Subgroups — C₁₃×#62142 #15748481

Order 3328.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3350	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3347	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3321	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3313	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3305	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3304	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3250	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3240	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×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3076	C₂	1	2	yes	maximal, complemented
23	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#559	—	2	1	no	—
25	C₁₃×#559	C₂²	1	1	yes	characteristic
26	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#557	C₂²	1	1	yes	characteristic
28	C₁₃×#556	—	2	1	no	—
29	C₁₃×#556	—	2	1	no	—
30	C₁₃×#556	—	2	2	no	—
31	C₁₃×#556	C₂²	1	1	yes	characteristic
32	C₁₃×#556	C₂²	1	2	yes	—
33	C₁₃×#556	C₂²	1	1	yes	characteristic
34	C₁₃×#555	C₂²	1	1	yes	characteristic
35	C₁₃×#555	C₂²	1	2	yes	—
36	C₁₃×#553	—	2	2	no	—
37	C₁₃×#553	C₂²	1	2	yes	—
38	C₁₃×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#548	—	2	1	no	—
41	C₁₃×#548	C₂²	1	2	yes	—
42	C₁₃×#542	—	2	2	no	—
43	C₁₃×#542	—	2	1	no	—
44	C₁₃×#533	C₂²	1	2	yes	—
45	C₁₃×#533	C₂²	1	1	yes	characteristic
46	C₁₃×#532	—	2	1	no	—
47	C₁₃×#532	C₂²	1	1	yes	characteristic
48	C₁₃×#529	—	2	2	no	—
49	C₁₃×#529	C₂²	1	1	yes	characteristic
50	C₁₃×#529	C₂²	1	2	yes	—
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	2	yes	—
55	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₁₃	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×#489	C₂²	1	2	yes	—
62	C₁₃×#489	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	2	yes	—
66	C₁₃×#485	C₂²	1	2	yes	—
67	C₁₃×#485	C₂²	1	2	yes	—
68	C₁₃×#483	C₂²	1	1	yes	characteristic
69	C₁₃×#482	C₂²	1	2	yes	—
70	C₁₃×#482	C₂²	1	2	yes	—
71	C₁₃×#482	C₂²	1	2	yes	—
72	C₁₃×#482	C₂²	1	2	yes	—
73	C₁₃×#482	C₂²	1	2	yes	—
74	C₁₃×#480	C₂²	1	1	yes	characteristic
75	C₁₃×#479	C₂²	1	1	yes	characteristic
76	C₁₃×#479	C₂²	1	2	yes	—
77	C₁₃×#479	C₂²	1	2	yes	—
78	C₁₃×#479	C₂²	1	2	yes	—
79	C₁₃×#479	C₂²	1	1	yes	characteristic
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×#477	C₂²	1	1	yes	characteristic
85	C₁₃×#477	C₂²	1	2	yes	—
86	C₁₃×#477	C₂²	1	1	yes	characteristic
87	C₁₃×#476	C₂²	1	2	yes	—
88	C₁₃×#475	C₂²	1	1	yes	characteristic
89	C₁₃×#475	C₂²	1	2	yes	—
90	C₁₃×#475	C₂²	1	1	yes	characteristic
91	C₁₃×#475	C₂²	1	1	yes	characteristic
92	C₁₃×#474	C₂²	1	2	yes	—
93	C₁₃×#474	C₂²	1	1	yes	characteristic
94	C₁₃×#469	C₂²	1	2	yes	—
95	C₁₃×#468	C₂²	1	2	yes	—
96	C₁₃×#467	C₂²	1	2	yes	—
97	C₁₃×#466	C₂²	1	2	yes	—
98	C₁₃×#465	C₂²	1	2	yes	—
99	C₁₃×#465	C₂²	1	2	yes	—
100	C₁₃×#464	C₂²	1	2	yes	—
101	C₁₃×#464	C₂²	1	1	yes	characteristic
102	C₁₃×#464	C₂²	1	1	yes	characteristic
103	C₁₃×#463	C₂²	1	2	yes	—
104	C₁₃×#463	C₂²	1	2	yes	—
105	C₁₃×#460	C₂²	1	1	yes	characteristic
106	C₁₃×#459	C₂²	1	1	yes	characteristic
107	C₁₃×#452	C₂²	1	2	yes	—
108	C₁₃×#451	C₂²	1	1	yes	characteristic
109	C₁₃×#449	C₂²	1	2	yes	—
110	C₁₃×#448	C₂²	1	1	yes	characteristic
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×Q₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
121	C₁₃×#435	C₂²	1	2	yes	—
122	C₁₃×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
125	C₁₃×#432	C₂²	1	2	yes	—
126	C₁₃×#431	C₂²	1	1	yes	characteristic
127	C₁₃×#428	C₂²	1	2	yes	—
128	C₁₃×#427	C₂²	1	2	yes	—
129	C₁₃×#427	C₂²	1	2	yes	—
130	C₁₃×#423	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
132	C₁₃×#419	C₂²	1	2	yes	—
133	C₁₃×#416	C₂²	1	2	yes	—
134	C₁₃×#416	C₂²	1	2	yes	—
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	2	yes	—
138	C₂²×Q₈×C₁₃	—	2	1	no	—
139	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
143	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×D₈	C₂³	1	2	yes	—
146	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
147	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
148	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
149	C₁₃×C₄⋊Q₈	—	2	1	no	—
150	C₁₃×C₄⋊Q₈	—	2	1	no	—
151	C₁₃×C₄⋊Q₈	—	2	2	no	—
152	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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×#127	—	2	1	no	—
158	C₁₃×#127	C₂³	1	1	yes	characteristic
159	C₁₃×#126	—	2	2	no	—
160	C₁₃×#126	—	2	2	no	—
161	C₁₃×#126	—	2	2	no	—
162	C₁₃×#126	—	2	2	no	—
163	C₁₃×#126	—	2	2	no	—
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	2	no	—
166	C₁₃×#126	—	2	1	no	—
167	C₁₃×#125	—	2	2	no	—
168	C₁₃×#125	C₂³	1	2	yes	—
169	C₁₃×#125	C₂³	1	1	yes	characteristic
170	C₁₃×#125	C₂³	1	2	yes	—
171	C₁₃×#124	—	2	1	no	—
172	C₁₃×#124	—	2	1	no	—
173	C₁₃×#124	—	2	1	no	—
174	C₁₃×#124	—	2	2	no	—
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×#124	C₂³	1	2	yes	—
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×#123	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	—	2	1	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	1	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	1	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×#121	—	2	2	no	—
198	C₁₃×#121	—	2	2	no	—
199	C₁₃×#121	—	2	1	no	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	1	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	C₂³	1	1	yes	characteristic
204	C₁₃×#121	C₂³	1	2	yes	—
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₄×Q₈×C₁₃	—	2	1	no	—
208	C₄×Q₈×C₁₃	—	2	1	no	—
209	C₄×Q₈×C₁₃	—	2	1	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
211	C₄×Q₈×C₁₃	—	2	2	no	—
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	2	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	—	2	2	no	—
217	C₄×Q₈×C₁₃	—	2	1	no	—
218	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₁₃	—	2	2	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	—	2	1	no	—
233	C₄×D₄×C₁₃	—	2	1	no	—
234	C₄×D₄×C₁₃	—	2	2	no	—
235	C₄×D₄×C₁₃	—	2	2	no	—
236	C₄×D₄×C₁₃	—	2	1	no	—
237	C₄×D₄×C₁₃	D₄	1	2	yes	—
238	C₄×D₄×C₁₃	D₄	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	C₄×D₄×C₁₃	C₂³	1	2	yes	—
245	C₁₃×#117	—	2	1	no	—
246	C₁₃×#117	—	2	2	no	—
247	C₁₃×#117	—	2	2	no	—
248	C₁₃×#117	—	2	2	no	—
249	C₁₃×#117	—	2	2	no	—
250	C₁₃×#117	—	2	1	no	—
251	C₁₃×#117	D₄	1	1	yes	characteristic
252	C₁₃×#117	D₄	1	2	yes	—
253	C₁₃×#117	C₂³	1	2	yes	—
254	C₁₃×#117	C₂³	1	2	yes	—
255	C₁₃×#117	C₂³	1	2	yes	—
256	C₁₃×#117	C₂³	1	2	yes	—
257	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₁₃	—	2	1	no	—
260	C₂×C₄²×C₁₃	—	2	2	no	—
261	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
262	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
269	C₁₃×#107	C₂³	1	2	yes	—
270	C₁₃×#106	C₂³	1	1	yes	characteristic
271	C₁₃×#106	C₂³	1	2	yes	—
272	C₁₃×#106	C₂³	1	2	yes	—
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	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	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	2	yes	—
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	1	yes	characteristic
291	C₁₃×#103	C₂³	1	1	yes	characteristic
292	C₁₃×#103	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	1	yes	characteristic
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#102	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	2	yes	—
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	#62142	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃×#41	—	2	4	no	—
314	C₁₃×#41	—	4	2	no	—
315	C₁₃×#41	—	4	2	no	—
316	C₁₃×#41	—	4	4	no	—
317	C₂×Q₈×C₁₃	—	2	1	no	—
318	C₂×Q₈×C₁₃	—	2	2	no	—
319	C₂×Q₈×C₁₃	—	2	1	no	—
320	C₂×Q₈×C₁₃	—	2	1	no	—
321	C₂×Q₈×C₁₃	—	2	2	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	2	2	no	—
324	C₂×Q₈×C₁₃	—	4	1	no	—
325	C₂×Q₈×C₁₃	—	4	4	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×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₁₃	—	2	2	no	—
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	1	no	—
335	C₂×D₄×C₁₃	—	2	1	no	—
336	C₂×D₄×C₁₃	—	2	1	no	—
337	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
340	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₁₃	—	2	1	no	—
342	C₂²×C₄×C₁₃	—	2	1	no	—
343	C₂²×C₄×C₁₃	—	2	2	no	—
344	C₂²×C₄×C₁₃	—	2	2	no	—
345	C₂²×C₄×C₁₃	—	2	2	no	—
346	C₂²×C₄×C₁₃	—	2	1	no	—
347	C₂²×C₄×C₁₃	—	2	2	no	—
348	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
352	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
354	C₁₃×Q₁₆	—	2	2	no	—
355	C₁₃×Q₁₆	—	4	1	no	—
356	C₁₃×SD₁₆	—	2	2	no	—
357	C₁₃×SD₁₆	—	4	1	no	—
358	C₁₃×SD₁₆	—	4	2	no	—
359	C₁₃×D₈	—	4	2	no	—
360	C₁₃×M₁₆	—	4	2	no	—
361	C₂×C₈×C₁₃	—	4	2	no	—
362	C₂×C₈×C₁₃	—	4	2	no	—
363	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
368	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
369	C₁₃×C₄⋊C₄	—	2	1	no	—
370	C₁₃×C₄⋊C₄	—	2	1	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	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	1	no	—
383	C₁₃×C₄⋊C₄	—	2	1	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	2	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	C₂×D₄	1	1	yes	characteristic
392	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
393	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
396	C₁₃×C₄⋊C₄	C₂⁴	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	1	yes	characteristic
400	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
401	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
402	C₁₃×C₂²⋊C₄	—	2	2	no	—
403	C₁₃×C₂²⋊C₄	—	2	2	no	—
404	C₁₃×C₂²⋊C₄	—	2	2	no	—
405	C₁₃×C₂²⋊C₄	—	2	2	no	—
406	C₁₃×C₂²⋊C₄	—	2	2	no	—
407	C₁₃×C₂²⋊C₄	—	2	2	no	—
408	C₁₃×C₂²⋊C₄	—	2	1	no	—
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	2	no	—
413	C₁₃×C₂²⋊C₄	—	2	2	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	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	1	no	—
421	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
422	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
423	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
424	C₄²×C₁₃	—	2	1	no	—
425	C₄²×C₁₃	—	2	1	no	—
426	C₄²×C₁₃	—	2	2	no	—
427	C₄²×C₁₃	—	2	2	no	—
428	C₄²×C₁₃	—	2	1	no	—
429	C₄²×C₁₃	—	2	1	no	—
430	C₄²×C₁₃	—	2	2	no	—
431	C₄²×C₁₃	—	2	2	no	—
432	C₄²×C₁₃	—	2	2	no	—
433	C₄²×C₁₃	—	2	2	no	—
434	C₄²×C₁₃	—	2	1	no	—
435	C₄²×C₁₃	C₂×D₄	1	2	yes	—
436	C₄²×C₁₃	C₂×D₄	1	2	yes	—
437	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
440	C₄²×C₁₃	C₂⁴	1	2	yes	—
441	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
442	#3518	C₂×C₁₃	1	1	yes	characteristic, complemented
443	#3480	C₂×C₁₃	1	1	yes	characteristic, complemented
444	#3387	C₂×C₁₃	1	1	yes	characteristic, complemented
445	#3386	C₂×C₁₃	1	1	yes	characteristic, complemented
446	#3375	C₂×C₁₃	1	1	yes	characteristic, complemented
447	#3373	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3350	C₂×C₁₃	1	2	yes	complemented
449	#3347	C₂×C₁₃	1	2	yes	complemented
450	#3342	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3340	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3321	C₂×C₁₃	1	2	yes	complemented
453	#3313	C₂×C₁₃	1	2	yes	complemented
454	#3305	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3304	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3251	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3250	C₂×C₁₃	1	2	yes	complemented
458	#3240	C₂×C₁₃	1	2	yes	complemented
459	#3228	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3111	C₂×C₁₃	1	2	yes	complemented
461	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3076	C₂×C₁₃	1	2	yes	complemented
464	#2990	C₂×C₁₃	1	1	yes	characteristic, complemented
465	C₂³×C₁₃	—	2	1	no	—
466	C₂³×C₁₃	—	2	2	no	—
467	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
468	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
469	Q₈×C₁₃	—	2	2	no	—
470	Q₈×C₁₃	—	2	1	no	—
471	Q₈×C₁₃	—	2	1	no	—
472	Q₈×C₁₃	—	2	1	no	—
473	Q₈×C₁₃	—	2	1	no	—
474	Q₈×C₁₃	—	2	1	no	—
475	Q₈×C₁₃	—	4	2	no	—
476	Q₈×C₁₃	—	4	4	no	—
477	Q₈×C₁₃	—	4	2	no	—
478	Q₈×C₁₃	—	4	2	no	—
479	Q₈×C₁₃	—	8	2	no	—
480	Q₈×C₁₃	—	8	1	no	—
481	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
482	D₄×C₁₃	—	2	2	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	—	4	2	no	—
488	D₄×C₁₃	—	4	4	no	—
489	D₄×C₁₃	—	4	4	no	—
490	D₄×C₁₃	—	4	2	no	—
491	D₄×C₁₃	—	8	1	no	—
492	D₄×C₁₃	—	8	2	no	—
493	D₄×C₁₃	—	8	1	no	—
494	D₄×C₁₃	—	8	2	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	2	no	—
497	C₂×C₄×C₁₃	—	2	1	no	—
498	C₂×C₄×C₁₃	—	2	2	no	—
499	C₂×C₄×C₁₃	—	2	2	no	—
500	C₂×C₄×C₁₃	—	2	1	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	2	no	—
505	C₂×C₄×C₁₃	—	2	1	no	—
506	C₂×C₄×C₁₃	—	2	2	no	—
507	C₂×C₄×C₁₃	—	2	2	no	—
508	C₂×C₄×C₁₃	—	2	1	no	—
509	C₂×C₄×C₁₃	—	2	1	no	—
510	C₂×C₄×C₁₃	—	4	2	no	—
511	C₂×C₄×C₁₃	—	4	1	no	—
512	C₂×C₄×C₁₃	—	4	2	no	—
513	C₂×C₄×C₁₃	—	4	4	no	—
514	C₂×C₄×C₁₃	—	4	2	no	—
515	C₂×C₄×C₁₃	—	4	4	no	—
516	C₂×C₄×C₁₃	—	4	4	no	—
517	C₂×C₄×C₁₃	—	4	2	no	—
518	C₂×C₄×C₁₃	—	8	2	no	—
519	C₂×C₄×C₁₃	—	8	1	no	—
520	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
527	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
529	C₈×C₁₃	—	2	1	no	—
530	C₈×C₁₃	—	2	1	no	—
531	C₈×C₁₃	—	2	1	no	—
532	C₈×C₁₃	—	2	1	no	—
533	C₈×C₁₃	—	2	2	no	—
534	C₈×C₁₃	—	2	2	no	—
535	#559	—	2	1	no	—
536	#559	C₂²×C₁₃	1	1	yes	characteristic
537	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
538	#557	C₂²×C₁₃	1	1	yes	characteristic
539	#556	—	2	1	no	—
540	#556	—	2	1	no	—
541	#556	—	2	2	no	—
542	#556	C₂²×C₁₃	1	1	yes	characteristic
543	#556	C₂²×C₁₃	1	1	yes	characteristic
544	#556	C₂²×C₁₃	1	2	yes	—
545	#555	C₂²×C₁₃	1	1	yes	characteristic
546	#555	C₂²×C₁₃	1	2	yes	—
547	#553	—	2	2	no	—
548	#553	C₂²×C₁₃	1	2	yes	—
549	#550	C₂²×C₁₃	1	1	yes	characteristic
550	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
551	#548	—	2	1	no	—
552	#548	C₂²×C₁₃	1	2	yes	—
553	#542	—	2	2	no	—
554	#542	—	2	1	no	—
555	#533	C₂²×C₁₃	1	2	yes	—
556	#533	C₂²×C₁₃	1	1	yes	characteristic
557	#532	—	2	1	no	—
558	#532	C₂²×C₁₃	1	1	yes	characteristic
559	#529	—	2	2	no	—
560	#529	C₂²×C₁₃	1	1	yes	characteristic
561	#529	C₂²×C₁₃	1	2	yes	—
562	#529	C₂²×C₁₃	1	2	yes	—
563	#519	—	2	1	no	—
564	C₄×#41	—	2	1	no	—
565	C₄×#41	C₂²×C₁₃	1	2	yes	—
566	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
567	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
568	#501	C₂²×C₁₃	1	2	yes	—
569	#501	C₂²×C₁₃	1	2	yes	—
570	#500	C₂²×C₁₃	1	1	yes	characteristic
571	#498	C₂²×C₁₃	1	1	yes	characteristic
572	#489	C₂²×C₁₃	1	2	yes	—
573	#489	C₂²×C₁₃	1	2	yes	—
574	#486	C₂²×C₁₃	1	1	yes	characteristic
575	#486	C₂²×C₁₃	1	1	yes	characteristic
576	#485	C₂²×C₁₃	1	2	yes	—
577	#485	C₂²×C₁₃	1	2	yes	—
578	#485	C₂²×C₁₃	1	2	yes	—
579	#483	C₂²×C₁₃	1	1	yes	characteristic
580	#482	C₂²×C₁₃	1	2	yes	—
581	#482	C₂²×C₁₃	1	2	yes	—
582	#482	C₂²×C₁₃	1	2	yes	—
583	#482	C₂²×C₁₃	1	2	yes	—
584	#482	C₂²×C₁₃	1	2	yes	—
585	#480	C₂²×C₁₃	1	1	yes	characteristic
586	#479	C₂²×C₁₃	1	1	yes	characteristic
587	#479	C₂²×C₁₃	1	2	yes	—
588	#479	C₂²×C₁₃	1	2	yes	—
589	#479	C₂²×C₁₃	1	2	yes	—
590	#479	C₂²×C₁₃	1	1	yes	characteristic
591	#478	C₂²×C₁₃	1	2	yes	—
592	#478	C₂²×C₁₃	1	2	yes	—
593	#478	C₂²×C₁₃	1	2	yes	—
594	#478	C₂²×C₁₃	1	2	yes	—
595	#477	C₂²×C₁₃	1	2	yes	—
596	#477	C₂²×C₁₃	1	1	yes	characteristic
597	#477	C₂²×C₁₃	1	1	yes	characteristic
598	#476	C₂²×C₁₃	1	2	yes	—
599	#475	C₂²×C₁₃	1	2	yes	—
600	#475	C₂²×C₁₃	1	1	yes	characteristic
601	#475	C₂²×C₁₃	1	1	yes	characteristic
602	#475	C₂²×C₁₃	1	1	yes	characteristic
603	#474	C₂²×C₁₃	1	2	yes	—
604	#474	C₂²×C₁₃	1	1	yes	characteristic
605	#469	C₂²×C₁₃	1	2	yes	—
606	#468	C₂²×C₁₃	1	2	yes	—
607	#467	C₂²×C₁₃	1	2	yes	—
608	#466	C₂²×C₁₃	1	2	yes	—
609	#465	C₂²×C₁₃	1	2	yes	—
610	#465	C₂²×C₁₃	1	2	yes	—
611	#464	C₂²×C₁₃	1	1	yes	characteristic
612	#464	C₂²×C₁₃	1	1	yes	characteristic
613	#464	C₂²×C₁₃	1	2	yes	—
614	#463	C₂²×C₁₃	1	2	yes	—
615	#463	C₂²×C₁₃	1	2	yes	—
616	#460	C₂²×C₁₃	1	1	yes	characteristic
617	#459	C₂²×C₁₃	1	1	yes	characteristic
618	#452	C₂²×C₁₃	1	2	yes	—
619	#451	C₂²×C₁₃	1	1	yes	characteristic
620	#449	C₂²×C₁₃	1	2	yes	—
621	#448	C₂²×C₁₃	1	1	yes	characteristic
622	#446	C₂²×C₁₃	1	1	yes	characteristic
623	#446	C₂²×C₁₃	1	1	yes	characteristic
624	#442	C₂²×C₁₃	1	2	yes	—
625	#441	C₂²×C₁₃	1	2	yes	—
626	#440	C₂²×C₁₃	1	2	yes	—
627	#440	C₂²×C₁₃	1	2	yes	—
628	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
629	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
630	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
631	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
632	#435	C₂²×C₁₃	1	2	yes	—
633	#435	C₂²×C₁₃	1	2	yes	—
634	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
635	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
636	#432	C₂²×C₁₃	1	2	yes	—
637	#431	C₂²×C₁₃	1	1	yes	characteristic
638	#428	C₂²×C₁₃	1	2	yes	—
639	#427	C₂²×C₁₃	1	2	yes	—
640	#427	C₂²×C₁₃	1	2	yes	—
641	#423	C₂²×C₁₃	1	1	yes	characteristic
642	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
643	#419	C₂²×C₁₃	1	2	yes	—
644	#416	C₂²×C₁₃	1	2	yes	—
645	#416	C₂²×C₁₃	1	2	yes	—
646	C₂²×C₁₃	—	2	1	no	—
647	C₂²×C₁₃	—	2	2	no	—
648	C₂²×C₁₃	—	2	1	no	—
649	C₂²×C₁₃	—	2	2	no	—
650	C₂²×C₁₃	—	2	1	no	—
651	C₂²×C₁₃	—	2	2	no	—
652	C₂²×C₁₃	—	4	2	no	—
653	C₂²×C₁₃	—	4	1	no	—
654	C₂²×C₁₃	—	4	2	no	—
655	C₂²×C₁₃	—	4	1	no	—
656	C₂²×C₁₃	—	4	1	no	—
657	C₂²×C₁₃	—	4	2	no	—
658	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
659	C₄×C₁₃	—	2	1	no	—
660	C₄×C₁₃	—	2	2	no	—
661	C₄×C₁₃	—	2	1	no	—
662	C₄×C₁₃	—	2	2	no	—
663	C₄×C₁₃	—	2	1	no	—
664	C₄×C₁₃	—	2	2	no	—
665	C₄×C₁₃	—	2	1	no	—
666	C₄×C₁₃	—	2	2	no	—
667	C₄×C₁₃	—	4	1	no	—
668	C₄×C₁₃	—	4	1	no	—
669	C₄×C₁₃	—	4	1	no	—
670	C₄×C₁₃	—	4	2	no	—
671	C₄×C₁₃	—	4	1	no	—
672	C₄×C₁₃	—	4	1	no	—
673	C₄×C₁₃	—	4	2	no	—
674	C₄×C₁₃	—	4	2	no	—
675	C₄×C₁₃	—	4	1	no	—
676	C₄×C₁₃	#575	1	2	yes	—
677	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
678	C₄×C₁₃	#585	1	1	yes	characteristic
679	C₂×#41	—	2	1	no	—
680	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
681	C₂×#41	C₂³×C₁₃	1	2	yes	—
682	C₂²×Q₈	—	2	1	no	—
683	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
685	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
686	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
687	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
688	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
689	C₂×D₈	C₂³×C₁₃	1	2	yes	—
690	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
691	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
692	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	2	no	—
696	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
699	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
701	#127	—	2	1	no	—
702	#127	C₂³×C₁₃	1	1	yes	characteristic
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	1	no	—
711	#125	—	2	2	no	—
712	#125	C₂³×C₁₃	1	1	yes	characteristic
713	#125	C₂³×C₁₃	1	2	yes	—
714	#125	C₂³×C₁₃	1	2	yes	—
715	#124	—	2	1	no	—
716	#124	—	2	1	no	—
717	#124	—	2	1	no	—
718	#124	—	2	2	no	—
719	#124	—	2	2	no	—
720	#124	—	2	2	no	—
721	#124	—	2	2	no	—
722	#124	—	2	2	no	—
723	#124	—	2	1	no	—
724	#124	C₂³×C₁₃	1	1	yes	characteristic
725	#124	C₂³×C₁₃	1	2	yes	—
726	#123	—	2	1	no	—
727	#123	—	2	2	no	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	1	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
739	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
740	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
741	#121	—	2	2	no	—
742	#121	—	2	2	no	—
743	#121	—	2	1	no	—
744	#121	—	2	2	no	—
745	#121	—	2	1	no	—
746	#121	—	2	2	no	—
747	#121	C₂³×C₁₃	1	2	yes	—
748	#121	C₂³×C₁₃	1	1	yes	characteristic
749	#121	C₂³×C₁₃	1	2	yes	—
750	#121	C₂³×C₁₃	1	2	yes	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	2	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	2	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	2	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
763	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
764	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
765	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
768	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
770	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	D₄×C₁₃	1	2	yes	—
782	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
783	C₄×D₄	C₂³×C₁₃	1	2	yes	—
784	C₄×D₄	C₂³×C₁₃	1	2	yes	—
785	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₁₃	1	2	yes	—
787	C₄×D₄	C₂³×C₁₃	1	2	yes	—
788	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
789	#117	—	2	1	no	—
790	#117	—	2	2	no	—
791	#117	—	2	2	no	—
792	#117	—	2	2	no	—
793	#117	—	2	2	no	—
794	#117	—	2	1	no	—
795	#117	D₄×C₁₃	1	1	yes	characteristic
796	#117	D₄×C₁₃	1	2	yes	—
797	#117	C₂³×C₁₃	1	2	yes	—
798	#117	C₂³×C₁₃	1	2	yes	—
799	#117	C₂³×C₁₃	1	2	yes	—
800	#117	C₂³×C₁₃	1	2	yes	—
801	C₂×C₄⋊C₄	—	2	1	no	—
802	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
803	C₂×C₄²	—	2	1	no	—
804	C₂×C₄²	—	2	2	no	—
805	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
806	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
807	#107	C₂³×C₁₃	1	1	yes	characteristic
808	#107	C₂³×C₁₃	1	2	yes	—
809	#107	C₂³×C₁₃	1	2	yes	—
810	#107	C₂³×C₁₃	1	2	yes	—
811	#107	C₂³×C₁₃	1	2	yes	—
812	#107	C₂³×C₁₃	1	1	yes	characteristic
813	#107	C₂³×C₁₃	1	2	yes	—
814	#106	C₂³×C₁₃	1	1	yes	characteristic
815	#106	C₂³×C₁₃	1	2	yes	—
816	#106	C₂³×C₁₃	1	2	yes	—
817	#106	C₂³×C₁₃	1	2	yes	—
818	#106	C₂³×C₁₃	1	2	yes	—
819	#106	C₂³×C₁₃	1	1	yes	characteristic
820	#106	C₂³×C₁₃	1	2	yes	—
821	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
823	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
824	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
825	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
828	#103	C₂³×C₁₃	1	1	yes	characteristic
829	#103	C₂³×C₁₃	1	1	yes	characteristic
830	#103	C₂³×C₁₃	1	2	yes	—
831	#103	C₂³×C₁₃	1	2	yes	—
832	#103	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
837	#103	C₂³×C₁₃	1	1	yes	characteristic
838	#103	C₂³×C₁₃	1	2	yes	—
839	#102	C₂³×C₁₃	1	2	yes	—
840	#102	C₂³×C₁₃	1	2	yes	—
841	#102	C₂³×C₁₃	1	2	yes	—
842	#102	C₂³×C₁₃	1	2	yes	—
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	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
849	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
850	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
851	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
852	#97	C₂³×C₁₃	1	2	yes	—
853	#97	C₂³×C₁₃	1	2	yes	—
854	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
855	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
856	C₂×C₁₃	—	4	1	no	—
857	C₂×C₁₃	—	4	2	no	—
858	C₂×C₁₃	—	8	2	no	—
859	C₂×C₁₃	—	8	1	no	—
860	C₂×C₁₃	#3489	1	1	yes	characteristic
861	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
862	C₂×C₁₃	#3584	1	1	yes	characteristic
863	#41	—	2	4	no	—
864	#41	—	4	2	no	—
865	#41	—	4	2	no	—
866	#41	—	4	4	no	—
867	C₂×Q₈	—	2	1	no	—
868	C₂×Q₈	—	2	2	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	2	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	4	1	no	—
875	C₂×Q₈	—	4	4	no	—
876	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
877	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
878	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
879	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
888	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
889	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
890	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
891	C₂²×C₄	—	2	1	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	2	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	C₂×D₄×C₁₃	1	1	yes	characteristic
899	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
900	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
901	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
904	Q₁₆	—	2	2	no	—
905	Q₁₆	—	4	1	no	—
906	SD₁₆	—	2	2	no	—
907	SD₁₆	—	4	1	no	—
908	SD₁₆	—	4	2	no	—
909	D₈	—	4	2	no	—
910	M₁₆	—	4	2	no	—
911	C₂×C₈	—	4	2	no	—
912	C₂×C₈	—	4	2	no	—
913	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
917	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
918	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
944	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
972	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
973	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	1	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	1	no	—
985	C₄²	C₂×D₄×C₁₃	1	2	yes	—
986	C₄²	C₂×D₄×C₁₃	1	2	yes	—
987	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
988	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
989	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
990	C₄²	C₂⁴×C₁₃	1	2	yes	—
991	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
992	C₁₃	#62142	1	1	yes	characteristic, direct product factor, Sylow
993	C₂³	—	2	1	no	—
994	C₂³	—	2	2	no	—
995	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
996	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
997	Q₈	—	2	2	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	2	1	no	—
1001	Q₈	—	2	1	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	4	4	no	—
1005	Q₈	—	4	2	no	—
1006	Q₈	—	4	2	no	—
1007	Q₈	—	8	2	no	—
1008	Q₈	—	8	1	no	—
1009	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
1010	D₄	—	2	2	no	—
1011	D₄	—	2	1	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	2	1	no	—
1014	D₄	—	2	2	no	—
1015	D₄	—	4	2	no	—
1016	D₄	—	4	4	no	—
1017	D₄	—	4	4	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	8	1	no	—
1020	D₄	—	8	2	no	—
1021	D₄	—	8	1	no	—
1022	D₄	—	8	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	2	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	1	no	—
1040	C₂×C₄	—	4	2	no	—
1041	C₂×C₄	—	4	4	no	—
1042	C₂×C₄	—	4	2	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	4	2	no	—
1046	C₂×C₄	—	8	2	no	—
1047	C₂×C₄	—	8	1	no	—
1048	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1049	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1051	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1052	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1053	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1054	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1055	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1056	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	1	no	—
1061	C₈	—	2	2	no	—
1062	C₈	—	2	2	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1076	C₄	—	2	1	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	1	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	2	no	—
1082	C₄	—	2	1	no	—
1083	C₄	—	2	2	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	C₁₃×#575	1	2	yes	—
1094	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1095	C₄	C₁₃×#585	1	1	yes	characteristic
1096	C₂	—	4	1	no	—
1097	C₂	—	4	2	no	—
1098	C₂	—	8	1	no	—
1099	C₂	—	8	2	no	—
1100	C₂	C₁₃×#3489	1	1	yes	characteristic
1101	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1102	C₂	C₁₃×#3584	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×#3518	C₂	semidirect
2. C₁₃×#3480	C₂	semidirect
3. C₁₃×#3387	C₂	semidirect
4. C₁₃×#3386	C₂	semidirect
5. C₁₃×#3375	C₂	semidirect
6. C₁₃×#3373	C₂	semidirect
7. C₁₃×#3350	C₂	semidirect
8. C₁₃×#3347	C₂	semidirect
9. C₁₃×#3342	C₂	semidirect
10. C₁₃×#3340	C₂	semidirect
11. C₁₃×#3321	C₂	semidirect
12. C₁₃×#3313	C₂	semidirect
13. C₁₃×#3305	C₂	semidirect
14. C₁₃×#3304	C₂	semidirect
15. C₁₃×#3251	C₂	semidirect
16. C₁₃×#3250	C₂	semidirect
17. C₁₃×#3240	C₂	semidirect
18. C₁₃×#3228	C₂	semidirect
19. C₁₃×#3111	C₂	semidirect
20. C₁₃×#3108	C₂	semidirect
21. C₁₃×#3078	C₂	semidirect
22. C₁₃×#3076	C₂	semidirect
23. C₁₃×#2990	C₂	semidirect
312. #62142	C₁₃	direct (N × H)
442. #3518	C₂×C₁₃	semidirect
443. #3480	C₂×C₁₃	semidirect
444. #3387	C₂×C₁₃	semidirect
445. #3386	C₂×C₁₃	semidirect
446. #3375	C₂×C₁₃	semidirect
447. #3373	C₂×C₁₃	semidirect
448. #3350	C₂×C₁₃	semidirect
449. #3347	C₂×C₁₃	semidirect
450. #3342	C₂×C₁₃	semidirect
451. #3340	C₂×C₁₃	semidirect
452. #3321	C₂×C₁₃	semidirect
453. #3313	C₂×C₁₃	semidirect
454. #3305	C₂×C₁₃	semidirect
455. #3304	C₂×C₁₃	semidirect
456. #3251	C₂×C₁₃	semidirect
457. #3250	C₂×C₁₃	semidirect
458. #3240	C₂×C₁₃	semidirect
459. #3228	C₂×C₁₃	semidirect
460. #3111	C₂×C₁₃	semidirect
461. #3108	C₂×C₁₃	semidirect
462. #3078	C₂×C₁₃	semidirect
463. #3076	C₂×C₁₃	semidirect
464. #2990	C₂×C₁₃	semidirect
992. C₁₃	#62142	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×#3518	2
C₁₃×#3480	2
C₁₃×#3387	2
C₁₃×#3386	2
C₁₃×#3375	2
C₁₃×#3373	2
C₁₃×#3350	2
C₁₃×#3347	2
C₁₃×#3342	2
C₁₃×#3340	2
C₁₃×#3321	2
C₁₃×#3313	2
C₁₃×#3305	2
C₁₃×#3304	2
C₁₃×#3251	2
C₁₃×#3250	2
C₁₃×#3240	2
C₁₃×#3228	2
C₁₃×#3111	2
C₁₃×#3108	2
C₁₃×#3078	2
C₁₃×#3076	2
C₁₃×#2990	2
#62142	13

Subgroups — C13×#62142 #15748481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62142 #15748481