Subgroups — C₁₃×#61000 #15747339

Order 3328.

1802 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3494	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3250	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3241	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3220	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3191	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3188	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3180	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3124	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3122	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3119	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3118	C₂	1	2	yes	maximal, complemented
19	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#555	—	2	2	no	—
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#553	—	2	2	no	—
23	C₁₃×#551	—	2	2	no	—
24	C₁₃×#551	—	2	2	no	—
25	C₁₃×#547	—	2	2	no	—
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#546	—	2	2	no	—
28	C₁₃×#544	C₂²	1	2	yes	complemented
29	C₁₃×#542	C₂²	1	2	yes	—
30	C₁₃×#542	C₂²	1	2	yes	—
31	C₁₃×#540	C₂²	1	2	yes	—
32	C₁₃×#540	C₂²	1	2	yes	—
33	C₁₃×#535	C₂²	1	2	yes	complemented
34	C₁₃×#532	C₂²	1	2	yes	complemented
35	C₁₃×#532	C₂²	1	2	yes	complemented
36	C₁₃×#529	C₂²	1	2	yes	complemented
37	C₁₃×#529	C₂²	1	2	yes	complemented
38	C₁₃×#525	C₂²	1	2	yes	—
39	C₂×C₁₃×#121	C₂²	1	2	yes	—
40	C₁₃×#520	C₂²	1	2	yes	complemented
41	C₁₃×#518	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
43	C₁₃×#501	C₂²	1	2	yes	complemented
44	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
46	C₁₃×#496	C₂²	1	2	yes	complemented
47	C₁₃×#495	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#490	C₂²	1	2	yes	complemented
50	C₁₃×#489	C₂²	1	2	yes	complemented
51	C₁₃×#488	C₂²	1	2	yes	complemented
52	C₁₃×#486	C₂²	1	2	yes	complemented
53	C₁₃×#485	C₂²	1	2	yes	complemented
54	C₁₃×#484	C₂²	1	2	yes	complemented
55	C₁₃×#482	C₂²	1	2	yes	—
56	C₁₃×#482	C₂²	1	2	yes	—
57	C₁₃×#482	C₂²	1	2	yes	complemented
58	C₁₃×#481	C₂²	1	2	yes	complemented
59	C₁₃×#480	C₂²	1	2	yes	—
60	C₁₃×#480	C₂²	1	2	yes	—
61	C₁₃×#479	C₂²	1	2	yes	complemented
62	C₁₃×#478	C₂²	1	2	yes	complemented
63	C₁₃×#478	C₂²	1	2	yes	complemented
64	C₁₃×#478	C₂²	1	2	yes	complemented
65	C₁₃×#477	C₂²	1	2	yes	complemented
66	C₁₃×#476	C₂²	1	2	yes	complemented
67	C₁₃×#474	C₂²	1	2	yes	complemented
68	C₁₃×#474	C₂²	1	2	yes	complemented
69	C₁₃×#467	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#466	C₂²	1	1	yes	characteristic
71	C₁₃×#466	C₂²	1	1	yes	characteristic
72	C₁₃×#466	C₂²	1	2	yes	—
73	C₁₃×#466	C₂²	1	2	yes	complemented
74	C₁₃×#466	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#466	C₂²	1	2	yes	complemented
76	C₁₃×#465	C₂²	1	2	yes	complemented
77	C₁₃×#465	C₂²	1	2	yes	complemented
78	C₁₃×#465	C₂²	1	2	yes	complemented
79	C₁₃×#464	C₂²	1	2	yes	complemented
80	C₁₃×#463	C₂²	1	2	yes	complemented
81	C₁₃×#463	C₂²	1	2	yes	complemented
82	C₁₃×#463	C₂²	1	2	yes	complemented
83	C₁₃×#460	C₂²	1	2	yes	complemented
84	C₁₃×#459	C₂²	1	2	yes	complemented
85	C₁₃×#459	C₂²	1	2	yes	complemented
86	C₁₃×#459	C₂²	1	2	yes	complemented
87	C₁₃×#452	C₂²	1	2	yes	complemented
88	C₁₃×#450	C₂²	1	2	yes	complemented
89	C₁₃×#449	C₂²	1	2	yes	—
90	C₁₃×#449	C₂²	1	2	yes	—
91	C₁₃×#449	C₂²	1	2	yes	complemented
92	C₁₃×#447	C₂²	1	2	yes	—
93	C₁₃×#447	C₂²	1	2	yes	—
94	C₁₃×#447	C₂²	1	2	yes	complemented
95	C₁₃×#442	C₂²	1	2	yes	complemented
96	C₁₃×#442	C₂²	1	2	yes	complemented
97	C₁₃×#440	C₂²	1	2	yes	complemented
98	C₁₃×#440	C₂²	1	2	yes	complemented
99	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
101	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
105	C₁₃×#433	C₂²	1	2	yes	complemented
106	C₁₃×#433	C₂²	1	2	yes	complemented
107	C₁₃×#433	C₂²	1	2	yes	complemented
108	C₁₃×#433	C₂²	1	2	yes	complemented
109	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
112	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
113	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₁₃×#41	—	2	2	no	—
116	C₂×C₁₃×#41	—	2	2	no	—
117	C₂×C₁₃×#41	C₂³	1	2	yes	—
118	C₂²×D₄×C₁₃	—	2	2	no	—
119	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
126	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
127	C₂×C₁₃×D₈	C₂³	1	2	yes	—
128	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
129	C₂×C₁₃×D₈	C₂³	1	2	yes	—
130	C₂×C₁₃×D₈	C₂³	1	2	yes	—
131	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₃×#127	C₂³	1	2	yes	—
139	C₁₃×#127	C₂³	1	2	yes	—
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#125	—	2	2	no	—
145	C₁₃×#125	C₂³	1	2	yes	—
146	C₁₃×#125	C₂³	1	2	yes	—
147	C₁₃×#124	—	2	2	no	—
148	C₁₃×#124	—	2	2	no	—
149	C₁₃×#124	—	2	2	no	—
150	C₁₃×#124	—	2	2	no	—
151	C₁₃×#124	C₂³	1	2	yes	—
152	C₁₃×#124	C₂³	1	2	yes	—
153	C₁₃×#123	—	2	2	no	—
154	C₁₃×#123	—	2	2	no	—
155	C₁₃×#123	—	2	2	no	—
156	C₁₃×#123	—	2	2	no	—
157	C₁₃×#123	—	2	2	no	—
158	C₁₃×#123	—	2	2	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×#123	—	2	2	no	—
162	C₁₃×C₂²⋊Q₈	—	2	2	no	—
163	C₁₃×C₂²⋊Q₈	—	2	2	no	—
164	C₁₃×C₂²⋊Q₈	—	2	2	no	—
165	C₁₃×C₂²⋊Q₈	—	2	2	no	—
166	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₁₃×#121	—	2	2	no	—
169	C₁₃×#121	—	2	2	no	—
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	2	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	—	2	2	no	—
177	C₁₃×#121	—	2	2	no	—
178	C₁₃×#121	C₂³	1	2	yes	—
179	C₁₃×#121	C₂³	1	2	yes	—
180	C₁₃×#121	C₂³	1	2	yes	—
181	C₁₃×#121	C₂³	1	2	yes	—
182	C₁₃×#121	C₂³	1	2	yes	—
183	C₁₃×#121	C₂³	1	2	yes	—
184	C₁₃×#120	—	2	2	no	—
185	C₁₃×#120	—	2	2	no	—
186	C₁₃×#120	—	2	2	no	—
187	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
188	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	2	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	—	2	2	no	—
194	C₄×D₄×C₁₃	—	2	2	no	—
195	C₄×D₄×C₁₃	—	2	2	no	—
196	C₄×D₄×C₁₃	—	2	2	no	—
197	C₄×D₄×C₁₃	—	2	2	no	—
198	C₄×D₄×C₁₃	—	2	2	no	—
199	C₄×D₄×C₁₃	C₂³	1	2	yes	—
200	C₄×D₄×C₁₃	C₂³	1	2	yes	—
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₄×D₄×C₁₃	C₂³	1	2	yes	—
203	C₄×D₄×C₁₃	C₂³	1	2	yes	—
204	C₄×D₄×C₁₃	C₂³	1	2	yes	—
205	C₁₃×#117	—	2	2	no	—
206	C₁₃×#117	—	2	2	no	—
207	C₁₃×#117	—	2	2	no	—
208	C₁₃×#117	D₄	1	2	yes	—
209	C₁₃×#117	D₄	1	2	yes	—
210	C₁₃×#117	C₂³	1	2	yes	—
211	C₁₃×#117	C₂³	1	2	yes	—
212	C₁₃×#117	C₂³	1	2	yes	—
213	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
215	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
216	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
217	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
218	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
219	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
221	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
224	C₁₃×#107	C₂³	1	1	yes	characteristic
225	C₁₃×#107	C₂³	1	1	yes	characteristic
226	C₁₃×#107	C₂³	1	2	yes	—
227	C₁₃×#107	C₂³	1	1	yes	characteristic
228	C₁₃×#107	C₂³	1	1	yes	characteristic
229	C₁₃×#107	C₂³	1	2	yes	—
230	C₁₃×#107	C₂³	1	2	yes	—
231	C₁₃×#106	C₂³	1	2	yes	—
232	C₁₃×#106	C₂³	1	2	yes	—
233	C₁₃×#106	C₂³	1	2	yes	—
234	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₁₃×#103	C₂³	1	2	yes	—
239	C₁₃×#103	C₂³	1	2	yes	—
240	C₁₃×#103	C₂³	1	2	yes	—
241	C₁₃×#103	C₂³	1	2	yes	—
242	C₁₃×#102	C₂³	1	2	yes	—
243	C₁₃×#102	C₂³	1	2	yes	—
244	C₁₃×#102	C₂³	1	2	yes	—
245	C₁₃×#102	C₂³	1	2	yes	—
246	C₁₃×#102	C₂³	1	2	yes	—
247	C₁₃×#102	C₂³	1	2	yes	—
248	C₁₃×#102	C₂³	1	2	yes	—
249	C₁₃×#102	C₂³	1	2	yes	—
250	C₁₃×#102	C₂³	1	2	yes	—
251	C₁₃×#102	C₂³	1	2	yes	—
252	C₁₃×#102	C₂³	1	2	yes	—
253	C₁₃×#102	C₂³	1	2	yes	—
254	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₁₃×#97	C₂³	1	2	yes	—
259	C₁₃×#97	C₂³	1	2	yes	—
260	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
264	#61000	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂⁴×C₁₃	—	2	2	no	—
266	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₁₃×#41	—	4	2	no	—
268	C₁₃×#41	—	4	2	no	—
269	C₁₃×#41	—	8	4	no	—
270	C₁₃×#41	—	8	4	no	—
271	C₂×Q₈×C₁₃	—	2	2	no	—
272	C₂×Q₈×C₁₃	—	2	2	no	—
273	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
274	C₂×D₄×C₁₃	—	2	2	no	—
275	C₂×D₄×C₁₃	—	2	2	no	—
276	C₂×D₄×C₁₃	—	2	2	no	—
277	C₂×D₄×C₁₃	—	2	2	no	—
278	C₂×D₄×C₁₃	—	2	2	no	—
279	C₂×D₄×C₁₃	—	2	2	no	—
280	C₂×D₄×C₁₃	—	2	2	no	—
281	C₂×D₄×C₁₃	—	2	2	no	—
282	C₂×D₄×C₁₃	—	2	2	no	—
283	C₂×D₄×C₁₃	—	2	2	no	—
284	C₂×D₄×C₁₃	—	2	2	no	—
285	C₂×D₄×C₁₃	—	2	2	no	—
286	C₂×D₄×C₁₃	—	4	2	no	—
287	C₂×D₄×C₁₃	—	4	2	no	—
288	C₂×D₄×C₁₃	—	8	4	no	—
289	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	2	no	—
294	C₂²×C₄×C₁₃	—	2	2	no	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	—	2	2	no	—
297	C₂²×C₄×C₁₃	—	2	2	no	—
298	C₂²×C₄×C₁₃	—	2	2	no	—
299	C₂²×C₄×C₁₃	—	2	2	no	—
300	C₂²×C₄×C₁₃	—	4	1	no	—
301	C₂²×C₄×C₁₃	—	4	1	no	—
302	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
307	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₁₃×Q₁₆	—	4	1	no	—
311	C₁₃×SD₁₆	—	4	2	no	—
312	C₁₃×SD₁₆	—	4	2	no	—
313	C₁₃×SD₁₆	—	4	2	no	—
314	C₁₃×D₈	—	4	2	no	—
315	C₁₃×D₈	—	4	1	no	—
316	C₁₃×D₈	—	4	1	no	—
317	C₁₃×D₈	—	4	2	no	—
318	C₁₃×D₈	—	4	2	no	—
319	C₁₃×D₈	—	4	1	no	—
320	C₂×C₈×C₁₃	—	4	1	no	—
321	C₂×C₈×C₁₃	—	4	1	no	—
322	C₂×C₈×C₁₃	—	4	1	no	—
323	C₂×C₈×C₁₃	—	4	1	no	—
324	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
329	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	2	no	—
335	C₁₃×C₄⋊C₄	—	2	2	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
342	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
343	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
344	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
345	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
347	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
348	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	2	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	2	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	2	no	—
357	C₁₃×C₂²⋊C₄	—	2	2	no	—
358	C₁₃×C₂²⋊C₄	—	2	2	no	—
359	C₁₃×C₂²⋊C₄	—	2	2	no	—
360	C₁₃×C₂²⋊C₄	—	2	2	no	—
361	C₁₃×C₂²⋊C₄	—	2	2	no	—
362	C₁₃×C₂²⋊C₄	—	2	2	no	—
363	C₁₃×C₂²⋊C₄	—	2	2	no	—
364	C₁₃×C₂²⋊C₄	—	2	2	no	—
365	C₁₃×C₂²⋊C₄	—	2	2	no	—
366	C₁₃×C₂²⋊C₄	—	2	2	no	—
367	C₁₃×C₂²⋊C₄	—	2	2	no	—
368	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
369	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
370	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
371	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
372	C₄²×C₁₃	—	2	2	no	—
373	C₄²×C₁₃	—	2	2	no	—
374	C₄²×C₁₃	—	2	2	no	—
375	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₁₃	C₂×D₄	1	2	yes	—
377	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₄²×C₁₃	C₂⁴	1	2	yes	—
381	#3494	C₂×C₁₃	1	2	yes	complemented
382	#3250	C₂×C₁₃	1	1	yes	characteristic, complemented
383	#3247	C₂×C₁₃	1	2	yes	complemented
384	#3245	C₂×C₁₃	1	1	yes	characteristic, complemented
385	#3243	C₂×C₁₃	1	2	yes	complemented
386	#3241	C₂×C₁₃	1	2	yes	complemented
387	#3224	C₂×C₁₃	1	2	yes	complemented
388	#3220	C₂×C₁₃	1	2	yes	complemented
389	#3191	C₂×C₁₃	1	1	yes	characteristic, complemented
390	#3188	C₂×C₁₃	1	2	yes	complemented
391	#3186	C₂×C₁₃	1	1	yes	characteristic, complemented
392	#3180	C₂×C₁₃	1	2	yes	complemented
393	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
394	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
395	#3124	C₂×C₁₃	1	2	yes	complemented
396	#3122	C₂×C₁₃	1	2	yes	complemented
397	#3119	C₂×C₁₃	1	2	yes	complemented
398	#3118	C₂×C₁₃	1	2	yes	complemented
399	C₂×#433	C₂×C₁₃	1	1	yes	characteristic, complemented
400	C₂³×C₁₃	—	2	2	no	—
401	C₂³×C₁₃	—	2	2	no	—
402	C₂³×C₁₃	—	2	2	no	—
403	C₂³×C₁₃	—	2	2	no	—
404	C₂³×C₁₃	—	4	1	no	—
405	C₂³×C₁₃	—	4	1	no	—
406	C₂³×C₁₃	—	4	4	no	—
407	C₂³×C₁₃	—	8	2	no	—
408	C₂³×C₁₃	—	8	2	no	—
409	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
410	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
411	Q₈×C₁₃	—	2	2	no	—
412	Q₈×C₁₃	—	2	2	no	—
413	Q₈×C₁₃	—	8	2	no	—
414	Q₈×C₁₃	—	8	2	no	—
415	D₄×C₁₃	—	2	2	no	—
416	D₄×C₁₃	—	2	2	no	—
417	D₄×C₁₃	—	2	2	no	—
418	D₄×C₁₃	—	2	2	no	—
419	D₄×C₁₃	—	2	2	no	—
420	D₄×C₁₃	—	2	2	no	—
421	D₄×C₁₃	—	4	4	no	—
422	D₄×C₁₃	—	4	4	no	—
423	D₄×C₁₃	—	4	4	no	—
424	D₄×C₁₃	—	4	4	no	—
425	D₄×C₁₃	—	4	4	no	—
426	D₄×C₁₃	—	8	2	no	—
427	D₄×C₁₃	—	8	2	no	—
428	D₄×C₁₃	—	8	2	no	—
429	D₄×C₁₃	—	8	2	no	—
430	D₄×C₁₃	—	8	2	no	—
431	D₄×C₁₃	—	8	2	no	—
432	D₄×C₁₃	—	8	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	2	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	4	1	no	—
445	C₂×C₄×C₁₃	—	4	2	no	—
446	C₂×C₄×C₁₃	—	4	1	no	—
447	C₂×C₄×C₁₃	—	4	1	no	—
448	C₂×C₄×C₁₃	—	4	4	no	—
449	C₂×C₄×C₁₃	—	8	2	no	—
450	C₂×C₄×C₁₃	—	8	2	no	—
451	C₂×C₄×C₁₃	—	8	2	no	—
452	C₂×C₄×C₁₃	—	8	2	no	—
453	C₂×C₄×C₁₃	—	8	2	no	—
454	C₂×C₄×C₁₃	—	8	2	no	—
455	C₂×C₄×C₁₃	—	8	2	no	—
456	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
465	C₈×C₁₃	—	2	1	no	—
466	C₈×C₁₃	—	2	1	no	—
467	C₈×C₁₃	—	2	2	no	—
468	C₈×C₁₃	—	2	2	no	—
469	C₈×C₁₃	—	2	1	no	—
470	C₈×C₁₃	—	2	1	no	—
471	#555	—	2	2	no	—
472	#553	—	2	2	no	—
473	#553	—	2	2	no	—
474	#551	—	2	2	no	—
475	#551	—	2	2	no	—
476	#547	—	2	2	no	—
477	#546	—	2	2	no	—
478	#546	—	2	2	no	—
479	#544	C₂²×C₁₃	1	2	yes	complemented
480	#542	C₂²×C₁₃	1	2	yes	—
481	#542	C₂²×C₁₃	1	2	yes	—
482	#540	C₂²×C₁₃	1	2	yes	—
483	#540	C₂²×C₁₃	1	2	yes	—
484	#535	C₂²×C₁₃	1	2	yes	complemented
485	#532	C₂²×C₁₃	1	2	yes	complemented
486	#532	C₂²×C₁₃	1	2	yes	complemented
487	#529	C₂²×C₁₃	1	2	yes	complemented
488	#529	C₂²×C₁₃	1	2	yes	complemented
489	#525	C₂²×C₁₃	1	2	yes	—
490	C₂×#121	C₂²×C₁₃	1	2	yes	—
491	#520	C₂²×C₁₃	1	2	yes	complemented
492	#518	C₂²×C₁₃	1	2	yes	complemented
493	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
494	#501	C₂²×C₁₃	1	2	yes	complemented
495	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
496	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
497	#496	C₂²×C₁₃	1	2	yes	complemented
498	#495	C₂²×C₁₃	1	1	yes	characteristic, complemented
499	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
500	#490	C₂²×C₁₃	1	2	yes	complemented
501	#489	C₂²×C₁₃	1	2	yes	complemented
502	#488	C₂²×C₁₃	1	2	yes	complemented
503	#486	C₂²×C₁₃	1	2	yes	complemented
504	#485	C₂²×C₁₃	1	2	yes	complemented
505	#484	C₂²×C₁₃	1	2	yes	complemented
506	#482	C₂²×C₁₃	1	2	yes	—
507	#482	C₂²×C₁₃	1	2	yes	—
508	#482	C₂²×C₁₃	1	2	yes	complemented
509	#481	C₂²×C₁₃	1	2	yes	complemented
510	#480	C₂²×C₁₃	1	2	yes	—
511	#480	C₂²×C₁₃	1	2	yes	—
512	#479	C₂²×C₁₃	1	2	yes	complemented
513	#478	C₂²×C₁₃	1	2	yes	complemented
514	#478	C₂²×C₁₃	1	2	yes	complemented
515	#478	C₂²×C₁₃	1	2	yes	complemented
516	#477	C₂²×C₁₃	1	2	yes	complemented
517	#476	C₂²×C₁₃	1	2	yes	complemented
518	#474	C₂²×C₁₃	1	2	yes	complemented
519	#474	C₂²×C₁₃	1	2	yes	complemented
520	#467	C₂²×C₁₃	1	1	yes	characteristic, complemented
521	#466	C₂²×C₁₃	1	1	yes	characteristic
522	#466	C₂²×C₁₃	1	1	yes	characteristic
523	#466	C₂²×C₁₃	1	2	yes	—
524	#466	C₂²×C₁₃	1	2	yes	complemented
525	#466	C₂²×C₁₃	1	1	yes	characteristic, complemented
526	#466	C₂²×C₁₃	1	2	yes	complemented
527	#465	C₂²×C₁₃	1	2	yes	complemented
528	#465	C₂²×C₁₃	1	2	yes	complemented
529	#465	C₂²×C₁₃	1	2	yes	complemented
530	#464	C₂²×C₁₃	1	2	yes	complemented
531	#463	C₂²×C₁₃	1	2	yes	complemented
532	#463	C₂²×C₁₃	1	2	yes	complemented
533	#463	C₂²×C₁₃	1	2	yes	complemented
534	#460	C₂²×C₁₃	1	2	yes	complemented
535	#459	C₂²×C₁₃	1	2	yes	complemented
536	#459	C₂²×C₁₃	1	2	yes	complemented
537	#459	C₂²×C₁₃	1	2	yes	complemented
538	#452	C₂²×C₁₃	1	2	yes	complemented
539	#450	C₂²×C₁₃	1	2	yes	complemented
540	#449	C₂²×C₁₃	1	2	yes	—
541	#449	C₂²×C₁₃	1	2	yes	—
542	#449	C₂²×C₁₃	1	2	yes	complemented
543	#447	C₂²×C₁₃	1	2	yes	—
544	#447	C₂²×C₁₃	1	2	yes	—
545	#447	C₂²×C₁₃	1	2	yes	complemented
546	#442	C₂²×C₁₃	1	2	yes	complemented
547	#442	C₂²×C₁₃	1	2	yes	complemented
548	#440	C₂²×C₁₃	1	2	yes	complemented
549	#440	C₂²×C₁₃	1	2	yes	complemented
550	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
551	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
552	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
553	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
554	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
555	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
556	#433	C₂²×C₁₃	1	2	yes	complemented
557	#433	C₂²×C₁₃	1	2	yes	complemented
558	#433	C₂²×C₁₃	1	2	yes	complemented
559	#433	C₂²×C₁₃	1	2	yes	complemented
560	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
561	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
562	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
563	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
564	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
565	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
566	C₂²×C₁₃	—	2	1	no	—
567	C₂²×C₁₃	—	2	1	no	—
568	C₂²×C₁₃	—	2	2	no	—
569	C₂²×C₁₃	—	2	2	no	—
570	C₂²×C₁₃	—	2	2	no	—
571	C₂²×C₁₃	—	4	2	no	—
572	C₂²×C₁₃	—	4	2	no	—
573	C₂²×C₁₃	—	4	2	no	—
574	C₂²×C₁₃	—	4	2	no	—
575	C₂²×C₁₃	—	4	2	no	—
576	C₂²×C₁₃	—	4	2	no	—
577	C₂²×C₁₃	—	4	2	no	—
578	C₂²×C₁₃	—	4	2	no	—
579	C₂²×C₁₃	—	4	2	no	—
580	C₂²×C₁₃	—	8	2	no	—
581	C₂²×C₁₃	—	16	4	no	—
582	C₂²×C₁₃	#576	1	2	yes	—
583	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
584	C₄×C₁₃	—	2	1	no	—
585	C₄×C₁₃	—	2	2	no	—
586	C₄×C₁₃	—	2	1	no	—
587	C₄×C₁₃	—	2	2	no	—
588	C₄×C₁₃	—	2	1	no	—
589	C₄×C₁₃	—	2	1	no	—
590	C₄×C₁₃	—	2	2	no	—
591	C₄×C₁₃	—	2	1	no	—
592	C₄×C₁₃	—	4	2	no	—
593	C₄×C₁₃	—	4	2	no	—
594	C₄×C₁₃	—	4	2	no	—
595	C₄×C₁₃	—	4	2	no	—
596	C₄×C₁₃	—	4	2	no	—
597	C₄×C₁₃	#585	1	1	yes	characteristic
598	C₄×C₁₃	#585	1	1	yes	characteristic
599	C₂×#41	—	2	2	no	—
600	C₂×#41	—	2	2	no	—
601	C₂×#41	C₂³×C₁₃	1	2	yes	—
602	C₂²×D₄	—	2	2	no	—
603	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
604	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
605	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
606	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
607	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
608	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
609	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
610	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
611	C₂×D₈	C₂³×C₁₃	1	2	yes	—
612	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
613	C₂×D₈	C₂³×C₁₃	1	2	yes	—
614	C₂×D₈	C₂³×C₁₃	1	2	yes	—
615	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
616	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
617	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
618	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
619	C₄⋊Q₈	—	2	2	no	—
620	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
621	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
622	#127	C₂³×C₁₃	1	2	yes	—
623	#127	C₂³×C₁₃	1	2	yes	—
624	#126	—	2	2	no	—
625	#126	—	2	2	no	—
626	#126	—	2	2	no	—
627	#126	—	2	2	no	—
628	#125	—	2	2	no	—
629	#125	C₂³×C₁₃	1	2	yes	—
630	#125	C₂³×C₁₃	1	2	yes	—
631	#124	—	2	2	no	—
632	#124	—	2	2	no	—
633	#124	—	2	2	no	—
634	#124	—	2	2	no	—
635	#124	C₂³×C₁₃	1	2	yes	—
636	#124	C₂³×C₁₃	1	2	yes	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	#123	—	2	2	no	—
644	#123	—	2	2	no	—
645	#123	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	—	2	2	no	—
648	C₂²⋊Q₈	—	2	2	no	—
649	C₂²⋊Q₈	—	2	2	no	—
650	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
651	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	—	2	2	no	—
658	#121	—	2	2	no	—
659	#121	—	2	2	no	—
660	#121	—	2	2	no	—
661	#121	—	2	2	no	—
662	#121	C₂³×C₁₃	1	2	yes	—
663	#121	C₂³×C₁₃	1	2	yes	—
664	#121	C₂³×C₁₃	1	2	yes	—
665	#121	C₂³×C₁₃	1	2	yes	—
666	#121	C₂³×C₁₃	1	2	yes	—
667	#121	C₂³×C₁₃	1	2	yes	—
668	#120	—	2	2	no	—
669	#120	—	2	2	no	—
670	#120	—	2	2	no	—
671	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
672	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	C₂³×C₁₃	1	2	yes	—
684	C₄×D₄	C₂³×C₁₃	1	2	yes	—
685	C₄×D₄	C₂³×C₁₃	1	2	yes	—
686	C₄×D₄	C₂³×C₁₃	1	2	yes	—
687	C₄×D₄	C₂³×C₁₃	1	2	yes	—
688	C₄×D₄	C₂³×C₁₃	1	2	yes	—
689	#117	—	2	2	no	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	D₄×C₁₃	1	2	yes	—
693	#117	D₄×C₁₃	1	2	yes	—
694	#117	C₂³×C₁₃	1	2	yes	—
695	#117	C₂³×C₁₃	1	2	yes	—
696	#117	C₂³×C₁₃	1	2	yes	—
697	C₂×C₄⋊C₄	—	2	2	no	—
698	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
699	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
701	C₂×C₂²⋊C₄	—	2	2	no	—
702	C₂×C₂²⋊C₄	—	2	2	no	—
703	C₂×C₂²⋊C₄	—	2	2	no	—
704	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
705	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
706	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
707	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
708	#107	C₂³×C₁₃	1	1	yes	characteristic
709	#107	C₂³×C₁₃	1	1	yes	characteristic
710	#107	C₂³×C₁₃	1	2	yes	—
711	#107	C₂³×C₁₃	1	1	yes	characteristic
712	#107	C₂³×C₁₃	1	1	yes	characteristic
713	#107	C₂³×C₁₃	1	2	yes	—
714	#107	C₂³×C₁₃	1	2	yes	—
715	#106	C₂³×C₁₃	1	2	yes	—
716	#106	C₂³×C₁₃	1	2	yes	—
717	#106	C₂³×C₁₃	1	2	yes	—
718	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
719	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
720	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
721	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
722	#103	C₂³×C₁₃	1	2	yes	—
723	#103	C₂³×C₁₃	1	2	yes	—
724	#103	C₂³×C₁₃	1	2	yes	—
725	#103	C₂³×C₁₃	1	2	yes	—
726	#102	C₂³×C₁₃	1	2	yes	—
727	#102	C₂³×C₁₃	1	2	yes	—
728	#102	C₂³×C₁₃	1	2	yes	—
729	#102	C₂³×C₁₃	1	2	yes	—
730	#102	C₂³×C₁₃	1	2	yes	—
731	#102	C₂³×C₁₃	1	2	yes	—
732	#102	C₂³×C₁₃	1	2	yes	—
733	#102	C₂³×C₁₃	1	2	yes	—
734	#102	C₂³×C₁₃	1	2	yes	—
735	#102	C₂³×C₁₃	1	2	yes	—
736	#102	C₂³×C₁₃	1	2	yes	—
737	#102	C₂³×C₁₃	1	2	yes	—
738	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
739	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
740	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
741	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
742	#97	C₂³×C₁₃	1	2	yes	—
743	#97	C₂³×C₁₃	1	2	yes	—
744	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
745	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
746	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
747	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
748	C₂×C₁₃	—	2	2	no	—
749	C₂×C₁₃	—	4	2	no	—
750	C₂×C₁₃	—	8	2	no	—
751	C₂×C₁₃	—	8	2	no	—
752	C₂×C₁₃	—	8	2	no	—
753	C₂×C₁₃	#3449	1	1	yes	characteristic
754	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
755	C₂×C₁₃	#3584	1	1	yes	characteristic
756	C₂⁴	—	2	2	no	—
757	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
758	#41	—	4	2	no	—
759	#41	—	4	2	no	—
760	#41	—	8	4	no	—
761	#41	—	8	4	no	—
762	C₂×Q₈	—	2	2	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	—	8	4	no	—
780	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
781	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
782	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	4	1	no	—
792	C₂²×C₄	—	4	1	no	—
793	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
797	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
798	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
800	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
801	Q₁₆	—	4	1	no	—
802	SD₁₆	—	4	2	no	—
803	SD₁₆	—	4	2	no	—
804	SD₁₆	—	4	2	no	—
805	D₈	—	4	2	no	—
806	D₈	—	4	1	no	—
807	D₈	—	4	1	no	—
808	D₈	—	4	2	no	—
809	D₈	—	4	2	no	—
810	D₈	—	4	1	no	—
811	C₂×C₈	—	4	1	no	—
812	C₂×C₈	—	4	1	no	—
813	C₂×C₈	—	4	1	no	—
814	C₂×C₈	—	4	1	no	—
815	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
816	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
817	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
818	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
819	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
820	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
833	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
834	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
835	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
838	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
839	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
860	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
861	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
862	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
863	C₄²	—	2	2	no	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	2	no	—
866	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
867	C₄²	C₂×D₄×C₁₃	1	2	yes	—
868	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
869	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
870	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
871	C₄²	C₂⁴×C₁₃	1	2	yes	—
872	C₁₃	#61000	1	1	yes	characteristic, direct product factor, Sylow
873	C₂³	—	2	2	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	4	1	no	—
878	C₂³	—	4	1	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	8	2	no	—
881	C₂³	—	8	2	no	—
882	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
883	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
884	Q₈	—	2	2	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	8	2	no	—
887	Q₈	—	8	2	no	—
888	D₄	—	2	2	no	—
889	D₄	—	2	2	no	—
890	D₄	—	2	2	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	4	no	—
895	D₄	—	4	4	no	—
896	D₄	—	4	4	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	4	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	2	no	—
903	D₄	—	8	2	no	—
904	D₄	—	8	2	no	—
905	D₄	—	8	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	2	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	—	8	2	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	8	2	no	—
927	C₂×C₄	—	8	2	no	—
928	C₂×C₄	—	8	2	no	—
929	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
931	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
932	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
936	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
937	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
938	C₈	—	2	1	no	—
939	C₈	—	2	1	no	—
940	C₈	—	2	2	no	—
941	C₈	—	2	2	no	—
942	C₈	—	2	1	no	—
943	C₈	—	2	1	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	8	2	no	—
959	C₂²	—	16	4	no	—
960	C₂²	C₁₃×#576	1	2	yes	—
961	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
962	C₄	—	2	1	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	2	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	1	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	C₁₃×#585	1	1	yes	characteristic
976	C₄	C₁₃×#585	1	1	yes	characteristic
977	C₂	—	2	2	no	—
978	C₂	—	4	2	no	—
979	C₂	—	8	2	no	—
980	C₂	—	8	2	no	—
981	C₂	—	8	2	no	—
982	C₂	C₁₃×#3449	1	1	yes	characteristic
983	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
984	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 ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3494	C₂	semidirect
2. C₁₃×#3250	C₂	semidirect
3. C₁₃×#3247	C₂	semidirect
4. C₁₃×#3245	C₂	semidirect
5. C₁₃×#3243	C₂	semidirect
6. C₁₃×#3241	C₂	semidirect
7. C₁₃×#3224	C₂	semidirect
8. C₁₃×#3220	C₂	semidirect
9. C₁₃×#3191	C₂	semidirect
10. C₁₃×#3188	C₂	semidirect
11. C₁₃×#3186	C₂	semidirect
12. C₁₃×#3180	C₂	semidirect
13. C₁₃×#3169	C₂	semidirect
14. C₁₃×#3168	C₂	semidirect
15. C₁₃×#3124	C₂	semidirect
16. C₁₃×#3122	C₂	semidirect
17. C₁₃×#3119	C₂	semidirect
18. C₁₃×#3118	C₂	semidirect
19. C₂×C₁₃×#433	C₂	semidirect
28. C₁₃×#544	C₂²	semidirect
33. C₁₃×#535	C₂²	semidirect
34. C₁₃×#532	C₂²	semidirect
35. C₁₃×#532	C₂²	semidirect
36. C₁₃×#529	C₂²	semidirect
37. C₁₃×#529	C₂²	semidirect
40. C₁₃×#520	C₂²	semidirect
41. C₁₃×#518	C₂²	semidirect
43. C₁₃×#501	C₂²	semidirect
44. C₁₃×#500	C₂²	semidirect
45. C₁₃×#499	C₂²	semidirect
46. C₁₃×#496	C₂²	semidirect
47. C₁₃×#495	C₂²	semidirect
48. C₁₃×#493	C₂²	semidirect
49. C₁₃×#490	C₂²	semidirect
50. C₁₃×#489	C₂²	semidirect
51. C₁₃×#488	C₂²	semidirect
52. C₁₃×#486	C₂²	semidirect
53. C₁₃×#485	C₂²	semidirect
54. C₁₃×#484	C₂²	semidirect
57. C₁₃×#482	C₂²	semidirect
58. C₁₃×#481	C₂²	semidirect
61. C₁₃×#479	C₂²	semidirect
62. C₁₃×#478	C₂²	semidirect
63. C₁₃×#478	C₂²	semidirect
64. C₁₃×#478	C₂²	semidirect
65. C₁₃×#477	C₂²	semidirect
66. C₁₃×#476	C₂²	semidirect
67. C₁₃×#474	C₂²	semidirect
68. C₁₃×#474	C₂²	semidirect
69. C₁₃×#467	C₂²	semidirect
73. C₁₃×#466	C₂²	semidirect
74. C₁₃×#466	C₂²	semidirect
75. C₁₃×#466	C₂²	semidirect
76. C₁₃×#465	C₂²	semidirect
77. C₁₃×#465	C₂²	semidirect
78. C₁₃×#465	C₂²	semidirect
79. C₁₃×#464	C₂²	semidirect
80. C₁₃×#463	C₂²	semidirect
81. C₁₃×#463	C₂²	semidirect
82. C₁₃×#463	C₂²	semidirect
83. C₁₃×#460	C₂²	semidirect
84. C₁₃×#459	C₂²	semidirect
85. C₁₃×#459	C₂²	semidirect
86. C₁₃×#459	C₂²	semidirect
87. C₁₃×#452	C₂²	semidirect
88. C₁₃×#450	C₂²	semidirect
91. C₁₃×#449	C₂²	semidirect
94. C₁₃×#447	C₂²	semidirect
95. C₁₃×#442	C₂²	semidirect
96. C₁₃×#442	C₂²	semidirect
97. C₁₃×#440	C₂²	semidirect
98. C₁₃×#440	C₂²	semidirect
99. C₄×C₁₃×Q₁₆	C₂²	semidirect
100. C₄×C₁₃×SD₁₆	C₂²	semidirect
101. C₄×C₁₃×D₈	C₂²	semidirect
102. C₄×C₁₃×D₈	C₂²	semidirect
103. C₄×C₁₃×D₈	C₂²	semidirect
104. C₄×C₁₃×D₈	C₂²	semidirect
105. C₁₃×#433	C₂²	semidirect
106. C₁₃×#433	C₂²	semidirect
107. C₁₃×#433	C₂²	semidirect
108. C₁₃×#433	C₂²	semidirect
109. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
110. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
113. C₂×C₁₃×#97	C₂²	semidirect
114. C₂×C₄×C₈×C₁₃	C₂²	semidirect
264. #61000	C₁₃	direct (N × H)
381. #3494	C₂×C₁₃	semidirect
382. #3250	C₂×C₁₃	semidirect
383. #3247	C₂×C₁₃	semidirect
384. #3245	C₂×C₁₃	semidirect
385. #3243	C₂×C₁₃	semidirect
386. #3241	C₂×C₁₃	semidirect
387. #3224	C₂×C₁₃	semidirect
388. #3220	C₂×C₁₃	semidirect
389. #3191	C₂×C₁₃	semidirect
390. #3188	C₂×C₁₃	semidirect
391. #3186	C₂×C₁₃	semidirect
392. #3180	C₂×C₁₃	semidirect
393. #3169	C₂×C₁₃	semidirect
394. #3168	C₂×C₁₃	semidirect
395. #3124	C₂×C₁₃	semidirect
396. #3122	C₂×C₁₃	semidirect
397. #3119	C₂×C₁₃	semidirect
398. #3118	C₂×C₁₃	semidirect
399. C₂×#433	C₂×C₁₃	semidirect
479. #544	C₂²×C₁₃	semidirect
484. #535	C₂²×C₁₃	semidirect
485. #532	C₂²×C₁₃	semidirect
486. #532	C₂²×C₁₃	semidirect
487. #529	C₂²×C₁₃	semidirect
488. #529	C₂²×C₁₃	semidirect
491. #520	C₂²×C₁₃	semidirect
492. #518	C₂²×C₁₃	semidirect
494. #501	C₂²×C₁₃	semidirect
495. #500	C₂²×C₁₃	semidirect
496. #499	C₂²×C₁₃	semidirect
497. #496	C₂²×C₁₃	semidirect
498. #495	C₂²×C₁₃	semidirect
499. #493	C₂²×C₁₃	semidirect
500. #490	C₂²×C₁₃	semidirect
501. #489	C₂²×C₁₃	semidirect
502. #488	C₂²×C₁₃	semidirect
503. #486	C₂²×C₁₃	semidirect
504. #485	C₂²×C₁₃	semidirect
505. #484	C₂²×C₁₃	semidirect
508. #482	C₂²×C₁₃	semidirect
509. #481	C₂²×C₁₃	semidirect
512. #479	C₂²×C₁₃	semidirect
513. #478	C₂²×C₁₃	semidirect
514. #478	C₂²×C₁₃	semidirect
515. #478	C₂²×C₁₃	semidirect
516. #477	C₂²×C₁₃	semidirect
517. #476	C₂²×C₁₃	semidirect
518. #474	C₂²×C₁₃	semidirect
519. #474	C₂²×C₁₃	semidirect
520. #467	C₂²×C₁₃	semidirect
524. #466	C₂²×C₁₃	semidirect
525. #466	C₂²×C₁₃	semidirect
526. #466	C₂²×C₁₃	semidirect
527. #465	C₂²×C₁₃	semidirect
528. #465	C₂²×C₁₃	semidirect
529. #465	C₂²×C₁₃	semidirect
530. #464	C₂²×C₁₃	semidirect
531. #463	C₂²×C₁₃	semidirect
532. #463	C₂²×C₁₃	semidirect
533. #463	C₂²×C₁₃	semidirect
534. #460	C₂²×C₁₃	semidirect
535. #459	C₂²×C₁₃	semidirect
536. #459	C₂²×C₁₃	semidirect
537. #459	C₂²×C₁₃	semidirect
538. #452	C₂²×C₁₃	semidirect
539. #450	C₂²×C₁₃	semidirect
542. #449	C₂²×C₁₃	semidirect
545. #447	C₂²×C₁₃	semidirect
546. #442	C₂²×C₁₃	semidirect
547. #442	C₂²×C₁₃	semidirect
548. #440	C₂²×C₁₃	semidirect
549. #440	C₂²×C₁₃	semidirect
550. C₄×Q₁₆	C₂²×C₁₃	semidirect
551. C₄×SD₁₆	C₂²×C₁₃	semidirect
552. C₄×D₈	C₂²×C₁₃	semidirect
553. C₄×D₈	C₂²×C₁₃	semidirect
554. C₄×D₈	C₂²×C₁₃	semidirect
555. C₄×D₈	C₂²×C₁₃	semidirect
556. #433	C₂²×C₁₃	semidirect
557. #433	C₂²×C₁₃	semidirect
558. #433	C₂²×C₁₃	semidirect
559. #433	C₂²×C₁₃	semidirect
560. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
561. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
564. C₂×#97	C₂²×C₁₃	semidirect
565. C₂×C₄×C₈	C₂²×C₁₃	semidirect
872. C₁₃	#61000	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×#3494	2
C₁₃×#3250	2
C₁₃×#3247	2
C₁₃×#3245	2
C₁₃×#3243	2
C₁₃×#3241	2
C₁₃×#3224	2
C₁₃×#3220	2
C₁₃×#3191	2
C₁₃×#3188	2
C₁₃×#3186	2
C₁₃×#3180	2
C₁₃×#3169	2
C₁₃×#3168	2
C₁₃×#3124	2
C₁₃×#3122	2
C₁₃×#3119	2
C₁₃×#3118	2
C₂×C₁₃×#433	2
#61000	13

Subgroups — C13×#61000 #15747339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61000 #15747339