Subgroups — C₁₃×#61859 #15748198

Order 3328.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1072 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	1	yes	maximal, characteristic, complemented
2	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3386	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3367	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3242	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3124	C₂	1	2	yes	maximal
20	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
21	C₁₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic
23	C₁₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#563	—	2	2	no	—
25	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
26	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
27	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#557	C₂²	1	1	yes	characteristic
29	C₁₃×#557	C₂²	1	2	yes	—
30	C₁₃×#557	C₂²	1	2	yes	—
31	C₁₃×#556	—	2	1	no	—
32	C₁₃×#556	C₂²	1	1	yes	characteristic
33	C₁₃×#556	C₂²	1	2	yes	—
34	C₁₃×#554	—	2	1	no	—
35	C₁₃×#554	—	2	1	no	—
36	C₁₃×#554	C₂²	1	1	yes	characteristic
37	C₁₃×#554	C₂²	1	1	yes	characteristic
38	C₁₃×#554	C₂²	1	1	yes	characteristic
39	C₁₃×#552	—	2	1	no	—
40	D₄×Q₈×C₁₃	—	2	2	no	—
41	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
42	C₁₃×#544	—	2	1	no	—
43	C₁₃×#544	—	2	2	no	—
44	C₁₃×#544	C₂²	1	2	yes	—
45	C₁₃×#542	C₂²	1	2	yes	—
46	C₁₃×#541	—	2	1	no	—
47	C₁₃×#541	—	2	2	no	—
48	C₁₃×#541	C₂²	1	2	yes	—
49	C₁₃×#533	—	2	1	no	—
50	C₁₃×#533	C₂²	1	1	yes	characteristic
51	C₁₃×#533	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
53	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₁₃×#529	C₂²	1	1	yes	characteristic
55	C₁₃×#520	C₂²	1	2	yes	—
56	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
57	C₁₃×#501	C₂²	1	2	yes	—
58	C₁₃×#501	C₂²	1	2	yes	—
59	C₁₃×#501	C₂²	1	2	yes	—
60	C₁₃×#500	C₂²	1	1	yes	characteristic
61	C₁₃×#500	C₂²	1	2	yes	—
62	C₁₃×#500	C₂²	1	1	yes	characteristic
63	C₁₃×#499	C₂²	1	2	yes	—
64	C₁₃×#491	C₂²	1	2	yes	—
65	C₁₃×#489	C₂²	1	2	yes	—
66	C₁₃×#489	C₂²	1	2	yes	—
67	C₁₃×#488	C₂²	1	2	yes	—
68	C₁₃×#487	C₂²	1	1	yes	characteristic
69	C₁₃×#487	C₂²	1	2	yes	—
70	C₁₃×#487	C₂²	1	1	yes	characteristic
71	C₁₃×#485	C₂²	1	1	yes	characteristic
72	C₁₃×#485	C₂²	1	2	yes	—
73	C₁₃×#484	C₂²	1	2	yes	—
74	C₁₃×#484	C₂²	1	2	yes	—
75	C₁₃×#483	C₂²	1	2	yes	—
76	C₁₃×#482	C₂²	1	1	yes	characteristic
77	C₁₃×#480	C₂²	1	2	yes	—
78	C₁₃×#479	C₂²	1	1	yes	characteristic
79	C₁₃×#479	C₂²	1	2	yes	—
80	C₁₃×#479	C₂²	1	2	yes	—
81	C₁₃×#479	C₂²	1	2	yes	—
82	C₁₃×#479	C₂²	1	2	yes	—
83	C₁₃×#478	C₂²	1	1	yes	characteristic
84	C₁₃×#478	C₂²	1	2	yes	—
85	C₁₃×#478	C₂²	1	2	yes	—
86	C₁₃×#477	C₂²	1	1	yes	characteristic
87	C₁₃×#477	C₂²	1	2	yes	—
88	C₁₃×#477	C₂²	1	2	yes	—
89	C₁₃×#477	C₂²	1	2	yes	—
90	C₁₃×#477	C₂²	1	1	yes	characteristic
91	C₁₃×#477	C₂²	1	1	yes	characteristic
92	C₁₃×#477	C₂²	1	2	yes	—
93	C₁₃×#477	C₂²	1	2	yes	—
94	C₁₃×#476	C₂²	1	1	yes	characteristic
95	C₁₃×#476	C₂²	1	1	yes	characteristic
96	C₁₃×#476	C₂²	1	1	yes	characteristic
97	C₁₃×#475	C₂²	1	2	yes	—
98	C₁₃×#474	C₂²	1	2	yes	—
99	C₁₃×#474	C₂²	1	2	yes	—
100	C₁₃×#464	C₂²	1	1	yes	characteristic
101	C₁₃×#464	C₂²	1	2	yes	—
102	C₁₃×#463	C₂²	1	1	yes	characteristic
103	C₁₃×#463	C₂²	1	2	yes	—
104	C₁₃×#462	C₂²	1	1	yes	characteristic
105	C₁₃×#462	C₂²	1	2	yes	—
106	C₁₃×#461	C₂²	1	1	yes	characteristic
107	C₁₃×#461	C₂²	1	2	yes	—
108	C₁₃×#452	C₂²	1	1	yes	characteristic
109	C₁₃×#452	C₂²	1	2	yes	—
110	C₁₃×#449	C₂²	1	1	yes	characteristic
111	C₁₃×#446	C₂²	1	2	yes	—
112	C₁₃×#446	C₂²	1	1	yes	characteristic
113	C₁₃×#446	C₂²	1	1	yes	characteristic
114	C₁₃×#446	C₂²	1	2	yes	—
115	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
117	C₁₃×#441	C₂²	1	2	yes	—
118	C₁₃×#441	C₂²	1	2	yes	—
119	C₁₃×#440	C₂²	1	2	yes	—
120	C₁₃×#440	C₂²	1	2	yes	—
121	C₁₃×#440	C₂²	1	2	yes	—
122	C₁₃×#440	C₂²	1	2	yes	—
123	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
124	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
125	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
126	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
127	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
128	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
129	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
130	C₄×C₁₃×D₈	C₂²	1	2	yes	—
131	C₁₃×#433	C₂²	1	2	yes	—
132	C₁₃×#433	C₂²	1	2	yes	—
133	C₁₃×#432	C₂²	1	1	yes	characteristic
134	C₁₃×#431	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₁₃	—	2	2	no	—
137	C₂²×Q₈×C₁₃	—	2	1	no	—
138	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
143	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
144	C₁₃×C₄⋊Q₈	—	2	2	no	—
145	C₁₃×C₄⋊Q₈	—	2	2	no	—
146	C₁₃×C₄⋊Q₈	—	2	2	no	—
147	C₁₃×C₄⋊Q₈	—	2	1	no	—
148	C₁₃×C₄⋊Q₈	—	2	1	no	—
149	C₁₃×C₄⋊Q₈	—	2	2	no	—
150	C₁₃×C₄⋊Q₈	—	2	2	no	—
151	C₁₃×C₄⋊Q₈	—	2	2	no	—
152	C₁₃×C₄⋊Q₈	—	2	1	no	—
153	C₁₃×C₄⋊Q₈	—	2	1	no	—
154	C₁₃×C₄⋊Q₈	—	2	1	no	—
155	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₁₃×#126	—	2	2	no	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#126	—	2	2	no	—
172	C₁₃×#126	—	2	1	no	—
173	C₁₃×#125	—	2	2	no	—
174	C₁₃×#125	—	2	2	no	—
175	C₁₃×#125	—	2	2	no	—
176	C₁₃×#125	—	2	2	no	—
177	C₁₃×#125	—	2	2	no	—
178	C₁₃×#125	—	2	2	no	—
179	C₁₃×#125	—	2	1	no	—
180	C₁₃×#125	—	2	2	no	—
181	C₁₃×#125	—	2	2	no	—
182	C₁₃×#125	—	2	1	no	—
183	C₁₃×#125	D₄	1	2	yes	—
184	C₁₃×#125	C₂³	1	2	yes	—
185	C₁₃×#125	C₂³	1	2	yes	—
186	C₁₃×#125	C₂³	1	1	yes	characteristic
187	C₁₃×#125	C₂³	1	2	yes	—
188	C₁₃×#124	—	2	2	no	—
189	C₁₃×#124	C₂³	1	2	yes	—
190	C₁₃×#124	C₂³	1	1	yes	characteristic
191	C₁₃×#123	—	2	1	no	—
192	C₁₃×#123	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	1	no	—
194	C₁₃×C₂²⋊Q₈	—	2	1	no	—
195	C₁₃×C₂²⋊Q₈	—	2	1	no	—
196	C₁₃×C₂²⋊Q₈	—	2	1	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	—	2	1	no	—
199	C₁₃×C₂²⋊Q₈	—	2	2	no	—
200	C₁₃×C₂²⋊Q₈	—	2	2	no	—
201	C₁₃×C₂²⋊Q₈	—	2	2	no	—
202	C₁₃×C₂²⋊Q₈	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	2	no	—
206	C₁₃×C₂²⋊Q₈	—	2	2	no	—
207	C₁₃×C₂²⋊Q₈	—	2	2	no	—
208	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
209	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₁₃×#121	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₁₃	—	2	1	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	—	2	1	no	—
217	C₄×Q₈×C₁₃	—	2	1	no	—
218	C₄×Q₈×C₁₃	—	2	2	no	—
219	C₄×Q₈×C₁₃	—	2	2	no	—
220	C₄×Q₈×C₁₃	—	2	1	no	—
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
228	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
233	C₄×D₄×C₁₃	—	2	1	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	1	no	—
236	C₄×D₄×C₁₃	—	2	2	no	—
237	C₄×D₄×C₁₃	—	2	2	no	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₁₃	C₂³	1	2	yes	—
241	C₄×D₄×C₁₃	C₂³	1	2	yes	—
242	C₄×D₄×C₁₃	C₂³	1	2	yes	—
243	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
244	C₁₃×#117	—	2	1	no	—
245	C₁₃×#117	—	2	2	no	—
246	C₁₃×#117	—	2	2	no	—
247	C₁₃×#117	—	2	1	no	—
248	C₁₃×#117	—	2	1	no	—
249	C₁₃×#117	—	2	1	no	—
250	C₁₃×#117	C₂³	1	1	yes	characteristic
251	C₁₃×#117	C₂³	1	2	yes	—
252	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₄²×C₁₃	—	2	1	no	—
259	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
260	C₁₃×#107	C₂³	1	2	yes	—
261	C₁₃×#107	C₂³	1	1	yes	characteristic
262	C₁₃×#107	C₂³	1	2	yes	—
263	C₁₃×#107	C₂³	1	1	yes	characteristic
264	C₁₃×#107	C₂³	1	2	yes	—
265	C₁₃×#107	C₂³	1	2	yes	—
266	C₁₃×#107	C₂³	1	2	yes	—
267	C₁₃×#107	C₂³	1	2	yes	—
268	C₁₃×#107	C₂³	1	2	yes	—
269	C₁₃×#106	C₂³	1	1	yes	characteristic
270	C₁₃×#106	C₂³	1	2	yes	—
271	C₁₃×#106	C₂³	1	1	yes	characteristic
272	C₁₃×#106	C₂³	1	2	yes	—
273	C₁₃×#106	C₂³	1	2	yes	—
274	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₃×#103	C₂³	1	1	yes	characteristic
283	C₁₃×#103	C₂³	1	2	yes	—
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	2	yes	—
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	1	yes	characteristic
299	C₁₃×#102	C₂³	1	1	yes	characteristic
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×#97	C₂³	1	2	yes	—
306	C₁₃×#97	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₃	C₂³	1	2	yes	—
311	C₄×C₈×C₁₃	C₂³	1	2	yes	—
312	#61859	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃×#41	—	2	2	no	—
314	C₁₃×#41	—	2	2	no	—
315	C₂×Q₈×C₁₃	—	2	2	no	—
316	C₂×Q₈×C₁₃	—	2	1	no	—
317	C₂×Q₈×C₁₃	—	2	2	no	—
318	C₂×Q₈×C₁₃	—	2	2	no	—
319	C₂×Q₈×C₁₃	—	2	2	no	—
320	C₂×Q₈×C₁₃	—	2	1	no	—
321	C₂×Q₈×C₁₃	—	2	1	no	—
322	C₂×Q₈×C₁₃	—	8	2	no	—
323	C₂×Q₈×C₁₃	—	8	4	no	—
324	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
327	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₁₃	—	2	1	no	—
331	C₂×D₄×C₁₃	—	2	1	no	—
332	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₁₃	—	2	1	no	—
335	C₂²×C₄×C₁₃	—	2	2	no	—
336	C₂²×C₄×C₁₃	—	2	1	no	—
337	C₂²×C₄×C₁₃	—	2	1	no	—
338	C₂²×C₄×C₁₃	—	2	1	no	—
339	C₂²×C₄×C₁₃	—	2	2	no	—
340	C₂²×C₄×C₁₃	—	2	2	no	—
341	C₂²×C₄×C₁₃	—	2	2	no	—
342	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
344	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₁₃×Q₁₆	—	2	2	no	—
346	C₁₃×Q₁₆	—	2	4	no	—
347	C₁₃×SD₁₆	—	2	2	no	—
348	C₁₃×SD₁₆	—	2	2	no	—
349	C₁₃×SD₁₆	—	2	4	no	—
350	C₁₃×D₈	—	2	2	no	—
351	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
354	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
357	C₁₃×C₄⋊C₄	—	2	1	no	—
358	C₁₃×C₄⋊C₄	—	2	1	no	—
359	C₁₃×C₄⋊C₄	—	2	2	no	—
360	C₁₃×C₄⋊C₄	—	2	1	no	—
361	C₁₃×C₄⋊C₄	—	2	2	no	—
362	C₁₃×C₄⋊C₄	—	2	2	no	—
363	C₁₃×C₄⋊C₄	—	2	2	no	—
364	C₁₃×C₄⋊C₄	—	2	2	no	—
365	C₁₃×C₄⋊C₄	—	2	2	no	—
366	C₁₃×C₄⋊C₄	—	2	2	no	—
367	C₁₃×C₄⋊C₄	—	2	1	no	—
368	C₁₃×C₄⋊C₄	—	2	1	no	—
369	C₁₃×C₄⋊C₄	—	2	1	no	—
370	C₁₃×C₄⋊C₄	—	2	2	no	—
371	C₁₃×C₄⋊C₄	—	2	1	no	—
372	C₁₃×C₄⋊C₄	—	2	1	no	—
373	C₁₃×C₄⋊C₄	—	2	1	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	—	2	2	no	—
376	C₁₃×C₄⋊C₄	—	2	2	no	—
377	C₁₃×C₄⋊C₄	—	2	2	no	—
378	C₁₃×C₄⋊C₄	—	2	2	no	—
379	C₁₃×C₄⋊C₄	—	2	2	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	2	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	2	no	—
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
389	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
390	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
391	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
393	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
394	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
398	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
399	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
400	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
403	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₁₃×C₂²⋊C₄	—	2	2	no	—
405	C₁₃×C₂²⋊C₄	—	2	1	no	—
406	C₁₃×C₂²⋊C₄	—	2	1	no	—
407	C₁₃×C₂²⋊C₄	—	2	1	no	—
408	C₁₃×C₂²⋊C₄	—	2	1	no	—
409	C₁₃×C₂²⋊C₄	—	2	1	no	—
410	C₁₃×C₂²⋊C₄	—	2	2	no	—
411	C₁₃×C₂²⋊C₄	—	2	2	no	—
412	C₁₃×C₂²⋊C₄	—	2	1	no	—
413	C₁₃×C₂²⋊C₄	—	2	1	no	—
414	C₁₃×C₂²⋊C₄	—	2	2	no	—
415	C₁₃×C₂²⋊C₄	—	2	2	no	—
416	C₁₃×C₂²⋊C₄	—	2	1	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
419	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
420	C₄²×C₁₃	—	2	1	no	—
421	C₄²×C₁₃	—	2	1	no	—
422	C₄²×C₁₃	—	2	1	no	—
423	C₄²×C₁₃	—	2	2	no	—
424	C₄²×C₁₃	—	2	2	no	—
425	C₄²×C₁₃	—	2	2	no	—
426	C₄²×C₁₃	—	2	1	no	—
427	C₄²×C₁₃	—	2	2	no	—
428	C₄²×C₁₃	—	2	2	no	—
429	C₄²×C₁₃	—	2	2	no	—
430	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
433	C₄²×C₁₃	C₂⁴	1	2	yes	—
434	C₄²×C₁₃	C₂⁴	1	2	yes	—
435	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
436	#3555	C₂×C₁₃	1	1	yes	characteristic, complemented
437	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
438	#3390	C₂×C₁₃	1	2	yes	complemented
439	#3386	C₂×C₁₃	1	2	yes	complemented
440	#3385	C₂×C₁₃	1	1	yes	characteristic, complemented
441	#3385	C₂×C₁₃	1	1	yes	characteristic, complemented
442	Q₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
443	#3380	C₂×C₁₃	1	1	yes	characteristic, complemented
444	#3377	C₂×C₁₃	1	2	yes	complemented
445	#3372	C₂×C₁₃	1	1	yes	characteristic, complemented
446	#3369	C₂×C₁₃	1	1	yes	characteristic, complemented
447	#3367	C₂×C₁₃	1	2	yes	complemented
448	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3243	C₂×C₁₃	1	2	yes	complemented
451	#3242	C₂×C₁₃	1	2	yes	complemented
452	#3238	C₂×C₁₃	1	1	yes	characteristic, complemented
453	#3230	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3124	C₂×C₁₃	1	2	yes	—
455	#3120	C₂×C₁₃	1	2	yes	complemented
456	#3116	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3102	C₂×C₁₃	1	1	yes	characteristic
458	#2985	C₂×C₁₃	1	1	yes	characteristic, complemented
459	C₂³×C₁₃	—	2	1	no	—
460	C₂³×C₁₃	—	2	1	no	—
461	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
462	Q₈×C₁₃	—	2	2	no	—
463	Q₈×C₁₃	—	2	2	no	—
464	Q₈×C₁₃	—	2	1	no	—
465	Q₈×C₁₃	—	2	2	no	—
466	Q₈×C₁₃	—	2	1	no	—
467	Q₈×C₁₃	—	2	1	no	—
468	Q₈×C₁₃	—	2	2	no	—
469	Q₈×C₁₃	—	4	2	no	—
470	Q₈×C₁₃	—	4	4	no	—
471	Q₈×C₁₃	—	8	1	no	—
472	Q₈×C₁₃	—	8	2	no	—
473	Q₈×C₁₃	—	8	1	no	—
474	Q₈×C₁₃	—	8	1	no	—
475	Q₈×C₁₃	—	8	2	no	—
476	Q₈×C₁₃	—	8	2	no	—
477	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
478	D₄×C₁₃	—	2	4	no	—
479	D₄×C₁₃	—	2	1	no	—
480	D₄×C₁₃	—	2	1	no	—
481	D₄×C₁₃	—	2	1	no	—
482	D₄×C₁₃	—	8	1	no	—
483	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
484	C₂×C₄×C₁₃	—	2	4	no	—
485	C₂×C₄×C₁₃	—	2	1	no	—
486	C₂×C₄×C₁₃	—	2	2	no	—
487	C₂×C₄×C₁₃	—	2	1	no	—
488	C₂×C₄×C₁₃	—	2	1	no	—
489	C₂×C₄×C₁₃	—	2	2	no	—
490	C₂×C₄×C₁₃	—	2	1	no	—
491	C₂×C₄×C₁₃	—	2	1	no	—
492	C₂×C₄×C₁₃	—	2	1	no	—
493	C₂×C₄×C₁₃	—	2	1	no	—
494	C₂×C₄×C₁₃	—	2	2	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	2	no	—
497	C₂×C₄×C₁₃	—	2	2	no	—
498	C₂×C₄×C₁₃	—	4	1	no	—
499	C₂×C₄×C₁₃	—	4	2	no	—
500	C₂×C₄×C₁₃	—	4	2	no	—
501	C₂×C₄×C₁₃	—	4	2	no	—
502	C₂×C₄×C₁₃	—	8	2	no	—
503	C₂×C₄×C₁₃	—	8	2	no	—
504	C₂×C₄×C₁₃	—	8	2	no	—
505	C₂×C₄×C₁₃	—	8	2	no	—
506	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
514	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
516	C₈×C₁₃	—	2	1	no	—
517	C₈×C₁₃	—	2	1	no	—
518	C₈×C₁₃	—	2	1	no	—
519	C₈×C₁₃	—	2	2	no	—
520	C₈×C₁₃	—	2	1	no	—
521	C₈×C₁₃	—	2	2	no	—
522	#563	—	2	2	no	—
523	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
524	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
525	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
526	#557	C₂²×C₁₃	1	1	yes	characteristic
527	#557	C₂²×C₁₃	1	2	yes	—
528	#557	C₂²×C₁₃	1	2	yes	—
529	#556	—	2	1	no	—
530	#556	C₂²×C₁₃	1	1	yes	characteristic
531	#556	C₂²×C₁₃	1	2	yes	—
532	#554	—	2	1	no	—
533	#554	—	2	1	no	—
534	#554	C₂²×C₁₃	1	1	yes	characteristic
535	#554	C₂²×C₁₃	1	1	yes	characteristic
536	#554	C₂²×C₁₃	1	1	yes	characteristic
537	#552	—	2	1	no	—
538	D₄×Q₈	—	2	2	no	—
539	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
540	#544	—	2	1	no	—
541	#544	—	2	2	no	—
542	#544	C₂²×C₁₃	1	2	yes	—
543	#542	C₂²×C₁₃	1	2	yes	—
544	#541	—	2	1	no	—
545	#541	—	2	2	no	—
546	#541	C₂²×C₁₃	1	2	yes	—
547	#533	—	2	1	no	—
548	#533	C₂²×C₁₃	1	1	yes	characteristic
549	#533	C₂²×C₁₃	1	1	yes	characteristic
550	C₂×C₄⋊Q₈	—	2	1	no	—
551	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
552	#529	C₂²×C₁₃	1	1	yes	characteristic
553	#520	C₂²×C₁₃	1	2	yes	—
554	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
555	#501	C₂²×C₁₃	1	2	yes	—
556	#501	C₂²×C₁₃	1	2	yes	—
557	#501	C₂²×C₁₃	1	2	yes	—
558	#500	C₂²×C₁₃	1	1	yes	characteristic
559	#500	C₂²×C₁₃	1	2	yes	—
560	#500	C₂²×C₁₃	1	1	yes	characteristic
561	#499	C₂²×C₁₃	1	2	yes	—
562	#491	C₂²×C₁₃	1	2	yes	—
563	#489	C₂²×C₁₃	1	2	yes	—
564	#489	C₂²×C₁₃	1	2	yes	—
565	#488	C₂²×C₁₃	1	2	yes	—
566	#487	C₂²×C₁₃	1	1	yes	characteristic
567	#487	C₂²×C₁₃	1	2	yes	—
568	#487	C₂²×C₁₃	1	1	yes	characteristic
569	#485	C₂²×C₁₃	1	1	yes	characteristic
570	#485	C₂²×C₁₃	1	2	yes	—
571	#484	C₂²×C₁₃	1	2	yes	—
572	#484	C₂²×C₁₃	1	2	yes	—
573	#483	C₂²×C₁₃	1	2	yes	—
574	#482	C₂²×C₁₃	1	1	yes	characteristic
575	#480	C₂²×C₁₃	1	2	yes	—
576	#479	C₂²×C₁₃	1	1	yes	characteristic
577	#479	C₂²×C₁₃	1	2	yes	—
578	#479	C₂²×C₁₃	1	2	yes	—
579	#479	C₂²×C₁₃	1	2	yes	—
580	#479	C₂²×C₁₃	1	2	yes	—
581	#478	C₂²×C₁₃	1	1	yes	characteristic
582	#478	C₂²×C₁₃	1	2	yes	—
583	#478	C₂²×C₁₃	1	2	yes	—
584	#477	C₂²×C₁₃	1	1	yes	characteristic
585	#477	C₂²×C₁₃	1	2	yes	—
586	#477	C₂²×C₁₃	1	2	yes	—
587	#477	C₂²×C₁₃	1	2	yes	—
588	#477	C₂²×C₁₃	1	1	yes	characteristic
589	#477	C₂²×C₁₃	1	1	yes	characteristic
590	#477	C₂²×C₁₃	1	2	yes	—
591	#477	C₂²×C₁₃	1	2	yes	—
592	#476	C₂²×C₁₃	1	1	yes	characteristic
593	#476	C₂²×C₁₃	1	1	yes	characteristic
594	#476	C₂²×C₁₃	1	1	yes	characteristic
595	#475	C₂²×C₁₃	1	2	yes	—
596	#474	C₂²×C₁₃	1	2	yes	—
597	#474	C₂²×C₁₃	1	2	yes	—
598	#464	C₂²×C₁₃	1	1	yes	characteristic
599	#464	C₂²×C₁₃	1	2	yes	—
600	#463	C₂²×C₁₃	1	1	yes	characteristic
601	#463	C₂²×C₁₃	1	2	yes	—
602	#462	C₂²×C₁₃	1	1	yes	characteristic
603	#462	C₂²×C₁₃	1	2	yes	—
604	#461	C₂²×C₁₃	1	1	yes	characteristic
605	#461	C₂²×C₁₃	1	2	yes	—
606	#452	C₂²×C₁₃	1	1	yes	characteristic
607	#452	C₂²×C₁₃	1	2	yes	—
608	#449	C₂²×C₁₃	1	1	yes	characteristic
609	#446	C₂²×C₁₃	1	2	yes	—
610	#446	C₂²×C₁₃	1	1	yes	characteristic
611	#446	C₂²×C₁₃	1	1	yes	characteristic
612	#446	C₂²×C₁₃	1	2	yes	—
613	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
614	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
615	#441	C₂²×C₁₃	1	2	yes	—
616	#441	C₂²×C₁₃	1	2	yes	—
617	#440	C₂²×C₁₃	1	2	yes	—
618	#440	C₂²×C₁₃	1	2	yes	—
619	#440	C₂²×C₁₃	1	2	yes	—
620	#440	C₂²×C₁₃	1	2	yes	—
621	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
622	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
623	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
624	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
625	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
626	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
627	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
628	C₄×D₈	C₂²×C₁₃	1	2	yes	—
629	#433	C₂²×C₁₃	1	2	yes	—
630	#433	C₂²×C₁₃	1	2	yes	—
631	#432	C₂²×C₁₃	1	1	yes	characteristic
632	#431	C₂²×C₁₃	1	1	yes	characteristic
633	C₂²×C₁₃	—	2	1	no	—
634	C₂²×C₁₃	—	2	1	no	—
635	C₂²×C₁₃	—	2	2	no	—
636	C₂²×C₁₃	—	2	1	no	—
637	C₂²×C₁₃	—	4	1	no	—
638	C₂²×C₁₃	—	4	1	no	—
639	C₂²×C₁₃	—	4	1	no	—
640	C₂²×C₁₃	—	4	1	no	—
641	C₂²×C₁₃	—	4	1	no	—
642	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
643	C₄×C₁₃	—	2	1	no	—
644	C₄×C₁₃	—	2	1	no	—
645	C₄×C₁₃	—	2	2	no	—
646	C₄×C₁₃	—	2	2	no	—
647	C₄×C₁₃	—	2	1	no	—
648	C₄×C₁₃	—	2	2	no	—
649	C₄×C₁₃	—	2	1	no	—
650	C₄×C₁₃	—	2	2	no	—
651	C₄×C₁₃	—	2	2	no	—
652	C₄×C₁₃	—	4	1	no	—
653	C₄×C₁₃	—	4	2	no	—
654	C₄×C₁₃	—	4	2	no	—
655	C₄×C₁₃	—	4	2	no	—
656	C₄×C₁₃	—	4	1	no	—
657	C₄×C₁₃	—	4	2	no	—
658	C₄×C₁₃	—	4	1	no	—
659	C₄×C₁₃	—	4	1	no	—
660	C₄×C₁₃	—	4	1	no	—
661	C₄×C₁₃	#578	1	2	yes	—
662	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
663	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
664	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
665	C₂²×Q₈	—	2	2	no	—
666	C₂²×Q₈	—	2	1	no	—
667	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
668	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
669	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
670	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
671	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
672	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
673	C₄⋊Q₈	—	2	2	no	—
674	C₄⋊Q₈	—	2	2	no	—
675	C₄⋊Q₈	—	2	2	no	—
676	C₄⋊Q₈	—	2	1	no	—
677	C₄⋊Q₈	—	2	1	no	—
678	C₄⋊Q₈	—	2	2	no	—
679	C₄⋊Q₈	—	2	2	no	—
680	C₄⋊Q₈	—	2	2	no	—
681	C₄⋊Q₈	—	2	1	no	—
682	C₄⋊Q₈	—	2	1	no	—
683	C₄⋊Q₈	—	2	1	no	—
684	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
685	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
686	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
687	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
688	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
689	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
690	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
693	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
694	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	1	no	—
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	—	2	2	no	—
705	#125	—	2	2	no	—
706	#125	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	1	no	—
709	#125	—	2	2	no	—
710	#125	—	2	2	no	—
711	#125	—	2	1	no	—
712	#125	D₄×C₁₃	1	2	yes	—
713	#125	C₂³×C₁₃	1	1	yes	characteristic
714	#125	C₂³×C₁₃	1	2	yes	—
715	#125	C₂³×C₁₃	1	2	yes	—
716	#125	C₂³×C₁₃	1	2	yes	—
717	#124	—	2	2	no	—
718	#124	C₂³×C₁₃	1	1	yes	characteristic
719	#124	C₂³×C₁₃	1	2	yes	—
720	#123	—	2	1	no	—
721	#123	—	2	2	no	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	1	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
738	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
739	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
740	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
741	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
742	#121	C₂³×C₁₃	1	1	yes	characteristic
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	2	no	—
748	C₄×Q₈	—	2	2	no	—
749	C₄×Q₈	—	2	1	no	—
750	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
751	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
752	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
753	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
754	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
756	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
757	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
758	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
759	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
760	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
761	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
762	C₄×D₄	—	2	1	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
768	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₁₃	1	2	yes	—
770	C₄×D₄	C₂³×C₁₃	1	2	yes	—
771	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₁₃	1	2	yes	—
773	#117	—	2	1	no	—
774	#117	—	2	2	no	—
775	#117	—	2	2	no	—
776	#117	—	2	1	no	—
777	#117	—	2	1	no	—
778	#117	—	2	1	no	—
779	#117	C₂³×C₁₃	1	1	yes	characteristic
780	#117	C₂³×C₁₃	1	2	yes	—
781	C₂×C₄⋊C₄	—	2	1	no	—
782	C₂×C₄⋊C₄	—	2	2	no	—
783	C₂×C₄⋊C₄	—	2	1	no	—
784	C₂×C₄⋊C₄	—	2	1	no	—
785	C₂×C₄⋊C₄	—	2	1	no	—
786	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
787	C₂×C₄²	—	2	1	no	—
788	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
789	#107	C₂³×C₁₃	1	2	yes	—
790	#107	C₂³×C₁₃	1	1	yes	characteristic
791	#107	C₂³×C₁₃	1	2	yes	—
792	#107	C₂³×C₁₃	1	1	yes	characteristic
793	#107	C₂³×C₁₃	1	2	yes	—
794	#107	C₂³×C₁₃	1	2	yes	—
795	#107	C₂³×C₁₃	1	2	yes	—
796	#107	C₂³×C₁₃	1	2	yes	—
797	#107	C₂³×C₁₃	1	2	yes	—
798	#106	C₂³×C₁₃	1	1	yes	characteristic
799	#106	C₂³×C₁₃	1	2	yes	—
800	#106	C₂³×C₁₃	1	1	yes	characteristic
801	#106	C₂³×C₁₃	1	2	yes	—
802	#106	C₂³×C₁₃	1	2	yes	—
803	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
804	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
805	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
806	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
807	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
808	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
809	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
810	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
811	#103	C₂³×C₁₃	1	1	yes	characteristic
812	#103	C₂³×C₁₃	1	2	yes	—
813	#103	C₂³×C₁₃	1	1	yes	characteristic
814	#103	C₂³×C₁₃	1	1	yes	characteristic
815	#103	C₂³×C₁₃	1	2	yes	—
816	#103	C₂³×C₁₃	1	2	yes	—
817	#103	C₂³×C₁₃	1	1	yes	characteristic
818	#103	C₂³×C₁₃	1	2	yes	—
819	#103	C₂³×C₁₃	1	2	yes	—
820	#103	C₂³×C₁₃	1	2	yes	—
821	#103	C₂³×C₁₃	1	2	yes	—
822	#103	C₂³×C₁₃	1	2	yes	—
823	#103	C₂³×C₁₃	1	2	yes	—
824	#102	C₂³×C₁₃	1	1	yes	characteristic
825	#102	C₂³×C₁₃	1	2	yes	—
826	#102	C₂³×C₁₃	1	2	yes	—
827	#102	C₂³×C₁₃	1	1	yes	characteristic
828	#102	C₂³×C₁₃	1	1	yes	characteristic
829	#102	C₂³×C₁₃	1	1	yes	characteristic
830	#102	C₂³×C₁₃	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
832	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
833	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
834	#97	C₂³×C₁₃	1	2	yes	—
835	#97	C₂³×C₁₃	1	2	yes	—
836	#97	C₂³×C₁₃	1	2	yes	—
837	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
838	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
839	C₄×C₈	C₂³×C₁₃	1	2	yes	—
840	C₄×C₈	C₂³×C₁₃	1	2	yes	—
841	C₂×C₁₃	—	4	1	no	—
842	C₂×C₁₃	—	4	2	no	—
843	C₂×C₁₃	—	8	1	no	—
844	C₂×C₁₃	#3486	1	1	yes	characteristic
845	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
846	C₂×C₁₃	#3585	1	1	yes	characteristic
847	#41	—	2	2	no	—
848	#41	—	2	2	no	—
849	C₂×Q₈	—	2	2	no	—
850	C₂×Q₈	—	2	1	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	2	2	no	—
853	C₂×Q₈	—	2	2	no	—
854	C₂×Q₈	—	2	1	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	8	2	no	—
857	C₂×Q₈	—	8	4	no	—
858	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
859	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
860	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
861	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
862	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
863	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
864	C₂×D₄	—	2	1	no	—
865	C₂×D₄	—	2	1	no	—
866	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
867	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	2	1	no	—
872	C₂²×C₄	—	2	1	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
877	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
878	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
879	Q₁₆	—	2	2	no	—
880	Q₁₆	—	2	4	no	—
881	SD₁₆	—	2	2	no	—
882	SD₁₆	—	2	2	no	—
883	SD₁₆	—	2	4	no	—
884	D₈	—	2	2	no	—
885	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
886	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
887	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
888	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
889	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
890	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
923	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
924	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
925	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
926	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
927	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
928	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
929	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
930	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
931	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
933	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
934	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
935	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
937	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
953	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
954	C₄²	—	2	1	no	—
955	C₄²	—	2	1	no	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	2	no	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
965	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
966	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
967	C₄²	C₂⁴×C₁₃	1	2	yes	—
968	C₄²	C₂⁴×C₁₃	1	2	yes	—
969	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
970	C₁₃	#61859	1	1	yes	characteristic, direct product factor, Sylow
971	C₂³	—	2	1	no	—
972	C₂³	—	2	1	no	—
973	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	1	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	1	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	4	2	no	—
982	Q₈	—	4	4	no	—
983	Q₈	—	8	1	no	—
984	Q₈	—	8	1	no	—
985	Q₈	—	8	2	no	—
986	Q₈	—	8	2	no	—
987	Q₈	—	8	1	no	—
988	Q₈	—	8	2	no	—
989	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
990	D₄	—	2	4	no	—
991	D₄	—	2	1	no	—
992	D₄	—	2	1	no	—
993	D₄	—	2	1	no	—
994	D₄	—	8	1	no	—
995	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
996	C₂×C₄	—	2	4	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	2	no	—
1012	C₂×C₄	—	4	2	no	—
1013	C₂×C₄	—	4	2	no	—
1014	C₂×C₄	—	8	2	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	2	no	—
1018	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1020	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1021	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1026	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1027	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	2	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1044	C₄	—	2	1	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	C₁₃×#578	1	2	yes	—
1063	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1064	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1065	C₂	—	4	1	no	—
1066	C₂	—	4	2	no	—
1067	C₂	—	8	1	no	—
1068	C₂	C₁₃×#3486	1	1	yes	characteristic
1069	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1070	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#449	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3555	C₂	semidirect
2. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3390	C₂	semidirect
4. C₁₃×#3386	C₂	semidirect
5. C₁₃×#3385	C₂	semidirect
6. C₁₃×#3385	C₂	semidirect
7. Q₈×C₁₃×Q₁₆	C₂	semidirect
8. C₁₃×#3380	C₂	semidirect
9. C₁₃×#3377	C₂	semidirect
10. C₁₃×#3372	C₂	semidirect
11. C₁₃×#3369	C₂	semidirect
12. C₁₃×#3367	C₂	semidirect
13. C₁₃×#3363	C₂	semidirect
14. C₁₃×#3360	C₂	semidirect
15. C₁₃×#3243	C₂	semidirect
16. C₁₃×#3242	C₂	semidirect
17. C₁₃×#3238	C₂	semidirect
18. C₁₃×#3230	C₂	semidirect
20. C₁₃×#3120	C₂	semidirect
21. C₁₃×#3116	C₂	semidirect
23. C₁₃×#2985	C₂	semidirect
312. #61859	C₁₃	direct (N × H)
436. #3555	C₂×C₁₃	semidirect
437. #3503	C₂×C₁₃	semidirect
438. #3390	C₂×C₁₃	semidirect
439. #3386	C₂×C₁₃	semidirect
440. #3385	C₂×C₁₃	semidirect
441. #3385	C₂×C₁₃	semidirect
442. Q₈×Q₁₆	C₂×C₁₃	semidirect
443. #3380	C₂×C₁₃	semidirect
444. #3377	C₂×C₁₃	semidirect
445. #3372	C₂×C₁₃	semidirect
446. #3369	C₂×C₁₃	semidirect
447. #3367	C₂×C₁₃	semidirect
448. #3363	C₂×C₁₃	semidirect
449. #3360	C₂×C₁₃	semidirect
450. #3243	C₂×C₁₃	semidirect
451. #3242	C₂×C₁₃	semidirect
452. #3238	C₂×C₁₃	semidirect
453. #3230	C₂×C₁₃	semidirect
455. #3120	C₂×C₁₃	semidirect
456. #3116	C₂×C₁₃	semidirect
458. #2985	C₂×C₁₃	semidirect
970. C₁₃	#61859	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×#3503	2
C₁₃×#3390	2
C₁₃×#3386	2
C₁₃×#3385	2
Q₈×C₁₃×Q₁₆	2
C₁₃×#3380	2
C₁₃×#3377	2
C₁₃×#3372	2
C₁₃×#3369	2
C₁₃×#3367	2
C₁₃×#3363	2
C₁₃×#3360	2
C₁₃×#3243	2
C₁₃×#3242	2
C₁₃×#3238	2
C₁₃×#3230	2
C₁₃×#3124	2
C₁₃×#3120	2
C₁₃×#3116	2
C₁₃×#3102	2
C₁₃×#2985	2
#61859	13

Subgroups — C13×#61859 #15748198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61859 #15748198