃	semidirect
524. #555	C₂²×C₁₃	semidirect
525. #555	C₂²×C₁₃	semidirect
526. #555	C₂²×C₁₃	semidirect
527. #555	C₂²×C₁₃	semidirect
528. #555	C₂²×C₁₃	semidirect
529. #555	C₂²×C₁₃	semidirect
530. #554	C₂²×C₁₃	semidirect
531. #553	C₂²×C₁₃	semidirect
532. #553	C₂²×C₁₃	semidirect
533. #553	C₂²×C₁₃	semidirect
534. #553	C₂²×C₁₃	semidirect
535. #552	C₂²×C₁₃	semidirect
536. #551	C₂²×C₁₃	semidirect
537. #550	C₂²×C₁₃	semidirect
538. #550	C₂²×C₁₃	semidirect
539. D₄×Q₈	C₂²×C₁₃	semidirect
540. #548	C₂²×C₁₃	semidirect
541. #548	C₂²×C₁₃	semidirect
542. #548	C₂²×C₁₃	semidirect
543. #547	C₂²×C₁₃	semidirect
544. #547	C₂²×C₁₃	semidirect
545. #547	C₂²×C₁₃	semidirect
546. #547	C₂²×C₁₃	semidirect
547. #546	C₂²×C₁₃	semidirect
548. #546	C₂²×C₁₃	semidirect
549. #546	C₂²×C₁₃	semidirect
550. #546	C₂²×C₁₃	semidirect
551. #546	C₂²×C₁₃	semidirect
552. #546	C₂²×C₁₃	semidirect
553. D₄²	C₂²×C₁₃	semidirect
554. D₄²	C₂²×C₁₃	semidirect
555. D₄²	C₂²×C₁₃	semidirect
556. D₄²	C₂²×C₁₃	semidirect
557. D₄²	C₂²×C₁₃	semidirect
558. D₄²	C₂²×C₁₃	semidirect
559. #544	C₂²×C₁₃	semidirect
560. #544	C₂²×C₁₃	semidirect
561. #542	C₂²×C₁₃	semidirect
562. #542	C₂²×C₁₃	semidirect
563. #542	C₂²×C₁₃	semidirect
564. #542	C₂²×C₁₃	semidirect
565. #540	C₂²×C₁₃	semidirect
566. #540	C₂²×C₁₃	semidirect
567. #540	C₂²×C₁₃	semidirect
568. #538	C₂²×C₁₃	semidirect
569. #538	C₂²×C₁₃	semidirect
570. #538	C₂²×C₁₃	semidirect
571. #538	C₂²×C₁₃	semidirect
572. #538	C₂²×C₁₃	semidirect
573. #537	C₂²×C₁₃	semidirect
574. #537	C₂²×C₁₃	semidirect
575. #537	C₂²×C₁₃	semidirect
576. #537	C₂²×C₁₃	semidirect
577. #536	C₂²×C₁₃	semidirect
578. #535	C₂²×C₁₃	semidirect
579. #535	C₂²×C₁₃	semidirect
580. #535	C₂²×C₁₃	semidirect
581. #535	C₂²×C₁₃	semidirect
582. #535	C₂²×C₁₃	semidirect
583. #535	C₂²×C₁₃	semidirect
584. #534	C₂²×C₁₃	semidirect
585. #534	C₂²×C₁₃	semidirect
586. #534	C₂²×C₁₃	semidirect
587. #533	C₂²×C₁₃	semidirect
588. #532	C₂²×C₁₃	semidirect
589. #532	C₂²×C₁₃	semidirect
590. #532	C₂²×C₁₃	semidirect
591. #532	C₂²×C₁₃	semidirect
592. #532	C₂²×C₁₃	semidirect
593. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
594. #529	C₂²×C₁₃	semidirect
595. #529	C₂²×C₁₃	semidirect
596. C₂×#124	C₂²×C₁₃	semidirect
597. #525	C₂²×C₁₃	semidirect
598. #525	C₂²×C₁₃	semidirect
599. #525	C₂²×C₁₃	semidirect
600. #525	C₂²×C₁₃	semidirect
601. #525	C₂²×C₁₃	semidirect
602. #525	C₂²×C₁₃	semidirect
603. C₂×#121	C₂²×C₁₃	semidirect
604. C₂×#121	C₂²×C₁₃	semidirect
605. C₂×#121	C₂²×C₁₃	semidirect
606. C₂×#121	C₂²×C₁₃	semidirect
607. #520	C₂²×C₁₃	semidirect
608. #520	C₂²×C₁₃	semidirect
609. #518	C₂²×C₁₃	semidirect
610. C₄×#41	C₂²×C₁₃	semidirect
611. C₂×C₄×D₄	C₂²×C₁₃	semidirect
612. C₂×C₄×D₄	C₂²×C₁₃	semidirect
613. C₂×C₄×D₄	C₂²×C₁₃	semidirect
614. C₂×#117	C₂²×C₁₃	semidirect
615. C₂×#117	C₂²×C₁₃	semidirect
962. C₁₃	#62930	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×#3558	2
C₁₃×#3549	2
C₁₃×#3547	2
C₁₃×#3542	2
C₁₃×#3540	2
C₁₃×#3537	2
C₁₃×#3519	2
C₁₃×#3511	2
C₁₃×#3506	2
C₁₃×#3496	2
C₁₃×#3494	2
C₁₃×#3493	2
C₁₃×#3488	2
C₂×C₁₃×#555	2
D₄×C₁₃×#41	2
C₁₃×#3460	2
C₁₃×#3449	2
#62930	13

Subgroups — C13×#62930 #15749269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62930 #15749269