Subgroups — C₁₃×#60925 #15747264

Order 3328.

1748 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3461	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3261	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3258	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3255	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3249	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3248	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3063	C₂	1	2	yes	maximal
13	C₁₃×#3059	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3044	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
20	C₂×C₁₃×#131	C₂²	1	2	yes	—
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#557	—	2	1	no	—
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#556	—	2	1	no	—
25	C₁₃×#552	—	2	2	no	—
26	C₁₃×#552	—	2	2	no	—
27	C₁₃×#544	C₂²	1	1	yes	characteristic
28	C₁₃×#542	—	2	1	no	—
29	C₁₃×#542	C₂²	1	2	yes	—
30	C₁₃×#541	—	2	1	no	—
31	C₁₃×#541	C₂²	1	2	yes	—
32	C₁₃×#541	C₂²	1	4	yes	—
33	C₁₃×#539	—	2	2	no	—
34	C₁₃×#537	C₂²	1	1	yes	characteristic
35	C₁₃×#536	C₂²	1	1	yes	characteristic
36	C₁₃×#536	C₂²	1	1	yes	characteristic
37	C₁₃×#536	C₂²	1	2	yes	—
38	C₁₃×#533	—	2	1	no	—
39	C₁₃×#533	C₂²	1	2	yes	—
40	C₁₃×#533	C₂²	1	2	yes	—
41	C₁₃×#533	C₂²	1	2	yes	—
42	C₁₃×#533	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	2	no	—
45	C₁₃×#529	—	2	1	no	—
46	C₁₃×#529	C₂²	1	2	yes	—
47	C₁₃×#519	C₂²	1	2	yes	—
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#479	C₂²	1	2	yes	—
52	C₁₃×#479	C₂²	1	4	yes	—
53	C₁₃×#479	C₂²	1	4	yes	—
54	C₁₃×#479	C₂²	1	4	yes	—
55	C₁₃×#478	C₂²	1	2	yes	—
56	C₁₃×#477	C₂²	1	1	yes	characteristic
57	C₁₃×#477	C₂²	1	2	yes	—
58	C₁₃×#477	C₂²	1	4	yes	—
59	C₁₃×#476	C₂²	1	1	yes	characteristic
60	C₁₃×#475	C₂²	1	1	yes	characteristic
61	C₁₃×#475	C₂²	1	2	yes	—
62	C₁₃×#475	C₂²	1	4	yes	—
63	C₁₃×#474	C₂²	1	1	yes	characteristic
64	C₁₃×#470	C₂²	1	4	yes	—
65	C₁₃×#470	C₂²	1	4	yes	—
66	C₁₃×#470	C₂²	1	4	yes	—
67	C₁₃×#468	C₂²	1	4	yes	—
68	C₁₃×#467	C₂²	1	4	yes	—
69	C₁₃×#467	C₂²	1	4	yes	—
70	C₁₃×#467	C₂²	1	4	yes	—
71	C₁₃×#465	C₂²	1	4	yes	—
72	C₁₃×#464	C₂²	1	4	yes	—
73	C₁₃×#464	C₂²	1	4	yes	—
74	C₁₃×#462	C₂²	1	2	yes	—
75	C₁₃×#462	C₂²	1	2	yes	—
76	C₁₃×#462	C₂²	1	4	yes	—
77	C₁₃×#462	C₂²	1	2	yes	—
78	C₁₃×#462	C₂²	1	2	yes	—
79	C₁₃×#462	C₂²	1	4	yes	—
80	C₁₃×#462	C₂²	1	4	yes	—
81	C₁₃×#461	C₂²	1	2	yes	—
82	C₁₃×#461	C₂²	1	2	yes	—
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₁₃×#427	C₂²	1	2	yes	—
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₁₃×#424	C₂²	1	4	yes	—
87	C₁₃×#423	C₂²	1	1	yes	characteristic
88	C₁₃×#423	C₂²	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
91	C₁₃×#419	C₂²	1	2	yes	—
92	C₁₃×#419	C₂²	1	2	yes	—
93	C₁₃×#416	C₂²	1	2	yes	—
94	C₂×C₁₃×#103	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#137	—	4	4	no	—
100	C₂×C₁₃×Q₁₆	—	4	4	no	—
101	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
105	C₁₃×#131	—	4	4	no	—
106	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
108	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
109	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	—	2	2	no	—
112	C₁₃×C₄⋊Q₈	—	2	1	no	—
113	C₁₃×C₄⋊Q₈	—	2	1	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₁₃×#126	—	2	2	no	—
122	C₁₃×#126	—	2	2	no	—
123	C₁₃×#126	—	2	2	no	—
124	C₁₃×#126	—	2	4	no	—
125	C₁₃×#126	—	2	4	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#125	—	2	2	no	—
128	C₁₃×#125	—	2	1	no	—
129	C₁₃×#125	—	2	2	no	—
130	C₁₃×#125	—	2	4	no	—
131	C₁₃×#125	—	2	4	no	—
132	C₁₃×#125	—	2	2	no	—
133	C₁₃×#125	—	2	2	no	—
134	C₁₃×#125	—	2	2	no	—
135	C₁₃×#125	C₂³	1	2	yes	—
136	C₁₃×#125	C₂³	1	2	yes	—
137	C₁₃×#124	—	2	1	no	—
138	C₁₃×#124	—	2	2	no	—
139	C₁₃×#124	—	2	2	no	—
140	C₁₃×#124	C₂³	1	2	yes	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	4	no	—
143	C₁₃×#123	—	2	2	no	—
144	C₁₃×#123	—	2	2	no	—
145	C₁₃×#123	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	1	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	1	no	—
149	C₁₃×C₂²⋊Q₈	—	2	1	no	—
150	C₁₃×C₂²⋊Q₈	—	2	2	no	—
151	C₁₃×C₂²⋊Q₈	—	2	2	no	—
152	C₁₃×C₂²⋊Q₈	—	2	1	no	—
153	C₁₃×C₂²⋊Q₈	—	2	1	no	—
154	C₁₃×C₂²⋊Q₈	—	2	2	no	—
155	C₁₃×C₂²⋊Q₈	—	2	2	no	—
156	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
157	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
158	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	—	2	1	no	—
163	C₁₃×#121	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₃	—	2	2	no	—
165	C₄×Q₈×C₁₃	—	2	2	no	—
166	C₄×Q₈×C₁₃	—	2	1	no	—
167	C₄×Q₈×C₁₃	—	2	1	no	—
168	C₄×Q₈×C₁₃	—	2	2	no	—
169	C₄×Q₈×C₁₃	—	2	2	no	—
170	C₄×Q₈×C₁₃	—	2	2	no	—
171	C₄×Q₈×C₁₃	—	2	1	no	—
172	C₄×Q₈×C₁₃	—	2	1	no	—
173	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
175	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
178	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
180	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
181	C₄×D₄×C₁₃	—	2	1	no	—
182	C₄×D₄×C₁₃	—	2	1	no	—
183	C₄×D₄×C₁₃	—	2	2	no	—
184	C₄×D₄×C₁₃	D₄	1	2	yes	—
185	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
186	C₄×D₄×C₁₃	D₄	1	2	yes	—
187	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	—	2	4	no	—
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	C₂³	1	2	yes	—
197	C₁₃×#117	C₂³	1	1	yes	characteristic
198	C₁₃×#117	C₂³	1	1	yes	characteristic
199	C₁₃×#117	C₂³	1	2	yes	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₁₃	—	2	1	no	—
205	C₂×C₄²×C₁₃	—	2	1	no	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₁₃×#107	C₂³	1	2	yes	—
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×#106	C₂³	1	2	yes	—
212	C₁₃×#106	C₂³	1	2	yes	—
213	C₁₃×#106	C₂³	1	4	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
219	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#103	C₂³	1	2	yes	—
224	C₁₃×#103	C₂³	1	2	yes	—
225	C₁₃×#103	C₂³	1	4	yes	—
226	C₁₃×#103	C₂³	1	4	yes	—
227	C₁₃×#103	C₂³	1	4	yes	—
228	C₁₃×#103	C₂³	1	4	yes	—
229	C₁₃×#102	C₂³	1	2	yes	—
230	C₁₃×#102	C₂³	1	2	yes	—
231	#60925	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₁₃×#41	—	2	2	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	2	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	1	no	—
238	C₂×Q₈×C₁₃	—	2	1	no	—
239	C₂×Q₈×C₁₃	—	2	2	no	—
240	C₂×Q₈×C₁₃	—	2	2	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	4	no	—
243	C₂×Q₈×C₁₃	—	2	4	no	—
244	C₂×Q₈×C₁₃	—	2	2	no	—
245	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
248	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₁₃	—	2	1	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₁₃×Q₁₆	—	4	4	no	—
267	C₁₃×Q₁₆	—	4	4	no	—
268	C₁₃×Q₁₆	—	4	4	no	—
269	C₁₃×SD₁₆	—	4	4	no	—
270	C₁₃×M₁₆	—	2	4	no	—
271	C₁₃×M₁₆	—	4	4	no	—
272	C₂×C₈×C₁₃	—	2	4	no	—
273	C₂×C₈×C₁₃	—	4	4	no	—
274	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
275	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	2	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	—	2	2	no	—
281	C₁₃×C₄⋊C₄	—	2	2	no	—
282	C₁₃×C₄⋊C₄	—	2	2	no	—
283	C₁₃×C₄⋊C₄	—	2	1	no	—
284	C₁₃×C₄⋊C₄	—	2	1	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	1	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	4	no	—
289	C₁₃×C₄⋊C₄	—	2	4	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	2	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	4	no	—
301	C₁₃×C₄⋊C₄	—	2	4	no	—
302	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
308	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
309	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
311	C₁₃×C₂²⋊C₄	—	2	2	no	—
312	C₁₃×C₂²⋊C₄	—	2	2	no	—
313	C₁₃×C₂²⋊C₄	—	2	2	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	—	2	4	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	—	2	1	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
324	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
325	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
326	C₄²×C₁₃	—	2	2	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	1	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	4	no	—
332	C₄²×C₁₃	—	2	4	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₁₃	C₂×D₄	1	2	yes	—
336	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₁₃	C₂×D₄	1	2	yes	—
338	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
340	C₄²×C₁₃	C₂⁴	1	2	yes	—
341	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#3461	C₂×C₁₃	1	1	yes	characteristic
343	#3261	C₂×C₁₃	1	4	yes	complemented
344	#3258	C₂×C₁₃	1	4	yes	complemented
345	#3255	C₂×C₁₃	1	2	yes	complemented
346	#3252	C₂×C₁₃	1	2	yes	complemented
347	#3249	C₂×C₁₃	1	2	yes	complemented
348	#3248	C₂×C₁₃	1	2	yes	complemented
349	#3082	C₂×C₁₃	1	2	yes	complemented
350	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#3063	C₂×C₁₃	1	2	yes	—
353	#3059	C₂×C₁₃	1	2	yes	complemented
354	#3044	C₂×C₁₃	1	2	yes	complemented
355	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
356	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
360	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	Q₈×C₁₃	—	2	2	no	—
362	Q₈×C₁₃	—	2	4	no	—
363	Q₈×C₁₃	—	2	2	no	—
364	Q₈×C₁₃	—	2	1	no	—
365	Q₈×C₁₃	—	2	2	no	—
366	Q₈×C₁₃	—	2	4	no	—
367	Q₈×C₁₃	—	2	1	no	—
368	Q₈×C₁₃	—	4	2	no	—
369	Q₈×C₁₃	—	4	2	no	—
370	Q₈×C₁₃	—	4	4	no	—
371	Q₈×C₁₃	—	4	2	no	—
372	Q₈×C₁₃	—	8	2	no	—
373	D₄×C₁₃	—	2	4	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	2	1	no	—
376	D₄×C₁₃	—	2	1	no	—
377	D₄×C₁₃	—	4	2	no	—
378	D₄×C₁₃	—	8	2	no	—
379	C₂×C₄×C₁₃	—	2	2	no	—
380	C₂×C₄×C₁₃	—	2	4	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	2	no	—
383	C₂×C₄×C₁₃	—	2	2	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	1	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	1	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	4	no	—
390	C₂×C₄×C₁₃	—	2	2	no	—
391	C₂×C₄×C₁₃	—	4	1	no	—
392	C₂×C₄×C₁₃	—	4	2	no	—
393	C₂×C₄×C₁₃	—	4	2	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	4	2	no	—
396	C₂×C₄×C₁₃	—	4	2	no	—
397	C₂×C₄×C₁₃	—	8	1	no	—
398	C₂×C₄×C₁₃	—	8	1	no	—
399	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
408	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
409	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
410	C₈×C₁₃	—	2	2	no	—
411	C₈×C₁₃	—	2	2	no	—
412	C₈×C₁₃	—	2	4	no	—
413	C₂×#137	C₂²×C₁₃	1	2	yes	—
414	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
415	C₂×#131	C₂²×C₁₃	1	2	yes	—
416	#557	—	2	1	no	—
417	#557	—	2	1	no	—
418	#556	—	2	1	no	—
419	#556	—	2	1	no	—
420	#552	—	2	2	no	—
421	#552	—	2	2	no	—
422	#544	C₂²×C₁₃	1	1	yes	characteristic
423	#542	—	2	1	no	—
424	#542	C₂²×C₁₃	1	2	yes	—
425	#541	—	2	1	no	—
426	#541	C₂²×C₁₃	1	2	yes	—
427	#541	C₂²×C₁₃	1	4	yes	—
428	#539	—	2	2	no	—
429	#537	C₂²×C₁₃	1	1	yes	characteristic
430	#536	C₂²×C₁₃	1	1	yes	characteristic
431	#536	C₂²×C₁₃	1	1	yes	characteristic
432	#536	C₂²×C₁₃	1	2	yes	—
433	#533	—	2	1	no	—
434	#533	C₂²×C₁₃	1	2	yes	—
435	#533	C₂²×C₁₃	1	2	yes	—
436	#533	C₂²×C₁₃	1	2	yes	—
437	#533	C₂²×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
439	#529	—	2	2	no	—
440	#529	—	2	1	no	—
441	#529	C₂²×C₁₃	1	2	yes	—
442	#519	C₂²×C₁₃	1	2	yes	—
443	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
444	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
446	#479	C₂²×C₁₃	1	2	yes	—
447	#479	C₂²×C₁₃	1	4	yes	—
448	#479	C₂²×C₁₃	1	4	yes	—
449	#479	C₂²×C₁₃	1	4	yes	—
450	#478	C₂²×C₁₃	1	2	yes	—
451	#477	C₂²×C₁₃	1	1	yes	characteristic
452	#477	C₂²×C₁₃	1	2	yes	—
453	#477	C₂²×C₁₃	1	4	yes	—
454	#476	C₂²×C₁₃	1	1	yes	characteristic
455	#475	C₂²×C₁₃	1	1	yes	characteristic
456	#475	C₂²×C₁₃	1	2	yes	—
457	#475	C₂²×C₁₃	1	4	yes	—
458	#474	C₂²×C₁₃	1	1	yes	characteristic
459	#470	C₂²×C₁₃	1	4	yes	—
460	#470	C₂²×C₁₃	1	4	yes	—
461	#470	C₂²×C₁₃	1	4	yes	—
462	#468	C₂²×C₁₃	1	4	yes	—
463	#467	C₂²×C₁₃	1	4	yes	—
464	#467	C₂²×C₁₃	1	4	yes	—
465	#467	C₂²×C₁₃	1	4	yes	—
466	#465	C₂²×C₁₃	1	4	yes	—
467	#464	C₂²×C₁₃	1	4	yes	—
468	#464	C₂²×C₁₃	1	4	yes	—
469	#462	C₂²×C₁₃	1	2	yes	—
470	#462	C₂²×C₁₃	1	2	yes	—
471	#462	C₂²×C₁₃	1	4	yes	—
472	#462	C₂²×C₁₃	1	2	yes	—
473	#462	C₂²×C₁₃	1	4	yes	—
474	#462	C₂²×C₁₃	1	4	yes	—
475	#462	C₂²×C₁₃	1	2	yes	—
476	#461	C₂²×C₁₃	1	2	yes	—
477	#461	C₂²×C₁₃	1	2	yes	—
478	#428	C₂²×C₁₃	1	2	yes	—
479	#427	C₂²×C₁₃	1	2	yes	—
480	#424	C₂²×C₁₃	1	2	yes	—
481	#424	C₂²×C₁₃	1	4	yes	—
482	#423	C₂²×C₁₃	1	1	yes	characteristic
483	#423	C₂²×C₁₃	1	2	yes	—
484	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
485	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
486	#419	C₂²×C₁₃	1	2	yes	—
487	#419	C₂²×C₁₃	1	2	yes	—
488	#416	C₂²×C₁₃	1	2	yes	—
489	C₂×#103	C₂²×C₁₃	1	2	yes	—
490	C₂²×C₁₃	—	2	1	no	—
491	C₂²×C₁₃	—	2	1	no	—
492	C₂²×C₁₃	—	2	2	no	—
493	C₂²×C₁₃	—	2	2	no	—
494	C₂²×C₁₃	—	2	2	no	—
495	C₂²×C₁₃	—	4	1	no	—
496	C₂²×C₁₃	—	4	1	no	—
497	C₂²×C₁₃	—	4	1	no	—
498	C₂²×C₁₃	#537	1	2	yes	—
499	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
500	C₄×C₁₃	—	2	1	no	—
501	C₄×C₁₃	—	2	1	no	—
502	C₄×C₁₃	—	2	2	no	—
503	C₄×C₁₃	—	2	2	no	—
504	C₄×C₁₃	—	2	1	no	—
505	C₄×C₁₃	—	2	2	no	—
506	C₄×C₁₃	—	4	2	no	—
507	C₄×C₁₃	—	4	1	no	—
508	C₄×C₁₃	—	4	2	no	—
509	C₄×C₁₃	—	4	1	no	—
510	C₄×C₁₃	—	4	2	no	—
511	C₄×C₁₃	—	4	4	no	—
512	C₄×C₁₃	—	4	1	no	—
513	C₄×C₁₃	—	4	2	no	—
514	C₄×C₁₃	#537	1	2	yes	—
515	C₄×C₁₃	#578	1	2	yes	—
516	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
517	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
518	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
519	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
520	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
521	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
522	#137	—	4	4	no	—
523	C₂×Q₁₆	—	4	4	no	—
524	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
525	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
526	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
527	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
528	#131	—	4	4	no	—
529	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
530	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
531	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
532	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
533	C₄⋊Q₈	—	2	1	no	—
534	C₄⋊Q₈	—	2	2	no	—
535	C₄⋊Q₈	—	2	1	no	—
536	C₄⋊Q₈	—	2	1	no	—
537	C₄⋊Q₈	—	2	1	no	—
538	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
539	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
540	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
541	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
544	#126	—	2	2	no	—
545	#126	—	2	2	no	—
546	#126	—	2	2	no	—
547	#126	—	2	4	no	—
548	#126	—	2	4	no	—
549	#126	—	2	2	no	—
550	#125	—	2	2	no	—
551	#125	—	2	1	no	—
552	#125	—	2	2	no	—
553	#125	—	2	4	no	—
554	#125	—	2	4	no	—
555	#125	—	2	2	no	—
556	#125	—	2	2	no	—
557	#125	—	2	2	no	—
558	#125	C₂³×C₁₃	1	2	yes	—
559	#125	C₂³×C₁₃	1	2	yes	—
560	#124	—	2	1	no	—
561	#124	—	2	2	no	—
562	#124	—	2	2	no	—
563	#124	C₂³×C₁₃	1	2	yes	—
564	#123	—	2	2	no	—
565	#123	—	2	4	no	—
566	#123	—	2	2	no	—
567	#123	—	2	2	no	—
568	#123	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	1	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	—	2	1	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
580	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
581	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
582	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
583	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
584	#121	—	2	2	no	—
585	#121	—	2	1	no	—
586	#121	C₂³×C₁₃	1	2	yes	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	2	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	1	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	—	2	2	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	1	no	—
596	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
597	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
599	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
600	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
603	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	D₄×C₁₃	1	2	yes	—
608	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
609	C₄×D₄	D₄×C₁₃	1	2	yes	—
610	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
611	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
612	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
613	#117	—	2	2	no	—
614	#117	—	2	2	no	—
615	#117	—	2	2	no	—
616	#117	—	2	4	no	—
617	#117	—	2	1	no	—
618	#117	—	2	2	no	—
619	#117	C₂³×C₁₃	1	1	yes	characteristic
620	#117	C₂³×C₁₃	1	2	yes	—
621	#117	C₂³×C₁₃	1	1	yes	characteristic
622	#117	C₂³×C₁₃	1	2	yes	—
623	C₂×C₄⋊C₄	—	2	1	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
627	C₂×C₄²	—	2	1	no	—
628	C₂×C₄²	—	2	1	no	—
629	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
630	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
631	#107	C₂³×C₁₃	1	2	yes	—
632	#107	C₂³×C₁₃	1	2	yes	—
633	#107	C₂³×C₁₃	1	4	yes	—
634	#106	C₂³×C₁₃	1	2	yes	—
635	#106	C₂³×C₁₃	1	2	yes	—
636	#106	C₂³×C₁₃	1	4	yes	—
637	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
638	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
639	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
640	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
641	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
642	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
643	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
644	#103	C₂³×C₁₃	1	4	yes	—
645	#103	C₂³×C₁₃	1	4	yes	—
646	#103	C₂³×C₁₃	1	2	yes	—
647	#103	C₂³×C₁₃	1	2	yes	—
648	#103	C₂³×C₁₃	1	4	yes	—
649	#103	C₂³×C₁₃	1	4	yes	—
650	#103	C₂³×C₁₃	1	4	yes	—
651	#103	C₂³×C₁₃	1	4	yes	—
652	#102	C₂³×C₁₃	1	2	yes	—
653	#102	C₂³×C₁₃	1	2	yes	—
654	C₂×C₁₃	—	2	2	no	—
655	C₂×C₁₃	—	4	2	no	—
656	C₂×C₁₃	—	8	1	no	—
657	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
658	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
659	C₂×C₁₃	#3586	1	1	yes	characteristic
660	#41	—	2	2	no	—
661	#41	—	2	2	no	—
662	#41	—	2	2	no	—
663	#41	—	2	2	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	4	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	4	no	—
673	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
674	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
676	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
680	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
681	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
690	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
694	Q₁₆	—	4	4	no	—
695	Q₁₆	—	4	4	no	—
696	Q₁₆	—	4	4	no	—
697	SD₁₆	—	4	4	no	—
698	M₁₆	—	2	4	no	—
699	M₁₆	—	4	4	no	—
700	C₂×C₈	—	2	4	no	—
701	C₂×C₈	—	4	4	no	—
702	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
703	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
704	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
731	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	1	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
752	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
754	C₄²	—	2	2	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	4	no	—
760	C₄²	—	2	4	no	—
761	C₄²	—	2	2	no	—
762	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₁₃	1	2	yes	—
764	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₄²	C₂×D₄×C₁₃	1	2	yes	—
766	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
767	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
768	C₄²	C₂⁴×C₁₃	1	2	yes	—
769	C₁₃	#60925	1	1	yes	characteristic, direct product factor, Sylow
770	C₂³	—	2	1	no	—
771	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
772	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
773	Q₈	—	2	2	no	—
774	Q₈	—	2	4	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	4	no	—
779	Q₈	—	2	1	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	4	2	no	—
782	Q₈	—	4	4	no	—
783	Q₈	—	4	2	no	—
784	Q₈	—	8	2	no	—
785	D₄	—	2	4	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	1	no	—
789	D₄	—	4	2	no	—
790	D₄	—	8	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	2	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	8	1	no	—
810	C₂×C₄	—	8	1	no	—
811	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
812	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
813	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
816	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
819	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
820	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
821	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
822	C₈	—	2	2	no	—
823	C₈	—	2	2	no	—
824	C₈	—	2	4	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	C₁₃×#537	1	2	yes	—
834	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
835	C₄	—	2	1	no	—
836	C₄	—	2	2	no	—
837	C₄	—	2	1	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	2	no	—
848	C₄	—	4	4	no	—
849	C₄	C₁₃×#537	1	2	yes	—
850	C₄	C₁₃×#578	1	2	yes	—
851	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
852	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
853	C₂	—	2	2	no	—
854	C₂	—	4	2	no	—
855	C₂	—	8	1	no	—
856	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
857	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
858	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#537	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3261	C₂	semidirect
4. C₁₃×#3258	C₂	semidirect
5. C₁₃×#3255	C₂	semidirect
6. C₁₃×#3252	C₂	semidirect
7. C₁₃×#3249	C₂	semidirect
8. C₁₃×#3248	C₂	semidirect
9. C₁₃×#3082	C₂	semidirect
10. C₁₃×#3078	C₂	semidirect
11. C₁₃×#3076	C₂	semidirect
13. C₁₃×#3059	C₂	semidirect
14. C₁₃×#3044	C₂	semidirect
15. C₁₃×#3039	C₂	semidirect
16. C₂×C₁₃×#462	C₂	semidirect
17. C₁₃×#2906	C₂	semidirect
231. #60925	C₁₃	direct (N × H)
341. #3509	C₂×C₁₃	semidirect
343. #3261	C₂×C₁₃	semidirect
344. #3258	C₂×C₁₃	semidirect
345. #3255	C₂×C₁₃	semidirect
346. #3252	C₂×C₁₃	semidirect
347. #3249	C₂×C₁₃	semidirect
348. #3248	C₂×C₁₃	semidirect
349. #3082	C₂×C₁₃	semidirect
350. #3078	C₂×C₁₃	semidirect
351. #3076	C₂×C₁₃	semidirect
353. #3059	C₂×C₁₃	semidirect
354. #3044	C₂×C₁₃	semidirect
355. #3039	C₂×C₁₃	semidirect
356. C₂×#462	C₂×C₁₃	semidirect
357. #2906	C₂×C₁₃	semidirect
769. C₁₃	#60925	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×#3509	2
C₁₃×#3461	2
C₁₃×#3261	2
C₁₃×#3258	2
C₁₃×#3255	2
C₁₃×#3252	2
C₁₃×#3249	2
C₁₃×#3248	2
C₁₃×#3082	2
C₁₃×#3078	2
C₁₃×#3076	2
C₁₃×#3063	2
C₁₃×#3059	2
C₁₃×#3044	2
C₁₃×#3039	2
C₂×C₁₃×#462	2
C₁₃×#2906	2
#60925	13

Subgroups — C13×#60925 #15747264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60925 #15747264