Subgroups — C₁₃×#61872 #15748211

Order 3328.

1722 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3389	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3384	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3384	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3373	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3370	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3370	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3366	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3244	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3241	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3122	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3118	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2987	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#562	—	2	2	no	—
21	C₁₃×#559	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#559	C₂²	1	2	yes	complemented
23	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#554	—	2	1	no	—
25	C₁₃×#554	—	2	2	no	—
26	C₁₃×#554	C₂²	1	2	yes	—
27	C₁₃×#554	C₂²	1	2	yes	—
28	C₁₃×#554	C₂²	1	2	yes	—
29	C₁₃×#554	C₂²	1	2	yes	complemented
30	C₁₃×#550	C₂²	1	1	yes	characteristic, complemented
31	D₄×Q₈×C₁₃	—	2	1	no	—
32	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
33	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#548	—	2	1	no	—
35	C₁₃×#547	—	2	1	no	—
36	C₁₃×#544	C₂²	1	2	yes	—
37	C₁₃×#543	—	2	1	no	—
38	C₁₃×#543	—	2	1	no	—
39	C₁₃×#542	—	2	1	no	—
40	C₁₃×#542	C₂²	1	2	yes	—
41	C₁₃×#540	C₂²	1	2	yes	—
42	C₁₃×#539	—	2	2	no	—
43	C₁₃×#536	—	2	1	no	—
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#533	C₂²	1	1	yes	characteristic
46	C₁₃×#532	C₂²	1	1	yes	characteristic
47	C₁₃×#529	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
49	C₁₃×#518	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#501	C₂²	1	2	yes	complemented
53	C₁₃×#501	C₂²	1	2	yes	complemented
54	C₁₃×#501	C₂²	1	2	yes	complemented
55	C₁₃×#501	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#499	C₂²	1	2	yes	complemented
57	C₁₃×#498	C₂²	1	2	yes	complemented
58	C₁₃×#490	C₂²	1	2	yes	complemented
59	C₁₃×#490	C₂²	1	2	yes	complemented
60	C₁₃×#489	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#489	C₂²	1	2	yes	complemented
62	C₁₃×#489	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#488	C₂²	1	2	yes	complemented
64	C₁₃×#486	C₂²	1	2	yes	complemented
65	C₁₃×#485	C₂²	1	2	yes	—
66	C₁₃×#483	C₂²	1	1	yes	characteristic
67	C₁₃×#482	C₂²	1	2	yes	—
68	C₁₃×#482	C₂²	1	2	yes	—
69	C₁₃×#482	C₂²	1	2	yes	—
70	C₁₃×#481	C₂²	1	2	yes	—
71	C₁₃×#480	C₂²	1	1	yes	characteristic
72	C₁₃×#479	C₂²	1	2	yes	complemented
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	—
75	C₁₃×#478	C₂²	1	2	yes	—
76	C₁₃×#478	C₂²	1	2	yes	—
77	C₁₃×#478	C₂²	1	2	yes	complemented
78	C₁₃×#478	C₂²	1	2	yes	complemented
79	C₁₃×#478	C₂²	1	2	yes	complemented
80	C₁₃×#478	C₂²	1	2	yes	complemented
81	C₁₃×#476	C₂²	1	2	yes	—
82	C₁₃×#476	C₂²	1	2	yes	—
83	C₁₃×#476	C₂²	1	2	yes	complemented
84	C₁₃×#476	C₂²	1	2	yes	complemented
85	C₁₃×#476	C₂²	1	2	yes	complemented
86	C₁₃×#475	C₂²	1	2	yes	complemented
87	C₁₃×#474	C₂²	1	2	yes	—
88	C₁₃×#474	C₂²	1	2	yes	complemented
89	C₁₃×#474	C₂²	1	2	yes	complemented
90	C₁₃×#463	C₂²	1	2	yes	—
91	C₁₃×#463	C₂²	1	2	yes	—
92	C₁₃×#463	C₂²	1	2	yes	—
93	C₁₃×#459	C₂²	1	2	yes	—
94	C₁₃×#459	C₂²	1	2	yes	—
95	C₁₃×#459	C₂²	1	2	yes	—
96	C₁₃×#450	C₂²	1	1	yes	characteristic
97	C₁₃×#447	C₂²	1	2	yes	—
98	C₁₃×#447	C₂²	1	1	yes	characteristic
99	C₁₃×#446	C₂²	1	2	yes	complemented
100	C₁₃×#446	C₂²	1	2	yes	complemented
101	C₁₃×#446	C₂²	1	2	yes	complemented
102	C₁₃×#446	C₂²	1	2	yes	complemented
103	C₁₃×#442	C₂²	1	2	yes	—
104	C₁₃×#442	C₂²	1	2	yes	—
105	C₁₃×#442	C₂²	1	2	yes	—
106	C₁₃×#442	C₂²	1	2	yes	—
107	C₁₃×#442	C₂²	1	2	yes	—
108	C₁₃×#442	C₂²	1	2	yes	—
109	C₁₃×#440	C₂²	1	2	yes	—
110	C₁₃×#440	C₂²	1	2	yes	—
111	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
112	C₄×C₁₃×D₈	C₂²	1	2	yes	—
113	C₄×C₁₃×D₈	C₂²	1	2	yes	—
114	C₄×C₁₃×D₈	C₂²	1	2	yes	—
115	C₁₃×#433	C₂²	1	2	yes	—
116	C₁₃×#433	C₂²	1	2	yes	—
117	C₁₃×#432	C₂²	1	1	yes	characteristic
118	C₁₃×#432	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	—	2	1	no	—
120	C₂×C₁₃×#41	—	2	1	no	—
121	C₂²×Q₈×C₁₃	—	2	2	no	—
122	C₂²×Q₈×C₁₃	—	2	1	no	—
123	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₁₃	—	2	1	no	—
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×D₈	C₂³	1	2	yes	—
127	C₂×C₁₃×D₈	C₂³	1	2	yes	—
128	C₂×C₁₃×D₈	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	—	2	1	no	—
130	C₁₃×C₄⋊Q₈	—	2	2	no	—
131	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
132	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
133	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
139	C₁₃×#127	C₂³	1	2	yes	—
140	C₁₃×#127	C₂³	1	1	yes	characteristic
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	1	no	—
143	C₁₃×#125	—	2	2	no	—
144	C₁₃×#125	—	2	2	no	—
145	C₁₃×#125	D₄	1	2	yes	—
146	C₁₃×#125	C₂³	1	2	yes	—
147	C₁₃×#125	C₂³	1	1	yes	characteristic
148	C₁₃×#125	C₂³	1	2	yes	—
149	C₁₃×#125	C₂³	1	2	yes	—
150	C₁₃×#125	C₂³	1	2	yes	—
151	C₁₃×#124	—	2	1	no	—
152	C₁₃×#124	—	2	2	no	—
153	C₁₃×#124	—	2	2	no	—
154	C₁₃×#124	—	2	1	no	—
155	C₁₃×#124	C₂³	1	2	yes	—
156	C₁₃×#124	C₂³	1	1	yes	characteristic
157	C₁₃×#123	—	2	1	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×#123	—	2	2	no	—
163	C₁₃×#123	—	2	2	no	—
164	C₁₃×C₂²⋊Q₈	—	2	2	no	—
165	C₁₃×C₂²⋊Q₈	—	2	2	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	—	2	1	no	—
169	C₁₃×C₂²⋊Q₈	—	2	1	no	—
170	C₁₃×C₂²⋊Q₈	—	2	2	no	—
171	C₁₃×C₂²⋊Q₈	—	2	2	no	—
172	C₁₃×C₂²⋊Q₈	—	2	2	no	—
173	C₁₃×C₂²⋊Q₈	—	2	2	no	—
174	C₁₃×C₂²⋊Q₈	—	2	2	no	—
175	C₁₃×C₂²⋊Q₈	—	2	2	no	—
176	C₁₃×C₂²⋊Q₈	—	2	2	no	—
177	C₁₃×C₂²⋊Q₈	—	2	1	no	—
178	C₁₃×C₂²⋊Q₈	—	2	2	no	—
179	C₁₃×C₂²⋊Q₈	—	2	2	no	—
180	C₁₃×C₂²⋊Q₈	—	2	2	no	—
181	C₁₃×C₂²⋊Q₈	—	2	2	no	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
187	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
189	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
190	C₁₃×#121	—	2	1	no	—
191	C₁₃×#121	—	2	2	no	—
192	C₁₃×#121	—	2	1	no	—
193	C₁₃×#121	—	2	2	no	—
194	C₁₃×#121	—	2	2	no	—
195	C₁₃×#121	C₂³	1	1	yes	characteristic
196	C₁₃×#121	C₂³	1	2	yes	—
197	C₄×Q₈×C₁₃	—	2	1	no	—
198	C₄×Q₈×C₁₃	—	2	1	no	—
199	C₄×Q₈×C₁₃	—	2	1	no	—
200	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
201	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
203	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
204	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
205	C₄×D₄×C₁₃	—	2	1	no	—
206	C₄×D₄×C₁₃	—	2	2	no	—
207	C₄×D₄×C₁₃	—	2	2	no	—
208	C₄×D₄×C₁₃	—	2	2	no	—
209	C₄×D₄×C₁₃	—	2	1	no	—
210	C₄×D₄×C₁₃	—	2	1	no	—
211	C₄×D₄×C₁₃	—	2	1	no	—
212	C₄×D₄×C₁₃	—	2	1	no	—
213	C₄×D₄×C₁₃	C₂³	1	2	yes	—
214	C₄×D₄×C₁₃	C₂³	1	2	yes	—
215	C₄×D₄×C₁₃	C₂³	1	2	yes	—
216	C₄×D₄×C₁₃	C₂³	1	2	yes	—
217	C₄×D₄×C₁₃	C₂³	1	2	yes	—
218	C₄×D₄×C₁₃	C₂³	1	2	yes	—
219	C₄×D₄×C₁₃	C₂³	1	2	yes	—
220	C₄×D₄×C₁₃	C₂³	1	2	yes	—
221	C₄×D₄×C₁₃	C₂³	1	2	yes	—
222	C₄×D₄×C₁₃	C₂³	1	2	yes	—
223	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
224	C₁₃×#117	—	2	1	no	—
225	C₁₃×#117	C₂³	1	2	yes	—
226	C₁₃×#117	C₂³	1	2	yes	—
227	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
231	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
232	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
233	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
236	C₁₃×#107	C₂³	1	2	yes	—
237	C₁₃×#107	C₂³	1	2	yes	—
238	C₁₃×#107	C₂³	1	2	yes	—
239	C₁₃×#107	C₂³	1	2	yes	—
240	C₁₃×#107	C₂³	1	2	yes	—
241	C₁₃×#106	C₂³	1	2	yes	—
242	C₁₃×#106	C₂³	1	2	yes	—
243	C₁₃×#106	C₂³	1	2	yes	—
244	C₁₃×#106	C₂³	1	2	yes	—
245	C₁₃×#106	C₂³	1	2	yes	—
246	C₁₃×#106	C₂³	1	2	yes	—
247	C₁₃×#106	C₂³	1	2	yes	—
248	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
249	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
251	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
252	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₃×#103	C₂³	1	2	yes	—
255	C₁₃×#103	C₂³	1	2	yes	—
256	C₁₃×#103	C₂³	1	2	yes	—
257	C₁₃×#102	C₂³	1	2	yes	—
258	C₁₃×#102	C₂³	1	2	yes	—
259	C₁₃×#102	C₂³	1	2	yes	—
260	C₁₃×#102	C₂³	1	2	yes	—
261	C₁₃×#102	C₂³	1	2	yes	—
262	C₁₃×#102	C₂³	1	2	yes	—
263	C₁₃×#102	C₂³	1	2	yes	—
264	C₁₃×#102	C₂³	1	2	yes	—
265	C₁₃×#102	C₂³	1	2	yes	—
266	C₁₃×#102	C₂³	1	2	yes	—
267	C₁₃×#102	C₂³	1	2	yes	—
268	C₁₃×#102	C₂³	1	2	yes	—
269	C₁₃×#102	C₂³	1	2	yes	—
270	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
271	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
272	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₁₃×#97	C₂³	1	2	yes	—
274	C₁₃×#97	C₂³	1	1	yes	characteristic
275	C₁₃×#97	C₂³	1	1	yes	characteristic
276	C₁₃×#97	C₂³	1	2	yes	—
277	C₁₃×#97	C₂³	1	2	yes	—
278	C₄×C₈×C₁₃	C₂³	1	2	yes	—
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#61872	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂⁴×C₁₃	—	2	1	no	—
282	C₁₃×#41	—	8	2	no	—
283	C₁₃×#41	—	8	2	no	—
284	C₂×Q₈×C₁₃	—	2	1	no	—
285	C₂×Q₈×C₁₃	—	2	1	no	—
286	C₂×Q₈×C₁₃	—	2	1	no	—
287	C₂×Q₈×C₁₃	—	2	2	no	—
288	C₂×Q₈×C₁₃	—	2	2	no	—
289	C₂×Q₈×C₁₃	—	2	2	no	—
290	C₂×Q₈×C₁₃	—	8	4	no	—
291	C₂×Q₈×C₁₃	—	8	2	no	—
292	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
294	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
295	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂×D₄×C₁₃	—	2	4	no	—
297	C₂×D₄×C₁₃	—	2	1	no	—
298	C₂×D₄×C₁₃	—	2	2	no	—
299	C₂×D₄×C₁₃	—	2	1	no	—
300	C₂×D₄×C₁₃	—	2	1	no	—
301	C₂×D₄×C₁₃	—	2	1	no	—
302	C₂×D₄×C₁₃	—	2	2	no	—
303	C₂×D₄×C₁₃	—	2	2	no	—
304	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
305	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₁₃	—	2	1	no	—
308	C₂²×C₄×C₁₃	—	2	2	no	—
309	C₂²×C₄×C₁₃	—	2	1	no	—
310	C₂²×C₄×C₁₃	—	2	2	no	—
311	C₂²×C₄×C₁₃	—	2	2	no	—
312	C₂²×C₄×C₁₃	—	2	2	no	—
313	C₂²×C₄×C₁₃	—	2	2	no	—
314	C₂²×C₄×C₁₃	—	2	2	no	—
315	C₂²×C₄×C₁₃	—	2	2	no	—
316	C₂²×C₄×C₁₃	—	2	2	no	—
317	C₂²×C₄×C₁₃	—	2	2	no	—
318	C₂²×C₄×C₁₃	—	2	2	no	—
319	C₂²×C₄×C₁₃	—	8	2	no	—
320	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
323	C₁₃×SD₁₆	—	2	4	no	—
324	C₁₃×D₈	—	2	4	no	—
325	C₁₃×D₈	—	2	4	no	—
326	C₁₃×D₈	—	2	4	no	—
327	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
328	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
329	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
330	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
331	C₁₃×C₄⋊C₄	—	2	1	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	1	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	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	1	no	—
343	C₁₃×C₄⋊C₄	—	2	1	no	—
344	C₁₃×C₄⋊C₄	—	2	1	no	—
345	C₁₃×C₄⋊C₄	—	2	1	no	—
346	C₁₃×C₄⋊C₄	—	2	2	no	—
347	C₁₃×C₄⋊C₄	—	2	2	no	—
348	C₁₃×C₄⋊C₄	—	2	1	no	—
349	C₁₃×C₄⋊C₄	—	2	2	no	—
350	C₁₃×C₄⋊C₄	—	2	1	no	—
351	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
352	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
353	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
354	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
355	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
356	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
357	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
358	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
359	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
360	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
362	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
364	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
366	C₁₃×C₂²⋊C₄	—	2	2	no	—
367	C₁₃×C₂²⋊C₄	—	2	1	no	—
368	C₁₃×C₂²⋊C₄	—	2	2	no	—
369	C₁₃×C₂²⋊C₄	—	2	2	no	—
370	C₁₃×C₂²⋊C₄	—	2	2	no	—
371	C₁₃×C₂²⋊C₄	—	2	2	no	—
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	1	no	—
375	C₁₃×C₂²⋊C₄	—	2	1	no	—
376	C₁₃×C₂²⋊C₄	—	2	1	no	—
377	C₁₃×C₂²⋊C₄	—	2	2	no	—
378	C₁₃×C₂²⋊C₄	—	2	2	no	—
379	C₁₃×C₂²⋊C₄	—	2	2	no	—
380	C₁₃×C₂²⋊C₄	—	2	1	no	—
381	C₁₃×C₂²⋊C₄	—	2	2	no	—
382	C₁₃×C₂²⋊C₄	—	2	2	no	—
383	C₁₃×C₂²⋊C₄	—	2	2	no	—
384	C₁₃×C₂²⋊C₄	—	2	2	no	—
385	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
386	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
387	C₄²×C₁₃	—	2	1	no	—
388	C₄²×C₁₃	—	2	2	no	—
389	C₄²×C₁₃	—	2	2	no	—
390	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
391	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
392	C₄²×C₁₃	C₂⁴	1	2	yes	—
393	C₄²×C₁₃	C₂⁴	1	2	yes	—
394	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
395	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
396	#3554	C₂×C₁₃	1	1	yes	characteristic, complemented
397	#3501	C₂×C₁₃	1	1	yes	characteristic, complemented
398	#3389	C₂×C₁₃	1	2	yes	complemented
399	#3388	C₂×C₁₃	1	2	yes	complemented
400	#3384	C₂×C₁₃	1	2	yes	complemented
401	#3384	C₂×C₁₃	1	2	yes	complemented
402	#3373	C₂×C₁₃	1	2	yes	complemented
403	#3370	C₂×C₁₃	1	2	yes	complemented
404	#3370	C₂×C₁₃	1	2	yes	complemented
405	#3366	C₂×C₁₃	1	2	yes	complemented
406	#3244	C₂×C₁₃	1	2	yes	complemented
407	#3241	C₂×C₁₃	1	2	yes	complemented
408	#3240	C₂×C₁₃	1	1	yes	characteristic, complemented
409	#3235	C₂×C₁₃	1	1	yes	characteristic, complemented
410	#3122	C₂×C₁₃	1	2	yes	complemented
411	#3118	C₂×C₁₃	1	2	yes	complemented
412	#3114	C₂×C₁₃	1	1	yes	characteristic, complemented
413	#3109	C₂×C₁₃	1	1	yes	characteristic, complemented
414	#2987	C₂×C₁₃	1	1	yes	characteristic, complemented
415	C₂³×C₁₃	—	2	4	no	—
416	C₂³×C₁₃	—	2	2	no	—
417	C₂³×C₁₃	—	2	1	no	—
418	C₂³×C₁₃	—	2	2	no	—
419	C₂³×C₁₃	—	8	1	no	—
420	C₂³×C₁₃	—	8	1	no	—
421	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
422	Q₈×C₁₃	—	2	2	no	—
423	Q₈×C₁₃	—	4	2	no	—
424	Q₈×C₁₃	—	4	1	no	—
425	Q₈×C₁₃	—	4	1	no	—
426	Q₈×C₁₃	—	4	2	no	—
427	Q₈×C₁₃	—	4	2	no	—
428	Q₈×C₁₃	—	8	1	no	—
429	Q₈×C₁₃	—	8	2	no	—
430	Q₈×C₁₃	—	8	2	no	—
431	Q₈×C₁₃	—	8	2	no	—
432	D₄×C₁₃	—	2	4	no	—
433	D₄×C₁₃	—	2	2	no	—
434	D₄×C₁₃	—	2	2	no	—
435	D₄×C₁₃	—	2	2	no	—
436	D₄×C₁₃	—	2	2	no	—
437	D₄×C₁₃	—	4	2	no	—
438	D₄×C₁₃	—	8	1	no	—
439	D₄×C₁₃	—	8	2	no	—
440	D₄×C₁₃	—	8	2	no	—
441	D₄×C₁₃	—	8	1	no	—
442	D₄×C₁₃	—	8	2	no	—
443	D₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	1	no	—
446	C₂×C₄×C₁₃	—	2	1	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	1	no	—
451	C₂×C₄×C₁₃	—	2	2	no	—
452	C₂×C₄×C₁₃	—	4	1	no	—
453	C₂×C₄×C₁₃	—	4	1	no	—
454	C₂×C₄×C₁₃	—	4	4	no	—
455	C₂×C₄×C₁₃	—	4	2	no	—
456	C₂×C₄×C₁₃	—	8	2	no	—
457	C₂×C₄×C₁₃	—	8	2	no	—
458	C₂×C₄×C₁₃	—	8	2	no	—
459	C₂×C₄×C₁₃	—	8	2	no	—
460	C₂×C₄×C₁₃	—	8	2	no	—
461	C₂×C₄×C₁₃	—	8	2	no	—
462	C₂×C₄×C₁₃	—	8	2	no	—
463	C₂×C₄×C₁₃	—	8	2	no	—
464	C₂×C₄×C₁₃	—	8	2	no	—
465	C₂×C₄×C₁₃	—	8	1	no	—
466	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
476	C₈×C₁₃	—	2	2	no	—
477	C₈×C₁₃	—	2	2	no	—
478	C₈×C₁₃	—	2	2	no	—
479	C₈×C₁₃	—	2	2	no	—
480	#562	—	2	2	no	—
481	#559	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	#559	C₂²×C₁₃	1	2	yes	complemented
483	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	#554	—	2	1	no	—
485	#554	—	2	2	no	—
486	#554	C₂²×C₁₃	1	2	yes	—
487	#554	C₂²×C₁₃	1	2	yes	—
488	#554	C₂²×C₁₃	1	2	yes	—
489	#554	C₂²×C₁₃	1	2	yes	complemented
490	#550	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	D₄×Q₈	—	2	1	no	—
492	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
493	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	#548	—	2	1	no	—
495	#547	—	2	1	no	—
496	#544	C₂²×C₁₃	1	2	yes	—
497	#543	—	2	1	no	—
498	#543	—	2	1	no	—
499	#542	—	2	1	no	—
500	#542	C₂²×C₁₃	1	2	yes	—
501	#540	C₂²×C₁₃	1	2	yes	—
502	#539	—	2	2	no	—
503	#536	—	2	1	no	—
504	#533	C₂²×C₁₃	1	1	yes	characteristic
505	#533	C₂²×C₁₃	1	1	yes	characteristic
506	#532	C₂²×C₁₃	1	1	yes	characteristic
507	#529	C₂²×C₁₃	1	1	yes	characteristic
508	C₂×C₂²⋊Q₈	—	2	2	no	—
509	#518	C₂²×C₁₃	1	2	yes	—
510	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
511	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
512	#501	C₂²×C₁₃	1	2	yes	complemented
513	#501	C₂²×C₁₃	1	2	yes	complemented
514	#501	C₂²×C₁₃	1	2	yes	complemented
515	#501	C₂²×C₁₃	1	1	yes	characteristic, complemented
516	#499	C₂²×C₁₃	1	2	yes	complemented
517	#498	C₂²×C₁₃	1	2	yes	complemented
518	#490	C₂²×C₁₃	1	2	yes	complemented
519	#490	C₂²×C₁₃	1	2	yes	complemented
520	#489	C₂²×C₁₃	1	1	yes	characteristic, complemented
521	#489	C₂²×C₁₃	1	2	yes	complemented
522	#489	C₂²×C₁₃	1	1	yes	characteristic, complemented
523	#488	C₂²×C₁₃	1	2	yes	complemented
524	#486	C₂²×C₁₃	1	2	yes	complemented
525	#485	C₂²×C₁₃	1	2	yes	—
526	#483	C₂²×C₁₃	1	1	yes	characteristic
527	#482	C₂²×C₁₃	1	2	yes	—
528	#482	C₂²×C₁₃	1	2	yes	—
529	#482	C₂²×C₁₃	1	2	yes	—
530	#481	C₂²×C₁₃	1	2	yes	—
531	#480	C₂²×C₁₃	1	1	yes	characteristic
532	#479	C₂²×C₁₃	1	2	yes	complemented
533	#479	C₂²×C₁₃	1	2	yes	complemented
534	#478	C₂²×C₁₃	1	2	yes	—
535	#478	C₂²×C₁₃	1	2	yes	—
536	#478	C₂²×C₁₃	1	2	yes	—
537	#478	C₂²×C₁₃	1	2	yes	complemented
538	#478	C₂²×C₁₃	1	2	yes	complemented
539	#478	C₂²×C₁₃	1	2	yes	complemented
540	#478	C₂²×C₁₃	1	2	yes	complemented
541	#476	C₂²×C₁₃	1	2	yes	—
542	#476	C₂²×C₁₃	1	2	yes	—
543	#476	C₂²×C₁₃	1	2	yes	complemented
544	#476	C₂²×C₁₃	1	2	yes	complemented
545	#476	C₂²×C₁₃	1	2	yes	complemented
546	#475	C₂²×C₁₃	1	2	yes	complemented
547	#474	C₂²×C₁₃	1	2	yes	—
548	#474	C₂²×C₁₃	1	2	yes	complemented
549	#474	C₂²×C₁₃	1	2	yes	complemented
550	#463	C₂²×C₁₃	1	2	yes	—
551	#463	C₂²×C₁₃	1	2	yes	—
552	#463	C₂²×C₁₃	1	2	yes	—
553	#459	C₂²×C₁₃	1	2	yes	—
554	#459	C₂²×C₁₃	1	2	yes	—
555	#459	C₂²×C₁₃	1	2	yes	—
556	#450	C₂²×C₁₃	1	1	yes	characteristic
557	#447	C₂²×C₁₃	1	2	yes	—
558	#447	C₂²×C₁₃	1	1	yes	characteristic
559	#446	C₂²×C₁₃	1	2	yes	complemented
560	#446	C₂²×C₁₃	1	2	yes	complemented
561	#446	C₂²×C₁₃	1	2	yes	complemented
562	#446	C₂²×C₁₃	1	2	yes	complemented
563	#442	C₂²×C₁₃	1	2	yes	—
564	#442	C₂²×C₁₃	1	2	yes	—
565	#442	C₂²×C₁₃	1	2	yes	—
566	#442	C₂²×C₁₃	1	2	yes	—
567	#442	C₂²×C₁₃	1	2	yes	—
568	#442	C₂²×C₁₃	1	2	yes	—
569	#440	C₂²×C₁₃	1	2	yes	—
570	#440	C₂²×C₁₃	1	2	yes	—
571	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
572	C₄×D₈	C₂²×C₁₃	1	2	yes	—
573	C₄×D₈	C₂²×C₁₃	1	2	yes	—
574	C₄×D₈	C₂²×C₁₃	1	2	yes	—
575	#433	C₂²×C₁₃	1	2	yes	—
576	#433	C₂²×C₁₃	1	2	yes	—
577	#432	C₂²×C₁₃	1	1	yes	characteristic
578	#432	C₂²×C₁₃	1	1	yes	characteristic
579	C₂²×C₁₃	—	2	1	no	—
580	C₂²×C₁₃	—	2	1	no	—
581	C₂²×C₁₃	—	2	1	no	—
582	C₂²×C₁₃	—	2	4	no	—
583	C₂²×C₁₃	—	4	2	no	—
584	C₂²×C₁₃	—	4	2	no	—
585	C₂²×C₁₃	—	4	1	no	—
586	C₂²×C₁₃	—	4	2	no	—
587	C₂²×C₁₃	—	4	2	no	—
588	C₂²×C₁₃	—	4	1	no	—
589	C₂²×C₁₃	—	4	1	no	—
590	C₂²×C₁₃	—	4	2	no	—
591	C₂²×C₁₃	—	8	4	no	—
592	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
593	C₄×C₁₃	—	2	1	no	—
594	C₄×C₁₃	—	2	1	no	—
595	C₄×C₁₃	—	2	1	no	—
596	C₄×C₁₃	—	2	1	no	—
597	C₄×C₁₃	—	2	2	no	—
598	C₄×C₁₃	—	2	2	no	—
599	C₄×C₁₃	—	2	2	no	—
600	C₄×C₁₃	—	2	2	no	—
601	C₄×C₁₃	—	2	1	no	—
602	C₄×C₁₃	—	4	1	no	—
603	C₄×C₁₃	—	4	2	no	—
604	C₄×C₁₃	—	4	1	no	—
605	C₄×C₁₃	—	4	2	no	—
606	C₄×C₁₃	—	4	2	no	—
607	C₄×C₁₃	—	4	2	no	—
608	C₄×C₁₃	—	4	1	no	—
609	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
610	C₂×#41	—	2	1	no	—
611	C₂×#41	—	2	1	no	—
612	C₂²×Q₈	—	2	2	no	—
613	C₂²×Q₈	—	2	1	no	—
614	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₂³×C₄	—	2	1	no	—
616	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
617	C₂×D₈	C₂³×C₁₃	1	2	yes	—
618	C₂×D₈	C₂³×C₁₃	1	2	yes	—
619	C₂×D₈	C₂³×C₁₃	1	2	yes	—
620	C₄⋊Q₈	—	2	1	no	—
621	C₄⋊Q₈	—	2	2	no	—
622	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
623	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
625	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
626	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
627	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
628	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
629	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
630	#127	C₂³×C₁₃	1	1	yes	characteristic
631	#127	C₂³×C₁₃	1	2	yes	—
632	#126	—	2	2	no	—
633	#126	—	2	1	no	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	D₄×C₁₃	1	2	yes	—
637	#125	C₂³×C₁₃	1	1	yes	characteristic
638	#125	C₂³×C₁₃	1	2	yes	—
639	#125	C₂³×C₁₃	1	2	yes	—
640	#125	C₂³×C₁₃	1	2	yes	—
641	#125	C₂³×C₁₃	1	2	yes	—
642	#124	—	2	1	no	—
643	#124	—	2	2	no	—
644	#124	—	2	2	no	—
645	#124	—	2	1	no	—
646	#124	C₂³×C₁₃	1	1	yes	characteristic
647	#124	C₂³×C₁₃	1	2	yes	—
648	#123	—	2	1	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	#123	—	2	2	no	—
654	#123	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	1	no	—
660	C₂²⋊Q₈	—	2	1	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	—	2	2	no	—
665	C₂²⋊Q₈	—	2	2	no	—
666	C₂²⋊Q₈	—	2	2	no	—
667	C₂²⋊Q₈	—	2	2	no	—
668	C₂²⋊Q₈	—	2	1	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	2	no	—
672	C₂²⋊Q₈	—	2	2	no	—
673	C₂²⋊Q₈	—	2	2	no	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
678	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
679	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
680	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
681	#121	—	2	1	no	—
682	#121	—	2	2	no	—
683	#121	—	2	1	no	—
684	#121	—	2	2	no	—
685	#121	—	2	2	no	—
686	#121	C₂³×C₁₃	1	1	yes	characteristic
687	#121	C₂³×C₁₃	1	2	yes	—
688	C₄×Q₈	—	2	1	no	—
689	C₄×Q₈	—	2	1	no	—
690	C₄×Q₈	—	2	1	no	—
691	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
692	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
693	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
694	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
695	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
696	C₄×D₄	—	2	1	no	—
697	C₄×D₄	—	2	2	no	—
698	C₄×D₄	—	2	2	no	—
699	C₄×D₄	—	2	2	no	—
700	C₄×D₄	—	2	1	no	—
701	C₄×D₄	—	2	1	no	—
702	C₄×D₄	—	2	1	no	—
703	C₄×D₄	—	2	1	no	—
704	C₄×D₄	C₂³×C₁₃	1	2	yes	—
705	C₄×D₄	C₂³×C₁₃	1	2	yes	—
706	C₄×D₄	C₂³×C₁₃	1	2	yes	—
707	C₄×D₄	C₂³×C₁₃	1	2	yes	—
708	C₄×D₄	C₂³×C₁₃	1	2	yes	—
709	C₄×D₄	C₂³×C₁₃	1	2	yes	—
710	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
711	C₄×D₄	C₂³×C₁₃	1	2	yes	—
712	C₄×D₄	C₂³×C₁₃	1	2	yes	—
713	C₄×D₄	C₂³×C₁₃	1	2	yes	—
714	C₄×D₄	C₂³×C₁₃	1	2	yes	—
715	#117	—	2	1	no	—
716	#117	C₂³×C₁₃	1	2	yes	—
717	#117	C₂³×C₁₃	1	2	yes	—
718	C₂×C₄⋊C₄	—	2	2	no	—
719	C₂×C₄⋊C₄	—	2	2	no	—
720	C₂×C₄⋊C₄	—	2	2	no	—
721	C₂×C₄⋊C₄	—	2	2	no	—
722	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	—	2	1	no	—
724	C₂×C₂²⋊C₄	—	2	2	no	—
725	C₂×C₂²⋊C₄	—	2	2	no	—
726	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
727	#107	C₂³×C₁₃	1	2	yes	—
728	#107	C₂³×C₁₃	1	2	yes	—
729	#107	C₂³×C₁₃	1	2	yes	—
730	#107	C₂³×C₁₃	1	2	yes	—
731	#107	C₂³×C₁₃	1	2	yes	—
732	#106	C₂³×C₁₃	1	2	yes	—
733	#106	C₂³×C₁₃	1	2	yes	—
734	#106	C₂³×C₁₃	1	2	yes	—
735	#106	C₂³×C₁₃	1	2	yes	—
736	#106	C₂³×C₁₃	1	2	yes	—
737	#106	C₂³×C₁₃	1	2	yes	—
738	#106	C₂³×C₁₃	1	2	yes	—
739	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
740	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
741	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
742	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
743	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
744	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
745	#103	C₂³×C₁₃	1	2	yes	—
746	#103	C₂³×C₁₃	1	2	yes	—
747	#103	C₂³×C₁₃	1	2	yes	—
748	#102	C₂³×C₁₃	1	2	yes	—
749	#102	C₂³×C₁₃	1	2	yes	—
750	#102	C₂³×C₁₃	1	2	yes	—
751	#102	C₂³×C₁₃	1	2	yes	—
752	#102	C₂³×C₁₃	1	2	yes	—
753	#102	C₂³×C₁₃	1	2	yes	—
754	#102	C₂³×C₁₃	1	2	yes	—
755	#102	C₂³×C₁₃	1	2	yes	—
756	#102	C₂³×C₁₃	1	2	yes	—
757	#102	C₂³×C₁₃	1	2	yes	—
758	#102	C₂³×C₁₃	1	2	yes	—
759	#102	C₂³×C₁₃	1	2	yes	—
760	#102	C₂³×C₁₃	1	2	yes	—
761	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
762	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
763	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
764	#97	C₂³×C₁₃	1	2	yes	—
765	#97	C₂³×C₁₃	1	1	yes	characteristic
766	#97	C₂³×C₁₃	1	1	yes	characteristic
767	#97	C₂³×C₁₃	1	2	yes	—
768	#97	C₂³×C₁₃	1	2	yes	—
769	C₄×C₈	C₂³×C₁₃	1	2	yes	—
770	C₄×C₈	C₂³×C₁₃	1	2	yes	—
771	C₂×C₁₃	—	4	1	no	—
772	C₂×C₁₃	—	4	4	no	—
773	C₂×C₁₃	—	8	1	no	—
774	C₂×C₁₃	—	8	2	no	—
775	C₂×C₁₃	#3486	1	1	yes	characteristic
776	C₂×C₁₃	#3585	1	1	yes	characteristic
777	C₂×C₁₃	#3585	1	1	yes	characteristic
778	C₂⁴	—	2	1	no	—
779	#41	—	8	2	no	—
780	#41	—	8	2	no	—
781	C₂×Q₈	—	2	1	no	—
782	C₂×Q₈	—	2	1	no	—
783	C₂×Q₈	—	2	1	no	—
784	C₂×Q₈	—	2	2	no	—
785	C₂×Q₈	—	2	2	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	8	4	no	—
788	C₂×Q₈	—	8	2	no	—
789	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
790	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
791	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
792	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
793	C₂×D₄	—	2	4	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	1	no	—
797	C₂×D₄	—	2	1	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
802	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
803	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	8	2	no	—
817	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
818	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
820	SD₁₆	—	2	4	no	—
821	D₈	—	2	4	no	—
822	D₈	—	2	4	no	—
823	D₈	—	2	4	no	—
824	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
825	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
826	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
827	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
849	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
850	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
851	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
852	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
853	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
854	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
855	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
856	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
857	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
858	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
859	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
860	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
861	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
862	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	1	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	1	no	—
872	C₂²⋊C₄	—	2	1	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	1	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
883	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
884	C₄²	—	2	1	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
888	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
889	C₄²	C₂⁴×C₁₃	1	2	yes	—
890	C₄²	C₂⁴×C₁₃	1	2	yes	—
891	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
892	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
893	C₁₃	#61872	1	1	yes	characteristic, direct product factor, Sylow
894	C₂³	—	2	4	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	8	1	no	—
899	C₂³	—	8	1	no	—
900	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
901	Q₈	—	2	2	no	—
902	Q₈	—	4	2	no	—
903	Q₈	—	4	1	no	—
904	Q₈	—	4	1	no	—
905	Q₈	—	4	2	no	—
906	Q₈	—	4	2	no	—
907	Q₈	—	8	2	no	—
908	Q₈	—	8	2	no	—
909	Q₈	—	8	2	no	—
910	Q₈	—	8	1	no	—
911	D₄	—	2	4	no	—
912	D₄	—	2	2	no	—
913	D₄	—	2	2	no	—
914	D₄	—	2	2	no	—
915	D₄	—	2	2	no	—
916	D₄	—	4	2	no	—
917	D₄	—	8	1	no	—
918	D₄	—	8	2	no	—
919	D₄	—	8	2	no	—
920	D₄	—	8	1	no	—
921	D₄	—	8	2	no	—
922	D₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	1	no	—
933	C₂×C₄	—	4	4	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	8	2	no	—
936	C₂×C₄	—	8	2	no	—
937	C₂×C₄	—	8	2	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	—	8	2	no	—
940	C₂×C₄	—	8	2	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	—	8	2	no	—
944	C₂×C₄	—	8	1	no	—
945	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
946	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
947	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
948	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
950	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
951	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
952	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
953	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
954	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
955	C₈	—	2	2	no	—
956	C₈	—	2	2	no	—
957	C₈	—	2	2	no	—
958	C₈	—	2	2	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	4	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	2	no	—
965	C₂²	—	4	1	no	—
966	C₂²	—	4	2	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	8	4	no	—
972	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
973	C₄	—	2	1	no	—
974	C₄	—	2	1	no	—
975	C₄	—	2	1	no	—
976	C₄	—	2	1	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	2	1	no	—
982	C₄	—	4	1	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	1	no	—
989	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
990	C₂	—	4	1	no	—
991	C₂	—	4	4	no	—
992	C₂	—	8	1	no	—
993	C₂	—	8	2	no	—
994	C₂	C₁₃×#3486	1	1	yes	characteristic
995	C₂	C₁₃×#3585	1	1	yes	characteristic
996	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 ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3554	C₂	semidirect
2. C₁₃×#3501	C₂	semidirect
3. C₁₃×#3389	C₂	semidirect
4. C₁₃×#3388	C₂	semidirect
5. C₁₃×#3384	C₂	semidirect
6. C₁₃×#3384	C₂	semidirect
7. C₁₃×#3373	C₂	semidirect
8. C₁₃×#3370	C₂	semidirect
9. C₁₃×#3370	C₂	semidirect
10. C₁₃×#3366	C₂	semidirect
11. C₁₃×#3244	C₂	semidirect
12. C₁₃×#3241	C₂	semidirect
13. C₁₃×#3240	C₂	semidirect
14. C₁₃×#3235	C₂	semidirect
15. C₁₃×#3122	C₂	semidirect
16. C₁₃×#3118	C₂	semidirect
17. C₁₃×#3114	C₂	semidirect
18. C₁₃×#3109	C₂	semidirect
19. C₁₃×#2987	C₂	semidirect
21. C₁₃×#559	C₂²	semidirect
22. C₁₃×#559	C₂²	semidirect
23. C₁₃×#557	C₂²	semidirect
29. C₁₃×#554	C₂²	semidirect
30. C₁₃×#550	C₂²	semidirect
33. D₄×Q₈×C₁₃	C₂²	semidirect
51. C₁₃×#501	C₂²	semidirect
52. C₁₃×#501	C₂²	semidirect
53. C₁₃×#501	C₂²	semidirect
54. C₁₃×#501	C₂²	semidirect
55. C₁₃×#501	C₂²	semidirect
56. C₁₃×#499	C₂²	semidirect
57. C₁₃×#498	C₂²	semidirect
58. C₁₃×#490	C₂²	semidirect
59. C₁₃×#490	C₂²	semidirect
60. C₁₃×#489	C₂²	semidirect
61. C₁₃×#489	C₂²	semidirect
62. C₁₃×#489	C₂²	semidirect
63. C₁₃×#488	C₂²	semidirect
64. C₁₃×#486	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
77. C₁₃×#478	C₂²	semidirect
78. C₁₃×#478	C₂²	semidirect
79. C₁₃×#478	C₂²	semidirect
80. C₁₃×#478	C₂²	semidirect
83. C₁₃×#476	C₂²	semidirect
84. C₁₃×#476	C₂²	semidirect
85. C₁₃×#476	C₂²	semidirect
86. C₁₃×#475	C₂²	semidirect
88. C₁₃×#474	C₂²	semidirect
89. C₁₃×#474	C₂²	semidirect
99. C₁₃×#446	C₂²	semidirect
100. C₁₃×#446	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₁₃×#446	C₂²	semidirect
280. #61872	C₁₃	direct (N × H)
396. #3554	C₂×C₁₃	semidirect
397. #3501	C₂×C₁₃	semidirect
398. #3389	C₂×C₁₃	semidirect
399. #3388	C₂×C₁₃	semidirect
400. #3384	C₂×C₁₃	semidirect
401. #3384	C₂×C₁₃	semidirect
402. #3373	C₂×C₁₃	semidirect
403. #3370	C₂×C₁₃	semidirect
404. #3370	C₂×C₁₃	semidirect
405. #3366	C₂×C₁₃	semidirect
406. #3244	C₂×C₁₃	semidirect
407. #3241	C₂×C₁₃	semidirect
408. #3240	C₂×C₁₃	semidirect
409. #3235	C₂×C₁₃	semidirect
410. #3122	C₂×C₁₃	semidirect
411. #3118	C₂×C₁₃	semidirect
412. #3114	C₂×C₁₃	semidirect
413. #3109	C₂×C₁₃	semidirect
414. #2987	C₂×C₁₃	semidirect
481. #559	C₂²×C₁₃	semidirect
482. #559	C₂²×C₁₃	semidirect
483. #557	C₂²×C₁₃	semidirect
489. #554	C₂²×C₁₃	semidirect
490. #550	C₂²×C₁₃	semidirect
493. D₄×Q₈	C₂²×C₁₃	semidirect
511. #501	C₂²×C₁₃	semidirect
512. #501	C₂²×C₁₃	semidirect
513. #501	C₂²×C₁₃	semidirect
514. #501	C₂²×C₁₃	semidirect
515. #501	C₂²×C₁₃	semidirect
516. #499	C₂²×C₁₃	semidirect
517. #498	C₂²×C₁₃	semidirect
518. #490	C₂²×C₁₃	semidirect
519. #490	C₂²×C₁₃	semidirect
520. #489	C₂²×C₁₃	semidirect
521. #489	C₂²×C₁₃	semidirect
522. #489	C₂²×C₁₃	semidirect
523. #488	C₂²×C₁₃	semidirect
524. #486	C₂²×C₁₃	semidirect
532. #479	C₂²×C₁₃	semidirect
533. #479	C₂²×C₁₃	semidirect
537. #478	C₂²×C₁₃	semidirect
538. #478	C₂²×C₁₃	semidirect
539. #478	C₂²×C₁₃	semidirect
540. #478	C₂²×C₁₃	semidirect
543. #476	C₂²×C₁₃	semidirect
544. #476	C₂²×C₁₃	semidirect
545. #476	C₂²×C₁₃	semidirect
546. #475	C₂²×C₁₃	semidirect
548. #474	C₂²×C₁₃	semidirect
549. #474	C₂²×C₁₃	semidirect
559. #446	C₂²×C₁₃	semidirect
560. #446	C₂²×C₁₃	semidirect
561. #446	C₂²×C₁₃	semidirect
562. #446	C₂²×C₁₃	semidirect
893. C₁₃	#61872	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×#3554	2
C₁₃×#3501	2
C₁₃×#3389	2
C₁₃×#3388	2
C₁₃×#3384	2
C₁₃×#3373	2
C₁₃×#3370	2
C₁₃×#3366	2
C₁₃×#3244	2
C₁₃×#3241	2
C₁₃×#3240	2
C₁₃×#3235	2
C₁₃×#3122	2
C₁₃×#3118	2
C₁₃×#3114	2
C₁₃×#3109	2
C₁₃×#2987	2
#61872	13

Subgroups — C13×#61872 #15748211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61872 #15748211