Subgroups — C₁₃×#62123 #15748462

Order 3328.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3348	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3347	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3317	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3309	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3251	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3234	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3111	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3080	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#557	C₂²	1	1	yes	characteristic
26	C₁₃×#555	—	2	1	no	—
27	C₁₃×#555	—	2	2	no	—
28	C₁₃×#555	C₂²	1	2	yes	—
29	C₁₃×#555	C₂²	1	1	yes	characteristic
30	C₁₃×#554	C₂²	1	1	yes	characteristic
31	C₁₃×#554	C₂²	1	1	yes	characteristic
32	C₁₃×#553	C₂²	1	2	yes	—
33	C₁₃×#552	—	2	2	no	—
34	C₁₃×#552	—	2	1	no	—
35	C₁₃×#552	C₂²	1	2	yes	—
36	C₁₃×#550	—	2	1	no	—
37	C₁₃×#550	C₂²	1	2	yes	—
38	C₁₃×#550	C₂²	1	1	yes	characteristic
39	C₁₃×#550	C₂²	1	1	yes	characteristic
40	C₁₃×#547	—	2	1	no	—
41	C₁₃×#547	C₂²	1	1	yes	characteristic
42	C₁₃×#541	—	2	1	no	—
43	C₁₃×#539	—	2	2	no	—
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#532	—	2	1	no	—
46	C₁₃×#532	—	2	2	no	—
47	C₁₃×#532	C₂²	1	1	yes	characteristic
48	C₁₃×#532	C₂²	1	2	yes	—
49	C₁₃×#529	C₂²	1	1	yes	characteristic
50	C₁₃×#529	C₂²	1	2	yes	—
51	C₂×C₁₃×#125	C₂²	1	2	yes	—
52	C₁₃×#520	—	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	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
57	C₁₃×#501	C₂²	1	2	yes	—
58	C₁₃×#501	C₂²	1	2	yes	—
59	C₁₃×#500	C₂²	1	1	yes	characteristic
60	C₁₃×#498	C₂²	1	1	yes	characteristic
61	C₁₃×#490	C₂²	1	2	yes	—
62	C₁₃×#490	C₂²	1	2	yes	—
63	C₁₃×#486	C₂²	1	1	yes	characteristic
64	C₁₃×#486	C₂²	1	1	yes	characteristic
65	C₁₃×#485	C₂²	1	1	yes	characteristic
66	C₁₃×#485	C₂²	1	2	yes	—
67	C₁₃×#482	C₂²	1	2	yes	—
68	C₁₃×#482	C₂²	1	2	yes	—
69	C₁₃×#482	C₂²	1	1	yes	characteristic
70	C₁₃×#482	C₂²	1	2	yes	—
71	C₁₃×#481	C₂²	1	2	yes	—
72	C₁₃×#481	C₂²	1	2	yes	—
73	C₁₃×#480	C₂²	1	2	yes	—
74	C₁₃×#480	C₂²	1	2	yes	—
75	C₁₃×#479	C₂²	1	2	yes	—
76	C₁₃×#479	C₂²	1	2	yes	—
77	C₁₃×#479	C₂²	1	2	yes	—
78	C₁₃×#479	C₂²	1	1	yes	characteristic
79	C₁₃×#478	C₂²	1	2	yes	—
80	C₁₃×#478	C₂²	1	2	yes	—
81	C₁₃×#478	C₂²	1	2	yes	—
82	C₁₃×#478	C₂²	1	2	yes	—
83	C₁₃×#478	C₂²	1	2	yes	—
84	C₁₃×#478	C₂²	1	1	yes	characteristic
85	C₁₃×#478	C₂²	1	2	yes	—
86	C₁₃×#477	C₂²	1	1	yes	characteristic
87	C₁₃×#477	C₂²	1	1	yes	characteristic
88	C₁₃×#476	C₂²	1	1	yes	characteristic
89	C₁₃×#476	C₂²	1	1	yes	characteristic
90	C₁₃×#475	C₂²	1	1	yes	characteristic
91	C₁₃×#475	C₂²	1	2	yes	—
92	C₁₃×#474	C₂²	1	1	yes	characteristic
93	C₁₃×#474	C₂²	1	2	yes	—
94	C₁₃×#469	C₂²	1	2	yes	—
95	C₁₃×#469	C₂²	1	2	yes	—
96	C₁₃×#468	C₂²	1	2	yes	—
97	C₁₃×#468	C₂²	1	2	yes	—
98	C₁₃×#466	C₂²	1	2	yes	—
99	C₁₃×#465	C₂²	1	2	yes	—
100	C₁₃×#464	C₂²	1	1	yes	characteristic
101	C₁₃×#463	C₂²	1	1	yes	characteristic
102	C₁₃×#463	C₂²	1	2	yes	—
103	C₁₃×#460	C₂²	1	2	yes	—
104	C₁₃×#460	C₂²	1	1	yes	characteristic
105	C₁₃×#459	C₂²	1	2	yes	—
106	C₁₃×#459	C₂²	1	1	yes	characteristic
107	C₁₃×#452	C₂²	1	1	yes	characteristic
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×#442	C₂²	1	2	yes	—
114	C₁₃×#441	C₂²	1	2	yes	—
115	C₁₃×#440	C₂²	1	2	yes	—
116	C₁₃×#440	C₂²	1	2	yes	—
117	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
118	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
121	C₁₃×#436	C₂²	1	1	yes	characteristic
122	C₁₃×#436	C₂²	1	1	yes	characteristic
123	C₁₃×#435	C₂²	1	2	yes	—
124	C₁₃×#435	C₂²	1	2	yes	—
125	C₁₃×#432	C₂²	1	2	yes	—
126	C₁₃×#431	C₂²	1	1	yes	characteristic
127	C₁₃×#428	C₂²	1	2	yes	—
128	C₁₃×#428	C₂²	1	2	yes	—
129	C₁₃×#427	C₂²	1	2	yes	—
130	C₁₃×#423	C₂²	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	C₁₃×#417	C₂²	1	2	yes	—
133	C₁₃×#417	C₂²	1	2	yes	—
134	C₁₃×#416	C₂²	1	2	yes	—
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	—	2	1	no	—
137	C₂×C₁₃×#41	—	2	2	no	—
138	C₂×C₁₃×#41	—	2	1	no	—
139	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
140	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×#41	C₂³	1	2	yes	—
142	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×D₈	C₂³	1	2	yes	—
148	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
150	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
151	C₁₃×C₄⋊Q₈	—	2	1	no	—
152	C₁₃×C₄⋊Q₈	—	2	1	no	—
153	C₁₃×C₄⋊Q₈	—	2	2	no	—
154	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₁₃×#127	—	2	1	no	—
159	C₁₃×#127	—	2	2	no	—
160	C₁₃×#127	C₂³	1	1	yes	characteristic
161	C₁₃×#127	C₂³	1	2	yes	—
162	C₁₃×#126	—	2	2	no	—
163	C₁₃×#126	—	2	2	no	—
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	1	no	—
166	C₁₃×#125	—	2	2	no	—
167	C₁₃×#125	—	2	2	no	—
168	C₁₃×#125	—	2	1	no	—
169	C₁₃×#125	—	2	2	no	—
170	C₁₃×#125	—	2	2	no	—
171	C₁₃×#125	C₂³	1	1	yes	characteristic
172	C₁₃×#125	C₂³	1	2	yes	—
173	C₁₃×#125	C₂³	1	2	yes	—
174	C₁₃×#125	C₂³	1	2	yes	—
175	C₁₃×#124	—	2	2	no	—
176	C₁₃×#124	—	2	2	no	—
177	C₁₃×#124	—	2	2	no	—
178	C₁₃×#124	—	2	2	no	—
179	C₁₃×#124	—	2	1	no	—
180	C₁₃×#124	C₂³	1	1	yes	characteristic
181	C₁₃×#123	—	2	2	no	—
182	C₁₃×#123	—	2	1	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×#123	—	2	2	no	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	1	no	—
187	C₁₃×C₂²⋊Q₈	—	2	1	no	—
188	C₁₃×C₂²⋊Q₈	—	2	1	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	1	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₁₃×#121	—	2	1	no	—
195	C₁₃×#121	—	2	2	no	—
196	C₁₃×#121	—	2	2	no	—
197	C₁₃×#121	—	2	1	no	—
198	C₁₃×#121	—	2	2	no	—
199	C₁₃×#121	—	2	1	no	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	C₂³	1	1	yes	characteristic
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₁₃×#121	C₂³	1	2	yes	—
208	C₁₃×#121	C₂³	1	2	yes	—
209	C₄×Q₈×C₁₃	—	2	1	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
217	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₁₃	—	2	1	no	—
221	C₄×D₄×C₁₃	—	2	2	no	—
222	C₄×D₄×C₁₃	—	2	1	no	—
223	C₄×D₄×C₁₃	—	2	1	no	—
224	C₄×D₄×C₁₃	—	2	2	no	—
225	C₄×D₄×C₁₃	—	2	2	no	—
226	C₄×D₄×C₁₃	—	2	1	no	—
227	C₄×D₄×C₁₃	—	2	1	no	—
228	C₄×D₄×C₁₃	—	2	2	no	—
229	C₄×D₄×C₁₃	—	2	2	no	—
230	C₄×D₄×C₁₃	—	2	1	no	—
231	C₄×D₄×C₁₃	—	2	2	no	—
232	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
233	C₄×D₄×C₁₃	D₄	1	2	yes	—
234	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₁₃	C₂³	1	2	yes	—
237	C₄×D₄×C₁₃	C₂³	1	2	yes	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	2	yes	—
240	C₄×D₄×C₁₃	C₂³	1	2	yes	—
241	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
242	C₁₃×#117	—	2	1	no	—
243	C₁₃×#117	—	2	2	no	—
244	C₁₃×#117	—	2	2	no	—
245	C₁₃×#117	—	2	2	no	—
246	C₁₃×#117	—	2	1	no	—
247	C₁₃×#117	—	2	1	no	—
248	C₁₃×#117	—	2	2	no	—
249	C₁₃×#117	D₄	1	1	yes	characteristic
250	C₁₃×#117	D₄	1	2	yes	—
251	C₁₃×#117	C₂³	1	2	yes	—
252	C₁₃×#117	C₂³	1	1	yes	characteristic
253	C₁₃×#117	C₂³	1	2	yes	—
254	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
258	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
259	C₂×C₄²×C₁₃	—	2	1	no	—
260	C₂×C₄²×C₁₃	—	2	2	no	—
261	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
263	C₁₃×#107	C₂³	1	2	yes	—
264	C₁₃×#107	C₂³	1	2	yes	—
265	C₁₃×#107	C₂³	1	1	yes	characteristic
266	C₁₃×#107	C₂³	1	2	yes	—
267	C₁₃×#107	C₂³	1	2	yes	—
268	C₁₃×#107	C₂³	1	1	yes	characteristic
269	C₁₃×#107	C₂³	1	2	yes	—
270	C₁₃×#106	C₂³	1	2	yes	—
271	C₁₃×#106	C₂³	1	2	yes	—
272	C₁₃×#106	C₂³	1	1	yes	characteristic
273	C₁₃×#106	C₂³	1	2	yes	—
274	C₁₃×#106	C₂³	1	2	yes	—
275	C₁₃×#106	C₂³	1	1	yes	characteristic
276	C₁₃×#106	C₂³	1	2	yes	—
277	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
278	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#102	C₂³	1	2	yes	—
292	C₁₃×#102	C₂³	1	2	yes	—
293	C₁₃×#102	C₂³	1	2	yes	—
294	C₁₃×#102	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₁₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	#62123	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃×#41	—	2	2	no	—
314	C₁₃×#41	—	2	4	no	—
315	C₁₃×#41	—	4	2	no	—
316	C₁₃×#41	—	4	1	no	—
317	C₁₃×#41	—	4	2	no	—
318	C₁₃×#41	—	4	4	no	—
319	C₁₃×#41	—	4	4	no	—
320	C₁₃×#41	—	8	4	no	—
321	C₁₃×#41	—	8	2	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	—	2	2	no	—
325	C₂×Q₈×C₁₃	—	2	1	no	—
326	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₁₃	—	2	1	no	—
330	C₂×D₄×C₁₃	—	2	2	no	—
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	1	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	1	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	2	1	no	—
340	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
344	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₁₃	—	2	2	no	—
346	C₂²×C₄×C₁₃	—	2	2	no	—
347	C₂²×C₄×C₁₃	—	2	1	no	—
348	C₂²×C₄×C₁₃	—	2	2	no	—
349	C₂²×C₄×C₁₃	—	2	2	no	—
350	C₂²×C₄×C₁₃	—	2	1	no	—
351	C₂²×C₄×C₁₃	—	2	1	no	—
352	C₂²×C₄×C₁₃	—	2	2	no	—
353	C₂²×C₄×C₁₃	—	2	1	no	—
354	C₂²×C₄×C₁₃	—	2	2	no	—
355	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
357	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
358	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
361	C₁₃×Q₁₆	—	2	2	no	—
362	C₁₃×SD₁₆	—	2	2	no	—
363	C₁₃×SD₁₆	—	4	2	no	—
364	C₁₃×SD₁₆	—	4	1	no	—
365	C₁₃×D₈	—	4	2	no	—
366	C₁₃×D₈	—	4	1	no	—
367	C₁₃×M₁₆	—	4	2	no	—
368	C₁₃×M₁₆	—	4	2	no	—
369	C₂×C₈×C₁₃	—	4	2	no	—
370	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
375	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
376	C₁₃×C₄⋊C₄	—	2	2	no	—
377	C₁₃×C₄⋊C₄	—	2	1	no	—
378	C₁₃×C₄⋊C₄	—	2	1	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	—	2	1	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	1	no	—
391	C₁₃×C₄⋊C₄	—	2	2	no	—
392	C₁₃×C₄⋊C₄	—	2	1	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	1	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
398	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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×C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
408	C₁₃×C₂²⋊C₄	—	2	2	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	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	1	no	—
418	C₁₃×C₂²⋊C₄	—	2	1	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	1	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	1	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
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	1	no	—
437	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₁₃	C₂×D₄	1	2	yes	—
439	C₄²×C₁₃	C₂×D₄	1	2	yes	—
440	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₁₃	C₂⁴	1	2	yes	—
443	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
444	#3515	C₂×C₁₃	1	1	yes	characteristic, complemented
445	#3483	C₂×C₁₃	1	1	yes	characteristic, complemented
446	#3387	C₂×C₁₃	1	1	yes	characteristic, complemented
447	#3385	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3368	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3366	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3357	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3354	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3348	C₂×C₁₃	1	2	yes	complemented
453	#3347	C₂×C₁₃	1	2	yes	complemented
454	#3333	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3332	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3317	C₂×C₁₃	1	2	yes	complemented
457	#3309	C₂×C₁₃	1	2	yes	complemented
458	#3251	C₂×C₁₃	1	2	yes	complemented
459	#3247	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3234	C₂×C₁₃	1	2	yes	complemented
461	#3228	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3111	C₂×C₁₃	1	2	yes	complemented
463	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3080	C₂×C₁₃	1	2	yes	complemented
465	#3076	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
467	C₂³×C₁₃	—	2	1	no	—
468	C₂³×C₁₃	—	2	2	no	—
469	C₂³×C₁₃	—	2	1	no	—
470	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
471	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
472	Q₈×C₁₃	—	2	2	no	—
473	Q₈×C₁₃	—	2	1	no	—
474	Q₈×C₁₃	—	2	1	no	—
475	Q₈×C₁₃	—	2	1	no	—
476	Q₈×C₁₃	—	4	2	no	—
477	Q₈×C₁₃	—	8	1	no	—
478	Q₈×C₁₃	—	8	2	no	—
479	Q₈×C₁₃	—	8	1	no	—
480	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
481	D₄×C₁₃	—	2	2	no	—
482	D₄×C₁₃	—	2	1	no	—
483	D₄×C₁₃	—	2	1	no	—
484	D₄×C₁₃	—	2	2	no	—
485	D₄×C₁₃	—	2	1	no	—
486	D₄×C₁₃	—	2	2	no	—
487	D₄×C₁₃	—	2	1	no	—
488	D₄×C₁₃	—	4	2	no	—
489	D₄×C₁₃	—	4	2	no	—
490	D₄×C₁₃	—	4	4	no	—
491	D₄×C₁₃	—	4	4	no	—
492	D₄×C₁₃	—	4	4	no	—
493	D₄×C₁₃	—	4	2	no	—
494	D₄×C₁₃	—	8	2	no	—
495	D₄×C₁₃	—	8	1	no	—
496	D₄×C₁₃	—	8	1	no	—
497	D₄×C₁₃	—	8	2	no	—
498	D₄×C₁₃	—	8	2	no	—
499	D₄×C₁₃	—	8	2	no	—
500	C₂×C₄×C₁₃	—	2	1	no	—
501	C₂×C₄×C₁₃	—	2	2	no	—
502	C₂×C₄×C₁₃	—	2	2	no	—
503	C₂×C₄×C₁₃	—	2	1	no	—
504	C₂×C₄×C₁₃	—	2	1	no	—
505	C₂×C₄×C₁₃	—	2	2	no	—
506	C₂×C₄×C₁₃	—	2	1	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	2	no	—
512	C₂×C₄×C₁₃	—	2	1	no	—
513	C₂×C₄×C₁₃	—	2	1	no	—
514	C₂×C₄×C₁₃	—	4	2	no	—
515	C₂×C₄×C₁₃	—	4	2	no	—
516	C₂×C₄×C₁₃	—	4	1	no	—
517	C₂×C₄×C₁₃	—	4	2	no	—
518	C₂×C₄×C₁₃	—	4	4	no	—
519	C₂×C₄×C₁₃	—	4	4	no	—
520	C₂×C₄×C₁₃	—	4	2	no	—
521	C₂×C₄×C₁₃	—	4	4	no	—
522	C₂×C₄×C₁₃	—	4	4	no	—
523	C₂×C₄×C₁₃	—	4	2	no	—
524	C₂×C₄×C₁₃	—	4	2	no	—
525	C₂×C₄×C₁₃	—	8	2	no	—
526	C₂×C₄×C₁₃	—	8	2	no	—
527	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
536	C₈×C₁₃	—	2	1	no	—
537	C₈×C₁₃	—	2	1	no	—
538	C₈×C₁₃	—	2	2	no	—
539	C₈×C₁₃	—	2	2	no	—
540	C₈×C₁₃	—	2	1	no	—
541	C₈×C₁₃	—	2	1	no	—
542	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
543	#557	C₂²×C₁₃	1	1	yes	characteristic
544	#555	—	2	1	no	—
545	#555	—	2	2	no	—
546	#555	C₂²×C₁₃	1	2	yes	—
547	#555	C₂²×C₁₃	1	1	yes	characteristic
548	#554	C₂²×C₁₃	1	1	yes	characteristic
549	#554	C₂²×C₁₃	1	1	yes	characteristic
550	#553	C₂²×C₁₃	1	2	yes	—
551	#552	—	2	2	no	—
552	#552	—	2	1	no	—
553	#552	C₂²×C₁₃	1	2	yes	—
554	#550	—	2	1	no	—
555	#550	C₂²×C₁₃	1	1	yes	characteristic
556	#550	C₂²×C₁₃	1	2	yes	—
557	#550	C₂²×C₁₃	1	1	yes	characteristic
558	#547	—	2	1	no	—
559	#547	C₂²×C₁₃	1	1	yes	characteristic
560	#541	—	2	1	no	—
561	#539	—	2	2	no	—
562	#533	C₂²×C₁₃	1	1	yes	characteristic
563	#532	—	2	1	no	—
564	#532	—	2	2	no	—
565	#532	C₂²×C₁₃	1	1	yes	characteristic
566	#532	C₂²×C₁₃	1	2	yes	—
567	#529	C₂²×C₁₃	1	1	yes	characteristic
568	#529	C₂²×C₁₃	1	2	yes	—
569	C₂×#125	C₂²×C₁₃	1	2	yes	—
570	#520	—	2	1	no	—
571	C₄×#41	—	2	1	no	—
572	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
573	C₄×#41	C₂²×C₁₃	1	2	yes	—
574	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
575	#501	C₂²×C₁₃	1	2	yes	—
576	#501	C₂²×C₁₃	1	2	yes	—
577	#500	C₂²×C₁₃	1	1	yes	characteristic
578	#498	C₂²×C₁₃	1	1	yes	characteristic
579	#490	C₂²×C₁₃	1	2	yes	—
580	#490	C₂²×C₁₃	1	2	yes	—
581	#486	C₂²×C₁₃	1	1	yes	characteristic
582	#486	C₂²×C₁₃	1	1	yes	characteristic
583	#485	C₂²×C₁₃	1	1	yes	characteristic
584	#485	C₂²×C₁₃	1	2	yes	—
585	#482	C₂²×C₁₃	1	1	yes	characteristic
586	#482	C₂²×C₁₃	1	2	yes	—
587	#482	C₂²×C₁₃	1	2	yes	—
588	#482	C₂²×C₁₃	1	2	yes	—
589	#481	C₂²×C₁₃	1	2	yes	—
590	#481	C₂²×C₁₃	1	2	yes	—
591	#480	C₂²×C₁₃	1	2	yes	—
592	#480	C₂²×C₁₃	1	2	yes	—
593	#479	C₂²×C₁₃	1	2	yes	—
594	#479	C₂²×C₁₃	1	1	yes	characteristic
595	#479	C₂²×C₁₃	1	2	yes	—
596	#479	C₂²×C₁₃	1	2	yes	—
597	#478	C₂²×C₁₃	1	2	yes	—
598	#478	C₂²×C₁₃	1	2	yes	—
599	#478	C₂²×C₁₃	1	2	yes	—
600	#478	C₂²×C₁₃	1	2	yes	—
601	#478	C₂²×C₁₃	1	2	yes	—
602	#478	C₂²×C₁₃	1	1	yes	characteristic
603	#478	C₂²×C₁₃	1	2	yes	—
604	#477	C₂²×C₁₃	1	1	yes	characteristic
605	#477	C₂²×C₁₃	1	1	yes	characteristic
606	#476	C₂²×C₁₃	1	1	yes	characteristic
607	#476	C₂²×C₁₃	1	1	yes	characteristic
608	#475	C₂²×C₁₃	1	1	yes	characteristic
609	#475	C₂²×C₁₃	1	2	yes	—
610	#474	C₂²×C₁₃	1	1	yes	characteristic
611	#474	C₂²×C₁₃	1	2	yes	—
612	#469	C₂²×C₁₃	1	2	yes	—
613	#469	C₂²×C₁₃	1	2	yes	—
614	#468	C₂²×C₁₃	1	2	yes	—
615	#468	C₂²×C₁₃	1	2	yes	—
616	#466	C₂²×C₁₃	1	2	yes	—
617	#465	C₂²×C₁₃	1	2	yes	—
618	#464	C₂²×C₁₃	1	1	yes	characteristic
619	#463	C₂²×C₁₃	1	1	yes	characteristic
620	#463	C₂²×C₁₃	1	2	yes	—
621	#460	C₂²×C₁₃	1	1	yes	characteristic
622	#460	C₂²×C₁₃	1	2	yes	—
623	#459	C₂²×C₁₃	1	1	yes	characteristic
624	#459	C₂²×C₁₃	1	2	yes	—
625	#452	C₂²×C₁₃	1	2	yes	—
626	#452	C₂²×C₁₃	1	1	yes	characteristic
627	#449	C₂²×C₁₃	1	2	yes	—
628	#449	C₂²×C₁₃	1	1	yes	characteristic
629	#446	C₂²×C₁₃	1	1	yes	characteristic
630	#446	C₂²×C₁₃	1	1	yes	characteristic
631	#442	C₂²×C₁₃	1	2	yes	—
632	#441	C₂²×C₁₃	1	2	yes	—
633	#440	C₂²×C₁₃	1	2	yes	—
634	#440	C₂²×C₁₃	1	2	yes	—
635	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
636	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
637	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
638	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
639	#436	C₂²×C₁₃	1	1	yes	characteristic
640	#436	C₂²×C₁₃	1	1	yes	characteristic
641	#435	C₂²×C₁₃	1	2	yes	—
642	#435	C₂²×C₁₃	1	2	yes	—
643	#432	C₂²×C₁₃	1	2	yes	—
644	#431	C₂²×C₁₃	1	1	yes	characteristic
645	#428	C₂²×C₁₃	1	2	yes	—
646	#428	C₂²×C₁₃	1	2	yes	—
647	#427	C₂²×C₁₃	1	2	yes	—
648	#423	C₂²×C₁₃	1	2	yes	—
649	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
650	#417	C₂²×C₁₃	1	2	yes	—
651	#417	C₂²×C₁₃	1	2	yes	—
652	#416	C₂²×C₁₃	1	2	yes	—
653	C₂²×C₁₃	—	2	2	no	—
654	C₂²×C₁₃	—	2	1	no	—
655	C₂²×C₁₃	—	2	1	no	—
656	C₂²×C₁₃	—	2	2	no	—
657	C₂²×C₁₃	—	2	1	no	—
658	C₂²×C₁₃	—	2	2	no	—
659	C₂²×C₁₃	—	4	1	no	—
660	C₂²×C₁₃	—	4	2	no	—
661	C₂²×C₁₃	—	4	1	no	—
662	C₂²×C₁₃	—	4	2	no	—
663	C₂²×C₁₃	—	4	1	no	—
664	C₂²×C₁₃	—	4	1	no	—
665	C₂²×C₁₃	—	4	2	no	—
666	C₂²×C₁₃	—	4	1	no	—
667	C₂²×C₁₃	—	4	1	no	—
668	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
669	C₄×C₁₃	—	2	1	no	—
670	C₄×C₁₃	—	2	2	no	—
671	C₄×C₁₃	—	2	1	no	—
672	C₄×C₁₃	—	2	1	no	—
673	C₄×C₁₃	—	2	2	no	—
674	C₄×C₁₃	—	2	2	no	—
675	C₄×C₁₃	—	2	1	no	—
676	C₄×C₁₃	—	2	2	no	—
677	C₄×C₁₃	—	4	1	no	—
678	C₄×C₁₃	—	4	2	no	—
679	C₄×C₁₃	—	4	1	no	—
680	C₄×C₁₃	—	4	2	no	—
681	C₄×C₁₃	—	4	1	no	—
682	C₄×C₁₃	—	4	1	no	—
683	C₄×C₁₃	—	4	1	no	—
684	C₄×C₁₃	—	4	2	no	—
685	C₄×C₁₃	#575	1	2	yes	—
686	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
687	C₄×C₁₃	#585	1	1	yes	characteristic
688	C₂×#41	—	2	1	no	—
689	C₂×#41	—	2	1	no	—
690	C₂×#41	—	2	2	no	—
691	C₂×#41	—	2	1	no	—
692	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
693	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
694	C₂×#41	C₂³×C₁₃	1	2	yes	—
695	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
696	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
697	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
698	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
699	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×D₈	C₂³×C₁₃	1	2	yes	—
701	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
702	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
703	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
704	C₄⋊Q₈	—	2	1	no	—
705	C₄⋊Q₈	—	2	1	no	—
706	C₄⋊Q₈	—	2	2	no	—
707	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
708	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
711	#127	—	2	1	no	—
712	#127	—	2	2	no	—
713	#127	C₂³×C₁₃	1	1	yes	characteristic
714	#127	C₂³×C₁₃	1	2	yes	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	1	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	1	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	C₂³×C₁₃	1	1	yes	characteristic
725	#125	C₂³×C₁₃	1	2	yes	—
726	#125	C₂³×C₁₃	1	2	yes	—
727	#125	C₂³×C₁₃	1	2	yes	—
728	#124	—	2	2	no	—
729	#124	—	2	2	no	—
730	#124	—	2	2	no	—
731	#124	—	2	2	no	—
732	#124	—	2	1	no	—
733	#124	C₂³×C₁₃	1	1	yes	characteristic
734	#123	—	2	2	no	—
735	#123	—	2	1	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
746	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
747	#121	—	2	1	no	—
748	#121	—	2	2	no	—
749	#121	—	2	2	no	—
750	#121	—	2	1	no	—
751	#121	—	2	2	no	—
752	#121	—	2	1	no	—
753	#121	—	2	2	no	—
754	#121	—	2	2	no	—
755	#121	—	2	2	no	—
756	#121	—	2	2	no	—
757	#121	C₂³×C₁₃	1	2	yes	—
758	#121	C₂³×C₁₃	1	1	yes	characteristic
759	#121	C₂³×C₁₃	1	2	yes	—
760	#121	C₂³×C₁₃	1	2	yes	—
761	#121	C₂³×C₁₃	1	2	yes	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
770	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
771	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	2	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
786	C₄×D₄	D₄×C₁₃	1	2	yes	—
787	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₁₃	1	2	yes	—
789	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₁₃	1	2	yes	—
791	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₁₃	1	2	yes	—
793	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₁₃	1	2	yes	—
795	#117	—	2	1	no	—
796	#117	—	2	2	no	—
797	#117	—	2	2	no	—
798	#117	—	2	2	no	—
799	#117	—	2	1	no	—
800	#117	—	2	1	no	—
801	#117	—	2	2	no	—
802	#117	D₄×C₁₃	1	1	yes	characteristic
803	#117	D₄×C₁₃	1	2	yes	—
804	#117	C₂³×C₁₃	1	1	yes	characteristic
805	#117	C₂³×C₁₃	1	2	yes	—
806	#117	C₂³×C₁₃	1	2	yes	—
807	C₂×C₄⋊C₄	—	2	2	no	—
808	C₂×C₄⋊C₄	—	2	2	no	—
809	C₂×C₄⋊C₄	—	2	1	no	—
810	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
811	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
812	C₂×C₄²	—	2	1	no	—
813	C₂×C₄²	—	2	2	no	—
814	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
815	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
816	#107	C₂³×C₁₃	1	2	yes	—
817	#107	C₂³×C₁₃	1	2	yes	—
818	#107	C₂³×C₁₃	1	1	yes	characteristic
819	#107	C₂³×C₁₃	1	2	yes	—
820	#107	C₂³×C₁₃	1	2	yes	—
821	#107	C₂³×C₁₃	1	1	yes	characteristic
822	#107	C₂³×C₁₃	1	2	yes	—
823	#106	C₂³×C₁₃	1	2	yes	—
824	#106	C₂³×C₁₃	1	2	yes	—
825	#106	C₂³×C₁₃	1	1	yes	characteristic
826	#106	C₂³×C₁₃	1	2	yes	—
827	#106	C₂³×C₁₃	1	2	yes	—
828	#106	C₂³×C₁₃	1	1	yes	characteristic
829	#106	C₂³×C₁₃	1	2	yes	—
830	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
831	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
835	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
836	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
837	#103	C₂³×C₁₃	1	2	yes	—
838	#103	C₂³×C₁₃	1	2	yes	—
839	#103	C₂³×C₁₃	1	1	yes	characteristic
840	#103	C₂³×C₁₃	1	1	yes	characteristic
841	#103	C₂³×C₁₃	1	1	yes	characteristic
842	#103	C₂³×C₁₃	1	1	yes	characteristic
843	#103	C₂³×C₁₃	1	2	yes	—
844	#102	C₂³×C₁₃	1	2	yes	—
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	#102	C₂³×C₁₃	1	1	yes	characteristic
851	#102	C₂³×C₁₃	1	1	yes	characteristic
852	#102	C₂³×C₁₃	1	1	yes	characteristic
853	#102	C₂³×C₁₃	1	1	yes	characteristic
854	#102	C₂³×C₁₃	1	2	yes	—
855	#102	C₂³×C₁₃	1	2	yes	—
856	#102	C₂³×C₁₃	1	2	yes	—
857	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
858	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
859	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
861	#97	C₂³×C₁₃	1	2	yes	—
862	#97	C₂³×C₁₃	1	2	yes	—
863	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
865	C₂×C₁₃	—	4	2	no	—
866	C₂×C₁₃	—	4	1	no	—
867	C₂×C₁₃	—	8	2	no	—
868	C₂×C₁₃	—	8	1	no	—
869	C₂×C₁₃	—	8	1	no	—
870	C₂×C₁₃	#3489	1	1	yes	characteristic
871	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
872	C₂×C₁₃	#3585	1	1	yes	characteristic
873	#41	—	2	2	no	—
874	#41	—	2	4	no	—
875	#41	—	4	2	no	—
876	#41	—	4	1	no	—
877	#41	—	4	2	no	—
878	#41	—	4	4	no	—
879	#41	—	4	4	no	—
880	#41	—	8	4	no	—
881	#41	—	8	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
887	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	1	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
901	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
902	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
903	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
904	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
916	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
917	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
918	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
920	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
921	Q₁₆	—	2	2	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	1	no	—
925	D₈	—	4	2	no	—
926	D₈	—	4	1	no	—
927	M₁₆	—	4	2	no	—
928	M₁₆	—	4	2	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
935	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
960	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
961	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
962	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
963	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
964	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
965	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
967	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	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	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
987	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
988	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	1	no	—
997	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
998	C₄²	C₂×D₄×C₁₃	1	2	yes	—
999	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1000	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1001	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1002	C₄²	C₂⁴×C₁₃	1	2	yes	—
1003	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1004	C₁₃	#62123	1	1	yes	characteristic, direct product factor, Sylow
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1009	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1010	Q₈	—	2	2	no	—
1011	Q₈	—	2	1	no	—
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	4	2	no	—
1015	Q₈	—	8	2	no	—
1016	Q₈	—	8	1	no	—
1017	Q₈	—	8	1	no	—
1018	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
1019	D₄	—	2	2	no	—
1020	D₄	—	2	1	no	—
1021	D₄	—	2	1	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	2	1	no	—
1026	D₄	—	4	2	no	—
1027	D₄	—	4	2	no	—
1028	D₄	—	4	4	no	—
1029	D₄	—	4	4	no	—
1030	D₄	—	4	4	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	8	2	no	—
1033	D₄	—	8	1	no	—
1034	D₄	—	8	1	no	—
1035	D₄	—	8	2	no	—
1036	D₄	—	8	2	no	—
1037	D₄	—	8	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	2	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	2	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	4	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	4	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1066	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1073	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1096	C₄	—	2	1	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	C₁₃×#575	1	2	yes	—
1113	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1114	C₄	C₁₃×#585	1	1	yes	characteristic
1115	C₂	—	4	1	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	8	2	no	—
1118	C₂	—	8	1	no	—
1119	C₂	—	8	1	no	—
1120	C₂	C₁₃×#3489	1	1	yes	characteristic
1121	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1122	C₂	C₁₃×#3585	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3515	C₂	semidirect
2. C₁₃×#3483	C₂	semidirect
3. C₁₃×#3387	C₂	semidirect
4. C₁₃×#3385	C₂	semidirect
5. C₁₃×#3368	C₂	semidirect
6. C₁₃×#3366	C₂	semidirect
7. C₁₃×#3357	C₂	semidirect
8. C₁₃×#3354	C₂	semidirect
9. C₁₃×#3348	C₂	semidirect
10. C₁₃×#3347	C₂	semidirect
11. C₁₃×#3333	C₂	semidirect
12. C₁₃×#3332	C₂	semidirect
13. C₁₃×#3317	C₂	semidirect
14. C₁₃×#3309	C₂	semidirect
15. C₁₃×#3251	C₂	semidirect
16. C₁₃×#3247	C₂	semidirect
17. C₁₃×#3234	C₂	semidirect
18. C₁₃×#3228	C₂	semidirect
19. C₁₃×#3111	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3080	C₂	semidirect
22. C₁₃×#3076	C₂	semidirect
23. C₁₃×#2989	C₂	semidirect
312. #62123	C₁₃	direct (N × H)
444. #3515	C₂×C₁₃	semidirect
445. #3483	C₂×C₁₃	semidirect
446. #3387	C₂×C₁₃	semidirect
447. #3385	C₂×C₁₃	semidirect
448. #3368	C₂×C₁₃	semidirect
449. #3366	C₂×C₁₃	semidirect
450. #3357	C₂×C₁₃	semidirect
451. #3354	C₂×C₁₃	semidirect
452. #3348	C₂×C₁₃	semidirect
453. #3347	C₂×C₁₃	semidirect
454. #3333	C₂×C₁₃	semidirect
455. #3332	C₂×C₁₃	semidirect
456. #3317	C₂×C₁₃	semidirect
457. #3309	C₂×C₁₃	semidirect
458. #3251	C₂×C₁₃	semidirect
459. #3247	C₂×C₁₃	semidirect
460. #3234	C₂×C₁₃	semidirect
461. #3228	C₂×C₁₃	semidirect
462. #3111	C₂×C₁₃	semidirect
463. #3102	C₂×C₁₃	semidirect
464. #3080	C₂×C₁₃	semidirect
465. #3076	C₂×C₁₃	semidirect
466. #2989	C₂×C₁₃	semidirect
1004. C₁₃	#62123	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×#3515	2
C₁₃×#3483	2
C₁₃×#3387	2
C₁₃×#3385	2
C₁₃×#3368	2
C₁₃×#3366	2
C₁₃×#3357	2
C₁₃×#3354	2
C₁₃×#3348	2
C₁₃×#3347	2
C₁₃×#3333	2
C₁₃×#3332	2
C₁₃×#3317	2
C₁₃×#3309	2
C₁₃×#3251	2
C₁₃×#3247	2
C₁₃×#3234	2
C₁₃×#3228	2
C₁₃×#3111	2
C₁₃×#3102	2
C₁₃×#3080	2
C₁₃×#3076	2
C₁₃×#2989	2
#62123	13

Subgroups — C13×#62123 #15748462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62123 #15748462