Subgroups — C₁₃×#61929 #15748268

Order 3328.

1654 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3402	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3393	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3225	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3212	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3124	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
21	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#563	—	2	2	no	—
25	C₁₃×#559	C₂²	1	1	yes	characteristic
26	C₁₃×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#557	C₂²	1	1	yes	characteristic
29	C₁₃×#557	C₂²	1	1	yes	characteristic
30	C₁₃×#557	C₂²	1	1	yes	characteristic
31	C₁₃×#557	C₂²	1	2	yes	—
32	C₁₃×#556	—	2	1	no	—
33	C₁₃×#556	—	2	1	no	—
34	C₁₃×#556	C₂²	1	2	yes	—
35	C₁₃×#556	C₂²	1	1	yes	characteristic
36	C₁₃×#556	C₂²	1	2	yes	—
37	C₁₃×#556	C₂²	1	2	yes	—
38	C₁₃×#554	—	2	1	no	—
39	C₁₃×#554	C₂²	1	1	yes	characteristic
40	C₁₃×#552	—	2	2	no	—
41	C₁₃×#552	—	2	1	no	—
42	C₁₃×#544	—	2	1	no	—
43	C₁₃×#542	C₂²	1	2	yes	—
44	C₁₃×#541	—	2	1	no	—
45	C₁₃×#541	—	2	2	no	—
46	C₁₃×#541	C₂²	1	2	yes	—
47	C₁₃×#539	—	2	2	no	—
48	C₁₃×#536	C₂²	1	2	yes	—
49	C₁₃×#533	C₂²	1	1	yes	characteristic
50	C₁₃×#533	C₂²	1	1	yes	characteristic
51	C₁₃×#532	C₂²	1	1	yes	characteristic
52	C₁₃×#529	—	2	1	no	—
53	C₁₃×#529	—	2	1	no	—
54	C₁₃×#529	C₂²	1	1	yes	characteristic
55	C₁₃×#520	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×#497	C₂²	1	2	yes	—
58	C₁₃×#497	C₂²	1	2	yes	—
59	C₁₃×#495	C₂²	1	2	yes	—
60	C₁₃×#495	C₂²	1	2	yes	—
61	C₁₃×#494	C₂²	1	2	yes	—
62	C₁₃×#494	C₂²	1	1	yes	characteristic
63	C₁₃×#492	C₂²	1	1	yes	characteristic
64	C₁₃×#491	C₂²	1	2	yes	—
65	C₁₃×#489	C₂²	1	2	yes	—
66	C₁₃×#488	C₂²	1	2	yes	—
67	C₁₃×#488	C₂²	1	2	yes	—
68	C₁₃×#487	C₂²	1	2	yes	—
69	C₁₃×#487	C₂²	1	1	yes	characteristic
70	C₁₃×#486	C₂²	1	1	yes	characteristic
71	C₁₃×#484	C₂²	1	2	yes	—
72	C₁₃×#483	C₂²	1	1	yes	characteristic
73	C₁₃×#480	C₂²	1	1	yes	characteristic
74	C₁₃×#479	C₂²	1	1	yes	characteristic
75	C₁₃×#479	C₂²	1	1	yes	characteristic
76	C₁₃×#479	C₂²	1	2	yes	—
77	C₁₃×#478	C₂²	1	2	yes	—
78	C₁₃×#477	C₂²	1	1	yes	characteristic
79	C₁₃×#477	C₂²	1	1	yes	characteristic
80	C₁₃×#477	C₂²	1	2	yes	—
81	C₁₃×#474	C₂²	1	2	yes	—
82	C₁₃×#464	C₂²	1	1	yes	characteristic
83	C₁₃×#464	C₂²	1	1	yes	characteristic
84	C₁₃×#464	C₂²	1	2	yes	—
85	C₁₃×#464	C₂²	1	2	yes	—
86	C₁₃×#464	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	2	yes	—
88	C₁₃×#464	C₂²	1	2	yes	—
89	C₁₃×#464	C₂²	1	2	yes	—
90	C₁₃×#463	C₂²	1	2	yes	—
91	C₁₃×#463	C₂²	1	2	yes	—
92	C₁₃×#462	C₂²	1	1	yes	characteristic
93	C₁₃×#462	C₂²	1	1	yes	characteristic
94	C₁₃×#462	C₂²	1	1	yes	characteristic
95	C₁₃×#462	C₂²	1	2	yes	—
96	C₁₃×#462	C₂²	1	2	yes	—
97	C₁₃×#462	C₂²	1	2	yes	—
98	C₁₃×#462	C₂²	1	2	yes	—
99	C₁₃×#461	C₂²	1	2	yes	—
100	C₁₃×#461	C₂²	1	1	yes	characteristic
101	C₁₃×#461	C₂²	1	2	yes	—
102	C₁₃×#460	C₂²	1	1	yes	characteristic
103	C₁₃×#459	C₂²	1	1	yes	characteristic
104	C₁₃×#452	C₂²	1	2	yes	—
105	C₁₃×#452	C₂²	1	2	yes	—
106	C₁₃×#452	C₂²	1	2	yes	—
107	C₁₃×#451	C₂²	1	2	yes	—
108	C₁₃×#451	C₂²	1	1	yes	characteristic
109	C₁₃×#449	C₂²	1	2	yes	—
110	C₁₃×#448	C₂²	1	1	yes	characteristic
111	C₁₃×#446	C₂²	1	1	yes	characteristic
112	C₁₃×#446	C₂²	1	1	yes	characteristic
113	C₁₃×#446	C₂²	1	2	yes	—
114	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
117	C₁₃×#441	C₂²	1	2	yes	—
118	C₁₃×#440	C₂²	1	2	yes	—
119	C₁₃×#440	C₂²	1	2	yes	—
120	C₁₃×#440	C₂²	1	2	yes	—
121	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
122	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
123	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
124	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
125	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
126	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
127	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
128	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
129	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
130	C₄×C₁₃×D₈	C₂²	1	2	yes	—
131	C₁₃×#433	C₂²	1	2	yes	—
132	C₁₃×#433	C₂²	1	2	yes	—
133	C₁₃×#431	C₂²	1	1	yes	characteristic
134	C₁₃×#431	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	C₂³	1	2	yes	—
136	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
138	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
143	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
147	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×D₈	C₂³	1	2	yes	—
151	C₁₃×C₄⋊Q₈	—	2	2	no	—
152	C₁₃×C₄⋊Q₈	—	2	2	no	—
153	C₁₃×C₄⋊Q₈	—	2	1	no	—
154	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₃×#127	C₂³	1	1	yes	characteristic
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	2	no	—
166	C₁₃×#126	—	2	2	no	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#126	—	2	2	no	—
172	C₁₃×#126	—	2	2	no	—
173	C₁₃×#126	—	2	2	no	—
174	C₁₃×#126	—	2	1	no	—
175	C₁₃×#125	—	2	1	no	—
176	C₁₃×#125	—	2	1	no	—
177	C₁₃×#125	—	2	2	no	—
178	C₁₃×#125	—	2	2	no	—
179	C₁₃×#125	—	2	2	no	—
180	C₁₃×#125	—	2	2	no	—
181	C₁₃×#125	—	2	2	no	—
182	C₁₃×#125	—	2	2	no	—
183	C₁₃×#125	—	2	2	no	—
184	C₁₃×#125	—	2	1	no	—
185	C₁₃×#125	—	2	1	no	—
186	C₁₃×#125	D₄	1	2	yes	—
187	C₁₃×#125	C₂³	1	2	yes	—
188	C₁₃×#125	C₂³	1	1	yes	characteristic
189	C₁₃×#124	—	2	1	no	—
190	C₁₃×#124	—	2	1	no	—
191	C₁₃×#124	—	2	2	no	—
192	C₁₃×#124	C₂³	1	2	yes	—
193	C₁₃×#124	C₂³	1	2	yes	—
194	C₁₃×#124	C₂³	1	2	yes	—
195	C₁₃×#124	C₂³	1	2	yes	—
196	C₁₃×#124	C₂³	1	1	yes	characteristic
197	C₁₃×#123	—	2	1	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×#123	—	2	2	no	—
201	C₁₃×#123	—	2	2	no	—
202	C₁₃×#123	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	1	no	—
206	C₁₃×C₂²⋊Q₈	—	2	1	no	—
207	C₁₃×C₂²⋊Q₈	—	2	2	no	—
208	C₁₃×C₂²⋊Q₈	—	2	1	no	—
209	C₁₃×C₂²⋊Q₈	—	2	2	no	—
210	C₁₃×C₂²⋊Q₈	—	2	2	no	—
211	C₁₃×C₂²⋊Q₈	—	2	2	no	—
212	C₁₃×C₂²⋊Q₈	—	2	2	no	—
213	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
214	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
215	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
216	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₁₃×#121	—	2	1	no	—
219	C₁₃×#121	—	2	1	no	—
220	C₁₃×#121	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	—	2	1	no	—
222	C₄×Q₈×C₁₃	—	2	1	no	—
223	C₄×Q₈×C₁₃	—	2	1	no	—
224	C₄×Q₈×C₁₃	—	2	1	no	—
225	C₄×Q₈×C₁₃	—	2	2	no	—
226	C₄×Q₈×C₁₃	—	2	1	no	—
227	C₄×Q₈×C₁₃	—	2	1	no	—
228	C₄×Q₈×C₁₃	—	2	1	no	—
229	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
232	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
234	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
237	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
240	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₁₃	—	2	1	no	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	—	2	1	no	—
246	C₄×D₄×C₁₃	—	2	2	no	—
247	C₄×D₄×C₁₃	—	2	2	no	—
248	C₄×D₄×C₁₃	—	2	1	no	—
249	C₄×D₄×C₁₃	—	2	1	no	—
250	C₄×D₄×C₁₃	C₂³	1	2	yes	—
251	C₄×D₄×C₁₃	C₂³	1	2	yes	—
252	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₃	C₂³	1	2	yes	—
254	C₁₃×#117	—	2	1	no	—
255	C₁₃×#117	—	2	2	no	—
256	C₁₃×#117	—	2	2	no	—
257	C₁₃×#117	—	2	2	no	—
258	C₁₃×#117	—	2	2	no	—
259	C₁₃×#117	—	2	1	no	—
260	C₁₃×#117	—	2	1	no	—
261	C₁₃×#117	C₂³	1	2	yes	—
262	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
264	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₄²×C₁₃	—	2	1	no	—
267	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
268	C₁₃×#107	C₂³	1	2	yes	—
269	C₁₃×#107	C₂³	1	1	yes	characteristic
270	C₁₃×#107	C₂³	1	2	yes	—
271	C₁₃×#107	C₂³	1	1	yes	characteristic
272	C₁₃×#106	C₂³	1	1	yes	characteristic
273	C₁₃×#106	C₂³	1	1	yes	characteristic
274	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₃×#103	C₂³	1	2	yes	—
283	C₁₃×#103	C₂³	1	1	yes	characteristic
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#102	C₂³	1	1	yes	characteristic
297	C₁₃×#102	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	1	yes	characteristic
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₁₃×#97	C₂³	1	2	yes	—
306	C₁₃×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₁₃	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	2	yes	—
311	C₄×C₈×C₁₃	C₂³	1	2	yes	—
312	#61929	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₁₃×#41	—	4	2	no	—
314	C₁₃×#41	—	4	2	no	—
315	C₂×Q₈×C₁₃	—	2	1	no	—
316	C₂×Q₈×C₁₃	—	2	1	no	—
317	C₂×Q₈×C₁₃	—	2	2	no	—
318	C₂×Q₈×C₁₃	—	4	1	no	—
319	C₂×Q₈×C₁₃	—	4	1	no	—
320	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
323	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
328	C₂×D₄×C₁₃	—	2	2	no	—
329	C₂×D₄×C₁₃	—	2	1	no	—
330	C₂×D₄×C₁₃	—	2	1	no	—
331	C₂×D₄×C₁₃	—	2	1	no	—
332	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
333	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₁₃	—	2	1	no	—
335	C₂²×C₄×C₁₃	—	2	1	no	—
336	C₂²×C₄×C₁₃	—	2	1	no	—
337	C₂²×C₄×C₁₃	—	2	2	no	—
338	C₂²×C₄×C₁₃	—	2	2	no	—
339	C₂²×C₄×C₁₃	—	2	2	no	—
340	C₂²×C₄×C₁₃	—	2	2	no	—
341	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₁₃×Q₁₆	—	4	2	no	—
345	C₁₃×Q₁₆	—	4	2	no	—
346	C₁₃×Q₁₆	—	4	2	no	—
347	C₁₃×Q₁₆	—	4	1	no	—
348	C₁₃×Q₁₆	—	4	2	no	—
349	C₁₃×Q₁₆	—	4	1	no	—
350	C₁₃×Q₁₆	—	4	2	no	—
351	C₁₃×SD₁₆	—	4	1	no	—
352	C₁₃×SD₁₆	—	4	2	no	—
353	C₁₃×SD₁₆	—	4	2	no	—
354	C₁₃×SD₁₆	—	4	2	no	—
355	C₁₃×SD₁₆	—	4	2	no	—
356	C₁₃×SD₁₆	—	4	1	no	—
357	C₁₃×D₈	—	4	2	no	—
358	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
360	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
364	C₁₃×C₄⋊C₄	—	2	1	no	—
365	C₁₃×C₄⋊C₄	—	2	1	no	—
366	C₁₃×C₄⋊C₄	—	2	2	no	—
367	C₁₃×C₄⋊C₄	—	2	2	no	—
368	C₁₃×C₄⋊C₄	—	2	1	no	—
369	C₁₃×C₄⋊C₄	—	2	1	no	—
370	C₁₃×C₄⋊C₄	—	2	1	no	—
371	C₁₃×C₄⋊C₄	—	2	1	no	—
372	C₁₃×C₄⋊C₄	—	2	2	no	—
373	C₁₃×C₄⋊C₄	—	2	1	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	—	2	2	no	—
376	C₁₃×C₄⋊C₄	—	2	2	no	—
377	C₁₃×C₄⋊C₄	—	2	1	no	—
378	C₁₃×C₄⋊C₄	—	2	1	no	—
379	C₁₃×C₄⋊C₄	—	2	1	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	1	no	—
387	C₁₃×C₄⋊C₄	—	2	2	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	2	no	—
391	C₁₃×C₄⋊C₄	—	2	2	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	1	no	—
394	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
396	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₁₃×C₂²⋊C₄	—	2	2	no	—
409	C₁₃×C₂²⋊C₄	—	2	1	no	—
410	C₁₃×C₂²⋊C₄	—	2	2	no	—
411	C₁₃×C₂²⋊C₄	—	2	1	no	—
412	C₁₃×C₂²⋊C₄	—	2	2	no	—
413	C₁₃×C₂²⋊C₄	—	2	2	no	—
414	C₁₃×C₂²⋊C₄	—	2	1	no	—
415	C₁₃×C₂²⋊C₄	—	2	1	no	—
416	C₁₃×C₂²⋊C₄	—	2	2	no	—
417	C₁₃×C₂²⋊C₄	—	2	2	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	1	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
426	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₄²×C₁₃	—	2	1	no	—
428	C₄²×C₁₃	—	2	1	no	—
429	C₄²×C₁₃	—	2	1	no	—
430	C₄²×C₁₃	—	2	1	no	—
431	C₄²×C₁₃	—	2	2	no	—
432	C₄²×C₁₃	—	2	2	no	—
433	C₄²×C₁₃	—	2	2	no	—
434	C₄²×C₁₃	—	2	1	no	—
435	C₄²×C₁₃	—	2	2	no	—
436	C₄²×C₁₃	—	2	2	no	—
437	C₄²×C₁₃	—	2	2	no	—
438	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
441	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₁₃	C₂⁴	1	2	yes	—
443	C₄²×C₁₃	C₂⁴	1	2	yes	—
444	#3555	C₂×C₁₃	1	1	yes	characteristic, complemented
445	#3507	C₂×C₁₃	1	1	yes	characteristic, complemented
446	#3402	C₂×C₁₃	1	2	yes	complemented
447	#3400	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3398	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3395	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3394	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3393	C₂×C₁₃	1	2	yes	complemented
452	#3377	C₂×C₁₃	1	2	yes	complemented
453	#3375	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3372	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3364	C₂×C₁₃	1	2	yes	complemented
456	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3361	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3225	C₂×C₁₃	1	2	yes	complemented
459	#3223	C₂×C₁₃	1	2	yes	complemented
460	#3212	C₂×C₁₃	1	1	yes	characteristic
461	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3124	C₂×C₁₃	1	2	yes	complemented
463	#3120	C₂×C₁₃	1	2	yes	complemented
464	#3108	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
467	C₂³×C₁₃	—	2	1	no	—
468	C₂³×C₁₃	—	2	2	no	—
469	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
470	Q₈×C₁₃	—	2	2	no	—
471	Q₈×C₁₃	—	2	2	no	—
472	Q₈×C₁₃	—	2	1	no	—
473	Q₈×C₁₃	—	2	2	no	—
474	Q₈×C₁₃	—	2	2	no	—
475	Q₈×C₁₃	—	2	1	no	—
476	Q₈×C₁₃	—	2	1	no	—
477	Q₈×C₁₃	—	2	2	no	—
478	Q₈×C₁₃	—	2	1	no	—
479	Q₈×C₁₃	—	2	1	no	—
480	Q₈×C₁₃	—	2	1	no	—
481	Q₈×C₁₃	—	2	2	no	—
482	Q₈×C₁₃	—	4	2	no	—
483	Q₈×C₁₃	—	4	2	no	—
484	Q₈×C₁₃	—	8	1	no	—
485	Q₈×C₁₃	—	8	2	no	—
486	D₄×C₁₃	—	2	1	no	—
487	D₄×C₁₃	—	2	2	no	—
488	D₄×C₁₃	—	2	1	no	—
489	D₄×C₁₃	—	2	2	no	—
490	D₄×C₁₃	—	4	4	no	—
491	D₄×C₁₃	—	4	2	no	—
492	D₄×C₁₃	—	8	1	no	—
493	D₄×C₁₃	—	8	1	no	—
494	C₂×C₄×C₁₃	—	2	2	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	1	no	—
497	C₂×C₄×C₁₃	—	2	1	no	—
498	C₂×C₄×C₁₃	—	2	1	no	—
499	C₂×C₄×C₁₃	—	2	2	no	—
500	C₂×C₄×C₁₃	—	2	1	no	—
501	C₂×C₄×C₁₃	—	2	1	no	—
502	C₂×C₄×C₁₃	—	2	1	no	—
503	C₂×C₄×C₁₃	—	2	1	no	—
504	C₂×C₄×C₁₃	—	2	1	no	—
505	C₂×C₄×C₁₃	—	2	2	no	—
506	C₂×C₄×C₁₃	—	2	2	no	—
507	C₂×C₄×C₁₃	—	4	1	no	—
508	C₂×C₄×C₁₃	—	4	4	no	—
509	C₂×C₄×C₁₃	—	4	2	no	—
510	C₂×C₄×C₁₃	—	4	2	no	—
511	C₂×C₄×C₁₃	—	8	2	no	—
512	C₂×C₄×C₁₃	—	8	2	no	—
513	C₂×C₄×C₁₃	—	8	2	no	—
514	C₂×C₄×C₁₃	—	8	1	no	—
515	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
525	C₈×C₁₃	—	2	2	no	—
526	C₈×C₁₃	—	2	1	no	—
527	C₈×C₁₃	—	2	1	no	—
528	C₈×C₁₃	—	2	2	no	—
529	C₈×C₁₃	—	2	1	no	—
530	C₈×C₁₃	—	2	1	no	—
531	#563	—	2	2	no	—
532	#559	C₂²×C₁₃	1	1	yes	characteristic
533	#559	C₂²×C₁₃	1	1	yes	characteristic
534	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
535	#557	C₂²×C₁₃	1	1	yes	characteristic
536	#557	C₂²×C₁₃	1	1	yes	characteristic
537	#557	C₂²×C₁₃	1	1	yes	characteristic
538	#557	C₂²×C₁₃	1	2	yes	—
539	#556	—	2	1	no	—
540	#556	—	2	1	no	—
541	#556	C₂²×C₁₃	1	2	yes	—
542	#556	C₂²×C₁₃	1	2	yes	—
543	#556	C₂²×C₁₃	1	2	yes	—
544	#556	C₂²×C₁₃	1	1	yes	characteristic
545	#554	—	2	1	no	—
546	#554	C₂²×C₁₃	1	1	yes	characteristic
547	#552	—	2	2	no	—
548	#552	—	2	1	no	—
549	#544	—	2	1	no	—
550	#542	C₂²×C₁₃	1	2	yes	—
551	#541	—	2	1	no	—
552	#541	—	2	2	no	—
553	#541	C₂²×C₁₃	1	2	yes	—
554	#539	—	2	2	no	—
555	#536	C₂²×C₁₃	1	2	yes	—
556	#533	C₂²×C₁₃	1	1	yes	characteristic
557	#533	C₂²×C₁₃	1	1	yes	characteristic
558	#532	C₂²×C₁₃	1	1	yes	characteristic
559	#529	—	2	1	no	—
560	#529	—	2	1	no	—
561	#529	C₂²×C₁₃	1	1	yes	characteristic
562	#520	C₂²×C₁₃	1	2	yes	—
563	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
564	#497	C₂²×C₁₃	1	2	yes	—
565	#497	C₂²×C₁₃	1	2	yes	—
566	#495	C₂²×C₁₃	1	2	yes	—
567	#495	C₂²×C₁₃	1	2	yes	—
568	#494	C₂²×C₁₃	1	2	yes	—
569	#494	C₂²×C₁₃	1	1	yes	characteristic
570	#492	C₂²×C₁₃	1	1	yes	characteristic
571	#491	C₂²×C₁₃	1	2	yes	—
572	#489	C₂²×C₁₃	1	2	yes	—
573	#488	C₂²×C₁₃	1	2	yes	—
574	#488	C₂²×C₁₃	1	2	yes	—
575	#487	C₂²×C₁₃	1	2	yes	—
576	#487	C₂²×C₁₃	1	1	yes	characteristic
577	#486	C₂²×C₁₃	1	1	yes	characteristic
578	#484	C₂²×C₁₃	1	2	yes	—
579	#483	C₂²×C₁₃	1	1	yes	characteristic
580	#480	C₂²×C₁₃	1	1	yes	characteristic
581	#479	C₂²×C₁₃	1	1	yes	characteristic
582	#479	C₂²×C₁₃	1	1	yes	characteristic
583	#479	C₂²×C₁₃	1	2	yes	—
584	#478	C₂²×C₁₃	1	2	yes	—
585	#477	C₂²×C₁₃	1	1	yes	characteristic
586	#477	C₂²×C₁₃	1	1	yes	characteristic
587	#477	C₂²×C₁₃	1	2	yes	—
588	#474	C₂²×C₁₃	1	2	yes	—
589	#464	C₂²×C₁₃	1	1	yes	characteristic
590	#464	C₂²×C₁₃	1	1	yes	characteristic
591	#464	C₂²×C₁₃	1	2	yes	—
592	#464	C₂²×C₁₃	1	2	yes	—
593	#464	C₂²×C₁₃	1	2	yes	—
594	#464	C₂²×C₁₃	1	2	yes	—
595	#464	C₂²×C₁₃	1	2	yes	—
596	#464	C₂²×C₁₃	1	2	yes	—
597	#463	C₂²×C₁₃	1	2	yes	—
598	#463	C₂²×C₁₃	1	2	yes	—
599	#462	C₂²×C₁₃	1	1	yes	characteristic
600	#462	C₂²×C₁₃	1	1	yes	characteristic
601	#462	C₂²×C₁₃	1	1	yes	characteristic
602	#462	C₂²×C₁₃	1	2	yes	—
603	#462	C₂²×C₁₃	1	2	yes	—
604	#462	C₂²×C₁₃	1	2	yes	—
605	#462	C₂²×C₁₃	1	2	yes	—
606	#461	C₂²×C₁₃	1	2	yes	—
607	#461	C₂²×C₁₃	1	1	yes	characteristic
608	#461	C₂²×C₁₃	1	2	yes	—
609	#460	C₂²×C₁₃	1	1	yes	characteristic
610	#459	C₂²×C₁₃	1	1	yes	characteristic
611	#452	C₂²×C₁₃	1	2	yes	—
612	#452	C₂²×C₁₃	1	2	yes	—
613	#452	C₂²×C₁₃	1	2	yes	—
614	#451	C₂²×C₁₃	1	2	yes	—
615	#451	C₂²×C₁₃	1	1	yes	characteristic
616	#449	C₂²×C₁₃	1	2	yes	—
617	#448	C₂²×C₁₃	1	1	yes	characteristic
618	#446	C₂²×C₁₃	1	1	yes	characteristic
619	#446	C₂²×C₁₃	1	1	yes	characteristic
620	#446	C₂²×C₁₃	1	2	yes	—
621	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
622	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
623	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
624	#441	C₂²×C₁₃	1	2	yes	—
625	#440	C₂²×C₁₃	1	2	yes	—
626	#440	C₂²×C₁₃	1	2	yes	—
627	#440	C₂²×C₁₃	1	2	yes	—
628	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
629	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
630	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
631	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
632	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
633	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
634	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
635	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
636	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
637	C₄×D₈	C₂²×C₁₃	1	2	yes	—
638	#433	C₂²×C₁₃	1	2	yes	—
639	#433	C₂²×C₁₃	1	2	yes	—
640	#431	C₂²×C₁₃	1	1	yes	characteristic
641	#431	C₂²×C₁₃	1	1	yes	characteristic
642	C₂²×C₁₃	—	2	1	no	—
643	C₂²×C₁₃	—	2	1	no	—
644	C₂²×C₁₃	—	2	1	no	—
645	C₂²×C₁₃	—	4	2	no	—
646	C₂²×C₁₃	—	4	1	no	—
647	C₂²×C₁₃	—	4	2	no	—
648	C₂²×C₁₃	—	4	1	no	—
649	C₂²×C₁₃	—	4	1	no	—
650	C₂²×C₁₃	—	4	2	no	—
651	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
652	C₄×C₁₃	—	2	1	no	—
653	C₄×C₁₃	—	2	1	no	—
654	C₄×C₁₃	—	2	2	no	—
655	C₄×C₁₃	—	2	2	no	—
656	C₄×C₁₃	—	2	1	no	—
657	C₄×C₁₃	—	2	1	no	—
658	C₄×C₁₃	—	2	2	no	—
659	C₄×C₁₃	—	2	2	no	—
660	C₄×C₁₃	—	4	1	no	—
661	C₄×C₁₃	—	4	1	no	—
662	C₄×C₁₃	—	4	2	no	—
663	C₄×C₁₃	—	4	1	no	—
664	C₄×C₁₃	—	4	2	no	—
665	C₄×C₁₃	—	4	1	no	—
666	C₄×C₁₃	—	4	1	no	—
667	C₄×C₁₃	—	4	1	no	—
668	C₄×C₁₃	—	4	2	no	—
669	C₄×C₁₃	—	4	1	no	—
670	C₄×C₁₃	#578	1	2	yes	—
671	C₄×C₁₃	#585	1	1	yes	characteristic
672	C₄×C₁₃	#585	1	1	yes	characteristic
673	C₂×#41	C₂³×C₁₃	1	2	yes	—
674	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
676	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
677	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
679	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
680	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
681	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
682	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
684	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
688	C₂×D₈	C₂³×C₁₃	1	2	yes	—
689	C₄⋊Q₈	—	2	2	no	—
690	C₄⋊Q₈	—	2	2	no	—
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
693	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
694	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
695	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
696	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
697	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
698	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
699	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
701	#127	C₂³×C₁₃	1	1	yes	characteristic
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	1	no	—
713	#125	—	2	1	no	—
714	#125	—	2	1	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	—	2	2	no	—
722	#125	—	2	1	no	—
723	#125	—	2	1	no	—
724	#125	D₄×C₁₃	1	2	yes	—
725	#125	C₂³×C₁₃	1	1	yes	characteristic
726	#125	C₂³×C₁₃	1	2	yes	—
727	#124	—	2	1	no	—
728	#124	—	2	1	no	—
729	#124	—	2	2	no	—
730	#124	C₂³×C₁₃	1	1	yes	characteristic
731	#124	C₂³×C₁₃	1	2	yes	—
732	#124	C₂³×C₁₃	1	2	yes	—
733	#124	C₂³×C₁₃	1	2	yes	—
734	#124	C₂³×C₁₃	1	2	yes	—
735	#123	—	2	1	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
752	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
753	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
755	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
756	#121	—	2	1	no	—
757	#121	—	2	1	no	—
758	#121	C₂³×C₁₃	1	1	yes	characteristic
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
772	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
773	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
776	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
777	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
778	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
780	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	C₂³×C₁₃	1	2	yes	—
789	C₄×D₄	C₂³×C₁₃	1	2	yes	—
790	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
791	C₄×D₄	C₂³×C₁₃	1	2	yes	—
792	#117	—	2	1	no	—
793	#117	—	2	2	no	—
794	#117	—	2	2	no	—
795	#117	—	2	2	no	—
796	#117	—	2	2	no	—
797	#117	—	2	1	no	—
798	#117	—	2	1	no	—
799	#117	C₂³×C₁₃	1	2	yes	—
800	C₂×C₄⋊C₄	—	2	1	no	—
801	C₂×C₄⋊C₄	—	2	2	no	—
802	C₂×C₄⋊C₄	—	2	1	no	—
803	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
804	C₂×C₄²	—	2	1	no	—
805	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
806	#107	C₂³×C₁₃	1	2	yes	—
807	#107	C₂³×C₁₃	1	1	yes	characteristic
808	#107	C₂³×C₁₃	1	2	yes	—
809	#107	C₂³×C₁₃	1	1	yes	characteristic
810	#106	C₂³×C₁₃	1	1	yes	characteristic
811	#106	C₂³×C₁₃	1	1	yes	characteristic
812	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
817	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
818	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
819	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
820	#103	C₂³×C₁₃	1	2	yes	—
821	#103	C₂³×C₁₃	1	1	yes	characteristic
822	#103	C₂³×C₁₃	1	1	yes	characteristic
823	#103	C₂³×C₁₃	1	1	yes	characteristic
824	#103	C₂³×C₁₃	1	1	yes	characteristic
825	#103	C₂³×C₁₃	1	2	yes	—
826	#103	C₂³×C₁₃	1	1	yes	characteristic
827	#103	C₂³×C₁₃	1	1	yes	characteristic
828	#103	C₂³×C₁₃	1	2	yes	—
829	#103	C₂³×C₁₃	1	2	yes	—
830	#103	C₂³×C₁₃	1	2	yes	—
831	#103	C₂³×C₁₃	1	2	yes	—
832	#103	C₂³×C₁₃	1	2	yes	—
833	#103	C₂³×C₁₃	1	2	yes	—
834	#102	C₂³×C₁₃	1	1	yes	characteristic
835	#102	C₂³×C₁₃	1	2	yes	—
836	#102	C₂³×C₁₃	1	1	yes	characteristic
837	#102	C₂³×C₁₃	1	2	yes	—
838	#102	C₂³×C₁₃	1	2	yes	—
839	#102	C₂³×C₁₃	1	2	yes	—
840	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
841	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
842	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
843	#97	C₂³×C₁₃	1	2	yes	—
844	#97	C₂³×C₁₃	1	2	yes	—
845	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
846	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
847	C₄×C₈	C₂³×C₁₃	1	2	yes	—
848	C₄×C₈	C₂³×C₁₃	1	2	yes	—
849	C₄×C₈	C₂³×C₁₃	1	2	yes	—
850	C₂×C₁₃	—	4	1	no	—
851	C₂×C₁₃	—	8	2	no	—
852	C₂×C₁₃	—	8	1	no	—
853	C₂×C₁₃	#3487	1	1	yes	characteristic
854	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
855	C₂×C₁₃	#3584	1	1	yes	characteristic
856	#41	—	4	2	no	—
857	#41	—	4	2	no	—
858	C₂×Q₈	—	2	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	4	1	no	—
862	C₂×Q₈	—	4	1	no	—
863	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
864	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
865	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
866	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
867	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
869	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
870	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
876	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	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	C₂×D₄×C₁₃	1	1	yes	characteristic
885	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
887	Q₁₆	—	4	2	no	—
888	Q₁₆	—	4	2	no	—
889	Q₁₆	—	4	2	no	—
890	Q₁₆	—	4	1	no	—
891	Q₁₆	—	4	2	no	—
892	Q₁₆	—	4	1	no	—
893	Q₁₆	—	4	2	no	—
894	SD₁₆	—	4	1	no	—
895	SD₁₆	—	4	2	no	—
896	SD₁₆	—	4	2	no	—
897	SD₁₆	—	4	2	no	—
898	SD₁₆	—	4	2	no	—
899	SD₁₆	—	4	1	no	—
900	D₈	—	4	2	no	—
901	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
903	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
940	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
948	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
949	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
969	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
982	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
983	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
984	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
985	C₄²	C₂⁴×C₁₃	1	2	yes	—
986	C₄²	C₂⁴×C₁₃	1	2	yes	—
987	C₁₃	#61929	1	1	yes	characteristic, direct product factor, Sylow
988	C₂³	—	2	1	no	—
989	C₂³	—	2	2	no	—
990	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
991	Q₈	—	2	2	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	2	2	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	2	1	no	—
1001	Q₈	—	2	1	no	—
1002	Q₈	—	2	2	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	4	2	no	—
1005	Q₈	—	8	1	no	—
1006	Q₈	—	8	2	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	2	2	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	2	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	2	no	—
1013	D₄	—	8	1	no	—
1014	D₄	—	8	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	4	1	no	—
1029	C₂×C₄	—	4	4	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	8	1	no	—
1036	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1037	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1042	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1044	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1045	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1046	C₈	—	2	2	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	2	no	—
1080	C₄	C₁₃×#578	1	2	yes	—
1081	C₄	C₁₃×#585	1	1	yes	characteristic
1082	C₄	C₁₃×#585	1	1	yes	characteristic
1083	C₂	—	4	1	no	—
1084	C₂	—	8	1	no	—
1085	C₂	—	8	2	no	—
1086	C₂	C₁₃×#3487	1	1	yes	characteristic
1087	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1088	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3212	C₂
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×#3555	C₂	semidirect
2. C₁₃×#3507	C₂	semidirect
3. C₁₃×#3402	C₂	semidirect
4. C₁₃×#3400	C₂	semidirect
5. C₁₃×#3398	C₂	semidirect
6. C₁₃×#3395	C₂	semidirect
7. C₁₃×#3394	C₂	semidirect
8. C₁₃×#3393	C₂	semidirect
9. C₁₃×#3377	C₂	semidirect
10. C₁₃×#3375	C₂	semidirect
11. C₁₃×#3372	C₂	semidirect
12. C₁₃×#3364	C₂	semidirect
13. C₁₃×#3363	C₂	semidirect
14. C₁₃×#3361	C₂	semidirect
15. C₁₃×#3225	C₂	semidirect
16. C₁₃×#3223	C₂	semidirect
18. C₁₃×#3210	C₂	semidirect
19. C₁₃×#3124	C₂	semidirect
20. C₁₃×#3120	C₂	semidirect
21. C₁₃×#3108	C₂	semidirect
22. C₁₃×#3104	C₂	semidirect
23. C₁₃×#2986	C₂	semidirect
312. #61929	C₁₃	direct (N × H)
444. #3555	C₂×C₁₃	semidirect
445. #3507	C₂×C₁₃	semidirect
446. #3402	C₂×C₁₃	semidirect
447. #3400	C₂×C₁₃	semidirect
448. #3398	C₂×C₁₃	semidirect
449. #3395	C₂×C₁₃	semidirect
450. #3394	C₂×C₁₃	semidirect
451. #3393	C₂×C₁₃	semidirect
452. #3377	C₂×C₁₃	semidirect
453. #3375	C₂×C₁₃	semidirect
454. #3372	C₂×C₁₃	semidirect
455. #3364	C₂×C₁₃	semidirect
456. #3363	C₂×C₁₃	semidirect
457. #3361	C₂×C₁₃	semidirect
458. #3225	C₂×C₁₃	semidirect
459. #3223	C₂×C₁₃	semidirect
461. #3210	C₂×C₁₃	semidirect
462. #3124	C₂×C₁₃	semidirect
463. #3120	C₂×C₁₃	semidirect
464. #3108	C₂×C₁₃	semidirect
465. #3104	C₂×C₁₃	semidirect
466. #2986	C₂×C₁₃	semidirect
987. C₁₃	#61929	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×#3555	2
C₁₃×#3507	2
C₁₃×#3402	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3395	2
C₁₃×#3394	2
C₁₃×#3393	2
C₁₃×#3377	2
C₁₃×#3375	2
C₁₃×#3372	2
C₁₃×#3364	2
C₁₃×#3363	2
C₁₃×#3361	2
C₁₃×#3225	2
C₁₃×#3223	2
C₁₃×#3212	2
C₁₃×#3210	2
C₁₃×#3124	2
C₁₃×#3120	2
C₁₃×#3108	2
C₁₃×#3104	2
C₁₃×#2986	2
#61929	13

Subgroups — C13×#61929 #15748268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61929 #15748268