Subgroups — C₁₃×#61008 #15747347

Order 3328.

1712 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3258	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3201	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3185	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3121	C₂	1	4	yes	maximal, complemented
18	C₁₃×#3120	C₂	1	4	yes	maximal, complemented
19	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#557	—	2	1	no	—
21	C₁₃×#557	—	2	1	no	—
22	C₁₃×#556	—	2	1	no	—
23	C₁₃×#556	—	2	1	no	—
24	C₁₃×#556	—	2	1	no	—
25	C₁₃×#555	—	2	1	no	—
26	C₁₃×#554	—	2	1	no	—
27	C₁₃×#553	—	2	1	no	—
28	C₁₃×#553	—	2	1	no	—
29	C₁₃×#552	—	2	1	no	—
30	C₁₃×#552	—	2	1	no	—
31	C₁₃×#552	—	2	1	no	—
32	C₁₃×#552	—	2	1	no	—
33	C₁₃×#548	—	2	1	no	—
34	C₁₃×#548	—	2	1	no	—
35	C₁₃×#547	—	2	1	no	—
36	C₁₃×#542	C₂²	1	2	yes	—
37	C₁₃×#542	C₂²	1	2	yes	—
38	C₁₃×#541	C₂²	1	2	yes	—
39	C₁₃×#541	C₂²	1	2	yes	—
40	C₁₃×#537	C₂²	1	2	yes	—
41	C₁₃×#536	C₂²	1	2	yes	—
42	C₁₃×#533	C₂²	1	1	yes	characteristic
43	C₁₃×#533	C₂²	1	1	yes	characteristic
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#533	C₂²	1	1	yes	characteristic
46	C₁₃×#533	C₂²	1	1	yes	characteristic
47	C₁₃×#533	C₂²	1	1	yes	characteristic
48	C₁₃×#533	C₂²	1	1	yes	characteristic
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#532	C₂²	1	1	yes	characteristic
51	C₁₃×#532	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₁₃×#520	C₂²	1	2	yes	—
55	C₁₃×#519	C₂²	1	2	yes	—
56	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
57	C₁₃×#500	C₂²	1	1	yes	characteristic
58	C₁₃×#500	C₂²	1	1	yes	characteristic
59	C₁₃×#498	C₂²	1	1	yes	characteristic
60	C₁₃×#498	C₂²	1	1	yes	characteristic
61	C₁₃×#494	C₂²	1	1	yes	characteristic
62	C₁₃×#494	C₂²	1	1	yes	characteristic
63	C₁₃×#492	C₂²	1	1	yes	characteristic
64	C₁₃×#492	C₂²	1	1	yes	characteristic
65	C₁₃×#487	C₂²	1	1	yes	characteristic
66	C₁₃×#487	C₂²	1	1	yes	characteristic
67	C₁₃×#487	C₂²	1	1	yes	characteristic
68	C₁₃×#487	C₂²	1	1	yes	characteristic
69	C₁₃×#487	C₂²	1	1	yes	characteristic
70	C₁₃×#487	C₂²	1	1	yes	characteristic
71	C₁₃×#486	C₂²	1	1	yes	characteristic
72	C₁₃×#486	C₂²	1	1	yes	characteristic
73	C₁₃×#485	C₂²	1	4	yes	—
74	C₁₃×#484	C₂²	1	4	yes	—
75	C₁₃×#483	C₂²	1	4	yes	—
76	C₁₃×#482	C₂²	1	4	yes	—
77	C₁₃×#479	C₂²	1	4	yes	—
78	C₁₃×#478	C₂²	1	4	yes	—
79	C₁₃×#477	C₂²	1	4	yes	—
80	C₁₃×#475	C₂²	1	4	yes	—
81	C₁₃×#470	C₂²	1	4	yes	—
82	C₁₃×#468	C₂²	1	4	yes	—
83	C₁₃×#467	C₂²	1	4	yes	—
84	C₁₃×#465	C₂²	1	4	yes	—
85	C₁₃×#464	C₂²	1	4	yes	—
86	C₁₃×#464	C₂²	1	4	yes	—
87	C₁₃×#462	C₂²	1	4	yes	—
88	C₁₃×#461	C₂²	1	4	yes	—
89	C₁₃×#452	C₂²	1	4	yes	—
90	C₁₃×#452	C₂²	1	4	yes	—
91	C₁₃×#451	C₂²	1	4	yes	—
92	C₁₃×#448	C₂²	1	4	yes	—
93	C₁₃×#441	C₂²	1	4	yes	—
94	C₁₃×#440	C₂²	1	4	yes	—
95	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
96	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
97	C₁₃×#433	C₂²	1	2	yes	—
98	C₁₃×#433	C₂²	1	2	yes	—
99	C₁₃×#431	C₂²	1	1	yes	characteristic
100	C₁₃×#431	C₂²	1	1	yes	characteristic
101	C₁₃×#431	C₂²	1	1	yes	characteristic
102	C₁₃×#431	C₂²	1	1	yes	characteristic
103	C₁₃×#424	C₂²	1	2	yes	—
104	C₁₃×#408	C₂²	1	2	yes	—
105	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
106	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
107	C₂×C₁₃×#41	—	2	1	no	—
108	C₂×C₁₃×#41	—	2	1	no	—
109	C₂×C₁₃×#41	C₂³	1	2	yes	—
110	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₁₃	—	2	1	no	—
112	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
113	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
118	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	—	2	2	no	—
120	C₁₃×C₄⋊Q₈	—	2	1	no	—
121	C₁₃×C₄⋊Q₈	—	2	1	no	—
122	C₁₃×C₄⋊Q₈	—	2	1	no	—
123	C₁₃×C₄⋊Q₈	—	2	1	no	—
124	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
125	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
127	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₁₃×#127	C₂³	1	1	yes	characteristic
134	C₁₃×#126	—	2	2	no	—
135	C₁₃×#126	—	2	2	no	—
136	C₁₃×#126	—	2	2	no	—
137	C₁₃×#126	—	2	2	no	—
138	C₁₃×#126	—	2	2	no	—
139	C₁₃×#126	—	2	2	no	—
140	C₁₃×#125	—	2	2	no	—
141	C₁₃×#125	—	2	2	no	—
142	C₁₃×#125	—	2	2	no	—
143	C₁₃×#125	—	2	2	no	—
144	C₁₃×#125	—	2	1	no	—
145	C₁₃×#125	—	2	1	no	—
146	C₁₃×#125	—	2	1	no	—
147	C₁₃×#125	—	2	1	no	—
148	C₁₃×#125	—	2	1	no	—
149	C₁₃×#125	—	2	1	no	—
150	C₁₃×#125	C₂³	1	2	yes	—
151	C₁₃×#124	—	2	2	no	—
152	C₁₃×#124	—	2	2	no	—
153	C₁₃×#124	—	2	2	no	—
154	C₁₃×#124	—	2	1	no	—
155	C₁₃×#124	—	2	1	no	—
156	C₁₃×#124	C₂³	1	2	yes	—
157	C₁₃×#123	—	2	2	no	—
158	C₁₃×#123	—	2	2	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×C₂²⋊Q₈	—	2	2	no	—
162	C₁₃×C₂²⋊Q₈	—	2	1	no	—
163	C₁₃×C₂²⋊Q₈	—	2	1	no	—
164	C₁₃×C₂²⋊Q₈	—	2	1	no	—
165	C₁₃×C₂²⋊Q₈	—	2	1	no	—
166	C₁₃×C₂²⋊Q₈	—	2	1	no	—
167	C₁₃×C₂²⋊Q₈	—	2	1	no	—
168	C₁₃×C₂²⋊Q₈	—	2	1	no	—
169	C₁₃×C₂²⋊Q₈	—	2	1	no	—
170	C₁₃×C₂²⋊Q₈	—	2	2	no	—
171	C₁₃×C₂²⋊Q₈	—	2	2	no	—
172	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₁₃×#121	—	2	2	no	—
179	C₁₃×#121	—	2	2	no	—
180	C₁₃×#121	—	2	2	no	—
181	C₁₃×#121	—	2	1	no	—
182	C₁₃×#121	—	2	1	no	—
183	C₁₃×#121	—	2	1	no	—
184	C₁₃×#121	—	2	1	no	—
185	C₁₃×#121	C₂³	1	2	yes	—
186	C₁₃×#121	C₂³	1	2	yes	—
187	C₄×Q₈×C₁₃	—	2	2	no	—
188	C₄×Q₈×C₁₃	—	2	2	no	—
189	C₄×Q₈×C₁₃	—	2	1	no	—
190	C₄×Q₈×C₁₃	—	2	1	no	—
191	C₄×Q₈×C₁₃	—	2	1	no	—
192	C₄×Q₈×C₁₃	—	2	1	no	—
193	C₄×Q₈×C₁₃	—	2	1	no	—
194	C₄×Q₈×C₁₃	—	2	1	no	—
195	C₄×Q₈×C₁₃	—	2	1	no	—
196	C₄×Q₈×C₁₃	—	2	1	no	—
197	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
198	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
199	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
200	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
201	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
202	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
203	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
204	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
205	C₄×D₄×C₁₃	—	2	2	no	—
206	C₄×D₄×C₁₃	—	2	2	no	—
207	C₄×D₄×C₁₃	—	2	1	no	—
208	C₄×D₄×C₁₃	—	2	1	no	—
209	C₄×D₄×C₁₃	—	2	1	no	—
210	C₄×D₄×C₁₃	—	2	1	no	—
211	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
212	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
213	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
214	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
215	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
216	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
217	C₄×D₄×C₁₃	C₂³	1	2	yes	—
218	C₄×D₄×C₁₃	C₂³	1	2	yes	—
219	C₁₃×#117	—	2	1	no	—
220	C₁₃×#117	—	2	1	no	—
221	C₁₃×#117	—	2	1	no	—
222	C₁₃×#117	—	2	1	no	—
223	C₁₃×#117	—	2	1	no	—
224	C₁₃×#117	—	2	1	no	—
225	C₁₃×#117	—	2	2	no	—
226	C₁₃×#117	—	2	2	no	—
227	C₁₃×#117	—	2	2	no	—
228	C₁₃×#117	C₂³	1	2	yes	—
229	C₁₃×#117	C₂³	1	1	yes	characteristic
230	C₁₃×#117	C₂³	1	1	yes	characteristic
231	C₁₃×#117	C₂³	1	1	yes	characteristic
232	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
235	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
236	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
238	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
240	C₁₃×#107	C₂³	1	4	yes	—
241	C₁₃×#107	C₂³	1	4	yes	—
242	C₁₃×#106	C₂³	1	4	yes	—
243	C₁₃×#106	C₂³	1	4	yes	—
244	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
245	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
246	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
247	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
248	C₁₃×#103	C₂³	1	4	yes	—
249	C₁₃×#103	C₂³	1	4	yes	—
250	C₁₃×#103	C₂³	1	4	yes	—
251	C₁₃×#103	C₂³	1	4	yes	—
252	C₁₃×#103	C₂³	1	4	yes	—
253	C₁₃×#103	C₂³	1	4	yes	—
254	C₁₃×#102	C₂³	1	4	yes	—
255	C₁₃×#102	C₂³	1	4	yes	—
256	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₁₃×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₁₃	C₂³	1	2	yes	—
264	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
266	#61008	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₁₃×#41	—	4	2	no	—
268	C₁₃×#41	—	4	4	no	—
269	C₁₃×#41	—	8	2	no	—
270	C₁₃×#41	—	8	2	no	—
271	C₂×Q₈×C₁₃	—	2	1	no	—
272	C₂×Q₈×C₁₃	—	2	1	no	—
273	C₂×Q₈×C₁₃	—	2	2	no	—
274	C₂×Q₈×C₁₃	—	2	1	no	—
275	C₂×Q₈×C₁₃	—	2	1	no	—
276	C₂×Q₈×C₁₃	—	2	2	no	—
277	C₂×Q₈×C₁₃	—	4	4	no	—
278	C₂×Q₈×C₁₃	—	8	2	no	—
279	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
281	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
282	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
283	C₂×D₄×C₁₃	—	2	2	no	—
284	C₂×D₄×C₁₃	—	2	2	no	—
285	C₂×D₄×C₁₃	—	2	2	no	—
286	C₂×D₄×C₁₃	—	2	1	no	—
287	C₂×D₄×C₁₃	—	2	1	no	—
288	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
290	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	2	no	—
294	C₂²×C₄×C₁₃	—	2	2	no	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	—	2	2	no	—
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₁₃×Q₁₆	—	4	4	no	—
307	C₁₃×Q₁₆	—	4	4	no	—
308	C₁₃×SD₁₆	—	4	4	no	—
309	C₁₃×SD₁₆	—	4	4	no	—
310	C₁₃×M₁₆	—	4	2	no	—
311	C₂×C₈×C₁₃	—	4	2	no	—
312	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
313	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
314	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	1	no	—
318	C₁₃×C₄⋊C₄	—	2	1	no	—
319	C₁₃×C₄⋊C₄	—	2	1	no	—
320	C₁₃×C₄⋊C₄	—	2	1	no	—
321	C₁₃×C₄⋊C₄	—	2	1	no	—
322	C₁₃×C₄⋊C₄	—	2	1	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	—	2	1	no	—
329	C₁₃×C₄⋊C₄	—	2	1	no	—
330	C₁₃×C₄⋊C₄	—	2	1	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	—	2	1	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	2	no	—
344	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
345	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
346	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
347	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
348	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
349	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
350	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
351	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
352	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
353	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	2	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	—	2	2	no	—
364	C₁₃×C₂²⋊C₄	—	2	2	no	—
365	C₁₃×C₂²⋊C₄	—	2	2	no	—
366	C₁₃×C₂²⋊C₄	—	2	2	no	—
367	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
368	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
369	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
370	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
371	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
372	C₁₃×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₁₃	—	2	2	no	—
374	C₄²×C₁₃	—	2	2	no	—
375	C₄²×C₁₃	—	2	2	no	—
376	C₄²×C₁₃	—	2	2	no	—
377	C₄²×C₁₃	—	2	2	no	—
378	C₄²×C₁₃	—	2	2	no	—
379	C₄²×C₁₃	—	2	2	no	—
380	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
384	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
386	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
388	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
389	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
390	#3511	C₂×C₁₃	1	1	yes	characteristic
391	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
392	#3258	C₂×C₁₃	1	4	yes	complemented
393	#3231	C₂×C₁₃	1	1	yes	characteristic, complemented
394	#3230	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#3229	C₂×C₁₃	1	1	yes	characteristic, complemented
396	#3228	C₂×C₁₃	1	1	yes	characteristic, complemented
397	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
398	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
399	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
400	#3206	C₂×C₁₃	1	1	yes	characteristic, complemented
401	#3201	C₂×C₁₃	1	4	yes	complemented
402	#3185	C₂×C₁₃	1	1	yes	characteristic, complemented
403	#3182	C₂×C₁₃	1	1	yes	characteristic, complemented
404	#3170	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
406	#3121	C₂×C₁₃	1	4	yes	complemented
407	#3120	C₂×C₁₃	1	4	yes	complemented
408	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
409	C₂³×C₁₃	—	2	2	no	—
410	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
412	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
413	Q₈×C₁₃	—	2	4	no	—
414	Q₈×C₁₃	—	2	4	no	—
415	Q₈×C₁₃	—	2	4	no	—
416	Q₈×C₁₃	—	4	1	no	—
417	Q₈×C₁₃	—	4	4	no	—
418	Q₈×C₁₃	—	4	2	no	—
419	Q₈×C₁₃	—	4	2	no	—
420	Q₈×C₁₃	—	4	2	no	—
421	Q₈×C₁₃	—	4	2	no	—
422	Q₈×C₁₃	—	8	2	no	—
423	D₄×C₁₃	—	2	4	no	—
424	D₄×C₁₃	—	4	1	no	—
425	D₄×C₁₃	—	4	1	no	—
426	D₄×C₁₃	—	4	1	no	—
427	D₄×C₁₃	—	4	4	no	—
428	D₄×C₁₃	—	4	2	no	—
429	D₄×C₁₃	—	4	2	no	—
430	D₄×C₁₃	—	8	2	no	—
431	D₄×C₁₃	—	8	2	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	2	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	2	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	4	4	no	—
449	C₂×C₄×C₁₃	—	4	4	no	—
450	C₂×C₄×C₁₃	—	8	2	no	—
451	C₂×C₄×C₁₃	—	8	2	no	—
452	C₂×C₄×C₁₃	—	8	2	no	—
453	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
465	C₈×C₁₃	—	2	2	no	—
466	C₈×C₁₃	—	2	2	no	—
467	C₈×C₁₃	—	2	2	no	—
468	C₈×C₁₃	—	2	2	no	—
469	#557	—	2	1	no	—
470	#557	—	2	1	no	—
471	#556	—	2	1	no	—
472	#556	—	2	1	no	—
473	#556	—	2	1	no	—
474	#555	—	2	1	no	—
475	#554	—	2	1	no	—
476	#553	—	2	1	no	—
477	#553	—	2	1	no	—
478	#552	—	2	1	no	—
479	#552	—	2	1	no	—
480	#552	—	2	1	no	—
481	#552	—	2	1	no	—
482	#548	—	2	1	no	—
483	#548	—	2	1	no	—
484	#547	—	2	1	no	—
485	#542	C₂²×C₁₃	1	2	yes	—
486	#542	C₂²×C₁₃	1	2	yes	—
487	#541	C₂²×C₁₃	1	2	yes	—
488	#541	C₂²×C₁₃	1	2	yes	—
489	#537	C₂²×C₁₃	1	2	yes	—
490	#536	C₂²×C₁₃	1	2	yes	—
491	#533	C₂²×C₁₃	1	1	yes	characteristic
492	#533	C₂²×C₁₃	1	1	yes	characteristic
493	#533	C₂²×C₁₃	1	1	yes	characteristic
494	#533	C₂²×C₁₃	1	1	yes	characteristic
495	#533	C₂²×C₁₃	1	1	yes	characteristic
496	#533	C₂²×C₁₃	1	1	yes	characteristic
497	#533	C₂²×C₁₃	1	1	yes	characteristic
498	#532	C₂²×C₁₃	1	1	yes	characteristic
499	#532	C₂²×C₁₃	1	1	yes	characteristic
500	#532	C₂²×C₁₃	1	1	yes	characteristic
501	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
502	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
503	#520	C₂²×C₁₃	1	2	yes	—
504	#519	C₂²×C₁₃	1	2	yes	—
505	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
506	#500	C₂²×C₁₃	1	1	yes	characteristic
507	#500	C₂²×C₁₃	1	1	yes	characteristic
508	#498	C₂²×C₁₃	1	1	yes	characteristic
509	#498	C₂²×C₁₃	1	1	yes	characteristic
510	#494	C₂²×C₁₃	1	1	yes	characteristic
511	#494	C₂²×C₁₃	1	1	yes	characteristic
512	#492	C₂²×C₁₃	1	1	yes	characteristic
513	#492	C₂²×C₁₃	1	1	yes	characteristic
514	#487	C₂²×C₁₃	1	1	yes	characteristic
515	#487	C₂²×C₁₃	1	1	yes	characteristic
516	#487	C₂²×C₁₃	1	1	yes	characteristic
517	#487	C₂²×C₁₃	1	1	yes	characteristic
518	#487	C₂²×C₁₃	1	1	yes	characteristic
519	#487	C₂²×C₁₃	1	1	yes	characteristic
520	#486	C₂²×C₁₃	1	1	yes	characteristic
521	#486	C₂²×C₁₃	1	1	yes	characteristic
522	#485	C₂²×C₁₃	1	4	yes	—
523	#484	C₂²×C₁₃	1	4	yes	—
524	#483	C₂²×C₁₃	1	4	yes	—
525	#482	C₂²×C₁₃	1	4	yes	—
526	#479	C₂²×C₁₃	1	4	yes	—
527	#478	C₂²×C₁₃	1	4	yes	—
528	#477	C₂²×C₁₃	1	4	yes	—
529	#475	C₂²×C₁₃	1	4	yes	—
530	#470	C₂²×C₁₃	1	4	yes	—
531	#468	C₂²×C₁₃	1	4	yes	—
532	#467	C₂²×C₁₃	1	4	yes	—
533	#465	C₂²×C₁₃	1	4	yes	—
534	#464	C₂²×C₁₃	1	4	yes	—
535	#464	C₂²×C₁₃	1	4	yes	—
536	#462	C₂²×C₁₃	1	4	yes	—
537	#461	C₂²×C₁₃	1	4	yes	—
538	#452	C₂²×C₁₃	1	4	yes	—
539	#452	C₂²×C₁₃	1	4	yes	—
540	#451	C₂²×C₁₃	1	4	yes	—
541	#448	C₂²×C₁₃	1	4	yes	—
542	#441	C₂²×C₁₃	1	4	yes	—
543	#440	C₂²×C₁₃	1	4	yes	—
544	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
545	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
546	#433	C₂²×C₁₃	1	2	yes	—
547	#433	C₂²×C₁₃	1	2	yes	—
548	#431	C₂²×C₁₃	1	1	yes	characteristic
549	#431	C₂²×C₁₃	1	1	yes	characteristic
550	#431	C₂²×C₁₃	1	1	yes	characteristic
551	#431	C₂²×C₁₃	1	1	yes	characteristic
552	#424	C₂²×C₁₃	1	2	yes	—
553	#408	C₂²×C₁₃	1	2	yes	—
554	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
555	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
556	C₂²×C₁₃	—	2	1	no	—
557	C₂²×C₁₃	—	2	1	no	—
558	C₂²×C₁₃	—	2	1	no	—
559	C₂²×C₁₃	—	2	1	no	—
560	C₂²×C₁₃	—	2	1	no	—
561	C₂²×C₁₃	—	2	1	no	—
562	C₂²×C₁₃	—	2	1	no	—
563	C₂²×C₁₃	—	2	1	no	—
564	C₂²×C₁₃	—	2	1	no	—
565	C₂²×C₁₃	—	4	2	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	—	4	2	no	—
568	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
569	C₄×C₁₃	—	2	1	no	—
570	C₄×C₁₃	—	2	1	no	—
571	C₄×C₁₃	—	2	1	no	—
572	C₄×C₁₃	—	2	1	no	—
573	C₄×C₁₃	—	2	1	no	—
574	C₄×C₁₃	—	2	1	no	—
575	C₄×C₁₃	—	2	1	no	—
576	C₄×C₁₃	—	2	1	no	—
577	C₄×C₁₃	—	2	1	no	—
578	C₄×C₁₃	—	4	2	no	—
579	C₄×C₁₃	—	4	2	no	—
580	C₄×C₁₃	—	4	2	no	—
581	C₄×C₁₃	—	4	2	no	—
582	C₄×C₁₃	—	4	2	no	—
583	C₄×C₁₃	—	4	2	no	—
584	C₄×C₁₃	—	4	2	no	—
585	C₄×C₁₃	#577	1	2	yes	—
586	C₄×C₁₃	#578	1	2	yes	—
587	C₄×C₁₃	#585	1	2	yes	—
588	C₂×#41	—	2	1	no	—
589	C₂×#41	—	2	1	no	—
590	C₂×#41	C₂³×C₁₃	1	2	yes	—
591	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
592	C₂²×Q₈	—	2	1	no	—
593	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
594	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
595	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
596	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
597	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
598	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
599	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
600	C₄⋊Q₈	—	2	2	no	—
601	C₄⋊Q₈	—	2	1	no	—
602	C₄⋊Q₈	—	2	1	no	—
603	C₄⋊Q₈	—	2	1	no	—
604	C₄⋊Q₈	—	2	1	no	—
605	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
606	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
607	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
608	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
609	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
610	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
611	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
612	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
613	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
614	#127	C₂³×C₁₃	1	1	yes	characteristic
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#126	—	2	2	no	—
618	#126	—	2	2	no	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#125	—	2	2	no	—
622	#125	—	2	2	no	—
623	#125	—	2	2	no	—
624	#125	—	2	2	no	—
625	#125	—	2	1	no	—
626	#125	—	2	1	no	—
627	#125	—	2	1	no	—
628	#125	—	2	1	no	—
629	#125	—	2	1	no	—
630	#125	—	2	1	no	—
631	#125	C₂³×C₁₃	1	2	yes	—
632	#124	—	2	2	no	—
633	#124	—	2	2	no	—
634	#124	—	2	2	no	—
635	#124	—	2	1	no	—
636	#124	—	2	1	no	—
637	#124	C₂³×C₁₃	1	2	yes	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	1	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	—	2	1	no	—
646	C₂²⋊Q₈	—	2	1	no	—
647	C₂²⋊Q₈	—	2	1	no	—
648	C₂²⋊Q₈	—	2	1	no	—
649	C₂²⋊Q₈	—	2	1	no	—
650	C₂²⋊Q₈	—	2	1	no	—
651	C₂²⋊Q₈	—	2	2	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
654	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
655	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
656	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
657	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
658	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
659	#121	—	2	2	no	—
660	#121	—	2	2	no	—
661	#121	—	2	2	no	—
662	#121	—	2	1	no	—
663	#121	—	2	1	no	—
664	#121	—	2	1	no	—
665	#121	—	2	1	no	—
666	#121	C₂³×C₁₃	1	2	yes	—
667	#121	C₂³×C₁₃	1	2	yes	—
668	C₄×Q₈	—	2	2	no	—
669	C₄×Q₈	—	2	2	no	—
670	C₄×Q₈	—	2	1	no	—
671	C₄×Q₈	—	2	1	no	—
672	C₄×Q₈	—	2	1	no	—
673	C₄×Q₈	—	2	1	no	—
674	C₄×Q₈	—	2	1	no	—
675	C₄×Q₈	—	2	1	no	—
676	C₄×Q₈	—	2	1	no	—
677	C₄×Q₈	—	2	1	no	—
678	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
679	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
680	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
681	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
682	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
683	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
684	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
685	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	1	no	—
689	C₄×D₄	—	2	1	no	—
690	C₄×D₄	—	2	1	no	—
691	C₄×D₄	—	2	1	no	—
692	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
693	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
694	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
695	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
696	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
697	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
698	C₄×D₄	C₂³×C₁₃	1	2	yes	—
699	C₄×D₄	C₂³×C₁₃	1	2	yes	—
700	#117	—	2	1	no	—
701	#117	—	2	1	no	—
702	#117	—	2	1	no	—
703	#117	—	2	1	no	—
704	#117	—	2	1	no	—
705	#117	—	2	1	no	—
706	#117	—	2	2	no	—
707	#117	—	2	2	no	—
708	#117	—	2	2	no	—
709	#117	C₂³×C₁₃	1	2	yes	—
710	#117	C₂³×C₁₃	1	1	yes	characteristic
711	#117	C₂³×C₁₃	1	1	yes	characteristic
712	#117	C₂³×C₁₃	1	1	yes	characteristic
713	C₂×C₄⋊C₄	—	2	1	no	—
714	C₂×C₄⋊C₄	—	2	1	no	—
715	C₂×C₄⋊C₄	—	2	1	no	—
716	C₂×C₄⋊C₄	—	2	2	no	—
717	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
718	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
721	#107	C₂³×C₁₃	1	4	yes	—
722	#107	C₂³×C₁₃	1	4	yes	—
723	#106	C₂³×C₁₃	1	4	yes	—
724	#106	C₂³×C₁₃	1	4	yes	—
725	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
726	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
727	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
728	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
729	#103	C₂³×C₁₃	1	4	yes	—
730	#103	C₂³×C₁₃	1	4	yes	—
731	#103	C₂³×C₁₃	1	4	yes	—
732	#103	C₂³×C₁₃	1	4	yes	—
733	#103	C₂³×C₁₃	1	4	yes	—
734	#103	C₂³×C₁₃	1	4	yes	—
735	#102	C₂³×C₁₃	1	4	yes	—
736	#102	C₂³×C₁₃	1	4	yes	—
737	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
738	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
739	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
740	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
741	#97	C₂³×C₁₃	1	2	yes	—
742	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
743	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
744	C₄×C₈	C₂³×C₁₃	1	2	yes	—
745	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
746	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
747	C₂×C₁₃	—	4	1	no	—
748	C₂×C₁₃	—	4	1	no	—
749	C₂×C₁₃	—	4	1	no	—
750	C₂×C₁₃	—	8	2	no	—
751	C₂×C₁₃	#3449	1	1	yes	characteristic
752	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
753	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
754	#41	—	4	2	no	—
755	#41	—	4	4	no	—
756	#41	—	8	2	no	—
757	#41	—	8	2	no	—
758	C₂×Q₈	—	2	1	no	—
759	C₂×Q₈	—	2	1	no	—
760	C₂×Q₈	—	2	2	no	—
761	C₂×Q₈	—	2	1	no	—
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	4	4	no	—
765	C₂×Q₈	—	8	2	no	—
766	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
768	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
769	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	1	no	—
774	C₂×D₄	—	2	1	no	—
775	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
776	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
777	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
778	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
790	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
792	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
793	Q₁₆	—	4	4	no	—
794	Q₁₆	—	4	4	no	—
795	SD₁₆	—	4	4	no	—
796	SD₁₆	—	4	4	no	—
797	M₁₆	—	4	2	no	—
798	C₂×C₈	—	4	2	no	—
799	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
800	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
801	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
802	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	1	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	1	no	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
832	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
833	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
834	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
835	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
836	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
837	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
838	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
839	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
840	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
855	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
856	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
857	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
858	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
859	C₂²⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
868	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
869	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
870	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
871	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
872	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
873	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
874	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
875	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
876	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
877	C₁₃	#61008	1	1	yes	characteristic, direct product factor, Sylow
878	C₂³	—	2	2	no	—
879	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
880	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
881	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
882	Q₈	—	2	4	no	—
883	Q₈	—	2	4	no	—
884	Q₈	—	2	4	no	—
885	Q₈	—	4	1	no	—
886	Q₈	—	4	4	no	—
887	Q₈	—	4	2	no	—
888	Q₈	—	4	2	no	—
889	Q₈	—	4	2	no	—
890	Q₈	—	4	2	no	—
891	Q₈	—	8	2	no	—
892	D₄	—	2	4	no	—
893	D₄	—	4	1	no	—
894	D₄	—	4	1	no	—
895	D₄	—	4	1	no	—
896	D₄	—	4	4	no	—
897	D₄	—	4	2	no	—
898	D₄	—	4	2	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
923	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
925	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
926	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
927	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
929	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
932	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
933	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
934	C₈	—	2	2	no	—
935	C₈	—	2	2	no	—
936	C₈	—	2	2	no	—
937	C₈	—	2	2	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	1	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	C₁₃×#577	1	2	yes	—
968	C₄	C₁₃×#578	1	2	yes	—
969	C₄	C₁₃×#585	1	2	yes	—
970	C₂	—	4	1	no	—
971	C₂	—	4	1	no	—
972	C₂	—	4	1	no	—
973	C₂	—	8	2	no	—
974	C₂	C₁₃×#3449	1	1	yes	characteristic
975	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
976	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3511	C₂
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
2. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3258	C₂	semidirect
4. C₁₃×#3231	C₂	semidirect
5. C₁₃×#3230	C₂	semidirect
6. C₁₃×#3229	C₂	semidirect
7. C₁₃×#3228	C₂	semidirect
8. C₁₃×#3210	C₂	semidirect
9. C₁₃×#3210	C₂	semidirect
10. C₁₃×#3209	C₂	semidirect
11. C₁₃×#3206	C₂	semidirect
12. C₁₃×#3201	C₂	semidirect
13. C₁₃×#3185	C₂	semidirect
14. C₁₃×#3182	C₂	semidirect
15. C₁₃×#3170	C₂	semidirect
16. C₁₃×#3167	C₂	semidirect
17. C₁₃×#3121	C₂	semidirect
18. C₁₃×#3120	C₂	semidirect
19. C₁₃×#2922	C₂	semidirect
266. #61008	C₁₃	direct (N × H)
391. #3509	C₂×C₁₃	semidirect
392. #3258	C₂×C₁₃	semidirect
393. #3231	C₂×C₁₃	semidirect
394. #3230	C₂×C₁₃	semidirect
395. #3229	C₂×C₁₃	semidirect
396. #3228	C₂×C₁₃	semidirect
397. #3210	C₂×C₁₃	semidirect
398. #3210	C₂×C₁₃	semidirect
399. #3209	C₂×C₁₃	semidirect
400. #3206	C₂×C₁₃	semidirect
401. #3201	C₂×C₁₃	semidirect
402. #3185	C₂×C₁₃	semidirect
403. #3182	C₂×C₁₃	semidirect
404. #3170	C₂×C₁₃	semidirect
405. #3167	C₂×C₁₃	semidirect
406. #3121	C₂×C₁₃	semidirect
407. #3120	C₂×C₁₃	semidirect
408. #2922	C₂×C₁₃	semidirect
877. C₁₃	#61008	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×#3511	2
C₁₃×#3509	2
C₁₃×#3258	2
C₁₃×#3231	2
C₁₃×#3230	2
C₁₃×#3229	2
C₁₃×#3228	2
C₁₃×#3210	2
C₁₃×#3209	2
C₁₃×#3206	2
C₁₃×#3201	2
C₁₃×#3185	2
C₁₃×#3182	2
C₁₃×#3170	2
C₁₃×#3167	2
C₁₃×#3121	2
C₁₃×#3120	2
C₁₃×#2922	2
#61008	13

Subgroups — C13×#61008 #15747347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61008 #15747347