Subgroups — C₁₃×#61897 #15748236

Order 3328.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3402	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3401	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3371	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3219	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3216	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3116	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3111	C₂	1	2	yes	maximal, complemented
21	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#559	C₂²	1	2	yes	—
25	C₁₃×#559	C₂²	1	1	yes	characteristic
26	C₁₃×#557	C₂²	1	1	yes	characteristic
27	C₁₃×#557	C₂²	1	1	yes	characteristic
28	C₁₃×#557	C₂²	1	1	yes	characteristic
29	C₁₃×#557	C₂²	1	2	yes	—
30	C₁₃×#556	C₂²	1	1	yes	characteristic
31	C₁₃×#556	C₂²	1	2	yes	—
32	C₁₃×#556	C₂²	1	1	yes	characteristic
33	C₁₃×#556	C₂²	1	2	yes	—
34	C₁₃×#553	—	2	1	no	—
35	C₁₃×#553	—	2	2	no	—
36	C₁₃×#552	—	2	1	no	—
37	C₁₃×#552	—	2	2	no	—
38	C₁₃×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₃	—	2	1	no	—
40	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
41	C₁₃×#548	—	2	1	no	—
42	C₁₃×#541	—	2	1	no	—
43	C₁₃×#541	—	2	2	no	—
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#533	C₂²	1	2	yes	—
46	C₁₃×#532	C₂²	1	1	yes	characteristic
47	C₁₃×#532	C₂²	1	2	yes	—
48	C₁₃×#529	—	2	1	no	—
49	C₁₃×#529	—	2	2	no	—
50	C₁₃×#529	C₂²	1	1	yes	characteristic
51	C₁₃×#529	C₂²	1	2	yes	—
52	C₁₃×#519	—	2	1	no	—
53	C₄×C₁₃×#41	—	2	1	no	—
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₄×C₁₃×#41	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×#497	C₂²	1	2	yes	—
58	C₁₃×#497	C₂²	1	2	yes	—
59	C₁₃×#497	C₂²	1	2	yes	—
60	C₁₃×#496	C₂²	1	2	yes	—
61	C₁₃×#495	C₂²	1	2	yes	—
62	C₁₃×#494	C₂²	1	1	yes	characteristic
63	C₁₃×#492	C₂²	1	1	yes	characteristic
64	C₁₃×#491	C₂²	1	2	yes	—
65	C₁₃×#490	C₂²	1	2	yes	—
66	C₁₃×#489	C₂²	1	2	yes	—
67	C₁₃×#489	C₂²	1	2	yes	—
68	C₁₃×#488	C₂²	1	2	yes	—
69	C₁₃×#487	C₂²	1	1	yes	characteristic
70	C₁₃×#486	C₂²	1	1	yes	characteristic
71	C₁₃×#485	C₂²	1	1	yes	characteristic
72	C₁₃×#485	C₂²	1	2	yes	—
73	C₁₃×#482	C₂²	1	1	yes	characteristic
74	C₁₃×#479	C₂²	1	1	yes	characteristic
75	C₁₃×#479	C₂²	1	2	yes	—
76	C₁₃×#478	C₂²	1	1	yes	characteristic
77	C₁₃×#478	C₂²	1	2	yes	—
78	C₁₃×#477	C₂²	1	2	yes	—
79	C₁₃×#476	C₂²	1	2	yes	—
80	C₁₃×#475	C₂²	1	1	yes	characteristic
81	C₁₃×#474	C₂²	1	1	yes	characteristic
82	C₁₃×#464	C₂²	1	1	yes	characteristic
83	C₁₃×#464	C₂²	1	2	yes	—
84	C₁₃×#464	C₂²	1	2	yes	—
85	C₁₃×#464	C₂²	1	2	yes	—
86	C₁₃×#464	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	2	yes	—
88	C₁₃×#463	C₂²	1	1	yes	characteristic
89	C₁₃×#463	C₂²	1	2	yes	—
90	C₁₃×#463	C₂²	1	2	yes	—
91	C₁₃×#463	C₂²	1	2	yes	—
92	C₁₃×#462	C₂²	1	1	yes	characteristic
93	C₁₃×#462	C₂²	1	2	yes	—
94	C₁₃×#462	C₂²	1	1	yes	characteristic
95	C₁₃×#462	C₂²	1	2	yes	—
96	C₁₃×#462	C₂²	1	2	yes	—
97	C₁₃×#461	C₂²	1	1	yes	characteristic
98	C₁₃×#461	C₂²	1	1	yes	characteristic
99	C₁₃×#461	C₂²	1	2	yes	—
100	C₁₃×#460	C₂²	1	1	yes	characteristic
101	C₁₃×#460	C₂²	1	2	yes	—
102	C₁₃×#460	C₂²	1	2	yes	—
103	C₁₃×#459	C₂²	1	1	yes	characteristic
104	C₁₃×#452	C₂²	1	1	yes	characteristic
105	C₁₃×#452	C₂²	1	2	yes	—
106	C₁₃×#452	C₂²	1	2	yes	—
107	C₁₃×#452	C₂²	1	2	yes	—
108	C₁₃×#452	C₂²	1	2	yes	—
109	C₁₃×#449	C₂²	1	1	yes	characteristic
110	C₁₃×#449	C₂²	1	2	yes	—
111	C₁₃×#446	C₂²	1	1	yes	characteristic
112	C₁₃×#446	C₂²	1	1	yes	characteristic
113	C₁₃×#446	C₂²	1	2	yes	—
114	C₁₃×#446	C₂²	1	1	yes	characteristic
115	C₁₃×#446	C₂²	1	1	yes	characteristic
116	C₁₃×#446	C₂²	1	2	yes	—
117	C₁₃×#442	C₂²	1	2	yes	—
118	C₁₃×#441	C₂²	1	2	yes	—
119	C₁₃×#441	C₂²	1	2	yes	—
120	C₁₃×#441	C₂²	1	2	yes	—
121	C₁₃×#440	C₂²	1	2	yes	—
122	C₁₃×#440	C₂²	1	2	yes	—
123	C₁₃×#440	C₂²	1	2	yes	—
124	C₁₃×#440	C₂²	1	2	yes	—
125	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
126	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
127	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
128	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
129	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
130	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
131	C₁₃×#432	C₂²	1	2	yes	—
132	C₁₃×#432	C₂²	1	2	yes	—
133	C₁₃×#431	C₂²	1	1	yes	characteristic
134	C₁₃×#431	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	2	yes	—
138	C₂²×Q₈×C₁₃	—	2	1	no	—
139	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
140	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
143	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×D₈	C₂³	1	2	yes	—
154	C₁₃×C₄⋊Q₈	—	2	1	no	—
155	C₁₃×C₄⋊Q₈	—	2	2	no	—
156	C₁₃×C₄⋊Q₈	C₂³	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	1	yes	characteristic
161	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₁₃×#127	C₂³	1	1	yes	characteristic
163	C₁₃×#127	C₂³	1	2	yes	—
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	2	no	—
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	1	no	—
172	C₁₃×#125	—	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	1	no	—
178	C₁₃×#125	—	2	2	no	—
179	C₁₃×#125	—	2	2	no	—
180	C₁₃×#125	—	2	1	no	—
181	C₁₃×#125	C₂³	1	1	yes	characteristic
182	C₁₃×#125	C₂³	1	2	yes	—
183	C₁₃×#124	—	2	1	no	—
184	C₁₃×#124	—	2	2	no	—
185	C₁₃×#124	C₂³	1	2	yes	—
186	C₁₃×#124	C₂³	1	2	yes	—
187	C₁₃×#124	C₂³	1	1	yes	characteristic
188	C₁₃×#124	C₂³	1	2	yes	—
189	C₁₃×#124	C₂³	1	2	yes	—
190	C₁₃×#123	—	2	1	no	—
191	C₁₃×#123	—	2	2	no	—
192	C₁₃×#123	—	2	2	no	—
193	C₁₃×#123	—	2	2	no	—
194	C₁₃×#123	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	1	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	—	2	1	no	—
198	C₁₃×C₂²⋊Q₈	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	—	2	1	no	—
200	C₁₃×C₂²⋊Q₈	—	2	2	no	—
201	C₁₃×C₂²⋊Q₈	—	2	1	no	—
202	C₁₃×C₂²⋊Q₈	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
204	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₁₃×#121	—	2	1	no	—
206	C₁₃×#121	—	2	2	no	—
207	C₁₃×#121	—	2	1	no	—
208	C₁₃×#121	—	2	2	no	—
209	C₁₃×#121	—	2	1	no	—
210	C₁₃×#121	—	2	2	no	—
211	C₁₃×#121	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	1	no	—
215	C₄×Q₈×C₁₃	—	2	2	no	—
216	C₄×Q₈×C₁₃	—	2	1	no	—
217	C₄×Q₈×C₁₃	—	2	2	no	—
218	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
220	C₄×Q₈×C₁₃	D₄	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	2	no	—
235	C₄×D₄×C₁₃	—	2	1	no	—
236	C₄×D₄×C₁₃	—	2	2	no	—
237	C₄×D₄×C₁₃	—	2	1	no	—
238	C₄×D₄×C₁₃	—	2	2	no	—
239	C₄×D₄×C₁₃	—	2	1	no	—
240	C₄×D₄×C₁₃	—	2	2	no	—
241	C₄×D₄×C₁₃	—	2	1	no	—
242	C₄×D₄×C₁₃	—	2	2	no	—
243	C₄×D₄×C₁₃	—	2	2	no	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₁₃	C₂³	1	2	yes	—
249	C₄×D₄×C₁₃	C₂³	1	2	yes	—
250	C₄×D₄×C₁₃	C₂³	1	2	yes	—
251	C₁₃×#117	—	2	1	no	—
252	C₁₃×#117	—	2	2	no	—
253	C₁₃×#117	—	2	1	no	—
254	C₁₃×#117	—	2	2	no	—
255	C₁₃×#117	—	2	1	no	—
256	C₁₃×#117	—	2	2	no	—
257	C₁₃×#117	—	2	2	no	—
258	C₁₃×#117	—	2	1	no	—
259	C₁₃×#117	—	2	1	no	—
260	C₁₃×#117	—	2	2	no	—
261	C₁₃×#117	C₂³	1	1	yes	characteristic
262	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
263	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
264	C₂×C₄²×C₁₃	—	2	1	no	—
265	C₂×C₄²×C₁₃	—	2	2	no	—
266	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
267	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
268	C₁₃×#107	C₂³	1	1	yes	characteristic
269	C₁₃×#107	C₂³	1	2	yes	—
270	C₁₃×#107	C₂³	1	1	yes	characteristic
271	C₁₃×#106	C₂³	1	1	yes	characteristic
272	C₁₃×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
286	C₁₃×#103	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	2	yes	—
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×#102	C₂³	1	1	yes	characteristic
294	C₁₃×#102	C₂³	1	1	yes	characteristic
295	C₁₃×#102	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	1	yes	characteristic
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₁₃×#97	C₂³	1	2	yes	—
306	C₁₃×#97	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	2	yes	—
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	2	yes	—
312	#61897	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃×#41	—	4	1	no	—
314	C₁₃×#41	—	4	2	no	—
315	C₁₃×#41	—	4	1	no	—
316	C₁₃×#41	—	4	2	no	—
317	C₁₃×#41	—	4	4	no	—
318	C₂×Q₈×C₁₃	—	2	2	no	—
319	C₂×Q₈×C₁₃	—	2	1	no	—
320	C₂×Q₈×C₁₃	—	4	2	no	—
321	C₂×Q₈×C₁₃	—	4	4	no	—
322	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
325	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
329	C₂×D₄×C₁₃	—	2	1	no	—
330	C₂×D₄×C₁₃	—	2	1	no	—
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	1	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	1	no	—
336	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
338	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₁₃	—	2	1	no	—
340	C₂²×C₄×C₁₃	—	2	2	no	—
341	C₂²×C₄×C₁₃	—	2	2	no	—
342	C₂²×C₄×C₁₃	—	2	1	no	—
343	C₂²×C₄×C₁₃	—	2	2	no	—
344	C₂²×C₄×C₁₃	—	2	1	no	—
345	C₂²×C₄×C₁₃	—	2	1	no	—
346	C₂²×C₄×C₁₃	—	2	2	no	—
347	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
350	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
352	C₁₃×Q₁₆	—	4	2	no	—
353	C₁₃×Q₁₆	—	4	2	no	—
354	C₁₃×Q₁₆	—	4	1	no	—
355	C₁₃×Q₁₆	—	4	2	no	—
356	C₁₃×Q₁₆	—	4	2	no	—
357	C₁₃×SD₁₆	—	4	2	no	—
358	C₁₃×SD₁₆	—	4	2	no	—
359	C₁₃×SD₁₆	—	4	2	no	—
360	C₁₃×SD₁₆	—	4	2	no	—
361	C₁₃×SD₁₆	—	4	2	no	—
362	C₁₃×SD₁₆	—	4	1	no	—
363	C₁₃×SD₁₆	—	4	1	no	—
364	C₁₃×D₈	—	4	1	no	—
365	C₁₃×D₈	—	4	2	no	—
366	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
370	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
371	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₁₃×C₄⋊C₄	—	2	2	no	—
373	C₁₃×C₄⋊C₄	—	2	1	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	—	2	1	no	—
376	C₁₃×C₄⋊C₄	—	2	2	no	—
377	C₁₃×C₄⋊C₄	—	2	1	no	—
378	C₁₃×C₄⋊C₄	—	2	2	no	—
379	C₁₃×C₄⋊C₄	—	2	1	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	2	no	—
382	C₁₃×C₄⋊C₄	—	2	1	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	1	no	—
386	C₁₃×C₄⋊C₄	—	2	2	no	—
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	—	2	1	no	—
390	C₁₃×C₄⋊C₄	—	2	2	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	2	no	—
396	C₁₃×C₄⋊C₄	—	2	1	no	—
397	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
398	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
406	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₁₃×C₂²⋊C₄	—	2	2	no	—
410	C₁₃×C₂²⋊C₄	—	2	1	no	—
411	C₁₃×C₂²⋊C₄	—	2	1	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	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	1	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	1	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	1	no	—
429	C₄²×C₁₃	—	2	1	no	—
430	C₄²×C₁₃	—	2	1	no	—
431	C₄²×C₁₃	—	2	2	no	—
432	C₄²×C₁₃	—	2	2	no	—
433	C₄²×C₁₃	—	2	1	no	—
434	C₄²×C₁₃	—	2	2	no	—
435	C₄²×C₁₃	—	2	2	no	—
436	C₄²×C₁₃	—	2	2	no	—
437	C₄²×C₁₃	—	2	2	no	—
438	C₄²×C₁₃	—	2	1	no	—
439	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₁₃	C₂×D₄	1	2	yes	—
441	C₄²×C₁₃	C₂×D₄	1	2	yes	—
442	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
444	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
445	C₄²×C₁₃	C₂⁴	1	2	yes	—
446	C₄²×C₁₃	C₂⁴	1	2	yes	—
447	#3523	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3402	C₂×C₁₃	1	2	yes	complemented
450	#3401	C₂×C₁₃	1	2	yes	complemented
451	#3400	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3398	C₂×C₁₃	1	1	yes	characteristic, complemented
453	#3398	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3397	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3377	C₂×C₁₃	1	2	yes	complemented
456	#3374	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3373	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3371	C₂×C₁₃	1	2	yes	complemented
459	#3368	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3367	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3219	C₂×C₁₃	1	2	yes	complemented
462	#3216	C₂×C₁₃	1	2	yes	complemented
463	#3212	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3116	C₂×C₁₃	1	2	yes	complemented
466	#3111	C₂×C₁₃	1	2	yes	complemented
467	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#2983	C₂×C₁₃	1	1	yes	characteristic, complemented
470	C₂³×C₁₃	—	2	1	no	—
471	C₂³×C₁₃	—	2	2	no	—
472	C₂³×C₁₃	—	2	1	no	—
473	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
474	Q₈×C₁₃	—	2	2	no	—
475	Q₈×C₁₃	—	2	2	no	—
476	Q₈×C₁₃	—	2	1	no	—
477	Q₈×C₁₃	—	2	2	no	—
478	Q₈×C₁₃	—	2	2	no	—
479	Q₈×C₁₃	—	2	2	no	—
480	Q₈×C₁₃	—	2	1	no	—
481	Q₈×C₁₃	—	2	1	no	—
482	Q₈×C₁₃	—	2	1	no	—
483	Q₈×C₁₃	—	2	2	no	—
484	Q₈×C₁₃	—	4	2	no	—
485	Q₈×C₁₃	—	4	4	no	—
486	Q₈×C₁₃	—	4	2	no	—
487	D₄×C₁₃	—	2	1	no	—
488	D₄×C₁₃	—	2	1	no	—
489	D₄×C₁₃	—	2	1	no	—
490	D₄×C₁₃	—	2	2	no	—
491	D₄×C₁₃	—	2	2	no	—
492	D₄×C₁₃	—	2	1	no	—
493	D₄×C₁₃	—	4	4	no	—
494	D₄×C₁₃	—	4	2	no	—
495	D₄×C₁₃	—	4	2	no	—
496	D₄×C₁₃	—	4	4	no	—
497	D₄×C₁₃	—	4	2	no	—
498	D₄×C₁₃	—	8	2	no	—
499	D₄×C₁₃	—	8	1	no	—
500	C₂×C₄×C₁₃	—	2	2	no	—
501	C₂×C₄×C₁₃	—	2	1	no	—
502	C₂×C₄×C₁₃	—	2	1	no	—
503	C₂×C₄×C₁₃	—	2	1	no	—
504	C₂×C₄×C₁₃	—	2	1	no	—
505	C₂×C₄×C₁₃	—	2	1	no	—
506	C₂×C₄×C₁₃	—	2	2	no	—
507	C₂×C₄×C₁₃	—	2	1	no	—
508	C₂×C₄×C₁₃	—	2	1	no	—
509	C₂×C₄×C₁₃	—	2	2	no	—
510	C₂×C₄×C₁₃	—	2	2	no	—
511	C₂×C₄×C₁₃	—	2	1	no	—
512	C₂×C₄×C₁₃	—	4	1	no	—
513	C₂×C₄×C₁₃	—	4	2	no	—
514	C₂×C₄×C₁₃	—	4	2	no	—
515	C₂×C₄×C₁₃	—	4	4	no	—
516	C₂×C₄×C₁₃	—	4	2	no	—
517	C₂×C₄×C₁₃	—	4	4	no	—
518	C₂×C₄×C₁₃	—	4	4	no	—
519	C₂×C₄×C₁₃	—	4	2	no	—
520	C₂×C₄×C₁₃	—	4	2	no	—
521	C₂×C₄×C₁₃	—	8	1	no	—
522	C₂×C₄×C₁₃	—	8	2	no	—
523	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
533	C₈×C₁₃	—	2	1	no	—
534	C₈×C₁₃	—	2	2	no	—
535	C₈×C₁₃	—	2	2	no	—
536	C₈×C₁₃	—	2	1	no	—
537	C₈×C₁₃	—	2	1	no	—
538	C₈×C₁₃	—	2	1	no	—
539	#559	C₂²×C₁₃	1	2	yes	—
540	#559	C₂²×C₁₃	1	1	yes	characteristic
541	#557	C₂²×C₁₃	1	1	yes	characteristic
542	#557	C₂²×C₁₃	1	1	yes	characteristic
543	#557	C₂²×C₁₃	1	1	yes	characteristic
544	#557	C₂²×C₁₃	1	2	yes	—
545	#556	C₂²×C₁₃	1	1	yes	characteristic
546	#556	C₂²×C₁₃	1	2	yes	—
547	#556	C₂²×C₁₃	1	1	yes	characteristic
548	#556	C₂²×C₁₃	1	2	yes	—
549	#553	—	2	1	no	—
550	#553	—	2	2	no	—
551	#552	—	2	1	no	—
552	#552	—	2	2	no	—
553	#550	C₂²×C₁₃	1	1	yes	characteristic
554	D₄×Q₈	—	2	1	no	—
555	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
556	#548	—	2	1	no	—
557	#541	—	2	1	no	—
558	#541	—	2	2	no	—
559	#533	C₂²×C₁₃	1	1	yes	characteristic
560	#533	C₂²×C₁₃	1	2	yes	—
561	#532	C₂²×C₁₃	1	1	yes	characteristic
562	#532	C₂²×C₁₃	1	2	yes	—
563	#529	—	2	1	no	—
564	#529	—	2	2	no	—
565	#529	C₂²×C₁₃	1	1	yes	characteristic
566	#529	C₂²×C₁₃	1	2	yes	—
567	#519	—	2	1	no	—
568	C₄×#41	—	2	1	no	—
569	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
570	C₄×#41	C₂²×C₁₃	1	2	yes	—
571	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
572	#497	C₂²×C₁₃	1	2	yes	—
573	#497	C₂²×C₁₃	1	2	yes	—
574	#497	C₂²×C₁₃	1	2	yes	—
575	#496	C₂²×C₁₃	1	2	yes	—
576	#495	C₂²×C₁₃	1	2	yes	—
577	#494	C₂²×C₁₃	1	1	yes	characteristic
578	#492	C₂²×C₁₃	1	1	yes	characteristic
579	#491	C₂²×C₁₃	1	2	yes	—
580	#490	C₂²×C₁₃	1	2	yes	—
581	#489	C₂²×C₁₃	1	2	yes	—
582	#489	C₂²×C₁₃	1	2	yes	—
583	#488	C₂²×C₁₃	1	2	yes	—
584	#487	C₂²×C₁₃	1	1	yes	characteristic
585	#486	C₂²×C₁₃	1	1	yes	characteristic
586	#485	C₂²×C₁₃	1	1	yes	characteristic
587	#485	C₂²×C₁₃	1	2	yes	—
588	#482	C₂²×C₁₃	1	1	yes	characteristic
589	#479	C₂²×C₁₃	1	1	yes	characteristic
590	#479	C₂²×C₁₃	1	2	yes	—
591	#478	C₂²×C₁₃	1	1	yes	characteristic
592	#478	C₂²×C₁₃	1	2	yes	—
593	#477	C₂²×C₁₃	1	2	yes	—
594	#476	C₂²×C₁₃	1	2	yes	—
595	#475	C₂²×C₁₃	1	1	yes	characteristic
596	#474	C₂²×C₁₃	1	1	yes	characteristic
597	#464	C₂²×C₁₃	1	1	yes	characteristic
598	#464	C₂²×C₁₃	1	2	yes	—
599	#464	C₂²×C₁₃	1	2	yes	—
600	#464	C₂²×C₁₃	1	2	yes	—
601	#464	C₂²×C₁₃	1	2	yes	—
602	#464	C₂²×C₁₃	1	2	yes	—
603	#463	C₂²×C₁₃	1	1	yes	characteristic
604	#463	C₂²×C₁₃	1	2	yes	—
605	#463	C₂²×C₁₃	1	2	yes	—
606	#463	C₂²×C₁₃	1	2	yes	—
607	#462	C₂²×C₁₃	1	1	yes	characteristic
608	#462	C₂²×C₁₃	1	2	yes	—
609	#462	C₂²×C₁₃	1	1	yes	characteristic
610	#462	C₂²×C₁₃	1	2	yes	—
611	#462	C₂²×C₁₃	1	2	yes	—
612	#461	C₂²×C₁₃	1	1	yes	characteristic
613	#461	C₂²×C₁₃	1	1	yes	characteristic
614	#461	C₂²×C₁₃	1	2	yes	—
615	#460	C₂²×C₁₃	1	1	yes	characteristic
616	#460	C₂²×C₁₃	1	2	yes	—
617	#460	C₂²×C₁₃	1	2	yes	—
618	#459	C₂²×C₁₃	1	1	yes	characteristic
619	#452	C₂²×C₁₃	1	1	yes	characteristic
620	#452	C₂²×C₁₃	1	2	yes	—
621	#452	C₂²×C₁₃	1	2	yes	—
622	#452	C₂²×C₁₃	1	2	yes	—
623	#452	C₂²×C₁₃	1	2	yes	—
624	#449	C₂²×C₁₃	1	1	yes	characteristic
625	#449	C₂²×C₁₃	1	2	yes	—
626	#446	C₂²×C₁₃	1	1	yes	characteristic
627	#446	C₂²×C₁₃	1	1	yes	characteristic
628	#446	C₂²×C₁₃	1	2	yes	—
629	#446	C₂²×C₁₃	1	1	yes	characteristic
630	#446	C₂²×C₁₃	1	1	yes	characteristic
631	#446	C₂²×C₁₃	1	2	yes	—
632	#442	C₂²×C₁₃	1	2	yes	—
633	#441	C₂²×C₁₃	1	2	yes	—
634	#441	C₂²×C₁₃	1	2	yes	—
635	#441	C₂²×C₁₃	1	2	yes	—
636	#440	C₂²×C₁₃	1	2	yes	—
637	#440	C₂²×C₁₃	1	2	yes	—
638	#440	C₂²×C₁₃	1	2	yes	—
639	#440	C₂²×C₁₃	1	2	yes	—
640	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
641	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
642	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
643	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
644	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
645	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
646	#432	C₂²×C₁₃	1	2	yes	—
647	#432	C₂²×C₁₃	1	2	yes	—
648	#431	C₂²×C₁₃	1	1	yes	characteristic
649	#431	C₂²×C₁₃	1	1	yes	characteristic
650	C₂²×C₁₃	—	2	1	no	—
651	C₂²×C₁₃	—	2	1	no	—
652	C₂²×C₁₃	—	2	1	no	—
653	C₂²×C₁₃	—	4	2	no	—
654	C₂²×C₁₃	—	4	1	no	—
655	C₂²×C₁₃	—	4	1	no	—
656	C₂²×C₁₃	—	4	2	no	—
657	C₂²×C₁₃	—	4	1	no	—
658	C₂²×C₁₃	—	4	1	no	—
659	C₂²×C₁₃	—	4	1	no	—
660	C₂²×C₁₃	—	4	2	no	—
661	C₂²×C₁₃	—	4	1	no	—
662	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
663	C₄×C₁₃	—	2	1	no	—
664	C₄×C₁₃	—	2	2	no	—
665	C₄×C₁₃	—	2	2	no	—
666	C₄×C₁₃	—	2	1	no	—
667	C₄×C₁₃	—	2	1	no	—
668	C₄×C₁₃	—	2	1	no	—
669	C₄×C₁₃	—	2	2	no	—
670	C₄×C₁₃	—	2	2	no	—
671	C₄×C₁₃	—	4	1	no	—
672	C₄×C₁₃	—	4	1	no	—
673	C₄×C₁₃	—	4	1	no	—
674	C₄×C₁₃	—	4	2	no	—
675	C₄×C₁₃	—	4	1	no	—
676	C₄×C₁₃	—	4	2	no	—
677	C₄×C₁₃	—	4	1	no	—
678	C₄×C₁₃	—	4	2	no	—
679	C₄×C₁₃	—	4	1	no	—
680	C₄×C₁₃	#575	1	2	yes	—
681	C₄×C₁₃	#585	1	1	yes	characteristic
682	C₄×C₁₃	#585	1	1	yes	characteristic
683	C₂×#41	—	2	1	no	—
684	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
685	C₂×#41	C₂³×C₁₃	1	2	yes	—
686	C₂²×Q₈	—	2	1	no	—
687	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
688	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
689	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
690	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
691	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
692	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
693	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
694	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
695	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
696	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
697	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
698	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
699	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
700	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
701	C₂×D₈	C₂³×C₁₃	1	2	yes	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
708	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
710	#127	C₂³×C₁₃	1	1	yes	characteristic
711	#127	C₂³×C₁₃	1	2	yes	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	1	no	—
720	#125	—	2	1	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	1	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	C₂³×C₁₃	1	1	yes	characteristic
730	#125	C₂³×C₁₃	1	2	yes	—
731	#124	—	2	1	no	—
732	#124	—	2	2	no	—
733	#124	C₂³×C₁₃	1	1	yes	characteristic
734	#124	C₂³×C₁₃	1	2	yes	—
735	#124	C₂³×C₁₃	1	2	yes	—
736	#124	C₂³×C₁₃	1	2	yes	—
737	#124	C₂³×C₁₃	1	2	yes	—
738	#123	—	2	1	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
752	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
753	#121	—	2	1	no	—
754	#121	—	2	2	no	—
755	#121	—	2	1	no	—
756	#121	—	2	2	no	—
757	#121	—	2	1	no	—
758	#121	—	2	2	no	—
759	#121	C₂³×C₁₃	1	1	yes	characteristic
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	2	no	—
766	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
767	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
768	C₄×Q₈	D₄×C₁₃	1	2	yes	—
769	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
771	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
773	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
776	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
777	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
778	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₁₃	1	2	yes	—
795	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
796	C₄×D₄	C₂³×C₁₃	1	2	yes	—
797	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₁₃	1	2	yes	—
799	#117	—	2	1	no	—
800	#117	—	2	2	no	—
801	#117	—	2	1	no	—
802	#117	—	2	2	no	—
803	#117	—	2	1	no	—
804	#117	—	2	2	no	—
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	—	2	1	no	—
808	#117	—	2	2	no	—
809	#117	C₂³×C₁₃	1	1	yes	characteristic
810	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
811	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
812	C₂×C₄²	—	2	1	no	—
813	C₂×C₄²	—	2	2	no	—
814	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
815	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
816	#107	C₂³×C₁₃	1	1	yes	characteristic
817	#107	C₂³×C₁₃	1	2	yes	—
818	#107	C₂³×C₁₃	1	1	yes	characteristic
819	#106	C₂³×C₁₃	1	1	yes	characteristic
820	#106	C₂³×C₁₃	1	1	yes	characteristic
821	#106	C₂³×C₁₃	1	2	yes	—
822	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
827	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
828	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
829	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
830	#103	C₂³×C₁₃	1	1	yes	characteristic
831	#103	C₂³×C₁₃	1	2	yes	—
832	#103	C₂³×C₁₃	1	1	yes	characteristic
833	#103	C₂³×C₁₃	1	2	yes	—
834	#103	C₂³×C₁₃	1	1	yes	characteristic
835	#103	C₂³×C₁₃	1	1	yes	characteristic
836	#103	C₂³×C₁₃	1	2	yes	—
837	#103	C₂³×C₁₃	1	2	yes	—
838	#103	C₂³×C₁₃	1	2	yes	—
839	#103	C₂³×C₁₃	1	2	yes	—
840	#103	C₂³×C₁₃	1	2	yes	—
841	#102	C₂³×C₁₃	1	1	yes	characteristic
842	#102	C₂³×C₁₃	1	1	yes	characteristic
843	#102	C₂³×C₁₃	1	1	yes	characteristic
844	#102	C₂³×C₁₃	1	1	yes	characteristic
845	#102	C₂³×C₁₃	1	2	yes	—
846	#102	C₂³×C₁₃	1	2	yes	—
847	#102	C₂³×C₁₃	1	2	yes	—
848	#102	C₂³×C₁₃	1	2	yes	—
849	#102	C₂³×C₁₃	1	2	yes	—
850	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
851	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
852	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
853	#97	C₂³×C₁₃	1	2	yes	—
854	#97	C₂³×C₁₃	1	2	yes	—
855	#97	C₂³×C₁₃	1	2	yes	—
856	#97	C₂³×C₁₃	1	2	yes	—
857	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
858	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
859	C₄×C₈	C₂³×C₁₃	1	2	yes	—
860	C₂×C₁₃	—	4	1	no	—
861	C₂×C₁₃	—	8	2	no	—
862	C₂×C₁₃	—	8	1	no	—
863	C₂×C₁₃	—	8	1	no	—
864	C₂×C₁₃	#3487	1	1	yes	characteristic
865	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
866	C₂×C₁₃	#3586	1	1	yes	characteristic
867	#41	—	4	1	no	—
868	#41	—	4	2	no	—
869	#41	—	4	1	no	—
870	#41	—	4	2	no	—
871	#41	—	4	4	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	—	2	1	no	—
874	C₂×Q₈	—	4	2	no	—
875	C₂×Q₈	—	4	4	no	—
876	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
877	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
878	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
879	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
880	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
881	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
882	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
883	C₂×D₄	—	2	1	no	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	2	no	—
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	2	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
891	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
892	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
902	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
903	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
904	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
905	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
906	Q₁₆	—	4	2	no	—
907	Q₁₆	—	4	2	no	—
908	Q₁₆	—	4	1	no	—
909	Q₁₆	—	4	2	no	—
910	Q₁₆	—	4	2	no	—
911	SD₁₆	—	4	2	no	—
912	SD₁₆	—	4	2	no	—
913	SD₁₆	—	4	2	no	—
914	SD₁₆	—	4	2	no	—
915	SD₁₆	—	4	2	no	—
916	SD₁₆	—	4	1	no	—
917	SD₁₆	—	4	1	no	—
918	D₈	—	4	1	no	—
919	D₈	—	4	2	no	—
920	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
922	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
923	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
924	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
925	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
953	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
955	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
956	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
957	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
958	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
960	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
961	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	1	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	1	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	2	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	1	no	—
993	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
994	C₄²	C₂×D₄×C₁₃	1	2	yes	—
995	C₄²	C₂×D₄×C₁₃	1	2	yes	—
996	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
997	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
998	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
999	C₄²	C₂⁴×C₁₃	1	2	yes	—
1000	C₄²	C₂⁴×C₁₃	1	2	yes	—
1001	C₁₃	#61897	1	1	yes	characteristic, direct product factor, Sylow
1002	C₂³	—	2	1	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	1	no	—
1005	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1006	Q₈	—	2	2	no	—
1007	Q₈	—	2	2	no	—
1008	Q₈	—	2	1	no	—
1009	Q₈	—	2	2	no	—
1010	Q₈	—	2	2	no	—
1011	Q₈	—	2	2	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	4	2	no	—
1017	Q₈	—	4	4	no	—
1018	Q₈	—	4	2	no	—
1019	D₄	—	2	1	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	2	no	—
1024	D₄	—	2	1	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	4	2	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	2	no	—
1030	D₄	—	8	2	no	—
1031	D₄	—	8	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	4	1	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	4	no	—
1048	C₂×C₄	—	4	4	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	4	4	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	8	1	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1056	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1057	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1058	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1059	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1060	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1061	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1062	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1063	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1064	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1065	C₈	—	2	1	no	—
1066	C₈	—	2	2	no	—
1067	C₈	—	2	2	no	—
1068	C₈	—	2	1	no	—
1069	C₈	—	2	1	no	—
1070	C₈	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	2	no	—
1101	C₄	C₁₃×#575	1	2	yes	—
1102	C₄	C₁₃×#585	1	1	yes	characteristic
1103	C₄	C₁₃×#585	1	1	yes	characteristic
1104	C₂	—	4	1	no	—
1105	C₂	—	8	1	no	—
1106	C₂	—	8	2	no	—
1107	C₂	—	8	1	no	—
1108	C₂	C₁₃×#3487	1	1	yes	characteristic
1109	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1110	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3523	C₂	semidirect
2. C₁₃×#3480	C₂	semidirect
3. C₁₃×#3402	C₂	semidirect
4. C₁₃×#3401	C₂	semidirect
5. C₁₃×#3400	C₂	semidirect
6. C₁₃×#3398	C₂	semidirect
7. C₁₃×#3398	C₂	semidirect
8. C₁₃×#3397	C₂	semidirect
9. C₁₃×#3377	C₂	semidirect
10. C₁₃×#3374	C₂	semidirect
11. C₁₃×#3373	C₂	semidirect
12. C₁₃×#3371	C₂	semidirect
13. C₁₃×#3368	C₂	semidirect
14. C₁₃×#3367	C₂	semidirect
15. C₁₃×#3219	C₂	semidirect
16. C₁₃×#3216	C₂	semidirect
17. C₁₃×#3212	C₂	semidirect
18. C₁₃×#3210	C₂	semidirect
19. C₁₃×#3116	C₂	semidirect
20. C₁₃×#3111	C₂	semidirect
21. C₁₃×#3107	C₂	semidirect
22. C₁₃×#3102	C₂	semidirect
23. C₁₃×#2983	C₂	semidirect
312. #61897	C₁₃	direct (N × H)
447. #3523	C₂×C₁₃	semidirect
448. #3480	C₂×C₁₃	semidirect
449. #3402	C₂×C₁₃	semidirect
450. #3401	C₂×C₁₃	semidirect
451. #3400	C₂×C₁₃	semidirect
452. #3398	C₂×C₁₃	semidirect
453. #3398	C₂×C₁₃	semidirect
454. #3397	C₂×C₁₃	semidirect
455. #3377	C₂×C₁₃	semidirect
456. #3374	C₂×C₁₃	semidirect
457. #3373	C₂×C₁₃	semidirect
458. #3371	C₂×C₁₃	semidirect
459. #3368	C₂×C₁₃	semidirect
460. #3367	C₂×C₁₃	semidirect
461. #3219	C₂×C₁₃	semidirect
462. #3216	C₂×C₁₃	semidirect
463. #3212	C₂×C₁₃	semidirect
464. #3210	C₂×C₁₃	semidirect
465. #3116	C₂×C₁₃	semidirect
466. #3111	C₂×C₁₃	semidirect
467. #3107	C₂×C₁₃	semidirect
468. #3102	C₂×C₁₃	semidirect
469. #2983	C₂×C₁₃	semidirect
1001. C₁₃	#61897	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×#3523	2
C₁₃×#3480	2
C₁₃×#3402	2
C₁₃×#3401	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3397	2
C₁₃×#3377	2
C₁₃×#3374	2
C₁₃×#3373	2
C₁₃×#3371	2
C₁₃×#3368	2
C₁₃×#3367	2
C₁₃×#3219	2
C₁₃×#3216	2
C₁₃×#3212	2
C₁₃×#3210	2
C₁₃×#3116	2
C₁₃×#3111	2
C₁₃×#3107	2
C₁₃×#3102	2
C₁₃×#2983	2
#61897	13

Subgroups — C13×#61897 #15748236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61897 #15748236