Subgroups — C₁₃×#62170 #15748509

Order 3328.

1740 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3370	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3346	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3345	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3334	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3309	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3308	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3301	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3257	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3243	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3119	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#563	—	2	1	no	—
21	C₁₃×#562	—	2	1	no	—
22	C₁₃×#559	—	2	1	no	—
23	C₁₃×#559	C₂²	1	1	yes	characteristic
24	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#554	—	2	1	no	—
26	C₁₃×#554	C₂²	1	2	yes	—
27	C₁₃×#554	C₂²	1	1	yes	characteristic
28	C₁₃×#553	C₂²	1	2	yes	—
29	C₁₃×#553	C₂²	1	2	yes	—
30	C₁₃×#550	C₂²	1	1	yes	characteristic
31	C₁₃×#548	C₂²	1	2	yes	—
32	C₁₃×#547	—	2	2	no	—
33	C₁₃×#547	—	2	2	no	—
34	C₁₃×#547	C₂²	1	2	yes	—
35	C₁₃×#547	C₂²	1	2	yes	—
36	C₁₃×#544	C₂²	1	2	yes	—
37	C₁₃×#542	—	2	2	no	—
38	C₁₃×#542	C₂²	1	2	yes	—
39	C₁₃×#540	C₂²	1	2	yes	—
40	C₁₃×#539	—	2	2	no	—
41	C₁₃×#539	—	2	1	no	—
42	C₁₃×#537	—	2	1	no	—
43	C₁₃×#532	—	2	1	no	—
44	C₁₃×#532	C₂²	1	1	yes	characteristic
45	C₁₃×#532	C₂²	1	1	yes	characteristic
46	C₁₃×#529	—	2	1	no	—
47	C₁₃×#529	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
49	C₁₃×#520	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	2	yes	—
52	C₁₃×#501	C₂²	1	2	yes	—
53	C₁₃×#500	C₂²	1	2	yes	—
54	C₁₃×#490	C₂²	1	2	yes	—
55	C₁₃×#489	C₂²	1	2	yes	—
56	C₁₃×#488	C₂²	1	2	yes	—
57	C₁₃×#485	C₂²	1	2	yes	—
58	C₁₃×#484	C₂²	1	2	yes	—
59	C₁₃×#482	C₂²	1	2	yes	—
60	C₁₃×#481	C₂²	1	2	yes	—
61	C₁₃×#481	C₂²	1	2	yes	—
62	C₁₃×#480	C₂²	1	2	yes	—
63	C₁₃×#480	C₂²	1	2	yes	—
64	C₁₃×#480	C₂²	1	2	yes	—
65	C₁₃×#480	C₂²	1	2	yes	—
66	C₁₃×#479	C₂²	1	2	yes	—
67	C₁₃×#479	C₂²	1	2	yes	—
68	C₁₃×#479	C₂²	1	2	yes	—
69	C₁₃×#479	C₂²	1	2	yes	—
70	C₁₃×#479	C₂²	1	2	yes	—
71	C₁₃×#478	C₂²	1	2	yes	—
72	C₁₃×#478	C₂²	1	2	yes	—
73	C₁₃×#478	C₂²	1	2	yes	—
74	C₁₃×#477	C₂²	1	2	yes	—
75	C₁₃×#477	C₂²	1	1	yes	characteristic
76	C₁₃×#477	C₂²	1	1	yes	characteristic
77	C₁₃×#476	C₂²	1	2	yes	—
78	C₁₃×#474	C₂²	1	2	yes	—
79	C₁₃×#474	C₂²	1	2	yes	—
80	C₁₃×#474	C₂²	1	2	yes	—
81	C₁₃×#474	C₂²	1	2	yes	—
82	C₁₃×#469	C₂²	1	2	yes	—
83	C₁₃×#468	C₂²	1	2	yes	—
84	C₁₃×#466	C₂²	1	2	yes	—
85	C₁₃×#466	C₂²	1	2	yes	—
86	C₁₃×#466	C₂²	1	2	yes	—
87	C₁₃×#465	C₂²	1	2	yes	—
88	C₁₃×#463	C₂²	1	2	yes	—
89	C₁₃×#463	C₂²	1	2	yes	—
90	C₁₃×#460	C₂²	1	1	yes	characteristic
91	C₁₃×#460	C₂²	1	1	yes	characteristic
92	C₁₃×#459	C₂²	1	2	yes	—
93	C₁₃×#459	C₂²	1	2	yes	—
94	C₁₃×#449	C₂²	1	2	yes	—
95	C₁₃×#449	C₂²	1	2	yes	—
96	C₁₃×#448	C₂²	1	2	yes	—
97	C₁₃×#446	C₂²	1	2	yes	—
98	C₁₃×#442	C₂²	1	2	yes	—
99	C₁₃×#440	C₂²	1	2	yes	—
100	C₁₃×#440	C₂²	1	2	yes	—
101	C₁₃×#440	C₂²	1	2	yes	—
102	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
103	C₄×C₁₃×D₈	C₂²	1	2	yes	—
104	C₁₃×#435	C₂²	1	2	yes	—
105	C₁₃×#435	C₂²	1	2	yes	—
106	C₈×D₄×C₁₃	C₂²	1	2	yes	—
107	C₁₃×#433	C₂²	1	2	yes	—
108	C₁₃×#432	C₂²	1	1	yes	characteristic
109	C₁₃×#428	C₂²	1	2	yes	—
110	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
111	C₂×C₁₃×#107	C₂²	1	2	yes	—
112	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
113	C₁₃×#424	C₂²	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₁₃×#417	C₂²	1	2	yes	—
116	C₁₃×#416	C₂²	1	2	yes	—
117	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
118	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	—	2	2	no	—
120	C₂×C₁₃×#41	—	2	2	no	—
121	C₂×C₁₃×#41	—	2	1	no	—
122	C₂×C₁₃×#41	—	2	1	no	—
123	C₂×C₁₃×#41	C₂³	1	2	yes	—
124	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×D₈	C₂³	1	2	yes	—
128	C₂×C₁₃×D₈	C₂³	1	2	yes	—
129	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
130	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
133	C₁₃×C₄⋊Q₈	—	2	1	no	—
134	C₁₃×C₄⋊Q₈	—	2	2	no	—
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₁₃×#127	—	2	1	no	—
141	C₁₃×#127	C₂³	1	1	yes	characteristic
142	C₁₃×#127	C₂³	1	1	yes	characteristic
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#126	—	2	2	no	—
146	C₁₃×#126	D₄	1	2	yes	—
147	C₁₃×#125	—	2	1	no	—
148	C₁₃×#125	—	2	2	no	—
149	C₁₃×#125	—	2	1	no	—
150	C₁₃×#125	—	2	1	no	—
151	C₁₃×#125	D₄	1	1	yes	characteristic
152	C₁₃×#125	C₂³	1	2	yes	—
153	C₁₃×#125	C₂³	1	2	yes	—
154	C₁₃×#125	C₂³	1	2	yes	—
155	C₁₃×#124	—	2	1	no	—
156	C₁₃×#124	—	2	2	no	—
157	C₁₃×#124	—	2	2	no	—
158	C₁₃×#124	—	2	1	no	—
159	C₁₃×#124	—	2	1	no	—
160	C₁₃×#124	D₄	1	1	yes	characteristic
161	C₁₃×#124	C₂³	1	2	yes	—
162	C₁₃×#123	—	2	2	no	—
163	C₁₃×#123	—	2	2	no	—
164	C₁₃×#123	—	2	2	no	—
165	C₁₃×#123	—	2	2	no	—
166	C₁₃×#123	—	2	2	no	—
167	C₁₃×#123	—	2	2	no	—
168	C₁₃×#123	—	2	2	no	—
169	C₁₃×#123	—	2	2	no	—
170	C₁₃×#123	—	2	2	no	—
171	C₁₃×#123	—	2	2	no	—
172	C₁₃×#123	D₄	1	2	yes	—
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	2	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	D₄	1	1	yes	characteristic
184	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
185	C₁₃×#121	—	2	2	no	—
186	C₁₃×#121	—	2	2	no	—
187	C₁₃×#121	—	2	2	no	—
188	C₁₃×#121	—	2	1	no	—
189	C₁₃×#121	—	2	1	no	—
190	C₁₃×#121	—	2	2	no	—
191	C₁₃×#121	—	2	2	no	—
192	C₁₃×#121	—	2	2	no	—
193	C₁₃×#121	D₄	1	1	yes	characteristic
194	C₁₃×#121	C₂³	1	2	yes	—
195	C₁₃×#121	C₂³	1	2	yes	—
196	C₁₃×#121	C₂³	1	2	yes	—
197	C₁₃×#121	C₂³	1	2	yes	—
198	C₁₃×#121	C₂³	1	2	yes	—
199	C₄×Q₈×C₁₃	—	2	1	no	—
200	C₄×Q₈×C₁₃	—	2	1	no	—
201	C₄×Q₈×C₁₃	—	2	1	no	—
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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
208	C₄×D₄×C₁₃	—	2	1	no	—
209	C₄×D₄×C₁₃	—	2	1	no	—
210	C₄×D₄×C₁₃	—	2	1	no	—
211	C₄×D₄×C₁₃	—	2	2	no	—
212	C₄×D₄×C₁₃	—	2	2	no	—
213	C₄×D₄×C₁₃	—	2	2	no	—
214	C₄×D₄×C₁₃	—	2	2	no	—
215	C₄×D₄×C₁₃	—	2	2	no	—
216	C₄×D₄×C₁₃	—	2	1	no	—
217	C₄×D₄×C₁₃	—	2	1	no	—
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	2	yes	—
224	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
225	C₁₃×#117	—	2	2	no	—
226	C₁₃×#117	C₂³	1	2	yes	—
227	C₁₃×#117	C₂³	1	2	yes	—
228	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
232	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
233	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
236	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
237	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
238	C₂×C₄²×C₁₃	—	2	1	no	—
239	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
240	C₁₃×#107	C₂³	1	2	yes	—
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#107	C₂³	1	2	yes	—
243	C₁₃×#107	C₂³	1	2	yes	—
244	C₁₃×#107	C₂³	1	2	yes	—
245	C₁₃×#107	C₂³	1	2	yes	—
246	C₁₃×#107	C₂³	1	2	yes	—
247	C₁₃×#107	C₂³	1	2	yes	—
248	C₁₃×#106	C₂³	1	2	yes	—
249	C₁₃×#106	C₂³	1	2	yes	—
250	C₁₃×#106	C₂³	1	2	yes	—
251	C₁₃×#106	C₂³	1	2	yes	—
252	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₁₃×#103	C₂³	1	2	yes	—
259	C₁₃×#103	C₂³	1	2	yes	—
260	C₁₃×#103	C₂³	1	2	yes	—
261	C₁₃×#103	C₂³	1	2	yes	—
262	C₁₃×#103	C₂³	1	2	yes	—
263	C₁₃×#103	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×#102	C₂³	1	2	yes	—
271	C₁₃×#102	C₂³	1	2	yes	—
272	C₁₃×#102	C₂³	1	2	yes	—
273	C₁₃×#102	C₂³	1	2	yes	—
274	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₁₃×#97	C₂³	1	2	yes	—
278	C₁₃×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#62170	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₁₃×#41	—	2	4	no	—
282	C₁₃×#41	—	4	2	no	—
283	C₁₃×#41	—	8	2	no	—
284	C₁₃×#41	—	8	2	no	—
285	C₁₃×#41	—	8	4	no	—
286	C₁₃×#41	—	8	4	no	—
287	C₂×Q₈×C₁₃	—	2	1	no	—
288	C₂×Q₈×C₁₃	—	2	2	no	—
289	C₂×Q₈×C₁₃	—	2	2	no	—
290	C₂×Q₈×C₁₃	—	2	1	no	—
291	C₂×Q₈×C₁₃	—	2	1	no	—
292	C₂×Q₈×C₁₃	—	2	2	no	—
293	C₂×Q₈×C₁₃	—	4	1	no	—
294	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
295	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
297	C₂×D₄×C₁₃	—	2	2	no	—
298	C₂×D₄×C₁₃	—	2	2	no	—
299	C₂×D₄×C₁₃	—	2	2	no	—
300	C₂×D₄×C₁₃	—	2	2	no	—
301	C₂×D₄×C₁₃	—	2	2	no	—
302	C₂×D₄×C₁₃	—	2	2	no	—
303	C₂×D₄×C₁₃	—	2	1	no	—
304	C₂×D₄×C₁₃	—	2	1	no	—
305	C₂×D₄×C₁₃	—	2	1	no	—
306	C₂×D₄×C₁₃	—	2	1	no	—
307	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
308	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
309	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
310	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₁₃	—	2	1	no	—
312	C₂²×C₄×C₁₃	—	2	1	no	—
313	C₂²×C₄×C₁₃	—	2	1	no	—
314	C₂²×C₄×C₁₃	—	2	1	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	—	2	2	no	—
320	C₂²×C₄×C₁₃	—	2	2	no	—
321	C₂²×C₄×C₁₃	—	2	2	no	—
322	C₂²×C₄×C₁₃	—	2	2	no	—
323	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
327	C₁₃×SD₁₆	—	2	4	no	—
328	C₁₃×SD₁₆	—	4	2	no	—
329	C₁₃×D₈	—	4	2	no	—
330	C₁₃×D₈	—	4	2	no	—
331	C₁₃×M₁₆	—	4	2	no	—
332	C₂×C₈×C₁₃	—	4	1	no	—
333	C₂×C₈×C₁₃	—	4	2	no	—
334	C₂×C₈×C₁₃	—	4	1	no	—
335	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
336	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
337	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
338	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
339	C₁₃×C₄⋊C₄	—	2	1	no	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
349	C₁₃×C₄⋊C₄	—	2	2	no	—
350	C₁₃×C₄⋊C₄	—	2	2	no	—
351	C₁₃×C₄⋊C₄	—	2	1	no	—
352	C₁₃×C₄⋊C₄	—	2	1	no	—
353	C₁₃×C₄⋊C₄	—	2	2	no	—
354	C₁₃×C₄⋊C₄	—	2	1	no	—
355	C₁₃×C₄⋊C₄	—	2	1	no	—
356	C₁₃×C₄⋊C₄	—	2	1	no	—
357	C₁₃×C₄⋊C₄	—	2	2	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	—	2	2	no	—
360	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
361	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
364	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
365	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
366	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
369	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
370	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
371	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	2	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	2	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	—	2	2	no	—
386	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
387	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
388	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
389	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
390	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
391	C₄²×C₁₃	—	2	1	no	—
392	C₄²×C₁₃	—	2	1	no	—
393	C₄²×C₁₃	—	2	1	no	—
394	C₄²×C₁₃	—	2	1	no	—
395	C₄²×C₁₃	—	2	2	no	—
396	C₄²×C₁₃	—	2	2	no	—
397	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₁₃	C₂⁴	1	2	yes	—
400	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
401	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
402	#3559	C₂×C₁₃	1	1	yes	characteristic, complemented
403	#3522	C₂×C₁₃	1	1	yes	characteristic, complemented
404	#3385	C₂×C₁₃	1	2	yes	complemented
405	#3370	C₂×C₁₃	1	2	yes	complemented
406	#3346	C₂×C₁₃	1	2	yes	complemented
407	#3345	C₂×C₁₃	1	2	yes	complemented
408	#3334	C₂×C₁₃	1	2	yes	complemented
409	#3309	C₂×C₁₃	1	2	yes	complemented
410	#3308	C₂×C₁₃	1	2	yes	complemented
411	#3301	C₂×C₁₃	1	2	yes	complemented
412	#3257	C₂×C₁₃	1	2	yes	complemented
413	#3245	C₂×C₁₃	1	1	yes	characteristic, complemented
414	#3243	C₂×C₁₃	1	2	yes	complemented
415	#3234	C₂×C₁₃	1	1	yes	characteristic, complemented
416	#3119	C₂×C₁₃	1	2	yes	complemented
417	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
418	#3083	C₂×C₁₃	1	2	yes	complemented
419	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
420	#2992	C₂×C₁₃	1	1	yes	characteristic, complemented
421	C₂³×C₁₃	—	2	2	no	—
422	C₂³×C₁₃	—	2	2	no	—
423	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
424	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	Q₈×C₁₃	—	2	1	no	—
426	Q₈×C₁₃	—	2	1	no	—
427	Q₈×C₁₃	—	2	1	no	—
428	Q₈×C₁₃	—	4	1	no	—
429	Q₈×C₁₃	—	4	2	no	—
430	Q₈×C₁₃	—	8	1	no	—
431	Q₈×C₁₃	—	8	1	no	—
432	Q₈×C₁₃	—	8	2	no	—
433	Q₈×C₁₃	—	8	2	no	—
434	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
435	D₄×C₁₃	—	2	4	no	—
436	D₄×C₁₃	—	2	2	no	—
437	D₄×C₁₃	—	2	2	no	—
438	D₄×C₁₃	—	2	2	no	—
439	D₄×C₁₃	—	2	2	no	—
440	D₄×C₁₃	—	4	1	no	—
441	D₄×C₁₃	—	4	4	no	—
442	D₄×C₁₃	—	4	2	no	—
443	D₄×C₁₃	—	4	4	no	—
444	D₄×C₁₃	—	4	4	no	—
445	D₄×C₁₃	—	8	1	no	—
446	D₄×C₁₃	—	8	1	no	—
447	D₄×C₁₃	—	8	1	no	—
448	D₄×C₁₃	—	8	2	no	—
449	D₄×C₁₃	—	8	2	no	—
450	D₄×C₁₃	—	8	2	no	—
451	C₂×C₄×C₁₃	—	2	2	no	—
452	C₂×C₄×C₁₃	—	2	1	no	—
453	C₂×C₄×C₁₃	—	2	1	no	—
454	C₂×C₄×C₁₃	—	2	2	no	—
455	C₂×C₄×C₁₃	—	2	1	no	—
456	C₂×C₄×C₁₃	—	2	2	no	—
457	C₂×C₄×C₁₃	—	2	1	no	—
458	C₂×C₄×C₁₃	—	2	1	no	—
459	C₂×C₄×C₁₃	—	2	1	no	—
460	C₂×C₄×C₁₃	—	2	2	no	—
461	C₂×C₄×C₁₃	—	2	2	no	—
462	C₂×C₄×C₁₃	—	2	2	no	—
463	C₂×C₄×C₁₃	—	2	2	no	—
464	C₂×C₄×C₁₃	—	4	1	no	—
465	C₂×C₄×C₁₃	—	4	4	no	—
466	C₂×C₄×C₁₃	—	4	2	no	—
467	C₂×C₄×C₁₃	—	4	2	no	—
468	C₂×C₄×C₁₃	—	4	2	no	—
469	C₂×C₄×C₁₃	—	8	2	no	—
470	C₂×C₄×C₁₃	—	8	2	no	—
471	C₂×C₄×C₁₃	—	8	2	no	—
472	C₂×C₄×C₁₃	—	8	2	no	—
473	C₂×C₄×C₁₃	—	8	2	no	—
474	C₂×C₄×C₁₃	—	8	1	no	—
475	C₂×C₄×C₁₃	—	8	2	no	—
476	C₂×C₄×C₁₃	—	8	2	no	—
477	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
486	C₈×C₁₃	—	2	2	no	—
487	C₈×C₁₃	—	2	2	no	—
488	C₈×C₁₃	—	2	2	no	—
489	C₈×C₁₃	—	2	2	no	—
490	#563	—	2	1	no	—
491	#562	—	2	1	no	—
492	#559	—	2	1	no	—
493	#559	C₂²×C₁₃	1	1	yes	characteristic
494	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
495	#554	—	2	1	no	—
496	#554	C₂²×C₁₃	1	2	yes	—
497	#554	C₂²×C₁₃	1	1	yes	characteristic
498	#553	C₂²×C₁₃	1	2	yes	—
499	#553	C₂²×C₁₃	1	2	yes	—
500	#550	C₂²×C₁₃	1	1	yes	characteristic
501	#548	C₂²×C₁₃	1	2	yes	—
502	#547	—	2	2	no	—
503	#547	—	2	2	no	—
504	#547	C₂²×C₁₃	1	2	yes	—
505	#547	C₂²×C₁₃	1	2	yes	—
506	#544	C₂²×C₁₃	1	2	yes	—
507	#542	—	2	2	no	—
508	#542	C₂²×C₁₃	1	2	yes	—
509	#540	C₂²×C₁₃	1	2	yes	—
510	#539	—	2	2	no	—
511	#539	—	2	1	no	—
512	#537	—	2	1	no	—
513	#532	—	2	1	no	—
514	#532	C₂²×C₁₃	1	1	yes	characteristic
515	#532	C₂²×C₁₃	1	1	yes	characteristic
516	#529	—	2	1	no	—
517	#529	C₂²×C₁₃	1	1	yes	characteristic
518	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
519	#520	C₂²×C₁₃	1	2	yes	—
520	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
521	#501	C₂²×C₁₃	1	2	yes	—
522	#501	C₂²×C₁₃	1	2	yes	—
523	#500	C₂²×C₁₃	1	2	yes	—
524	#490	C₂²×C₁₃	1	2	yes	—
525	#489	C₂²×C₁₃	1	2	yes	—
526	#488	C₂²×C₁₃	1	2	yes	—
527	#485	C₂²×C₁₃	1	2	yes	—
528	#484	C₂²×C₁₃	1	2	yes	—
529	#482	C₂²×C₁₃	1	2	yes	—
530	#481	C₂²×C₁₃	1	2	yes	—
531	#481	C₂²×C₁₃	1	2	yes	—
532	#480	C₂²×C₁₃	1	2	yes	—
533	#480	C₂²×C₁₃	1	2	yes	—
534	#480	C₂²×C₁₃	1	2	yes	—
535	#480	C₂²×C₁₃	1	2	yes	—
536	#479	C₂²×C₁₃	1	2	yes	—
537	#479	C₂²×C₁₃	1	2	yes	—
538	#479	C₂²×C₁₃	1	2	yes	—
539	#479	C₂²×C₁₃	1	2	yes	—
540	#479	C₂²×C₁₃	1	2	yes	—
541	#478	C₂²×C₁₃	1	2	yes	—
542	#478	C₂²×C₁₃	1	2	yes	—
543	#478	C₂²×C₁₃	1	2	yes	—
544	#477	C₂²×C₁₃	1	1	yes	characteristic
545	#477	C₂²×C₁₃	1	2	yes	—
546	#477	C₂²×C₁₃	1	1	yes	characteristic
547	#476	C₂²×C₁₃	1	2	yes	—
548	#474	C₂²×C₁₃	1	2	yes	—
549	#474	C₂²×C₁₃	1	2	yes	—
550	#474	C₂²×C₁₃	1	2	yes	—
551	#474	C₂²×C₁₃	1	2	yes	—
552	#469	C₂²×C₁₃	1	2	yes	—
553	#468	C₂²×C₁₃	1	2	yes	—
554	#466	C₂²×C₁₃	1	2	yes	—
555	#466	C₂²×C₁₃	1	2	yes	—
556	#466	C₂²×C₁₃	1	2	yes	—
557	#465	C₂²×C₁₃	1	2	yes	—
558	#463	C₂²×C₁₃	1	2	yes	—
559	#463	C₂²×C₁₃	1	2	yes	—
560	#460	C₂²×C₁₃	1	1	yes	characteristic
561	#460	C₂²×C₁₃	1	1	yes	characteristic
562	#459	C₂²×C₁₃	1	2	yes	—
563	#459	C₂²×C₁₃	1	2	yes	—
564	#449	C₂²×C₁₃	1	2	yes	—
565	#449	C₂²×C₁₃	1	2	yes	—
566	#448	C₂²×C₁₃	1	2	yes	—
567	#446	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	#440	C₂²×C₁₃	1	2	yes	—
572	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
573	C₄×D₈	C₂²×C₁₃	1	2	yes	—
574	#435	C₂²×C₁₃	1	2	yes	—
575	#435	C₂²×C₁₃	1	2	yes	—
576	C₈×D₄	C₂²×C₁₃	1	2	yes	—
577	#433	C₂²×C₁₃	1	2	yes	—
578	#432	C₂²×C₁₃	1	1	yes	characteristic
579	#428	C₂²×C₁₃	1	2	yes	—
580	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
581	C₂×#107	C₂²×C₁₃	1	2	yes	—
582	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
583	#424	C₂²×C₁₃	1	2	yes	—
584	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
585	#417	C₂²×C₁₃	1	2	yes	—
586	#416	C₂²×C₁₃	1	2	yes	—
587	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
588	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
589	C₂²×C₁₃	—	2	1	no	—
590	C₂²×C₁₃	—	2	1	no	—
591	C₂²×C₁₃	—	2	2	no	—
592	C₂²×C₁₃	—	2	2	no	—
593	C₂²×C₁₃	—	2	2	no	—
594	C₂²×C₁₃	—	4	2	no	—
595	C₂²×C₁₃	—	4	2	no	—
596	C₂²×C₁₃	—	4	2	no	—
597	C₂²×C₁₃	—	4	2	no	—
598	C₂²×C₁₃	—	4	2	no	—
599	C₂²×C₁₃	—	4	2	no	—
600	C₂²×C₁₃	#576	1	2	yes	—
601	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
602	C₄×C₁₃	—	2	1	no	—
603	C₄×C₁₃	—	2	1	no	—
604	C₄×C₁₃	—	2	2	no	—
605	C₄×C₁₃	—	2	2	no	—
606	C₄×C₁₃	—	2	1	no	—
607	C₄×C₁₃	—	2	2	no	—
608	C₄×C₁₃	—	2	1	no	—
609	C₄×C₁₃	—	2	1	no	—
610	C₄×C₁₃	—	2	2	no	—
611	C₄×C₁₃	—	4	2	no	—
612	C₄×C₁₃	—	4	1	no	—
613	C₄×C₁₃	—	4	1	no	—
614	C₄×C₁₃	—	4	2	no	—
615	C₄×C₁₃	—	4	1	no	—
616	C₄×C₁₃	—	4	2	no	—
617	C₄×C₁₃	—	4	2	no	—
618	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
619	C₄×C₁₃	#585	1	1	yes	characteristic
620	C₂×#41	—	2	2	no	—
621	C₂×#41	—	2	2	no	—
622	C₂×#41	—	2	1	no	—
623	C₂×#41	—	2	1	no	—
624	C₂×#41	C₂³×C₁₃	1	2	yes	—
625	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
626	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
627	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
628	C₂×D₈	C₂³×C₁₃	1	2	yes	—
629	C₂×D₈	C₂³×C₁₃	1	2	yes	—
630	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
631	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
632	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
633	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
634	C₄⋊Q₈	—	2	1	no	—
635	C₄⋊Q₈	—	2	2	no	—
636	C₄⋊Q₈	—	2	2	no	—
637	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
638	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
639	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
640	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
641	#127	—	2	1	no	—
642	#127	C₂³×C₁₃	1	1	yes	characteristic
643	#127	C₂³×C₁₃	1	1	yes	characteristic
644	#126	—	2	2	no	—
645	#126	—	2	2	no	—
646	#126	—	2	2	no	—
647	#126	D₄×C₁₃	1	2	yes	—
648	#125	—	2	1	no	—
649	#125	—	2	2	no	—
650	#125	—	2	1	no	—
651	#125	—	2	1	no	—
652	#125	D₄×C₁₃	1	1	yes	characteristic
653	#125	C₂³×C₁₃	1	2	yes	—
654	#125	C₂³×C₁₃	1	2	yes	—
655	#125	C₂³×C₁₃	1	2	yes	—
656	#124	—	2	1	no	—
657	#124	—	2	2	no	—
658	#124	—	2	2	no	—
659	#124	—	2	1	no	—
660	#124	—	2	1	no	—
661	#124	D₄×C₁₃	1	1	yes	characteristic
662	#124	C₂³×C₁₃	1	2	yes	—
663	#123	—	2	2	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	D₄×C₁₃	1	2	yes	—
674	C₂²⋊Q₈	—	2	2	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	2	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
685	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
686	#121	—	2	2	no	—
687	#121	—	2	2	no	—
688	#121	—	2	2	no	—
689	#121	—	2	1	no	—
690	#121	—	2	1	no	—
691	#121	—	2	2	no	—
692	#121	—	2	2	no	—
693	#121	—	2	2	no	—
694	#121	D₄×C₁₃	1	1	yes	characteristic
695	#121	C₂³×C₁₃	1	2	yes	—
696	#121	C₂³×C₁₃	1	2	yes	—
697	#121	C₂³×C₁₃	1	2	yes	—
698	#121	C₂³×C₁₃	1	2	yes	—
699	#121	C₂³×C₁₃	1	2	yes	—
700	C₄×Q₈	—	2	1	no	—
701	C₄×Q₈	—	2	1	no	—
702	C₄×Q₈	—	2	1	no	—
703	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
704	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
705	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
706	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
707	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
708	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	—	2	1	no	—
711	C₄×D₄	—	2	1	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	2	no	—
714	C₄×D₄	—	2	2	no	—
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	—	2	2	no	—
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	C₂³×C₁₃	1	2	yes	—
720	C₄×D₄	C₂³×C₁₃	1	2	yes	—
721	C₄×D₄	C₂³×C₁₃	1	2	yes	—
722	C₄×D₄	C₂³×C₁₃	1	2	yes	—
723	C₄×D₄	C₂³×C₁₃	1	2	yes	—
724	C₄×D₄	C₂³×C₁₃	1	2	yes	—
725	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
726	#117	—	2	2	no	—
727	#117	C₂³×C₁₃	1	2	yes	—
728	#117	C₂³×C₁₃	1	2	yes	—
729	C₂×C₄⋊C₄	—	2	1	no	—
730	C₂×C₄⋊C₄	—	2	1	no	—
731	C₂×C₄⋊C₄	—	2	1	no	—
732	C₂×C₄⋊C₄	—	2	2	no	—
733	C₂×C₄⋊C₄	—	2	2	no	—
734	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
736	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
739	C₂×C₄²	—	2	1	no	—
740	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
741	#107	C₂³×C₁₃	1	2	yes	—
742	#107	C₂³×C₁₃	1	2	yes	—
743	#107	C₂³×C₁₃	1	2	yes	—
744	#107	C₂³×C₁₃	1	2	yes	—
745	#107	C₂³×C₁₃	1	2	yes	—
746	#107	C₂³×C₁₃	1	2	yes	—
747	#107	C₂³×C₁₃	1	2	yes	—
748	#107	C₂³×C₁₃	1	2	yes	—
749	#106	C₂³×C₁₃	1	2	yes	—
750	#106	C₂³×C₁₃	1	2	yes	—
751	#106	C₂³×C₁₃	1	2	yes	—
752	#106	C₂³×C₁₃	1	2	yes	—
753	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
754	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
755	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
756	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
757	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
758	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
759	#103	C₂³×C₁₃	1	2	yes	—
760	#103	C₂³×C₁₃	1	2	yes	—
761	#103	C₂³×C₁₃	1	2	yes	—
762	#103	C₂³×C₁₃	1	2	yes	—
763	#103	C₂³×C₁₃	1	2	yes	—
764	#103	C₂³×C₁₃	1	2	yes	—
765	#102	C₂³×C₁₃	1	2	yes	—
766	#102	C₂³×C₁₃	1	2	yes	—
767	#102	C₂³×C₁₃	1	2	yes	—
768	#102	C₂³×C₁₃	1	2	yes	—
769	#102	C₂³×C₁₃	1	2	yes	—
770	#102	C₂³×C₁₃	1	2	yes	—
771	#102	C₂³×C₁₃	1	2	yes	—
772	#102	C₂³×C₁₃	1	2	yes	—
773	#102	C₂³×C₁₃	1	2	yes	—
774	#102	C₂³×C₁₃	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
778	#97	C₂³×C₁₃	1	2	yes	—
779	#97	C₂³×C₁₃	1	2	yes	—
780	C₄×C₈	C₂³×C₁₃	1	2	yes	—
781	C₂×C₁₃	—	2	2	no	—
782	C₂×C₁₃	—	4	2	no	—
783	C₂×C₁₃	—	8	2	no	—
784	C₂×C₁₃	—	8	2	no	—
785	C₂×C₁₃	#3489	1	1	yes	characteristic
786	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
787	C₂×C₁₃	#3586	1	1	yes	characteristic
788	#41	—	2	4	no	—
789	#41	—	4	2	no	—
790	#41	—	8	2	no	—
791	#41	—	8	2	no	—
792	#41	—	8	4	no	—
793	#41	—	8	4	no	—
794	C₂×Q₈	—	2	1	no	—
795	C₂×Q₈	—	2	2	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	1	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	2	no	—
800	C₂×Q₈	—	4	1	no	—
801	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
802	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
803	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
815	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
816	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
817	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
831	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
834	SD₁₆	—	2	4	no	—
835	SD₁₆	—	4	2	no	—
836	D₈	—	4	2	no	—
837	D₈	—	4	2	no	—
838	M₁₆	—	4	2	no	—
839	C₂×C₈	—	4	1	no	—
840	C₂×C₈	—	4	2	no	—
841	C₂×C₈	—	4	1	no	—
842	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
843	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
844	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
845	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	1	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
868	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
869	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
870	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
871	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
872	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
873	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
876	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
877	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
878	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
894	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
898	C₄²	—	2	1	no	—
899	C₄²	—	2	1	no	—
900	C₄²	—	2	1	no	—
901	C₄²	—	2	1	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
905	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
906	C₄²	C₂⁴×C₁₃	1	2	yes	—
907	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
908	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
909	C₁₃	#62170	1	1	yes	characteristic, direct product factor, Sylow
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
913	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
914	Q₈	—	2	1	no	—
915	Q₈	—	2	1	no	—
916	Q₈	—	2	1	no	—
917	Q₈	—	4	1	no	—
918	Q₈	—	4	2	no	—
919	Q₈	—	8	1	no	—
920	Q₈	—	8	1	no	—
921	Q₈	—	8	2	no	—
922	Q₈	—	8	2	no	—
923	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
924	D₄	—	2	4	no	—
925	D₄	—	2	2	no	—
926	D₄	—	2	2	no	—
927	D₄	—	2	2	no	—
928	D₄	—	2	2	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	4	no	—
931	D₄	—	4	2	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	4	no	—
934	D₄	—	8	1	no	—
935	D₄	—	8	1	no	—
936	D₄	—	8	1	no	—
937	D₄	—	8	2	no	—
938	D₄	—	8	2	no	—
939	D₄	—	8	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	4	1	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	8	2	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	—	8	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	2	no	—
963	C₂×C₄	—	8	1	no	—
964	C₂×C₄	—	8	2	no	—
965	C₂×C₄	—	8	2	no	—
966	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
968	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
969	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
970	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
971	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
972	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
973	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
974	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
975	C₈	—	2	2	no	—
976	C₈	—	2	2	no	—
977	C₈	—	2	2	no	—
978	C₈	—	2	2	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	C₁₃×#576	1	2	yes	—
991	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
992	C₄	—	2	1	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	2	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	2	no	—
998	C₄	—	2	2	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	4	1	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	1	no	—
1004	C₄	—	4	2	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	1	no	—
1008	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1009	C₄	C₁₃×#585	1	1	yes	characteristic
1010	C₂	—	2	2	no	—
1011	C₂	—	4	2	no	—
1012	C₂	—	8	2	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₁₃×#3489	1	1	yes	characteristic
1015	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1016	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3559	C₂	semidirect
2. C₁₃×#3522	C₂	semidirect
3. C₁₃×#3385	C₂	semidirect
4. C₁₃×#3370	C₂	semidirect
5. C₁₃×#3346	C₂	semidirect
6. C₁₃×#3345	C₂	semidirect
7. C₁₃×#3334	C₂	semidirect
8. C₁₃×#3309	C₂	semidirect
9. C₁₃×#3308	C₂	semidirect
10. C₁₃×#3301	C₂	semidirect
11. C₁₃×#3257	C₂	semidirect
12. C₁₃×#3245	C₂	semidirect
13. C₁₃×#3243	C₂	semidirect
14. C₁₃×#3234	C₂	semidirect
15. C₁₃×#3119	C₂	semidirect
16. C₁₃×#3112	C₂	semidirect
17. C₁₃×#3083	C₂	semidirect
18. C₂×C₁₃×#479	C₂	semidirect
19. C₁₃×#2992	C₂	semidirect
280. #62170	C₁₃	direct (N × H)
402. #3559	C₂×C₁₃	semidirect
403. #3522	C₂×C₁₃	semidirect
404. #3385	C₂×C₁₃	semidirect
405. #3370	C₂×C₁₃	semidirect
406. #3346	C₂×C₁₃	semidirect
407. #3345	C₂×C₁₃	semidirect
408. #3334	C₂×C₁₃	semidirect
409. #3309	C₂×C₁₃	semidirect
410. #3308	C₂×C₁₃	semidirect
411. #3301	C₂×C₁₃	semidirect
412. #3257	C₂×C₁₃	semidirect
413. #3245	C₂×C₁₃	semidirect
414. #3243	C₂×C₁₃	semidirect
415. #3234	C₂×C₁₃	semidirect
416. #3119	C₂×C₁₃	semidirect
417. #3112	C₂×C₁₃	semidirect
418. #3083	C₂×C₁₃	semidirect
419. C₂×#479	C₂×C₁₃	semidirect
420. #2992	C₂×C₁₃	semidirect
909. C₁₃	#62170	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×#3559	2
C₁₃×#3522	2
C₁₃×#3385	2
C₁₃×#3370	2
C₁₃×#3346	2
C₁₃×#3345	2
C₁₃×#3334	2
C₁₃×#3309	2
C₁₃×#3308	2
C₁₃×#3301	2
C₁₃×#3257	2
C₁₃×#3245	2
C₁₃×#3243	2
C₁₃×#3234	2
C₁₃×#3119	2
C₁₃×#3112	2
C₁₃×#3083	2
C₂×C₁₃×#479	2
C₁₃×#2992	2
#62170	13

Subgroups — C13×#62170 #15748509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62170 #15748509