Subgroups — C₁₃×#62881 #15749220

Order 3328.

6610 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3559	C₂	1	8	yes	maximal, complemented
2	C₁₃×#3557	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3554	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3548	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3547	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3536	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3535	C₂	1	8	yes	maximal, complemented
8	C₁₃×#3508	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3506	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3504	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3501	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3494	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#563	C₂²	1	16	yes	complemented
17	C₁₃×#562	C₂²	1	16	yes	complemented
18	C₁₃×#562	C₂²	1	16	yes	complemented
19	C₁₃×#562	C₂²	1	16	yes	complemented
20	C₁₃×#559	C₂²	1	8	yes	complemented
21	C₁₃×#559	C₂²	1	8	yes	complemented
22	C₁₃×#557	C₂²	1	8	yes	complemented
23	C₁₃×#556	C₂²	1	4	yes	complemented
24	C₁₃×#555	C₂²	1	8	yes	complemented
25	C₁₃×#555	C₂²	1	4	yes	complemented
26	C₁₃×#554	C₂²	1	16	yes	—
27	C₁₃×#554	C₂²	1	8	yes	complemented
28	C₁₃×#554	C₂²	1	8	yes	complemented
29	C₁₃×#554	C₂²	1	8	yes	complemented
30	C₁₃×#554	C₂²	1	4	yes	complemented
31	C₁₃×#554	C₂²	1	4	yes	complemented
32	C₁₃×#553	C₂²	1	8	yes	complemented
33	C₁₃×#553	C₂²	1	8	yes	complemented
34	C₁₃×#553	C₂²	1	8	yes	complemented
35	C₁₃×#552	C₂²	1	16	yes	complemented
36	C₁₃×#551	C₂²	1	16	yes	—
37	C₁₃×#550	C₂²	1	4	yes	complemented
38	C₁₃×#550	C₂²	1	8	yes	complemented
39	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
40	D₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
41	C₁₃×#548	C₂²	1	16	yes	complemented
42	C₁₃×#547	C₂²	1	16	yes	complemented
43	C₁₃×#547	C₂²	1	16	yes	complemented
44	C₁₃×#547	C₂²	1	8	yes	complemented
45	C₁₃×#547	C₂²	1	4	yes	complemented
46	C₁₃×#546	C₂²	1	16	yes	—
47	C₁₃×#546	C₂²	1	16	yes	—
48	C₁₃×#544	C₂²	1	4	yes	—
49	C₁₃×#544	C₂²	1	4	yes	—
50	C₁₃×#544	C₂²	1	4	yes	complemented
51	C₁₃×#544	C₂²	1	8	yes	complemented
52	C₁₃×#544	C₂²	1	4	yes	complemented
53	C₁₃×#543	C₂²	1	8	yes	—
54	C₁₃×#543	C₂²	1	4	yes	—
55	C₁₃×#542	C₂²	1	16	yes	complemented
56	C₁₃×#542	C₂²	1	16	yes	complemented
57	C₁₃×#542	C₂²	1	4	yes	complemented
58	C₁₃×#542	C₂²	1	8	yes	complemented
59	C₁₃×#541	C₂²	1	2	yes	complemented
60	C₁₃×#540	C₂²	1	8	yes	—
61	C₁₃×#540	C₂²	1	4	yes	—
62	C₁₃×#540	C₂²	1	4	yes	—
63	C₁₃×#540	C₂²	1	4	yes	complemented
64	C₁₃×#540	C₂²	1	2	yes	complemented
65	C₁₃×#540	C₂²	1	8	yes	complemented
66	C₁₃×#540	C₂²	1	4	yes	complemented
67	C₁₃×#539	C₂²	1	4	yes	—
68	C₁₃×#539	C₂²	1	16	yes	complemented
69	C₁₃×#539	C₂²	1	16	yes	complemented
70	C₁₃×#539	C₂²	1	16	yes	complemented
71	C₁₃×#538	C₂²	1	8	yes	—
72	C₁₃×#538	C₂²	1	4	yes	—
73	C₁₃×#537	C₂²	1	16	yes	complemented
74	C₁₃×#537	C₂²	1	16	yes	complemented
75	C₁₃×#536	C₂²	1	16	yes	complemented
76	C₁₃×#535	C₂²	1	4	yes	—
77	C₁₃×#533	C₂²	1	1	yes	characteristic
78	C₁₃×#533	C₂²	1	2	yes	—
79	C₁₃×#533	C₂²	1	2	yes	—
80	C₁₃×#533	C₂²	1	4	yes	complemented
81	C₁₃×#533	C₂²	1	4	yes	complemented
82	C₁₃×#533	C₂²	1	4	yes	complemented
83	C₁₃×#532	C₂²	1	1	yes	characteristic
84	C₁₃×#532	C₂²	1	8	yes	complemented
85	C₁₃×#532	C₂²	1	8	yes	complemented
86	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
87	C₁₃×#529	C₂²	1	8	yes	complemented
88	C₁₃×#529	C₂²	1	8	yes	complemented
89	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
90	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
91	C₁₃×#525	C₂²	1	8	yes	—
92	C₁₃×#525	C₂²	1	2	yes	—
93	C₂×C₁₃×#123	C₂²	1	4	yes	—
94	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	—
95	C₂×C₁₃×#121	C₂²	1	4	yes	—
96	C₂×C₁₃×#121	C₂²	1	2	yes	—
97	C₁₃×#520	C₂²	1	4	yes	—
98	C₁₃×#518	C₂²	1	4	yes	—
99	C₄×C₁₃×#41	C₂²	1	2	yes	—
100	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
101	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
102	C₂×C₁₃×#117	C₂²	1	2	yes	—
103	C₂×C₁₃×#41	C₂³	1	2	yes	—
104	C₂×C₁₃×#41	C₂³	1	8	yes	—
105	C₂×C₁₃×#41	C₂³	1	16	yes	—
106	C₂×C₁₃×#41	C₂³	1	16	yes	—
107	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
108	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
111	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
113	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	—
123	C₁₃×#127	C₂³	1	4	yes	—
124	C₁₃×#127	C₂³	1	4	yes	—
125	C₁₃×#127	C₂³	1	1	yes	characteristic
126	C₁₃×#127	C₂³	1	8	yes	—
127	C₁₃×#126	C₂³	1	8	yes	—
128	C₁₃×#126	C₂³	1	8	yes	—
129	C₁₃×#126	C₂³	1	16	yes	—
130	C₁₃×#126	C₂³	1	16	yes	—
131	C₁₃×#126	C₂³	1	16	yes	—
132	C₁₃×#125	C₂³	1	4	yes	—
133	C₁₃×#125	C₂³	1	4	yes	—
134	C₁₃×#125	C₂³	1	2	yes	—
135	C₁₃×#125	C₂³	1	16	yes	—
136	C₁₃×#125	C₂³	1	8	yes	—
137	C₁₃×#125	C₂³	1	8	yes	—
138	C₁₃×#125	C₂³	1	8	yes	—
139	C₁₃×#125	C₂³	1	2	yes	—
140	C₁₃×#125	C₂³	1	2	yes	—
141	C₁₃×#125	C₂³	1	4	yes	—
142	C₁₃×#125	C₂³	1	8	yes	—
143	C₁₃×#125	C₂³	1	8	yes	—
144	C₁₃×#125	C₂³	1	16	yes	—
145	C₁₃×#124	C₂³	1	8	yes	—
146	C₁₃×#124	C₂³	1	8	yes	—
147	C₁₃×#124	C₂³	1	2	yes	—
148	C₁₃×#124	C₂³	1	16	yes	—
149	C₁₃×#124	C₂³	1	16	yes	—
150	C₁₃×#124	C₂³	1	16	yes	—
151	C₁₃×#124	C₂³	1	16	yes	—
152	C₁₃×#123	C₂³	1	16	yes	—
153	C₁₃×#123	C₂³	1	16	yes	—
154	C₁₃×#123	C₂³	1	16	yes	—
155	C₁₃×#123	C₂³	1	4	yes	—
156	C₁₃×#123	C₂³	1	8	yes	—
157	C₁₃×#123	C₂³	1	8	yes	—
158	C₁₃×#123	C₂³	1	16	yes	—
159	C₁₃×#123	C₂³	1	16	yes	—
160	C₁₃×#123	C₂³	1	16	yes	—
161	C₁₃×#123	C₂³	1	16	yes	—
162	C₁₃×#123	C₂³	1	16	yes	—
163	C₁₃×#123	C₂³	1	16	yes	—
164	C₁₃×#123	C₂³	1	16	yes	—
165	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
166	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
167	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
168	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
169	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
170	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
171	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
172	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
173	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
174	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	8	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	16	yes	—
184	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
185	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
188	C₁₃×#121	C₂³	1	8	yes	—
189	C₁₃×#121	C₂³	1	16	yes	—
190	C₁₃×#121	C₂³	1	16	yes	—
191	C₁₃×#121	C₂³	1	8	yes	—
192	C₁₃×#121	C₂³	1	4	yes	—
193	C₁₃×#121	C₂³	1	4	yes	—
194	C₁₃×#121	C₂³	1	8	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	16	yes	—
199	C₁₃×#121	C₂³	1	16	yes	—
200	C₁₃×#121	C₂³	1	16	yes	—
201	C₁₃×#121	C₂³	1	16	yes	—
202	C₁₃×#121	C₂³	1	16	yes	—
203	C₁₃×#121	C₂³	1	16	yes	—
204	C₁₃×#121	C₂³	1	16	yes	—
205	C₁₃×#120	C₂³	1	16	yes	—
206	C₁₃×#120	C₂³	1	4	yes	—
207	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
208	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
209	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
210	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
211	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
214	C₄×D₄×C₁₃	C₂³	1	4	yes	—
215	C₄×D₄×C₁₃	C₂³	1	4	yes	—
216	C₄×D₄×C₁₃	C₂³	1	4	yes	—
217	C₄×D₄×C₁₃	C₂³	1	4	yes	—
218	C₄×D₄×C₁₃	C₂³	1	8	yes	—
219	C₄×D₄×C₁₃	C₂³	1	4	yes	—
220	C₄×D₄×C₁₃	C₂³	1	8	yes	—
221	C₄×D₄×C₁₃	C₂³	1	8	yes	—
222	C₄×D₄×C₁₃	C₂³	1	8	yes	—
223	C₄×D₄×C₁₃	C₂³	1	8	yes	—
224	C₄×D₄×C₁₃	C₂³	1	16	yes	—
225	C₄×D₄×C₁₃	C₂³	1	8	yes	—
226	C₄×D₄×C₁₃	C₂³	1	8	yes	—
227	C₄×D₄×C₁₃	C₂³	1	16	yes	—
228	C₄×D₄×C₁₃	C₂³	1	4	yes	—
229	C₄×D₄×C₁₃	C₂³	1	16	yes	—
230	C₄×D₄×C₁₃	C₂³	1	16	yes	—
231	C₄×D₄×C₁₃	C₂³	1	16	yes	—
232	C₁₃×#117	C₂³	1	4	yes	—
233	C₁₃×#117	C₂³	1	4	yes	—
234	C₁₃×#117	C₂³	1	2	yes	—
235	C₁₃×#117	C₂³	1	2	yes	—
236	C₁₃×#117	C₂³	1	4	yes	—
237	C₁₃×#117	C₂³	1	4	yes	—
238	C₁₃×#117	C₂³	1	2	yes	—
239	C₁₃×#117	C₂³	1	2	yes	—
240	C₁₃×#117	C₂³	1	2	yes	—
241	C₁₃×#117	C₂³	1	4	yes	—
242	C₁₃×#117	C₂³	1	8	yes	—
243	C₁₃×#117	C₂³	1	8	yes	—
244	C₁₃×#117	C₂³	1	16	yes	—
245	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
246	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
247	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
248	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
249	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
250	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
251	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
252	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
253	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
254	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
255	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
256	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
257	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
258	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
260	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
261	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
262	#62881	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
265	C₁₃×#41	—	2	8	no	—
266	C₁₃×#41	—	8	8	no	—
267	C₁₃×#41	—	8	16	no	—
268	C₁₃×#41	—	8	16	no	—
269	C₂×Q₈×C₁₃	—	8	8	no	—
270	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
271	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
272	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
273	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
274	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
275	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
276	C₂×D₄×C₁₃	—	2	8	no	—
277	C₂×D₄×C₁₃	—	8	4	no	—
278	C₂×D₄×C₁₃	—	8	4	no	—
279	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
280	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
281	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
282	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
283	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
284	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
285	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
286	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
287	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
288	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
289	C₂²×C₄×C₁₃	—	2	4	no	—
290	C₂²×C₄×C₁₃	—	8	4	no	—
291	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
298	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
301	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
302	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
305	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
323	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
324	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
325	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
330	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
331	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
332	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
334	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
335	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
336	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
337	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
338	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
339	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
340	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
341	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
342	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
343	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
344	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
345	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
346	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
347	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
348	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
349	C₄²×C₁₃	C₂⁴	1	2	yes	—
350	C₄²×C₁₃	C₂⁴	1	4	yes	—
351	C₄²×C₁₃	C₂⁴	1	2	yes	—
352	C₄²×C₁₃	C₂⁴	1	4	yes	—
353	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₄²×C₁₃	C₂⁴	1	4	yes	—
356	C₄²×C₁₃	C₂⁴	1	8	yes	—
357	C₄²×C₁₃	C₂⁴	1	2	yes	—
358	C₄²×C₁₃	C₂⁴	1	8	yes	—
359	C₄²×C₁₃	C₂⁴	1	16	yes	—
360	#3559	C₂×C₁₃	1	8	yes	complemented
361	#3557	C₂×C₁₃	1	4	yes	complemented
362	#3554	C₂×C₁₃	1	8	yes	complemented
363	#3548	C₂×C₁₃	1	4	yes	complemented
364	#3547	C₂×C₁₃	1	8	yes	complemented
365	#3536	C₂×C₁₃	1	8	yes	complemented
366	#3535	C₂×C₁₃	1	8	yes	complemented
367	#3508	C₂×C₁₃	1	2	yes	complemented
368	#3506	C₂×C₁₃	1	2	yes	complemented
369	#3504	C₂×C₁₃	1	2	yes	complemented
370	#3501	C₂×C₁₃	1	2	yes	complemented
371	#3494	C₂×C₁₃	1	4	yes	complemented
372	#3458	C₂×C₁₃	1	1	yes	characteristic, complemented
373	#3455	C₂×C₁₃	1	1	yes	characteristic, complemented
374	C₂×#540	C₂×C₁₃	1	1	yes	characteristic, complemented
375	C₂³×C₁₃	—	2	2	no	—
376	C₂³×C₁₃	—	2	8	no	—
377	C₂³×C₁₃	—	4	4	no	—
378	C₂³×C₁₃	—	4	2	no	—
379	C₂³×C₁₃	—	4	4	no	—
380	C₂³×C₁₃	C₂⁵	1	2	yes	—
381	C₂³×C₁₃	C₂⁵	1	8	yes	—
382	C₂³×C₁₃	C₂⁵	1	4	yes	—
383	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
384	Q₈×C₁₃	—	2	4	no	—
385	Q₈×C₁₃	—	4	4	no	—
386	Q₈×C₁₃	—	4	4	no	—
387	Q₈×C₁₃	—	4	16	no	—
388	Q₈×C₁₃	—	4	4	no	—
389	Q₈×C₁₃	—	4	8	no	—
390	D₄×C₁₃	—	2	8	no	—
391	D₄×C₁₃	—	2	8	no	—
392	D₄×C₁₃	—	2	8	no	—
393	D₄×C₁₃	—	2	4	no	—
394	D₄×C₁₃	—	4	16	no	—
395	D₄×C₁₃	—	4	16	no	—
396	D₄×C₁₃	—	4	16	no	—
397	D₄×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	4	8	no	—
399	D₄×C₁₃	—	4	16	no	—
400	C₂×C₄×C₁₃	—	2	2	no	—
401	C₂×C₄×C₁₃	—	2	4	no	—
402	C₂×C₄×C₁₃	—	2	4	no	—
403	C₂×C₄×C₁₃	—	2	8	no	—
404	C₂×C₄×C₁₃	—	4	2	no	—
405	C₂×C₄×C₁₃	—	4	4	no	—
406	C₂×C₄×C₁₃	—	4	8	no	—
407	C₂×C₄×C₁₃	—	4	8	no	—
408	C₂×C₄×C₁₃	—	4	2	no	—
409	C₂×C₄×C₁₃	—	4	16	no	—
410	C₂×C₄×C₁₃	—	4	16	no	—
411	C₂×C₄×C₁₃	—	4	16	no	—
412	C₂×C₄×C₁₃	—	4	8	no	—
413	C₂×C₄×C₁₃	—	4	8	no	—
414	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
415	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
416	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
417	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
418	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
419	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
420	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
421	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
422	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
423	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
424	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
426	#563	C₂²×C₁₃	1	16	yes	complemented
427	#562	C₂²×C₁₃	1	16	yes	complemented
428	#562	C₂²×C₁₃	1	16	yes	complemented
429	#562	C₂²×C₁₃	1	16	yes	complemented
430	#559	C₂²×C₁₃	1	8	yes	complemented
431	#559	C₂²×C₁₃	1	8	yes	complemented
432	#557	C₂²×C₁₃	1	8	yes	complemented
433	#556	C₂²×C₁₃	1	4	yes	complemented
434	#555	C₂²×C₁₃	1	8	yes	complemented
435	#555	C₂²×C₁₃	1	4	yes	complemented
436	#554	C₂²×C₁₃	1	16	yes	—
437	#554	C₂²×C₁₃	1	8	yes	complemented
438	#554	C₂²×C₁₃	1	8	yes	complemented
439	#554	C₂²×C₁₃	1	4	yes	complemented
440	#554	C₂²×C₁₃	1	4	yes	complemented
441	#554	C₂²×C₁₃	1	8	yes	complemented
442	#553	C₂²×C₁₃	1	8	yes	complemented
443	#553	C₂²×C₁₃	1	8	yes	complemented
444	#553	C₂²×C₁₃	1	8	yes	complemented
445	#552	C₂²×C₁₃	1	16	yes	complemented
446	#551	C₂²×C₁₃	1	16	yes	—
447	#550	C₂²×C₁₃	1	4	yes	complemented
448	#550	C₂²×C₁₃	1	8	yes	complemented
449	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
450	D₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
451	#548	C₂²×C₁₃	1	16	yes	complemented
452	#547	C₂²×C₁₃	1	8	yes	complemented
453	#547	C₂²×C₁₃	1	4	yes	complemented
454	#547	C₂²×C₁₃	1	16	yes	complemented
455	#547	C₂²×C₁₃	1	16	yes	complemented
456	#546	C₂²×C₁₃	1	16	yes	—
457	#546	C₂²×C₁₃	1	16	yes	—
458	#544	C₂²×C₁₃	1	4	yes	—
459	#544	C₂²×C₁₃	1	4	yes	—
460	#544	C₂²×C₁₃	1	4	yes	complemented
461	#544	C₂²×C₁₃	1	4	yes	complemented
462	#544	C₂²×C₁₃	1	8	yes	complemented
463	#543	C₂²×C₁₃	1	4	yes	—
464	#543	C₂²×C₁₃	1	8	yes	—
465	#542	C₂²×C₁₃	1	4	yes	complemented
466	#542	C₂²×C₁₃	1	8	yes	complemented
467	#542	C₂²×C₁₃	1	16	yes	complemented
468	#542	C₂²×C₁₃	1	16	yes	complemented
469	#541	C₂²×C₁₃	1	2	yes	complemented
470	#540	C₂²×C₁₃	1	8	yes	—
471	#540	C₂²×C₁₃	1	4	yes	—
472	#540	C₂²×C₁₃	1	4	yes	—
473	#540	C₂²×C₁₃	1	2	yes	complemented
474	#540	C₂²×C₁₃	1	8	yes	complemented
475	#540	C₂²×C₁₃	1	4	yes	complemented
476	#540	C₂²×C₁₃	1	4	yes	complemented
477	#539	C₂²×C₁₃	1	4	yes	—
478	#539	C₂²×C₁₃	1	16	yes	complemented
479	#539	C₂²×C₁₃	1	16	yes	complemented
480	#539	C₂²×C₁₃	1	16	yes	complemented
481	#538	C₂²×C₁₃	1	4	yes	—
482	#538	C₂²×C₁₃	1	8	yes	—
483	#537	C₂²×C₁₃	1	16	yes	complemented
484	#537	C₂²×C₁₃	1	16	yes	complemented
485	#536	C₂²×C₁₃	1	16	yes	complemented
486	#535	C₂²×C₁₃	1	4	yes	—
487	#533	C₂²×C₁₃	1	1	yes	characteristic
488	#533	C₂²×C₁₃	1	2	yes	—
489	#533	C₂²×C₁₃	1	2	yes	—
490	#533	C₂²×C₁₃	1	4	yes	complemented
491	#533	C₂²×C₁₃	1	4	yes	complemented
492	#533	C₂²×C₁₃	1	4	yes	complemented
493	#532	C₂²×C₁₃	1	1	yes	characteristic
494	#532	C₂²×C₁₃	1	8	yes	complemented
495	#532	C₂²×C₁₃	1	8	yes	complemented
496	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
497	#529	C₂²×C₁₃	1	8	yes	complemented
498	#529	C₂²×C₁₃	1	8	yes	complemented
499	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
500	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
501	#525	C₂²×C₁₃	1	2	yes	—
502	#525	C₂²×C₁₃	1	8	yes	—
503	C₂×#123	C₂²×C₁₃	1	4	yes	—
504	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	—
505	C₂×#121	C₂²×C₁₃	1	2	yes	—
506	C₂×#121	C₂²×C₁₃	1	4	yes	—
507	#520	C₂²×C₁₃	1	4	yes	—
508	#518	C₂²×C₁₃	1	4	yes	—
509	C₄×#41	C₂²×C₁₃	1	2	yes	—
510	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
511	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
512	C₂×#117	C₂²×C₁₃	1	2	yes	—
513	C₂²×C₁₃	—	2	2	no	—
514	C₂²×C₁₃	—	2	2	no	—
515	C₂²×C₁₃	—	2	4	no	—
516	C₂²×C₁₃	—	2	8	no	—
517	C₂²×C₁₃	—	2	8	no	—
518	C₂²×C₁₃	—	2	8	no	—
519	C₂²×C₁₃	—	2	4	no	—
520	C₂²×C₁₃	—	2	8	no	—
521	C₂²×C₁₃	—	8	2	no	—
522	C₂²×C₁₃	—	8	8	no	—
523	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
524	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
525	C₄×C₁₃	—	2	2	no	—
526	C₄×C₁₃	—	2	4	no	—
527	C₄×C₁₃	—	2	2	no	—
528	C₄×C₁₃	—	2	8	no	—
529	C₄×C₁₃	—	2	8	no	—
530	C₄×C₁₃	—	2	8	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	2	4	no	—
533	C₄×C₁₃	—	2	8	no	—
534	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
535	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
536	C₂×#41	C₂³×C₁₃	1	2	yes	—
537	C₂×#41	C₂³×C₁₃	1	8	yes	—
538	C₂×#41	C₂³×C₁₃	1	16	yes	—
539	C₂×#41	C₂³×C₁₃	1	16	yes	—
540	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
541	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
542	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
543	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
544	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
546	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
547	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
548	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
549	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
551	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
553	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
554	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
555	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	—
556	#127	C₂³×C₁₃	1	4	yes	—
557	#127	C₂³×C₁₃	1	4	yes	—
558	#127	C₂³×C₁₃	1	1	yes	characteristic
559	#127	C₂³×C₁₃	1	8	yes	—
560	#126	C₂³×C₁₃	1	8	yes	—
561	#126	C₂³×C₁₃	1	8	yes	—
562	#126	C₂³×C₁₃	1	16	yes	—
563	#126	C₂³×C₁₃	1	16	yes	—
564	#126	C₂³×C₁₃	1	16	yes	—
565	#125	C₂³×C₁₃	1	4	yes	—
566	#125	C₂³×C₁₃	1	4	yes	—
567	#125	C₂³×C₁₃	1	2	yes	—
568	#125	C₂³×C₁₃	1	16	yes	—
569	#125	C₂³×C₁₃	1	8	yes	—
570	#125	C₂³×C₁₃	1	8	yes	—
571	#125	C₂³×C₁₃	1	8	yes	—
572	#125	C₂³×C₁₃	1	2	yes	—
573	#125	C₂³×C₁₃	1	2	yes	—
574	#125	C₂³×C₁₃	1	4	yes	—
575	#125	C₂³×C₁₃	1	8	yes	—
576	#125	C₂³×C₁₃	1	8	yes	—
577	#125	C₂³×C₁₃	1	16	yes	—
578	#124	C₂³×C₁₃	1	8	yes	—
579	#124	C₂³×C₁₃	1	8	yes	—
580	#124	C₂³×C₁₃	1	2	yes	—
581	#124	C₂³×C₁₃	1	16	yes	—
582	#124	C₂³×C₁₃	1	16	yes	—
583	#124	C₂³×C₁₃	1	16	yes	—
584	#124	C₂³×C₁₃	1	16	yes	—
585	#123	C₂³×C₁₃	1	16	yes	—
586	#123	C₂³×C₁₃	1	16	yes	—
587	#123	C₂³×C₁₃	1	16	yes	—
588	#123	C₂³×C₁₃	1	4	yes	—
589	#123	C₂³×C₁₃	1	8	yes	—
590	#123	C₂³×C₁₃	1	8	yes	—
591	#123	C₂³×C₁₃	1	16	yes	—
592	#123	C₂³×C₁₃	1	16	yes	—
593	#123	C₂³×C₁₃	1	16	yes	—
594	#123	C₂³×C₁₃	1	16	yes	—
595	#123	C₂³×C₁₃	1	16	yes	—
596	#123	C₂³×C₁₃	1	16	yes	—
597	#123	C₂³×C₁₃	1	16	yes	—
598	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
599	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
600	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
601	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
602	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
603	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
604	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
605	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
606	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
607	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
608	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
609	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
610	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
611	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
612	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
613	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
614	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
615	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
616	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
617	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
618	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
619	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
620	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
621	#121	C₂³×C₁₃	1	8	yes	—
622	#121	C₂³×C₁₃	1	16	yes	—
623	#121	C₂³×C₁₃	1	16	yes	—
624	#121	C₂³×C₁₃	1	8	yes	—
625	#121	C₂³×C₁₃	1	4	yes	—
626	#121	C₂³×C₁₃	1	4	yes	—
627	#121	C₂³×C₁₃	1	8	yes	—
628	#121	C₂³×C₁₃	1	8	yes	—
629	#121	C₂³×C₁₃	1	8	yes	—
630	#121	C₂³×C₁₃	1	8	yes	—
631	#121	C₂³×C₁₃	1	16	yes	—
632	#121	C₂³×C₁₃	1	16	yes	—
633	#121	C₂³×C₁₃	1	16	yes	—
634	#121	C₂³×C₁₃	1	16	yes	—
635	#121	C₂³×C₁₃	1	16	yes	—
636	#121	C₂³×C₁₃	1	16	yes	—
637	#121	C₂³×C₁₃	1	16	yes	—
638	#120	C₂³×C₁₃	1	16	yes	—
639	#120	C₂³×C₁₃	1	4	yes	—
640	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
641	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
642	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
643	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
644	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
645	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
646	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
647	C₄×D₄	C₂³×C₁₃	1	4	yes	—
648	C₄×D₄	C₂³×C₁₃	1	4	yes	—
649	C₄×D₄	C₂³×C₁₃	1	4	yes	—
650	C₄×D₄	C₂³×C₁₃	1	4	yes	—
651	C₄×D₄	C₂³×C₁₃	1	8	yes	—
652	C₄×D₄	C₂³×C₁₃	1	4	yes	—
653	C₄×D₄	C₂³×C₁₃	1	8	yes	—
654	C₄×D₄	C₂³×C₁₃	1	8	yes	—
655	C₄×D₄	C₂³×C₁₃	1	8	yes	—
656	C₄×D₄	C₂³×C₁₃	1	8	yes	—
657	C₄×D₄	C₂³×C₁₃	1	16	yes	—
658	C₄×D₄	C₂³×C₁₃	1	8	yes	—
659	C₄×D₄	C₂³×C₁₃	1	8	yes	—
660	C₄×D₄	C₂³×C₁₃	1	16	yes	—
661	C₄×D₄	C₂³×C₁₃	1	4	yes	—
662	C₄×D₄	C₂³×C₁₃	1	16	yes	—
663	C₄×D₄	C₂³×C₁₃	1	16	yes	—
664	C₄×D₄	C₂³×C₁₃	1	16	yes	—
665	#117	C₂³×C₁₃	1	4	yes	—
666	#117	C₂³×C₁₃	1	4	yes	—
667	#117	C₂³×C₁₃	1	2	yes	—
668	#117	C₂³×C₁₃	1	2	yes	—
669	#117	C₂³×C₁₃	1	4	yes	—
670	#117	C₂³×C₁₃	1	4	yes	—
671	#117	C₂³×C₁₃	1	2	yes	—
672	#117	C₂³×C₁₃	1	2	yes	—
673	#117	C₂³×C₁₃	1	2	yes	—
674	#117	C₂³×C₁₃	1	4	yes	—
675	#117	C₂³×C₁₃	1	8	yes	—
676	#117	C₂³×C₁₃	1	8	yes	—
677	#117	C₂³×C₁₃	1	16	yes	—
678	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
680	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
681	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
682	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
683	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
684	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
685	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
691	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
694	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
695	C₂×C₁₃	—	2	2	no	—
696	C₂×C₁₃	—	4	4	no	—
697	C₂×C₁₃	—	4	2	no	—
698	C₂×C₁₃	—	4	8	no	—
699	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
700	C₂×C₁₃	H(7,𝔽₂)	1	2	yes	—
701	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
702	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
703	#41	—	2	8	no	—
704	#41	—	8	8	no	—
705	#41	—	8	16	no	—
706	#41	—	8	16	no	—
707	C₂×Q₈	—	8	8	no	—
708	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
709	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
710	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
711	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
712	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
713	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
714	C₂×D₄	—	2	8	no	—
715	C₂×D₄	—	8	4	no	—
716	C₂×D₄	—	8	4	no	—
717	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
718	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
719	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
720	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
722	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
723	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
724	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
725	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
726	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	8	4	no	—
729	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
731	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
736	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
737	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
738	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
739	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
740	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
741	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
742	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
743	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
744	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
745	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
746	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
747	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
748	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
749	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
751	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
752	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
753	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
754	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
755	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
756	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
757	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
758	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
759	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
760	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
761	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
762	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
763	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
764	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
765	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
766	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
767	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
768	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
769	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
770	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
771	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
772	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
773	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
774	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
775	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
776	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
777	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
778	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
779	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
780	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
781	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
782	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
783	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
784	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
785	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
786	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
787	C₄²	C₂⁴×C₁₃	1	2	yes	—
788	C₄²	C₂⁴×C₁₃	1	4	yes	—
789	C₄²	C₂⁴×C₁₃	1	2	yes	—
790	C₄²	C₂⁴×C₁₃	1	4	yes	—
791	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
792	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
793	C₄²	C₂⁴×C₁₃	1	4	yes	—
794	C₄²	C₂⁴×C₁₃	1	8	yes	—
795	C₄²	C₂⁴×C₁₃	1	2	yes	—
796	C₄²	C₂⁴×C₁₃	1	8	yes	—
797	C₄²	C₂⁴×C₁₃	1	16	yes	—
798	C₁₃	#62881	1	1	yes	characteristic, direct product factor, Sylow
799	C₂³	—	2	2	no	—
800	C₂³	—	2	8	no	—
801	C₂³	—	4	4	no	—
802	C₂³	—	4	2	no	—
803	C₂³	—	4	4	no	—
804	C₂³	C₂⁵×C₁₃	1	2	yes	—
805	C₂³	C₂⁵×C₁₃	1	8	yes	—
806	C₂³	C₂⁵×C₁₃	1	4	yes	—
807	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
808	Q₈	—	2	4	no	—
809	Q₈	—	4	4	no	—
810	Q₈	—	4	4	no	—
811	Q₈	—	4	16	no	—
812	Q₈	—	4	4	no	—
813	Q₈	—	4	8	no	—
814	D₄	—	2	8	no	—
815	D₄	—	2	8	no	—
816	D₄	—	2	8	no	—
817	D₄	—	2	4	no	—
818	D₄	—	4	16	no	—
819	D₄	—	4	16	no	—
820	D₄	—	4	16	no	—
821	D₄	—	4	4	no	—
822	D₄	—	4	8	no	—
823	D₄	—	4	16	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	8	no	—
831	C₂×C₄	—	4	8	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	16	no	—
834	C₂×C₄	—	4	16	no	—
835	C₂×C₄	—	4	16	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
839	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
840	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
841	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
842	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
843	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
844	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
845	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
846	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
847	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
848	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
849	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	8	no	—
854	C₂²	—	2	8	no	—
855	C₂²	—	2	8	no	—
856	C₂²	—	2	4	no	—
857	C₂²	—	2	8	no	—
858	C₂²	—	8	2	no	—
859	C₂²	—	8	8	no	—
860	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
861	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
862	C₄	—	2	2	no	—
863	C₄	—	2	4	no	—
864	C₄	—	2	2	no	—
865	C₄	—	2	8	no	—
866	C₄	—	2	8	no	—
867	C₄	—	2	8	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	8	no	—
871	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
872	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
873	C₂	—	2	2	no	—
874	C₂	—	4	2	no	—
875	C₂	—	4	8	no	—
876	C₂	—	4	4	no	—
877	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
878	C₂	C₁₃×H(7,𝔽₂)	1	2	yes	—

	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×#3559	C₂	semidirect
2. C₁₃×#3557	C₂	semidirect
3. C₁₃×#3554	C₂	semidirect
4. C₁₃×#3548	C₂	semidirect
5. C₁₃×#3547	C₂	semidirect
6. C₁₃×#3536	C₂	semidirect
7. C₁₃×#3535	C₂	semidirect
8. C₁₃×#3508	C₂	semidirect
9. C₁₃×#3506	C₂	semidirect
10. C₁₃×#3504	C₂	semidirect
11. C₁₃×#3501	C₂	semidirect
12. C₁₃×#3494	C₂	semidirect
13. C₁₃×#3458	C₂	semidirect
14. C₁₃×#3455	C₂	semidirect
15. C₂×C₁₃×#540	C₂	semidirect
16. C₁₃×#563	C₂²	semidirect
17. C₁₃×#562	C₂²	semidirect
18. C₁₃×#562	C₂²	semidirect
19. C₁₃×#562	C₂²	semidirect
20. C₁₃×#559	C₂²	semidirect
21. C₁₃×#559	C₂²	semidirect
22. C₁₃×#557	C₂²	semidirect
23. C₁₃×#556	C₂²	semidirect
24. C₁₃×#555	C₂²	semidirect
25. C₁₃×#555	C₂²	semidirect
27. C₁₃×#554	C₂²	semidirect
28. C₁₃×#554	C₂²	semidirect
29. C₁₃×#554	C₂²	semidirect
30. C₁₃×#554	C₂²	semidirect
31. C₁₃×#554	C₂²	semidirect
32. C₁₃×#553	C₂²	semidirect
33. C₁₃×#553	C₂²	semidirect
34. C₁₃×#553	C₂²	semidirect
35. C₁₃×#552	C₂²	semidirect
37. C₁₃×#550	C₂²	semidirect
38. C₁₃×#550	C₂²	semidirect
39. D₄×Q₈×C₁₃	C₂²	semidirect
40. D₄×Q₈×C₁₃	C₂²	semidirect
41. C₁₃×#548	C₂²	semidirect
42. C₁₃×#547	C₂²	semidirect
43. C₁₃×#547	C₂²	semidirect
44. C₁₃×#547	C₂²	semidirect
45. C₁₃×#547	C₂²	semidirect
50. C₁₃×#544	C₂²	semidirect
51. C₁₃×#544	C₂²	semidirect
52. C₁₃×#544	C₂²	semidirect
55. C₁₃×#542	C₂²	semidirect
56. C₁₃×#542	C₂²	semidirect
57. C₁₃×#542	C₂²	semidirect
58. C₁₃×#542	C₂²	semidirect
59. C₁₃×#541	C₂²	semidirect
63. C₁₃×#540	C₂²	semidirect
64. C₁₃×#540	C₂²	semidirect
65. C₁₃×#540	C₂²	semidirect
66. C₁₃×#540	C₂²	semidirect
68. C₁₃×#539	C₂²	semidirect
69. C₁₃×#539	C₂²	semidirect
70. C₁₃×#539	C₂²	semidirect
73. C₁₃×#537	C₂²	semidirect
74. C₁₃×#537	C₂²	semidirect
75. C₁₃×#536	C₂²	semidirect
80. C₁₃×#533	C₂²	semidirect
81. C₁₃×#533	C₂²	semidirect
82. C₁₃×#533	C₂²	semidirect
84. C₁₃×#532	C₂²	semidirect
85. C₁₃×#532	C₂²	semidirect
87. C₁₃×#529	C₂²	semidirect
88. C₁₃×#529	C₂²	semidirect
90. C₂×C₁₃×#125	C₂²	semidirect
262. #62881	C₁₃	direct (N × H)
360. #3559	C₂×C₁₃	semidirect
361. #3557	C₂×C₁₃	semidirect
362. #3554	C₂×C₁₃	semidirect
363. #3548	C₂×C₁₃	semidirect
364. #3547	C₂×C₁₃	semidirect
365. #3536	C₂×C₁₃	semidirect
366. #3535	C₂×C₁₃	semidirect
367. #3508	C₂×C₁₃	semidirect
368. #3506	C₂×C₁₃	semidirect
369. #3504	C₂×C₁₃	semidirect
370. #3501	C₂×C₁₃	semidirect
371. #3494	C₂×C₁₃	semidirect
372. #3458	C₂×C₁₃	semidirect
373. #3455	C₂×C₁₃	semidirect
374. C₂×#540	C₂×C₁₃	semidirect
426. #563	C₂²×C₁₃	semidirect
427. #562	C₂²×C₁₃	semidirect
428. #562	C₂²×C₁₃	semidirect
429. #562	C₂²×C₁₃	semidirect
430. #559	C₂²×C₁₃	semidirect
431. #559	C₂²×C₁₃	semidirect
432. #557	C₂²×C₁₃	semidirect
433. #556	C₂²×C₁₃	semidirect
434. #555	C₂²×C₁₃	semidirect
435. #555	C₂²×C₁₃	semidirect
437. #554	C₂²×C₁₃	semidirect
438. #554	C₂²×C₁₃	semidirect
439. #554	C₂²×C₁₃	semidirect
440. #554	C₂²×C₁₃	semidirect
441. #554	C₂²×C₁₃	semidirect
442. #553	C₂²×C₁₃	semidirect
443. #553	C₂²×C₁₃	semidirect
444. #553	C₂²×C₁₃	semidirect
445. #552	C₂²×C₁₃	semidirect
447. #550	C₂²×C₁₃	semidirect
448. #550	C₂²×C₁₃	semidirect
449. D₄×Q₈	C₂²×C₁₃	semidirect
450. D₄×Q₈	C₂²×C₁₃	semidirect
451. #548	C₂²×C₁₃	semidirect
452. #547	C₂²×C₁₃	semidirect
453. #547	C₂²×C₁₃	semidirect
454. #547	C₂²×C₁₃	semidirect
455. #547	C₂²×C₁₃	semidirect
460. #544	C₂²×C₁₃	semidirect
461. #544	C₂²×C₁₃	semidirect
462. #544	C₂²×C₁₃	semidirect
465. #542	C₂²×C₁₃	semidirect
466. #542	C₂²×C₁₃	semidirect
467. #542	C₂²×C₁₃	semidirect
468. #542	C₂²×C₁₃	semidirect
469. #541	C₂²×C₁₃	semidirect
473. #540	C₂²×C₁₃	semidirect
474. #540	C₂²×C₁₃	semidirect
475. #540	C₂²×C₁₃	semidirect
476. #540	C₂²×C₁₃	semidirect
478. #539	C₂²×C₁₃	semidirect
479. #539	C₂²×C₁₃	semidirect
480. #539	C₂²×C₁₃	semidirect
483. #537	C₂²×C₁₃	semidirect
484. #537	C₂²×C₁₃	semidirect
485. #536	C₂²×C₁₃	semidirect
490. #533	C₂²×C₁₃	semidirect
491. #533	C₂²×C₁₃	semidirect
492. #533	C₂²×C₁₃	semidirect
494. #532	C₂²×C₁₃	semidirect
495. #532	C₂²×C₁₃	semidirect
497. #529	C₂²×C₁₃	semidirect
498. #529	C₂²×C₁₃	semidirect
500. C₂×#125	C₂²×C₁₃	semidirect
798. C₁₃	#62881	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×#3559	2
C₁₃×#3557	2
C₁₃×#3554	2
C₁₃×#3548	2
C₁₃×#3547	2
C₁₃×#3536	2
C₁₃×#3535	2
C₁₃×#3508	2
C₁₃×#3506	2
C₁₃×#3504	2
C₁₃×#3501	2
C₁₃×#3494	2
C₁₃×#3458	2
C₁₃×#3455	2
C₂×C₁₃×#540	2
#62881	13

Subgroups — C13×#62881 #15749220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62881 #15749220