Subgroups — C₁₃×#61386 #15747725

Order 3328.

1690 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3504	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3390	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3388	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3388	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3387	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3385	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3383	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3381	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3164	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3084	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#3083	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic
19	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2947	C₂	1	1	yes	maximal, characteristic
22	C₁₃×#2947	C₂	1	1	yes	maximal, characteristic
23	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
24	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
25	Q₈²×C₁₃	—	2	1	no	—
26	Q₈²×C₁₃	C₂²	1	2	yes	—
27	C₁₃×#557	—	2	1	no	—
28	C₁₃×#557	—	2	1	no	—
29	C₁₃×#557	—	2	1	no	—
30	C₁₃×#557	C₂²	1	2	yes	—
31	C₁₃×#557	C₂²	1	2	yes	—
32	C₁₃×#557	C₂²	1	2	yes	—
33	C₁₃×#557	C₂²	1	2	yes	—
34	C₁₃×#557	C₂²	1	2	yes	—
35	C₁₃×#554	—	2	2	no	—
36	C₁₃×#554	—	2	2	no	—
37	C₁₃×#554	C₂²	1	2	yes	—
38	C₁₃×#554	C₂²	1	2	yes	—
39	C₁₃×#544	—	2	1	no	—
40	C₁₃×#544	—	2	1	no	—
41	C₁₃×#544	—	2	2	no	—
42	C₁₃×#544	C₂²	1	1	yes	characteristic
43	C₁₃×#544	C₂²	1	1	yes	characteristic
44	C₁₃×#544	C₂²	1	1	yes	characteristic
45	C₁₃×#544	C₂²	1	1	yes	characteristic
46	C₁₃×#533	—	2	1	no	—
47	C₁₃×#533	—	2	2	no	—
48	C₁₃×#533	C₂²	1	1	yes	characteristic
49	C₁₃×#533	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#125	—	2	1	no	—
51	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
52	C₁₃×#520	C₂²	1	1	yes	characteristic
53	C₁₃×#520	C₂²	1	1	yes	characteristic
54	C₁₃×#519	C₂²	1	1	yes	characteristic
55	C₁₃×#519	C₂²	1	1	yes	characteristic
56	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
58	C₁₃×#501	C₂²	1	2	yes	—
59	C₁₃×#501	C₂²	1	2	yes	—
60	C₁₃×#501	C₂²	1	2	yes	—
61	C₁₃×#501	C₂²	1	2	yes	—
62	C₁₃×#501	C₂²	1	2	yes	—
63	C₁₃×#501	C₂²	1	2	yes	—
64	C₁₃×#500	C₂²	1	2	yes	—
65	C₁₃×#499	C₂²	1	2	yes	—
66	C₁₃×#499	C₂²	1	2	yes	—
67	C₁₃×#499	C₂²	1	2	yes	—
68	C₁₃×#499	C₂²	1	2	yes	—
69	C₁₃×#498	C₂²	1	2	yes	—
70	C₁₃×#479	C₂²	1	2	yes	—
71	C₁₃×#479	C₂²	1	2	yes	—
72	C₁₃×#479	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	—
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×#479	C₂²	1	2	yes	—
78	C₁₃×#479	C₂²	1	2	yes	—
79	C₁₃×#479	C₂²	1	2	yes	—
80	C₁₃×#479	C₂²	1	2	yes	—
81	C₁₃×#479	C₂²	1	2	yes	—
82	C₁₃×#478	C₂²	1	1	yes	characteristic
83	C₁₃×#478	C₂²	1	1	yes	characteristic
84	C₁₃×#478	C₂²	1	2	yes	—
85	C₁₃×#478	C₂²	1	2	yes	—
86	C₁₃×#477	C₂²	1	1	yes	characteristic
87	C₁₃×#477	C₂²	1	2	yes	—
88	C₁₃×#477	C₂²	1	2	yes	—
89	C₁₃×#477	C₂²	1	2	yes	—
90	C₁₃×#476	C₂²	1	1	yes	characteristic
91	C₁₃×#476	C₂²	1	2	yes	—
92	C₁₃×#475	C₂²	1	1	yes	characteristic
93	C₁₃×#475	C₂²	1	2	yes	—
94	C₁₃×#475	C₂²	1	2	yes	—
95	C₁₃×#475	C₂²	1	2	yes	—
96	C₁₃×#474	C₂²	1	1	yes	characteristic
97	C₁₃×#474	C₂²	1	2	yes	—
98	C₁₃×#446	C₂²	1	2	yes	—
99	C₁₃×#446	C₂²	1	2	yes	—
100	C₁₃×#446	C₂²	1	2	yes	—
101	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
102	C₁₃×#441	C₂²	1	2	yes	—
103	C₁₃×#441	C₂²	1	2	yes	—
104	C₁₃×#441	C₂²	1	2	yes	—
105	C₁₃×#440	C₂²	1	2	yes	—
106	C₁₃×#440	C₂²	1	2	yes	—
107	C₁₃×#440	C₂²	1	2	yes	—
108	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
109	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
110	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
111	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
112	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
114	C₁₃×#428	C₂²	1	1	yes	characteristic
115	C₁₃×#428	C₂²	1	1	yes	characteristic
116	C₁₃×#428	C₂²	1	1	yes	characteristic
117	C₁₃×#428	C₂²	1	1	yes	characteristic
118	C₁₃×#428	C₂²	1	1	yes	characteristic
119	C₁₃×#427	C₂²	1	1	yes	characteristic
120	C₁₃×#427	C₂²	1	1	yes	characteristic
121	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
122	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
123	C₁₃×#424	C₂²	1	1	yes	characteristic
124	C₁₃×#424	C₂²	1	1	yes	characteristic
125	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₁₃×#419	C₂²	1	1	yes	characteristic
127	C₁₃×#417	C₂²	1	1	yes	characteristic
128	C₁₃×#416	C₂²	1	1	yes	characteristic
129	C₁₃×#416	C₂²	1	1	yes	characteristic
130	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
132	C₁₃×#405	C₂²	1	1	yes	characteristic
133	C₁₃×#405	C₂²	1	1	yes	characteristic
134	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
137	C₁₃×#137	Q₈	1	8	yes	complemented
138	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₁₃×C₄⋊Q₈	—	2	2	no	—
145	C₁₃×C₄⋊Q₈	—	2	2	no	—
146	C₁₃×C₄⋊Q₈	—	2	2	no	—
147	C₁₃×C₄⋊Q₈	—	2	2	no	—
148	C₁₃×C₄⋊Q₈	—	2	2	no	—
149	C₁₃×C₄⋊Q₈	—	2	1	no	—
150	C₁₃×C₄⋊Q₈	—	2	1	no	—
151	C₁₃×C₄⋊Q₈	—	2	2	no	—
152	C₁₃×C₄⋊Q₈	—	2	2	no	—
153	C₁₃×C₄⋊Q₈	—	2	2	no	—
154	C₁₃×C₄⋊Q₈	—	2	1	no	—
155	C₁₃×C₄⋊Q₈	—	2	1	no	—
156	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×#125	—	2	1	no	—
165	C₁₃×#125	—	2	1	no	—
166	C₁₃×#125	—	2	2	no	—
167	C₁₃×#125	—	2	2	no	—
168	C₁₃×#125	—	2	2	no	—
169	C₁₃×#125	—	2	2	no	—
170	C₁₃×#125	—	2	2	no	—
171	C₁₃×#125	—	2	2	no	—
172	C₁₃×#125	—	2	2	no	—
173	C₁₃×#125	—	2	2	no	—
174	C₁₃×#125	—	2	2	no	—
175	C₁₃×#125	—	2	2	no	—
176	C₁₃×#125	—	2	1	no	—
177	C₁₃×#125	—	2	1	no	—
178	C₁₃×#125	—	2	1	no	—
179	C₁₃×#125	—	2	1	no	—
180	C₁₃×#125	D₄	1	1	yes	characteristic
181	C₁₃×#125	D₄	1	1	yes	characteristic
182	C₁₃×#125	C₂³	1	1	yes	characteristic
183	C₁₃×#125	C₂³	1	1	yes	characteristic
184	C₁₃×#125	C₂³	1	2	yes	—
185	C₁₃×#125	C₂³	1	2	yes	—
186	C₁₃×#125	C₂³	1	2	yes	—
187	C₁₃×#125	C₂³	1	2	yes	—
188	C₁₃×#125	C₂³	1	2	yes	—
189	C₁₃×#125	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	1	no	—
193	C₁₃×C₂²⋊Q₈	—	2	1	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	—	2	2	no	—
200	C₁₃×C₂²⋊Q₈	—	2	2	no	—
201	C₁₃×C₂²⋊Q₈	—	2	2	no	—
202	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
203	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
204	C₄×Q₈×C₁₃	—	2	2	no	—
205	C₄×Q₈×C₁₃	—	2	1	no	—
206	C₄×Q₈×C₁₃	—	2	1	no	—
207	C₄×Q₈×C₁₃	—	2	1	no	—
208	C₄×Q₈×C₁₃	—	2	1	no	—
209	C₄×Q₈×C₁₃	—	2	2	no	—
210	C₄×Q₈×C₁₃	—	2	2	no	—
211	C₄×Q₈×C₁₃	—	2	2	no	—
212	C₄×Q₈×C₁₃	—	2	2	no	—
213	C₄×Q₈×C₁₃	—	2	2	no	—
214	C₄×Q₈×C₁₃	—	2	1	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	—	2	1	no	—
217	C₄×Q₈×C₁₃	—	2	1	no	—
218	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
219	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
229	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
230	C₄×D₄×C₁₃	—	2	1	no	—
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	—	2	2	no	—
233	C₄×D₄×C₁₃	—	2	2	no	—
234	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₁₃	C₂³	1	2	yes	—
236	C₄×D₄×C₁₃	C₂³	1	2	yes	—
237	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
238	C₁₃×#117	—	2	1	no	—
239	C₁₃×#117	—	2	1	no	—
240	C₁₃×#117	—	2	2	no	—
241	C₁₃×#117	—	2	2	no	—
242	C₁₃×#117	—	2	1	no	—
243	C₁₃×#117	C₂³	1	1	yes	characteristic
244	C₁₃×#117	C₂³	1	1	yes	characteristic
245	C₁₃×#117	C₂³	1	1	yes	characteristic
246	C₁₃×#117	C₂³	1	1	yes	characteristic
247	C₁₃×#117	C₂³	1	1	yes	characteristic
248	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
256	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₁₃	—	2	1	no	—
259	C₂×C₄²×C₁₃	—	2	1	no	—
260	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
261	C₁₃×#107	C₂³	1	2	yes	—
262	C₁₃×#107	C₂³	1	2	yes	—
263	C₁₃×#107	C₂³	1	1	yes	characteristic
264	C₁₃×#107	C₂³	1	1	yes	characteristic
265	C₁₃×#107	C₂³	1	1	yes	characteristic
266	C₁₃×#107	C₂³	1	1	yes	characteristic
267	C₁₃×#107	C₂³	1	2	yes	—
268	C₁₃×#107	C₂³	1	2	yes	—
269	C₁₃×#107	C₂³	1	2	yes	—
270	C₁₃×#107	C₂³	1	2	yes	—
271	C₁₃×#107	C₂³	1	2	yes	—
272	C₁₃×#106	C₂³	1	2	yes	—
273	C₁₃×#106	C₂³	1	2	yes	—
274	C₁₃×#106	C₂³	1	1	yes	characteristic
275	C₁₃×#106	C₂³	1	1	yes	characteristic
276	C₁₃×#106	C₂³	1	1	yes	characteristic
277	C₁₃×#106	C₂³	1	1	yes	characteristic
278	C₁₃×#106	C₂³	1	2	yes	—
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×#106	C₂³	1	2	yes	—
281	C₁₃×#106	C₂³	1	2	yes	—
282	C₁₃×#106	C₂³	1	2	yes	—
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
288	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
289	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
290	C₁₃×C₄⋊C₈	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	1	yes	characteristic
296	C₁₃×#103	C₂³	1	1	yes	characteristic
297	C₁₃×#103	C₂³	1	1	yes	characteristic
298	C₁₃×#103	C₂³	1	1	yes	characteristic
299	C₁₃×#103	C₂³	1	2	yes	—
300	C₁₃×#103	C₂³	1	2	yes	—
301	C₁₃×#103	C₂³	1	2	yes	—
302	C₁₃×#102	C₂³	1	1	yes	characteristic
303	C₁₃×#102	C₂³	1	1	yes	characteristic
304	C₁₃×#102	C₂³	1	1	yes	characteristic
305	C₁₃×#102	C₂³	1	1	yes	characteristic
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	2	yes	—
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₁₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	2	yes	—
311	C₄×C₈×C₁₃	C₂³	1	2	yes	—
312	C₄×C₈×C₁₃	C₂³	1	2	yes	—
313	#61386	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₁₃×#41	—	2	2	no	—
315	C₁₃×#41	C₂×Q₈	1	4	yes	—
316	C₂×Q₈×C₁₃	—	2	1	no	—
317	C₂×Q₈×C₁₃	—	2	1	no	—
318	C₂×Q₈×C₁₃	—	2	2	no	—
319	C₂×Q₈×C₁₃	—	2	2	no	—
320	C₂×Q₈×C₁₃	—	2	1	no	—
321	C₂×Q₈×C₁₃	—	2	2	no	—
322	C₂×Q₈×C₁₃	—	2	2	no	—
323	C₂×Q₈×C₁₃	—	2	2	no	—
324	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
325	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
327	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₁₃	—	2	1	no	—
330	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₁₃	—	2	1	no	—
332	C₂²×C₄×C₁₃	—	2	1	no	—
333	C₂²×C₄×C₁₃	—	2	1	no	—
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	1	no	—
338	C₂²×C₄×C₁₃	—	2	2	no	—
339	C₂²×C₄×C₁₃	—	2	2	no	—
340	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₁₃×Q₁₆	C₂×Q₈	1	8	yes	—
344	C₁₃×SD₁₆	C₂×Q₈	1	8	yes	—
345	C₁₃×M₁₆	—	2	2	no	—
346	C₁₃×M₁₆	C₂×Q₈	1	4	yes	—
347	C₂×C₈×C₁₃	—	2	2	no	—
348	C₂×C₈×C₁₃	—	2	2	no	—
349	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
352	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
355	C₁₃×C₄⋊C₄	—	2	2	no	—
356	C₁₃×C₄⋊C₄	—	2	2	no	—
357	C₁₃×C₄⋊C₄	—	2	1	no	—
358	C₁₃×C₄⋊C₄	—	2	1	no	—
359	C₁₃×C₄⋊C₄	—	2	2	no	—
360	C₁₃×C₄⋊C₄	—	2	2	no	—
361	C₁₃×C₄⋊C₄	—	2	2	no	—
362	C₁₃×C₄⋊C₄	—	2	2	no	—
363	C₁₃×C₄⋊C₄	—	2	2	no	—
364	C₁₃×C₄⋊C₄	—	2	2	no	—
365	C₁₃×C₄⋊C₄	—	2	2	no	—
366	C₁₃×C₄⋊C₄	—	2	2	no	—
367	C₁₃×C₄⋊C₄	—	2	2	no	—
368	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	—	2	2	no	—
376	C₁₃×C₄⋊C₄	—	2	1	no	—
377	C₁₃×C₄⋊C₄	—	2	1	no	—
378	C₁₃×C₄⋊C₄	—	2	1	no	—
379	C₁₃×C₄⋊C₄	—	2	2	no	—
380	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
391	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
392	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
393	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
394	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
399	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
401	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
405	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
406	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
407	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
408	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₁₃×C₂²⋊C₄	—	2	1	no	—
410	C₁₃×C₂²⋊C₄	—	2	1	no	—
411	C₁₃×C₂²⋊C₄	—	2	1	no	—
412	C₁₃×C₂²⋊C₄	—	2	1	no	—
413	C₁₃×C₂²⋊C₄	—	2	1	no	—
414	C₁₃×C₂²⋊C₄	—	2	2	no	—
415	C₁₃×C₂²⋊C₄	—	2	2	no	—
416	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
417	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
418	C₄²×C₁₃	—	2	1	no	—
419	C₄²×C₁₃	—	2	1	no	—
420	C₄²×C₁₃	—	2	1	no	—
421	C₄²×C₁₃	—	2	2	no	—
422	C₄²×C₁₃	—	2	2	no	—
423	C₄²×C₁₃	—	2	2	no	—
424	C₄²×C₁₃	—	2	2	no	—
425	C₄²×C₁₃	—	2	2	no	—
426	C₄²×C₁₃	—	2	2	no	—
427	C₄²×C₁₃	—	2	2	no	—
428	C₄²×C₁₃	—	2	2	no	—
429	C₄²×C₁₃	—	2	1	no	—
430	C₄²×C₁₃	—	2	1	no	—
431	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
433	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
434	C₄²×C₁₃	C₂⁴	1	2	yes	—
435	C₄²×C₁₃	C₂⁴	1	2	yes	—
436	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
437	#3504	C₂×C₁₃	1	1	yes	characteristic
438	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
439	#3390	C₂×C₁₃	1	2	yes	complemented
440	#3390	C₂×C₁₃	1	2	yes	complemented
441	#3388	C₂×C₁₃	1	2	yes	complemented
442	#3388	C₂×C₁₃	1	2	yes	complemented
443	#3387	C₂×C₁₃	1	2	yes	complemented
444	#3385	C₂×C₁₃	1	2	yes	complemented
445	#3383	C₂×C₁₃	1	2	yes	complemented
446	#3381	C₂×C₁₃	1	2	yes	complemented
447	#3166	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3164	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3163	C₂×C₁₃	1	1	yes	characteristic, complemented
450	#3084	C₂×C₁₃	1	1	yes	characteristic
451	#3083	C₂×C₁₃	1	1	yes	characteristic
452	#3082	C₂×C₁₃	1	1	yes	characteristic, complemented
453	#3082	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3076	C₂×C₁₃	1	1	yes	characteristic
455	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#2947	C₂×C₁₃	1	1	yes	characteristic
458	#2947	C₂×C₁₃	1	1	yes	characteristic
459	C₄×#137	C₂×C₁₃	1	1	yes	characteristic
460	C₂³×C₁₃	—	2	1	no	—
461	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
462	Q₈×C₁₃	—	2	4	no	—
463	Q₈×C₁₃	—	2	2	no	—
464	Q₈×C₁₃	—	2	1	no	—
465	Q₈×C₁₃	—	4	2	no	—
466	Q₈×C₁₃	—	4	2	no	—
467	Q₈×C₁₃	—	4	2	no	—
468	Q₈×C₁₃	—	8	1	no	—
469	Q₈×C₁₃	—	8	2	no	—
470	Q₈×C₁₃	—	8	2	no	—
471	Q₈×C₁₃	—	8	2	no	—
472	Q₈×C₁₃	—	8	2	no	—
473	Q₈×C₁₃	C₂²×Q₈	1	4	yes	—
474	Q₈×C₁₃	C₂²×Q₈	1	2	yes	—
475	D₄×C₁₃	—	2	4	no	—
476	D₄×C₁₃	—	2	1	no	—
477	D₄×C₁₃	C₂²×Q₈	1	2	yes	—
478	C₂×C₄×C₁₃	—	2	4	no	—
479	C₂×C₄×C₁₃	—	2	1	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	2	4	no	—
482	C₂×C₄×C₁₃	—	2	1	no	—
483	C₂×C₄×C₁₃	—	2	1	no	—
484	C₂×C₄×C₁₃	—	2	1	no	—
485	C₂×C₄×C₁₃	—	2	1	no	—
486	C₂×C₄×C₁₃	—	2	1	no	—
487	C₂×C₄×C₁₃	—	2	1	no	—
488	C₂×C₄×C₁₃	—	2	2	no	—
489	C₂×C₄×C₁₃	—	2	2	no	—
490	C₂×C₄×C₁₃	—	2	2	no	—
491	C₂×C₄×C₁₃	—	4	1	no	—
492	C₂×C₄×C₁₃	—	4	1	no	—
493	C₂×C₄×C₁₃	—	8	1	no	—
494	C₂×C₄×C₁₃	—	8	2	no	—
495	C₂×C₄×C₁₃	—	8	1	no	—
496	C₂×C₄×C₁₃	—	8	2	no	—
497	C₂×C₄×C₁₃	—	8	1	no	—
498	C₂×C₄×C₁₃	—	8	1	no	—
499	C₂×C₄×C₁₃	—	8	1	no	—
500	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
510	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
511	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
512	C₈×C₁₃	—	2	1	no	—
513	C₈×C₁₃	—	2	1	no	—
514	C₈×C₁₃	—	2	1	no	—
515	C₈×C₁₃	—	2	1	no	—
516	C₈×C₁₃	—	2	2	no	—
517	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
518	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
519	Q₈²	—	2	1	no	—
520	Q₈²	C₂²×C₁₃	1	2	yes	—
521	#557	—	2	1	no	—
522	#557	—	2	1	no	—
523	#557	—	2	1	no	—
524	#557	C₂²×C₁₃	1	2	yes	—
525	#557	C₂²×C₁₃	1	2	yes	—
526	#557	C₂²×C₁₃	1	2	yes	—
527	#557	C₂²×C₁₃	1	2	yes	—
528	#557	C₂²×C₁₃	1	2	yes	—
529	#554	—	2	2	no	—
530	#554	—	2	2	no	—
531	#554	C₂²×C₁₃	1	2	yes	—
532	#554	C₂²×C₁₃	1	2	yes	—
533	#544	—	2	1	no	—
534	#544	—	2	1	no	—
535	#544	—	2	2	no	—
536	#544	C₂²×C₁₃	1	1	yes	characteristic
537	#544	C₂²×C₁₃	1	1	yes	characteristic
538	#544	C₂²×C₁₃	1	1	yes	characteristic
539	#544	C₂²×C₁₃	1	1	yes	characteristic
540	#533	—	2	1	no	—
541	#533	—	2	2	no	—
542	#533	C₂²×C₁₃	1	1	yes	characteristic
543	#533	C₂²×C₁₃	1	1	yes	characteristic
544	C₂×#125	—	2	1	no	—
545	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
546	#520	C₂²×C₁₃	1	1	yes	characteristic
547	#520	C₂²×C₁₃	1	1	yes	characteristic
548	#519	C₂²×C₁₃	1	1	yes	characteristic
549	#519	C₂²×C₁₃	1	1	yes	characteristic
550	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
551	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
552	#501	C₂²×C₁₃	1	2	yes	—
553	#501	C₂²×C₁₃	1	2	yes	—
554	#501	C₂²×C₁₃	1	2	yes	—
555	#501	C₂²×C₁₃	1	2	yes	—
556	#501	C₂²×C₁₃	1	2	yes	—
557	#501	C₂²×C₁₃	1	2	yes	—
558	#500	C₂²×C₁₃	1	2	yes	—
559	#499	C₂²×C₁₃	1	2	yes	—
560	#499	C₂²×C₁₃	1	2	yes	—
561	#499	C₂²×C₁₃	1	2	yes	—
562	#499	C₂²×C₁₃	1	2	yes	—
563	#498	C₂²×C₁₃	1	2	yes	—
564	#479	C₂²×C₁₃	1	2	yes	—
565	#479	C₂²×C₁₃	1	2	yes	—
566	#479	C₂²×C₁₃	1	2	yes	—
567	#479	C₂²×C₁₃	1	2	yes	—
568	#479	C₂²×C₁₃	1	1	yes	characteristic
569	#479	C₂²×C₁₃	1	1	yes	characteristic
570	#479	C₂²×C₁₃	1	2	yes	—
571	#479	C₂²×C₁₃	1	2	yes	—
572	#479	C₂²×C₁₃	1	2	yes	—
573	#479	C₂²×C₁₃	1	2	yes	—
574	#479	C₂²×C₁₃	1	2	yes	—
575	#479	C₂²×C₁₃	1	2	yes	—
576	#478	C₂²×C₁₃	1	1	yes	characteristic
577	#478	C₂²×C₁₃	1	1	yes	characteristic
578	#478	C₂²×C₁₃	1	2	yes	—
579	#478	C₂²×C₁₃	1	2	yes	—
580	#477	C₂²×C₁₃	1	1	yes	characteristic
581	#477	C₂²×C₁₃	1	2	yes	—
582	#477	C₂²×C₁₃	1	2	yes	—
583	#477	C₂²×C₁₃	1	2	yes	—
584	#476	C₂²×C₁₃	1	1	yes	characteristic
585	#476	C₂²×C₁₃	1	2	yes	—
586	#475	C₂²×C₁₃	1	1	yes	characteristic
587	#475	C₂²×C₁₃	1	2	yes	—
588	#475	C₂²×C₁₃	1	2	yes	—
589	#475	C₂²×C₁₃	1	2	yes	—
590	#474	C₂²×C₁₃	1	1	yes	characteristic
591	#474	C₂²×C₁₃	1	2	yes	—
592	#446	C₂²×C₁₃	1	2	yes	—
593	#446	C₂²×C₁₃	1	2	yes	—
594	#446	C₂²×C₁₃	1	2	yes	—
595	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
596	#441	C₂²×C₁₃	1	2	yes	—
597	#441	C₂²×C₁₃	1	2	yes	—
598	#441	C₂²×C₁₃	1	2	yes	—
599	#440	C₂²×C₁₃	1	2	yes	—
600	#440	C₂²×C₁₃	1	2	yes	—
601	#440	C₂²×C₁₃	1	2	yes	—
602	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
603	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
604	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
605	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
606	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
607	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
608	#428	C₂²×C₁₃	1	1	yes	characteristic
609	#428	C₂²×C₁₃	1	1	yes	characteristic
610	#428	C₂²×C₁₃	1	1	yes	characteristic
611	#428	C₂²×C₁₃	1	1	yes	characteristic
612	#428	C₂²×C₁₃	1	1	yes	characteristic
613	#427	C₂²×C₁₃	1	1	yes	characteristic
614	#427	C₂²×C₁₃	1	1	yes	characteristic
615	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
616	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
617	#424	C₂²×C₁₃	1	1	yes	characteristic
618	#424	C₂²×C₁₃	1	1	yes	characteristic
619	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
620	#419	C₂²×C₁₃	1	1	yes	characteristic
621	#417	C₂²×C₁₃	1	1	yes	characteristic
622	#416	C₂²×C₁₃	1	1	yes	characteristic
623	#416	C₂²×C₁₃	1	1	yes	characteristic
624	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
625	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
626	#405	C₂²×C₁₃	1	1	yes	characteristic
627	#405	C₂²×C₁₃	1	1	yes	characteristic
628	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
629	C₂²×C₁₃	—	2	1	no	—
630	C₂²×C₁₃	—	2	1	no	—
631	C₂²×C₁₃	—	2	2	no	—
632	C₂²×C₁₃	—	4	1	no	—
633	C₂²×C₁₃	—	4	1	no	—
634	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
635	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
636	C₄×C₁₃	—	2	1	no	—
637	C₄×C₁₃	—	2	1	no	—
638	C₄×C₁₃	—	2	2	no	—
639	C₄×C₁₃	—	2	2	no	—
640	C₄×C₁₃	—	2	1	no	—
641	C₄×C₁₃	—	2	1	no	—
642	C₄×C₁₃	—	2	2	no	—
643	C₄×C₁₃	—	2	2	no	—
644	C₄×C₁₃	—	2	2	no	—
645	C₄×C₁₃	—	2	4	no	—
646	C₄×C₁₃	—	4	2	no	—
647	C₄×C₁₃	—	4	1	no	—
648	C₄×C₁₃	—	4	2	no	—
649	C₄×C₁₃	—	4	1	no	—
650	C₄×C₁₃	—	4	1	no	—
651	C₄×C₁₃	—	4	2	no	—
652	C₄×C₁₃	—	4	1	no	—
653	C₄×C₁₃	—	4	1	no	—
654	C₄×C₁₃	—	4	1	no	—
655	C₄×C₁₃	D₄×Q₈	1	2	yes	—
656	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
657	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
658	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
659	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
660	#137	Q₈×C₁₃	1	8	yes	complemented
661	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
662	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
663	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
664	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
665	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
666	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
667	C₄⋊Q₈	—	2	2	no	—
668	C₄⋊Q₈	—	2	2	no	—
669	C₄⋊Q₈	—	2	2	no	—
670	C₄⋊Q₈	—	2	2	no	—
671	C₄⋊Q₈	—	2	2	no	—
672	C₄⋊Q₈	—	2	1	no	—
673	C₄⋊Q₈	—	2	1	no	—
674	C₄⋊Q₈	—	2	2	no	—
675	C₄⋊Q₈	—	2	2	no	—
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	—	2	1	no	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
680	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
681	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
682	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
683	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
684	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
685	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
686	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
687	#125	—	2	1	no	—
688	#125	—	2	1	no	—
689	#125	—	2	2	no	—
690	#125	—	2	2	no	—
691	#125	—	2	2	no	—
692	#125	—	2	2	no	—
693	#125	—	2	2	no	—
694	#125	—	2	2	no	—
695	#125	—	2	2	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	1	no	—
700	#125	—	2	1	no	—
701	#125	—	2	1	no	—
702	#125	—	2	1	no	—
703	#125	D₄×C₁₃	1	1	yes	characteristic
704	#125	D₄×C₁₃	1	1	yes	characteristic
705	#125	C₂³×C₁₃	1	2	yes	—
706	#125	C₂³×C₁₃	1	2	yes	—
707	#125	C₂³×C₁₃	1	1	yes	characteristic
708	#125	C₂³×C₁₃	1	1	yes	characteristic
709	#125	C₂³×C₁₃	1	2	yes	—
710	#125	C₂³×C₁₃	1	2	yes	—
711	#125	C₂³×C₁₃	1	2	yes	—
712	#125	C₂³×C₁₃	1	2	yes	—
713	C₂²⋊Q₈	—	2	2	no	—
714	C₂²⋊Q₈	—	2	2	no	—
715	C₂²⋊Q₈	—	2	1	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
726	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
727	C₄×Q₈	—	2	2	no	—
728	C₄×Q₈	—	2	1	no	—
729	C₄×Q₈	—	2	1	no	—
730	C₄×Q₈	—	2	1	no	—
731	C₄×Q₈	—	2	1	no	—
732	C₄×Q₈	—	2	2	no	—
733	C₄×Q₈	—	2	2	no	—
734	C₄×Q₈	—	2	2	no	—
735	C₄×Q₈	—	2	2	no	—
736	C₄×Q₈	—	2	2	no	—
737	C₄×Q₈	—	2	1	no	—
738	C₄×Q₈	—	2	1	no	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
742	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
743	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
744	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
745	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
746	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
747	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
748	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
749	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
750	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
751	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
752	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
753	C₄×D₄	—	2	1	no	—
754	C₄×D₄	—	2	1	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
758	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
759	C₄×D₄	C₂³×C₁₃	1	2	yes	—
760	C₄×D₄	C₂³×C₁₃	1	2	yes	—
761	#117	—	2	1	no	—
762	#117	—	2	1	no	—
763	#117	—	2	2	no	—
764	#117	—	2	2	no	—
765	#117	—	2	1	no	—
766	#117	C₂³×C₁₃	1	1	yes	characteristic
767	#117	C₂³×C₁₃	1	1	yes	characteristic
768	#117	C₂³×C₁₃	1	1	yes	characteristic
769	#117	C₂³×C₁₃	1	1	yes	characteristic
770	#117	C₂³×C₁₃	1	1	yes	characteristic
771	C₂×C₄⋊C₄	—	2	1	no	—
772	C₂×C₄⋊C₄	—	2	1	no	—
773	C₂×C₄⋊C₄	—	2	1	no	—
774	C₂×C₄⋊C₄	—	2	1	no	—
775	C₂×C₄⋊C₄	—	2	1	no	—
776	C₂×C₄⋊C₄	—	2	2	no	—
777	C₂×C₄⋊C₄	—	2	2	no	—
778	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
779	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
780	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
781	C₂×C₄²	—	2	1	no	—
782	C₂×C₄²	—	2	1	no	—
783	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
784	#107	C₂³×C₁₃	1	2	yes	—
785	#107	C₂³×C₁₃	1	2	yes	—
786	#107	C₂³×C₁₃	1	1	yes	characteristic
787	#107	C₂³×C₁₃	1	1	yes	characteristic
788	#107	C₂³×C₁₃	1	1	yes	characteristic
789	#107	C₂³×C₁₃	1	1	yes	characteristic
790	#107	C₂³×C₁₃	1	2	yes	—
791	#107	C₂³×C₁₃	1	2	yes	—
792	#107	C₂³×C₁₃	1	2	yes	—
793	#107	C₂³×C₁₃	1	2	yes	—
794	#107	C₂³×C₁₃	1	2	yes	—
795	#106	C₂³×C₁₃	1	2	yes	—
796	#106	C₂³×C₁₃	1	2	yes	—
797	#106	C₂³×C₁₃	1	1	yes	characteristic
798	#106	C₂³×C₁₃	1	1	yes	characteristic
799	#106	C₂³×C₁₃	1	1	yes	characteristic
800	#106	C₂³×C₁₃	1	1	yes	characteristic
801	#106	C₂³×C₁₃	1	2	yes	—
802	#106	C₂³×C₁₃	1	2	yes	—
803	#106	C₂³×C₁₃	1	2	yes	—
804	#106	C₂³×C₁₃	1	2	yes	—
805	#106	C₂³×C₁₃	1	2	yes	—
806	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
807	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
808	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
809	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
810	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
811	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
812	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
813	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
814	#103	C₂³×C₁₃	1	2	yes	—
815	#103	C₂³×C₁₃	1	2	yes	—
816	#103	C₂³×C₁₃	1	2	yes	—
817	#103	C₂³×C₁₃	1	2	yes	—
818	#103	C₂³×C₁₃	1	1	yes	characteristic
819	#103	C₂³×C₁₃	1	1	yes	characteristic
820	#103	C₂³×C₁₃	1	1	yes	characteristic
821	#103	C₂³×C₁₃	1	1	yes	characteristic
822	#103	C₂³×C₁₃	1	2	yes	—
823	#103	C₂³×C₁₃	1	2	yes	—
824	#103	C₂³×C₁₃	1	2	yes	—
825	#102	C₂³×C₁₃	1	1	yes	characteristic
826	#102	C₂³×C₁₃	1	1	yes	characteristic
827	#102	C₂³×C₁₃	1	1	yes	characteristic
828	#102	C₂³×C₁₃	1	1	yes	characteristic
829	#102	C₂³×C₁₃	1	2	yes	—
830	#97	C₂³×C₁₃	1	2	yes	—
831	#97	C₂³×C₁₃	1	2	yes	—
832	#97	C₂³×C₁₃	1	2	yes	—
833	C₄×C₈	C₂³×C₁₃	1	2	yes	—
834	C₄×C₈	C₂³×C₁₃	1	2	yes	—
835	C₄×C₈	C₂³×C₁₃	1	2	yes	—
836	C₂×C₁₃	—	2	2	no	—
837	C₂×C₁₃	—	4	2	no	—
838	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
839	C₂×C₁₃	#3584	1	1	yes	characteristic
840	C₂×C₁₃	#3586	1	1	yes	characteristic
841	#41	—	2	2	no	—
842	#41	C₂×Q₈×C₁₃	1	4	yes	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	2	no	—
846	C₂×Q₈	—	2	2	no	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	2	2	no	—
849	C₂×Q₈	—	2	2	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
852	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
853	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
854	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
855	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
858	C₂²×C₄	—	2	1	no	—
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
868	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
870	Q₁₆	C₂×Q₈×C₁₃	1	8	yes	—
871	SD₁₆	C₂×Q₈×C₁₃	1	8	yes	—
872	M₁₆	—	2	2	no	—
873	M₁₆	C₂×Q₈×C₁₃	1	4	yes	—
874	C₂×C₈	—	2	2	no	—
875	C₂×C₈	—	2	2	no	—
876	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
877	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
878	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
879	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
880	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
881	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	1	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
918	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
920	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
921	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
922	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
923	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
924	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
925	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
926	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
927	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
928	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
929	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
933	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
934	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
936	C₂²⋊C₄	—	2	1	no	—
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
944	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
945	C₄²	—	2	1	no	—
946	C₄²	—	2	1	no	—
947	C₄²	—	2	1	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	1	no	—
957	C₄²	—	2	1	no	—
958	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
959	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
960	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
961	C₄²	C₂⁴×C₁₃	1	2	yes	—
962	C₄²	C₂⁴×C₁₃	1	2	yes	—
963	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
964	C₁₃	#61386	1	1	yes	characteristic, direct product factor, Sylow
965	C₂³	—	2	1	no	—
966	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
967	Q₈	—	2	4	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	2	1	no	—
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	4	2	no	—
973	Q₈	—	8	1	no	—
974	Q₈	—	8	2	no	—
975	Q₈	—	8	2	no	—
976	Q₈	—	8	2	no	—
977	Q₈	—	8	2	no	—
978	Q₈	C₂²×Q₈×C₁₃	1	4	yes	—
979	Q₈	C₂²×Q₈×C₁₃	1	2	yes	—
980	D₄	—	2	4	no	—
981	D₄	—	2	1	no	—
982	D₄	C₂²×Q₈×C₁₃	1	2	yes	—
983	C₂×C₄	—	2	4	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	4	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	4	1	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	8	1	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	8	1	no	—
1001	C₂×C₄	—	8	2	no	—
1002	C₂×C₄	—	8	1	no	—
1003	C₂×C₄	—	8	1	no	—
1004	C₂×C₄	—	8	1	no	—
1005	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1006	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1007	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1008	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1009	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1010	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1011	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1012	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1013	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1014	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
1015	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
1016	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	1	no	—
1020	C₈	—	2	1	no	—
1021	C₈	—	2	2	no	—
1022	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
1029	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1030	C₄	—	2	1	no	—
1031	C₄	—	2	1	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	2	no	—
1034	C₄	—	2	1	no	—
1035	C₄	—	2	1	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	D₄×Q₈×C₁₃	1	2	yes	—
1050	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
1051	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1052	C₂	—	2	2	no	—
1053	C₂	—	4	2	no	—
1054	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
1055	C₂	C₁₃×#3584	1	1	yes	characteristic
1056	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
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
2. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3390	C₂	semidirect
4. C₁₃×#3390	C₂	semidirect
5. C₁₃×#3388	C₂	semidirect
6. C₁₃×#3388	C₂	semidirect
7. C₁₃×#3387	C₂	semidirect
8. C₁₃×#3385	C₂	semidirect
9. C₁₃×#3383	C₂	semidirect
10. C₁₃×#3381	C₂	semidirect
11. C₁₃×#3166	C₂	semidirect
12. C₁₃×#3164	C₂	semidirect
13. C₁₃×#3163	C₂	semidirect
16. C₁₃×#3082	C₂	semidirect
17. C₁₃×#3082	C₂	semidirect
19. C₂×C₁₃×#479	C₂	semidirect
20. C₁₃×#2962	C₂	semidirect
137. C₁₃×#137	Q₈	semidirect
313. #61386	C₁₃	direct (N × H)
438. #3502	C₂×C₁₃	semidirect
439. #3390	C₂×C₁₃	semidirect
440. #3390	C₂×C₁₃	semidirect
441. #3388	C₂×C₁₃	semidirect
442. #3388	C₂×C₁₃	semidirect
443. #3387	C₂×C₁₃	semidirect
444. #3385	C₂×C₁₃	semidirect
445. #3383	C₂×C₁₃	semidirect
446. #3381	C₂×C₁₃	semidirect
447. #3166	C₂×C₁₃	semidirect
448. #3164	C₂×C₁₃	semidirect
449. #3163	C₂×C₁₃	semidirect
452. #3082	C₂×C₁₃	semidirect
453. #3082	C₂×C₁₃	semidirect
455. C₂×#479	C₂×C₁₃	semidirect
456. #2962	C₂×C₁₃	semidirect
660. #137	Q₈×C₁₃	semidirect
964. C₁₃	#61386	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×#3504	2
C₁₃×#3502	2
C₁₃×#3390	2
C₁₃×#3388	2
C₁₃×#3387	2
C₁₃×#3385	2
C₁₃×#3383	2
C₁₃×#3381	2
C₁₃×#3166	2
C₁₃×#3164	2
C₁₃×#3163	2
C₁₃×#3084	2
C₁₃×#3083	2
C₁₃×#3082	2
C₁₃×#3076	2
C₂×C₁₃×#479	2
C₁₃×#2962	2
C₁₃×#2947	2
C₄×C₁₃×#137	2
#61386	13

Subgroups — C13×#61386 #15747725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61386 #15747725