Subgroups — C₁₃×#62943 #15749282

Order 3328.

6458 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×#3555	C₂	1	6	yes	maximal, complemented
2	C₁₃×#3555	C₂	1	6	yes	maximal, complemented
3	C₁₃×#3552	C₂	1	12	yes	maximal, complemented
4	C₁₃×#3550	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3544	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3522	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3518	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3516	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3511	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3507	C₂	1	3	yes	maximal, complemented
11	C₁₃×#3503	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3503	C₂	1	3	yes	maximal, complemented
13	C₁₃×#3502	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3461	C₂	1	3	yes	maximal, complemented
18	C₁₃×#563	C₂²	1	24	yes	—
19	C₁₃×#563	C₂²	1	24	yes	—
20	C₁₃×#559	C₂²	1	6	yes	—
21	C₁₃×#559	C₂²	1	3	yes	—
22	Q₈²×C₁₃	C₂²	1	2	yes	—
23	Q₈²×C₁₃	C₂²	1	2	yes	—
24	Q₈²×C₁₃	C₂²	1	6	yes	—
25	Q₈²×C₁₃	C₂²	1	6	yes	—
26	Q₈²×C₁₃	C₂²	1	6	yes	—
27	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#557	C₂²	1	12	yes	—
29	C₁₃×#557	C₂²	1	3	yes	—
30	C₁₃×#557	C₂²	1	6	yes	—
31	C₁₃×#557	C₂²	1	6	yes	—
32	C₁₃×#557	C₂²	1	1	yes	characteristic
33	C₁₃×#557	C₂²	1	4	yes	—
34	C₁₃×#556	C₂²	1	12	yes	—
35	C₁₃×#556	C₂²	1	6	yes	—
36	C₁₃×#556	C₂²	1	12	yes	—
37	C₁₃×#556	C₂²	1	12	yes	—
38	C₁₃×#556	C₂²	1	3	yes	—
39	C₁₃×#556	C₂²	1	6	yes	—
40	C₁₃×#555	C₂²	1	6	yes	—
41	C₁₃×#554	C₂²	1	6	yes	—
42	C₁₃×#554	C₂²	1	3	yes	—
43	C₁₃×#554	C₂²	1	6	yes	—
44	C₁₃×#554	C₂²	1	6	yes	—
45	C₁₃×#554	C₂²	1	12	yes	—
46	C₁₃×#554	C₂²	1	6	yes	—
47	C₁₃×#553	C₂²	1	6	yes	—
48	C₁₃×#553	C₂²	1	12	yes	—
49	C₁₃×#552	C₂²	1	12	yes	—
50	C₁₃×#552	C₂²	1	12	yes	—
51	C₁₃×#550	C₂²	1	1	yes	characteristic
52	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
53	D₄×Q₈×C₁₃	C₂²	1	6	yes	—
54	D₄×Q₈×C₁₃	C₂²	1	12	yes	—
55	D₄×Q₈×C₁₃	C₂²	1	12	yes	—
56	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
57	C₁₃×#548	C₂²	1	4	yes	—
58	C₁₃×#548	C₂²	1	12	yes	—
59	C₁₃×#548	C₂²	1	2	yes	—
60	C₁₃×#547	C₂²	1	12	yes	—
61	C₁₃×#547	C₂²	1	6	yes	—
62	C₁₃×#544	C₂²	1	12	yes	—
63	C₁₃×#544	C₂²	1	12	yes	—
64	C₁₃×#544	C₂²	1	12	yes	—
65	C₁₃×#544	C₂²	1	3	yes	—
66	C₁₃×#542	C₂²	1	12	yes	—
67	C₁₃×#542	C₂²	1	12	yes	—
68	C₁₃×#542	C₂²	1	6	yes	—
69	C₁₃×#542	C₂²	1	12	yes	—
70	C₁₃×#542	C₂²	1	6	yes	—
71	C₁₃×#542	C₂²	1	12	yes	—
72	C₁₃×#541	C₂²	1	24	yes	—
73	C₁₃×#541	C₂²	1	6	yes	—
74	C₁₃×#541	C₂²	1	6	yes	—
75	C₁₃×#541	C₂²	1	12	yes	—
76	C₁₃×#539	C₂²	1	12	yes	—
77	C₁₃×#539	C₂²	1	12	yes	—
78	C₁₃×#537	C₂²	1	3	yes	—
79	C₁₃×#536	C₂²	1	24	yes	—
80	C₁₃×#536	C₂²	1	1	yes	characteristic
81	C₁₃×#536	C₂²	1	3	yes	—
82	C₁₃×#533	C₂²	1	6	yes	—
83	C₁₃×#533	C₂²	1	6	yes	—
84	C₁₃×#533	C₂²	1	6	yes	—
85	C₁₃×#533	C₂²	1	6	yes	—
86	C₁₃×#533	C₂²	1	6	yes	—
87	C₁₃×#533	C₂²	1	3	yes	—
88	C₁₃×#532	C₂²	1	6	yes	—
89	C₁₃×#532	C₂²	1	3	yes	—
90	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	—
91	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	—
92	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
93	C₁₃×#529	C₂²	1	6	yes	—
94	C₁₃×#529	C₂²	1	6	yes	—
95	C₁₃×#529	C₂²	1	6	yes	—
96	C₁₃×#529	C₂²	1	12	yes	—
97	C₁₃×#529	C₂²	1	12	yes	—
98	C₁₃×#520	C₂²	1	4	yes	—
99	C₁₃×#520	C₂²	1	6	yes	—
100	C₁₃×#519	C₂²	1	4	yes	—
101	C₄×C₁₃×#41	C₂²	1	2	yes	—
102	C₄×C₁₃×#41	C₂²	1	3	yes	—
103	C₄×C₁₃×#41	C₂²	1	3	yes	—
104	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
105	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
106	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
107	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
108	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×#41	C₂³	1	3	yes	—
110	C₂×C₁₃×#41	C₂³	1	2	yes	—
111	C₂×C₁₃×#41	C₂³	1	12	yes	—
112	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
115	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
116	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
123	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
124	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
126	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
127	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
128	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
129	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
130	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
131	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
132	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
133	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
135	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
136	C₁₃×#127	C₂³	1	3	yes	—
137	C₁₃×#126	C₂³	1	12	yes	—
138	C₁₃×#126	C₂³	1	12	yes	—
139	C₁₃×#126	C₂³	1	12	yes	—
140	C₁₃×#126	C₂³	1	12	yes	—
141	C₁₃×#126	C₂³	1	24	yes	—
142	C₁₃×#126	C₂³	1	12	yes	—
143	C₁₃×#126	C₂³	1	24	yes	—
144	C₁₃×#126	C₂³	1	24	yes	—
145	C₁₃×#125	C₂³	1	6	yes	—
146	C₁₃×#125	C₂³	1	12	yes	—
147	C₁₃×#125	C₂³	1	6	yes	—
148	C₁₃×#125	C₂³	1	12	yes	—
149	C₁₃×#125	C₂³	1	6	yes	—
150	C₁₃×#125	C₂³	1	12	yes	—
151	C₁₃×#125	C₂³	1	12	yes	—
152	C₁₃×#125	C₂³	1	12	yes	—
153	C₁₃×#125	C₂³	1	12	yes	—
154	C₁₃×#125	C₂³	1	6	yes	—
155	C₁₃×#125	C₂³	1	24	yes	—
156	C₁₃×#125	C₂³	1	24	yes	—
157	C₁₃×#124	C₂³	1	2	yes	—
158	C₁₃×#124	C₂³	1	12	yes	—
159	C₁₃×#124	C₂³	1	6	yes	—
160	C₁₃×#124	C₂³	1	6	yes	—
161	C₁₃×#124	C₂³	1	12	yes	—
162	C₁₃×#124	C₂³	1	12	yes	—
163	C₁₃×#124	C₂³	1	6	yes	—
164	C₁₃×#124	C₂³	1	24	yes	—
165	C₁₃×#123	C₂³	1	4	yes	—
166	C₁₃×#123	C₂³	1	12	yes	—
167	C₁₃×#123	C₂³	1	12	yes	—
168	C₁₃×#123	C₂³	1	12	yes	—
169	C₁₃×#123	C₂³	1	12	yes	—
170	C₁₃×#123	C₂³	1	24	yes	—
171	C₁₃×#123	C₂³	1	24	yes	—
172	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
174	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
179	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
180	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
181	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
182	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
183	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
184	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
185	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
187	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
188	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
190	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
191	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
194	C₁₃×#121	C₂³	1	6	yes	—
195	C₁₃×#121	C₂³	1	6	yes	—
196	C₁₃×#121	C₂³	1	12	yes	—
197	C₁₃×#121	C₂³	1	6	yes	—
198	C₁₃×#121	C₂³	1	6	yes	—
199	C₁₃×#121	C₂³	1	6	yes	—
200	C₁₃×#121	C₂³	1	12	yes	—
201	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
203	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
204	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
205	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
206	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
207	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
208	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
209	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
210	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
211	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
212	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
213	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
214	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
216	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
221	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
222	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
223	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
225	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
226	C₄×D₄×C₁₃	C₂³	1	6	yes	—
227	C₄×D₄×C₁₃	C₂³	1	6	yes	—
228	C₄×D₄×C₁₃	C₂³	1	3	yes	—
229	C₄×D₄×C₁₃	C₂³	1	3	yes	—
230	C₄×D₄×C₁₃	C₂³	1	6	yes	—
231	C₄×D₄×C₁₃	C₂³	1	6	yes	—
232	C₄×D₄×C₁₃	C₂³	1	6	yes	—
233	C₄×D₄×C₁₃	C₂³	1	3	yes	—
234	C₄×D₄×C₁₃	C₂³	1	6	yes	—
235	C₄×D₄×C₁₃	C₂³	1	3	yes	—
236	C₄×D₄×C₁₃	C₂³	1	24	yes	—
237	C₄×D₄×C₁₃	C₂³	1	12	yes	—
238	C₄×D₄×C₁₃	C₂³	1	12	yes	—
239	C₄×D₄×C₁₃	C₂³	1	12	yes	—
240	C₄×D₄×C₁₃	C₂³	1	12	yes	—
241	C₄×D₄×C₁₃	C₂³	1	6	yes	—
242	C₁₃×#117	C₂³	1	1	yes	characteristic
243	C₁₃×#117	C₂³	1	3	yes	—
244	C₁₃×#117	C₂³	1	6	yes	—
245	C₁₃×#117	C₂³	1	6	yes	—
246	C₁₃×#117	C₂³	1	6	yes	—
247	C₁₃×#117	C₂³	1	12	yes	—
248	C₁₃×#117	C₂³	1	12	yes	—
249	C₁₃×#117	C₂³	1	12	yes	—
250	C₁₃×#117	C₂³	1	12	yes	—
251	C₁₃×#117	C₂³	1	24	yes	—
252	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
253	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
254	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
255	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
256	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
258	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
259	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
260	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
261	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
262	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
263	#62943	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₁₃×#41	—	2	8	no	—
265	C₁₃×#41	—	2	4	no	—
266	C₁₃×#41	—	2	12	no	—
267	C₁₃×#41	—	8	12	no	—
268	C₂×Q₈×C₁₃	—	2	4	no	—
269	C₂×Q₈×C₁₃	—	2	8	no	—
270	C₂×Q₈×C₁₃	—	2	4	no	—
271	C₂×Q₈×C₁₃	—	8	6	no	—
272	C₂×Q₈×C₁₃	—	8	12	no	—
273	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
276	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
277	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
278	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
279	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
280	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
281	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
282	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
283	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
285	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
288	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
289	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
290	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
291	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
296	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
297	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
298	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
300	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
301	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
302	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
304	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
305	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
310	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
316	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
317	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
318	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
319	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
320	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
321	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
322	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
324	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
325	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
326	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
327	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
330	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
332	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
333	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
334	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
335	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
336	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
337	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
338	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
339	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
340	C₁₃×C₂²⋊C₄	C₂⁴	1	2	yes	—
341	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
342	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
343	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
344	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
345	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
346	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
347	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
348	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
349	C₁₃×C₂²⋊C₄	C₂⁴	1	4	yes	—
350	C₄²×C₁₃	C₂⁴	1	2	yes	—
351	C₄²×C₁₃	C₂⁴	1	3	yes	—
352	C₄²×C₁₃	C₂⁴	1	3	yes	—
353	C₄²×C₁₃	C₂⁴	1	3	yes	—
354	C₄²×C₁₃	C₂⁴	1	6	yes	—
355	C₄²×C₁₃	C₂⁴	1	12	yes	—
356	C₄²×C₁₃	C₂⁴	1	6	yes	—
357	C₄²×C₁₃	C₂⁴	1	6	yes	—
358	C₄²×C₁₃	C₂⁴	1	3	yes	—
359	C₄²×C₁₃	C₂⁴	1	6	yes	—
360	C₄²×C₁₃	C₂⁴	1	12	yes	—
361	C₄²×C₁₃	C₂⁴	1	6	yes	—
362	C₄²×C₁₃	C₂⁴	1	24	yes	—
363	#3555	C₂×C₁₃	1	6	yes	complemented
364	#3555	C₂×C₁₃	1	6	yes	complemented
365	#3552	C₂×C₁₃	1	12	yes	complemented
366	#3550	C₂×C₁₃	1	6	yes	complemented
367	#3544	C₂×C₁₃	1	6	yes	complemented
368	#3522	C₂×C₁₃	1	2	yes	complemented
369	#3518	C₂×C₁₃	1	2	yes	complemented
370	#3516	C₂×C₁₃	1	4	yes	complemented
371	#3511	C₂×C₁₃	1	3	yes	complemented
372	#3507	C₂×C₁₃	1	3	yes	complemented
373	#3503	C₂×C₁₃	1	3	yes	complemented
374	#3503	C₂×C₁₃	1	2	yes	complemented
375	#3502	C₂×C₁₃	1	2	yes	complemented
376	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
377	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
378	C₂×Q₈²	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#3461	C₂×C₁₃	1	3	yes	complemented
380	C₂³×C₁₃	C₂⁵	1	2	yes	—
381	C₂³×C₁₃	C₂⁵	1	6	yes	—
382	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
383	Q₈×C₁₃	—	2	4	no	—
384	Q₈×C₁₃	—	2	6	no	—
385	Q₈×C₁₃	—	2	12	no	—
386	Q₈×C₁₃	—	2	4	no	—
387	Q₈×C₁₃	—	2	2	no	—
388	Q₈×C₁₃	—	2	6	no	—
389	Q₈×C₁₃	—	4	6	no	—
390	Q₈×C₁₃	—	4	12	no	—
391	Q₈×C₁₃	—	4	12	no	—
392	Q₈×C₁₃	—	4	12	no	—
393	Q₈×C₁₃	2₋¹⁺⁴	1	4	yes	—
394	D₄×C₁₃	—	2	12	no	—
395	D₄×C₁₃	—	2	4	no	—
396	D₄×C₁₃	—	2	2	no	—
397	D₄×C₁₃	—	2	12	no	—
398	D₄×C₁₃	—	2	6	no	—
399	D₄×C₁₃	—	4	6	no	—
400	D₄×C₁₃	—	4	12	no	—
401	C₂×C₄×C₁₃	—	2	4	no	—
402	C₂×C₄×C₁₃	—	2	6	no	—
403	C₂×C₄×C₁₃	—	2	12	no	—
404	C₂×C₄×C₁₃	—	2	12	no	—
405	C₂×C₄×C₁₃	—	2	12	no	—
406	C₂×C₄×C₁₃	—	2	4	no	—
407	C₂×C₄×C₁₃	—	4	3	no	—
408	C₂×C₄×C₁₃	—	4	6	no	—
409	C₂×C₄×C₁₃	—	4	6	no	—
410	C₂×C₄×C₁₃	—	4	24	no	—
411	C₂×C₄×C₁₃	—	4	6	no	—
412	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
413	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
414	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
415	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
416	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
417	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
418	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
419	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
420	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
421	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
422	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
423	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
424	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
426	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
427	#563	C₂²×C₁₃	1	24	yes	—
428	#563	C₂²×C₁₃	1	24	yes	—
429	#559	C₂²×C₁₃	1	3	yes	—
430	#559	C₂²×C₁₃	1	6	yes	—
431	Q₈²	C₂²×C₁₃	1	2	yes	—
432	Q₈²	C₂²×C₁₃	1	2	yes	—
433	Q₈²	C₂²×C₁₃	1	6	yes	—
434	Q₈²	C₂²×C₁₃	1	6	yes	—
435	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
436	Q₈²	C₂²×C₁₃	1	6	yes	—
437	#557	C₂²×C₁₃	1	3	yes	—
438	#557	C₂²×C₁₃	1	1	yes	characteristic
439	#557	C₂²×C₁₃	1	4	yes	—
440	#557	C₂²×C₁₃	1	6	yes	—
441	#557	C₂²×C₁₃	1	12	yes	—
442	#557	C₂²×C₁₃	1	6	yes	—
443	#556	C₂²×C₁₃	1	3	yes	—
444	#556	C₂²×C₁₃	1	6	yes	—
445	#556	C₂²×C₁₃	1	12	yes	—
446	#556	C₂²×C₁₃	1	6	yes	—
447	#556	C₂²×C₁₃	1	12	yes	—
448	#556	C₂²×C₁₃	1	12	yes	—
449	#555	C₂²×C₁₃	1	6	yes	—
450	#554	C₂²×C₁₃	1	3	yes	—
451	#554	C₂²×C₁₃	1	6	yes	—
452	#554	C₂²×C₁₃	1	6	yes	—
453	#554	C₂²×C₁₃	1	6	yes	—
454	#554	C₂²×C₁₃	1	12	yes	—
455	#554	C₂²×C₁₃	1	6	yes	—
456	#553	C₂²×C₁₃	1	6	yes	—
457	#553	C₂²×C₁₃	1	12	yes	—
458	#552	C₂²×C₁₃	1	12	yes	—
459	#552	C₂²×C₁₃	1	12	yes	—
460	#550	C₂²×C₁₃	1	1	yes	characteristic
461	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
462	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
463	D₄×Q₈	C₂²×C₁₃	1	6	yes	—
464	D₄×Q₈	C₂²×C₁₃	1	12	yes	—
465	D₄×Q₈	C₂²×C₁₃	1	12	yes	—
466	#548	C₂²×C₁₃	1	2	yes	—
467	#548	C₂²×C₁₃	1	12	yes	—
468	#548	C₂²×C₁₃	1	4	yes	—
469	#547	C₂²×C₁₃	1	6	yes	—
470	#547	C₂²×C₁₃	1	12	yes	—
471	#544	C₂²×C₁₃	1	3	yes	—
472	#544	C₂²×C₁₃	1	12	yes	—
473	#544	C₂²×C₁₃	1	12	yes	—
474	#544	C₂²×C₁₃	1	12	yes	—
475	#542	C₂²×C₁₃	1	6	yes	—
476	#542	C₂²×C₁₃	1	6	yes	—
477	#542	C₂²×C₁₃	1	12	yes	—
478	#542	C₂²×C₁₃	1	12	yes	—
479	#542	C₂²×C₁₃	1	12	yes	—
480	#542	C₂²×C₁₃	1	12	yes	—
481	#541	C₂²×C₁₃	1	6	yes	—
482	#541	C₂²×C₁₃	1	6	yes	—
483	#541	C₂²×C₁₃	1	12	yes	—
484	#541	C₂²×C₁₃	1	24	yes	—
485	#539	C₂²×C₁₃	1	12	yes	—
486	#539	C₂²×C₁₃	1	12	yes	—
487	#537	C₂²×C₁₃	1	3	yes	—
488	#536	C₂²×C₁₃	1	1	yes	characteristic
489	#536	C₂²×C₁₃	1	3	yes	—
490	#536	C₂²×C₁₃	1	24	yes	—
491	#533	C₂²×C₁₃	1	6	yes	—
492	#533	C₂²×C₁₃	1	6	yes	—
493	#533	C₂²×C₁₃	1	3	yes	—
494	#533	C₂²×C₁₃	1	6	yes	—
495	#533	C₂²×C₁₃	1	6	yes	—
496	#533	C₂²×C₁₃	1	6	yes	—
497	#532	C₂²×C₁₃	1	3	yes	—
498	#532	C₂²×C₁₃	1	6	yes	—
499	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
500	C₂×C₄⋊Q₈	C₂²×C₁₃	1	6	yes	—
501	C₂×C₄⋊Q₈	C₂²×C₁₃	1	6	yes	—
502	#529	C₂²×C₁₃	1	12	yes	—
503	#529	C₂²×C₁₃	1	6	yes	—
504	#529	C₂²×C₁₃	1	6	yes	—
505	#529	C₂²×C₁₃	1	6	yes	—
506	#529	C₂²×C₁₃	1	12	yes	—
507	#520	C₂²×C₁₃	1	6	yes	—
508	#520	C₂²×C₁₃	1	4	yes	—
509	#519	C₂²×C₁₃	1	4	yes	—
510	C₄×#41	C₂²×C₁₃	1	3	yes	—
511	C₄×#41	C₂²×C₁₃	1	3	yes	—
512	C₄×#41	C₂²×C₁₃	1	2	yes	—
513	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
514	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
515	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
516	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
517	C₂²×C₁₃	—	2	1	no	—
518	C₂²×C₁₃	—	2	1	no	—
519	C₂²×C₁₃	—	2	2	no	—
520	C₂²×C₁₃	—	2	2	no	—
521	C₂²×C₁₃	—	2	6	no	—
522	C₂²×C₁₃	—	2	6	no	—
523	C₂²×C₁₃	—	2	6	no	—
524	C₂²×C₁₃	—	2	2	no	—
525	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
526	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
527	C₄×C₁₃	—	2	2	no	—
528	C₄×C₁₃	—	2	6	no	—
529	C₄×C₁₃	—	2	2	no	—
530	C₄×C₁₃	—	2	4	no	—
531	C₄×C₁₃	—	2	3	no	—
532	C₄×C₁₃	—	2	6	no	—
533	C₄×C₁₃	—	2	6	no	—
534	C₄×C₁₃	—	2	3	no	—
535	C₄×C₁₃	—	2	12	no	—
536	C₄×C₁₃	—	2	3	no	—
537	C₄×C₁₃	—	2	2	no	—
538	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
539	C₄×C₁₃	C₂×2₋¹⁺⁴	1	6	yes	—
540	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
541	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
542	C₂×#41	C₂³×C₁₃	1	3	yes	—
543	C₂×#41	C₂³×C₁₃	1	2	yes	—
544	C₂×#41	C₂³×C₁₃	1	12	yes	—
545	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
546	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
547	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
548	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
549	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
550	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
551	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
552	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
553	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
554	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
555	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
556	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
557	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
558	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
559	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
560	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
561	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
562	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
563	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
564	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
565	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
566	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
567	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
568	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
569	#127	C₂³×C₁₃	1	3	yes	—
570	#126	C₂³×C₁₃	1	12	yes	—
571	#126	C₂³×C₁₃	1	12	yes	—
572	#126	C₂³×C₁₃	1	12	yes	—
573	#126	C₂³×C₁₃	1	12	yes	—
574	#126	C₂³×C₁₃	1	24	yes	—
575	#126	C₂³×C₁₃	1	12	yes	—
576	#126	C₂³×C₁₃	1	24	yes	—
577	#126	C₂³×C₁₃	1	24	yes	—
578	#125	C₂³×C₁₃	1	6	yes	—
579	#125	C₂³×C₁₃	1	12	yes	—
580	#125	C₂³×C₁₃	1	6	yes	—
581	#125	C₂³×C₁₃	1	12	yes	—
582	#125	C₂³×C₁₃	1	6	yes	—
583	#125	C₂³×C₁₃	1	12	yes	—
584	#125	C₂³×C₁₃	1	12	yes	—
585	#125	C₂³×C₁₃	1	12	yes	—
586	#125	C₂³×C₁₃	1	12	yes	—
587	#125	C₂³×C₁₃	1	6	yes	—
588	#125	C₂³×C₁₃	1	24	yes	—
589	#125	C₂³×C₁₃	1	24	yes	—
590	#124	C₂³×C₁₃	1	2	yes	—
591	#124	C₂³×C₁₃	1	12	yes	—
592	#124	C₂³×C₁₃	1	6	yes	—
593	#124	C₂³×C₁₃	1	6	yes	—
594	#124	C₂³×C₁₃	1	12	yes	—
595	#124	C₂³×C₁₃	1	12	yes	—
596	#124	C₂³×C₁₃	1	6	yes	—
597	#124	C₂³×C₁₃	1	24	yes	—
598	#123	C₂³×C₁₃	1	4	yes	—
599	#123	C₂³×C₁₃	1	12	yes	—
600	#123	C₂³×C₁₃	1	12	yes	—
601	#123	C₂³×C₁₃	1	12	yes	—
602	#123	C₂³×C₁₃	1	12	yes	—
603	#123	C₂³×C₁₃	1	24	yes	—
604	#123	C₂³×C₁₃	1	24	yes	—
605	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
606	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
607	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
608	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
609	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
610	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
611	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
612	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
613	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
614	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
615	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
616	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
617	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
618	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
619	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
620	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
621	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
622	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
623	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
624	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
625	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
626	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
627	#121	C₂³×C₁₃	1	6	yes	—
628	#121	C₂³×C₁₃	1	6	yes	—
629	#121	C₂³×C₁₃	1	12	yes	—
630	#121	C₂³×C₁₃	1	6	yes	—
631	#121	C₂³×C₁₃	1	6	yes	—
632	#121	C₂³×C₁₃	1	6	yes	—
633	#121	C₂³×C₁₃	1	12	yes	—
634	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
635	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
636	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
637	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
638	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
639	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
640	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
641	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
642	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
643	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
644	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
645	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
646	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
647	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
648	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
649	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
650	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
651	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
652	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
653	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
654	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
655	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
656	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
657	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
658	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
659	C₄×D₄	C₂³×C₁₃	1	6	yes	—
660	C₄×D₄	C₂³×C₁₃	1	6	yes	—
661	C₄×D₄	C₂³×C₁₃	1	3	yes	—
662	C₄×D₄	C₂³×C₁₃	1	3	yes	—
663	C₄×D₄	C₂³×C₁₃	1	6	yes	—
664	C₄×D₄	C₂³×C₁₃	1	6	yes	—
665	C₄×D₄	C₂³×C₁₃	1	6	yes	—
666	C₄×D₄	C₂³×C₁₃	1	3	yes	—
667	C₄×D₄	C₂³×C₁₃	1	6	yes	—
668	C₄×D₄	C₂³×C₁₃	1	3	yes	—
669	C₄×D₄	C₂³×C₁₃	1	24	yes	—
670	C₄×D₄	C₂³×C₁₃	1	12	yes	—
671	C₄×D₄	C₂³×C₁₃	1	12	yes	—
672	C₄×D₄	C₂³×C₁₃	1	12	yes	—
673	C₄×D₄	C₂³×C₁₃	1	12	yes	—
674	C₄×D₄	C₂³×C₁₃	1	6	yes	—
675	#117	C₂³×C₁₃	1	1	yes	characteristic
676	#117	C₂³×C₁₃	1	3	yes	—
677	#117	C₂³×C₁₃	1	6	yes	—
678	#117	C₂³×C₁₃	1	6	yes	—
679	#117	C₂³×C₁₃	1	6	yes	—
680	#117	C₂³×C₁₃	1	12	yes	—
681	#117	C₂³×C₁₃	1	12	yes	—
682	#117	C₂³×C₁₃	1	12	yes	—
683	#117	C₂³×C₁₃	1	12	yes	—
684	#117	C₂³×C₁₃	1	24	yes	—
685	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
686	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
687	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
688	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
689	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
690	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
691	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
692	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
693	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
694	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
695	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
696	C₂×C₁₃	—	2	2	no	—
697	C₂×C₁₃	—	4	2	no	—
698	C₂×C₁₃	—	4	6	no	—
699	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
700	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
701	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
702	#41	—	2	8	no	—
703	#41	—	2	4	no	—
704	#41	—	2	12	no	—
705	#41	—	8	12	no	—
706	C₂×Q₈	—	2	4	no	—
707	C₂×Q₈	—	2	8	no	—
708	C₂×Q₈	—	2	4	no	—
709	C₂×Q₈	—	8	6	no	—
710	C₂×Q₈	—	8	12	no	—
711	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
712	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
713	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
714	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
715	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
716	C₂×Q₈	C₂⁴×C₁₃	1	3	yes	—
717	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
718	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
719	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
720	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
721	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
723	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
724	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
725	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
726	C₂×D₄	C₂⁴×C₁₃	1	3	yes	—
727	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
728	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
729	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
730	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
733	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
734	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
735	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
736	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
737	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
738	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
739	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
740	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
741	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
742	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
743	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
744	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
745	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
746	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
747	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
748	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
749	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
750	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
751	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
752	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
753	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
754	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
755	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
756	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
757	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
758	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
759	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
760	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
761	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
763	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
764	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
765	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
766	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
767	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
768	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
769	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
770	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
771	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
772	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
773	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
774	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
775	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
776	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
777	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
778	C₂²⋊C₄	C₂⁴×C₁₃	1	2	yes	—
779	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
780	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
781	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
782	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
783	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
784	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
785	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
786	C₂²⋊C₄	C₂⁴×C₁₃	1	6	yes	—
787	C₂²⋊C₄	C₂⁴×C₁₃	1	4	yes	—
788	C₄²	C₂⁴×C₁₃	1	2	yes	—
789	C₄²	C₂⁴×C₁₃	1	3	yes	—
790	C₄²	C₂⁴×C₁₃	1	3	yes	—
791	C₄²	C₂⁴×C₁₃	1	3	yes	—
792	C₄²	C₂⁴×C₁₃	1	6	yes	—
793	C₄²	C₂⁴×C₁₃	1	12	yes	—
794	C₄²	C₂⁴×C₁₃	1	6	yes	—
795	C₄²	C₂⁴×C₁₃	1	6	yes	—
796	C₄²	C₂⁴×C₁₃	1	3	yes	—
797	C₄²	C₂⁴×C₁₃	1	6	yes	—
798	C₄²	C₂⁴×C₁₃	1	12	yes	—
799	C₄²	C₂⁴×C₁₃	1	6	yes	—
800	C₄²	C₂⁴×C₁₃	1	24	yes	—
801	C₁₃	#62943	1	1	yes	characteristic, direct product factor, Sylow
802	C₂³	C₂⁵×C₁₃	1	2	yes	—
803	C₂³	C₂⁵×C₁₃	1	6	yes	—
804	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
805	Q₈	—	2	4	no	—
806	Q₈	—	2	6	no	—
807	Q₈	—	2	12	no	—
808	Q₈	—	2	4	no	—
809	Q₈	—	2	2	no	—
810	Q₈	—	2	6	no	—
811	Q₈	—	4	6	no	—
812	Q₈	—	4	12	no	—
813	Q₈	—	4	12	no	—
814	Q₈	—	4	12	no	—
815	Q₈	C₁₃×2₋¹⁺⁴	1	4	yes	—
816	D₄	—	2	12	no	—
817	D₄	—	2	4	no	—
818	D₄	—	2	2	no	—
819	D₄	—	2	12	no	—
820	D₄	—	2	6	no	—
821	D₄	—	4	6	no	—
822	D₄	—	4	12	no	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	6	no	—
825	C₂×C₄	—	2	12	no	—
826	C₂×C₄	—	2	12	no	—
827	C₂×C₄	—	2	12	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	4	3	no	—
830	C₂×C₄	—	4	6	no	—
831	C₂×C₄	—	4	6	no	—
832	C₂×C₄	—	4	24	no	—
833	C₂×C₄	—	4	6	no	—
834	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
835	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
836	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
837	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
838	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
839	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
840	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
841	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
842	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
843	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
844	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
845	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
846	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
847	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
848	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	6	no	—
854	C₂²	—	2	6	no	—
855	C₂²	—	2	6	no	—
856	C₂²	—	2	2	no	—
857	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
858	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
859	C₄	—	2	2	no	—
860	C₄	—	2	6	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	4	no	—
863	C₄	—	2	3	no	—
864	C₄	—	2	6	no	—
865	C₄	—	2	6	no	—
866	C₄	—	2	3	no	—
867	C₄	—	2	12	no	—
868	C₄	—	2	3	no	—
869	C₄	—	2	2	no	—
870	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
871	C₄	C₂×C₁₃×2₋¹⁺⁴	1	6	yes	—
872	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
873	C₂	—	2	2	no	—
874	C₂	—	4	2	no	—
875	C₂	—	4	6	no	—
876	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
877	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
878	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×#3555	C₂	semidirect
2. C₁₃×#3555	C₂	semidirect
3. C₁₃×#3552	C₂	semidirect
4. C₁₃×#3550	C₂	semidirect
5. C₁₃×#3544	C₂	semidirect
6. C₁₃×#3522	C₂	semidirect
7. C₁₃×#3518	C₂	semidirect
8. C₁₃×#3516	C₂	semidirect
9. C₁₃×#3511	C₂	semidirect
10. C₁₃×#3507	C₂	semidirect
11. C₁₃×#3503	C₂	semidirect
12. C₁₃×#3503	C₂	semidirect
13. C₁₃×#3502	C₂	semidirect
14. C₁₃×#3480	C₂	semidirect
15. Q₈×C₁₃×#41	C₂	semidirect
16. C₂×Q₈²×C₁₃	C₂	semidirect
17. C₁₃×#3461	C₂	semidirect
263. #62943	C₁₃	direct (N × H)
363. #3555	C₂×C₁₃	semidirect
364. #3555	C₂×C₁₃	semidirect
365. #3552	C₂×C₁₃	semidirect
366. #3550	C₂×C₁₃	semidirect
367. #3544	C₂×C₁₃	semidirect
368. #3522	C₂×C₁₃	semidirect
369. #3518	C₂×C₁₃	semidirect
370. #3516	C₂×C₁₃	semidirect
371. #3511	C₂×C₁₃	semidirect
372. #3507	C₂×C₁₃	semidirect
373. #3503	C₂×C₁₃	semidirect
374. #3503	C₂×C₁₃	semidirect
375. #3502	C₂×C₁₃	semidirect
376. #3480	C₂×C₁₃	semidirect
377. Q₈×#41	C₂×C₁₃	semidirect
378. C₂×Q₈²	C₂×C₁₃	semidirect
379. #3461	C₂×C₁₃	semidirect
801. C₁₃	#62943	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×#3555	2
C₁₃×#3552	2
C₁₃×#3550	2
C₁₃×#3544	2
C₁₃×#3522	2
C₁₃×#3518	2
C₁₃×#3516	2
C₁₃×#3511	2
C₁₃×#3507	2
C₁₃×#3503	2
C₁₃×#3502	2
C₁₃×#3480	2
Q₈×C₁₃×#41	2
C₂×Q₈²×C₁₃	2
C₁₃×#3461	2
#62943	13

Subgroups — C13×#62943 #15749282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62943 #15749282