Subgroups — C₁₃×#62168 #15748507

Order 3328.

1628 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3563	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3523	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3349	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3344	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3336	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3299	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3261	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3242	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3127	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3082	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
20	C₁₃×#564	—	2	1	no	—
21	C₁₃×#563	—	2	1	no	—
22	C₁₃×#557	—	2	1	no	—
23	C₁₃×#557	C₂²	1	1	yes	characteristic
24	C₁₃×#557	C₂²	1	1	yes	characteristic
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#556	—	2	1	no	—
27	C₁₃×#556	C₂²	1	1	yes	characteristic
28	C₁₃×#554	C₂²	1	2	yes	—
29	C₁₃×#552	—	2	2	no	—
30	C₁₃×#552	—	2	2	no	—
31	C₁₃×#552	C₂²	1	2	yes	—
32	C₁₃×#552	C₂²	1	2	yes	—
33	C₁₃×#552	C₂²	1	2	yes	—
34	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
35	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#544	—	2	1	no	—
37	C₁₃×#544	C₂²	1	2	yes	—
38	C₁₃×#541	—	2	2	no	—
39	C₁₃×#541	—	2	2	no	—
40	C₁₃×#541	C₂²	1	2	yes	—
41	C₁₃×#541	C₂²	1	2	yes	—
42	C₁₃×#539	—	2	1	no	—
43	C₁₃×#533	—	2	1	no	—
44	C₁₃×#533	C₂²	1	1	yes	characteristic
45	C₁₃×#533	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×#519	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×#499	C₂²	1	2	yes	—
54	C₁₃×#491	C₂²	1	2	yes	—
55	C₁₃×#491	C₂²	1	2	yes	—
56	C₁₃×#487	C₂²	1	2	yes	—
57	C₁₃×#485	C₂²	1	2	yes	—
58	C₁₃×#485	C₂²	1	2	yes	—
59	C₁₃×#485	C₂²	1	2	yes	—
60	C₁₃×#485	C₂²	1	2	yes	—
61	C₁₃×#484	C₂²	1	2	yes	—
62	C₁₃×#484	C₂²	1	2	yes	—
63	C₁₃×#483	C₂²	1	2	yes	—
64	C₁₃×#483	C₂²	1	2	yes	—
65	C₁₃×#483	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×#479	C₂²	1	2	yes	—
72	C₁₃×#479	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	—
74	C₁₃×#479	C₂²	1	2	yes	—
75	C₁₃×#479	C₂²	1	2	yes	—
76	C₁₃×#477	C₂²	1	2	yes	—
77	C₁₃×#477	C₂²	1	2	yes	—
78	C₁₃×#477	C₂²	1	2	yes	—
79	C₁₃×#475	C₂²	1	1	yes	characteristic
80	C₁₃×#475	C₂²	1	2	yes	—
81	C₁₃×#475	C₂²	1	1	yes	characteristic
82	C₁₃×#470	C₂²	1	2	yes	—
83	C₁₃×#470	C₂²	1	2	yes	—
84	C₁₃×#467	C₂²	1	2	yes	—
85	C₁₃×#467	C₂²	1	2	yes	—
86	C₁₃×#467	C₂²	1	2	yes	—
87	C₁₃×#467	C₂²	1	2	yes	—
88	C₁₃×#462	C₂²	1	2	yes	—
89	C₁₃×#462	C₂²	1	2	yes	—
90	C₁₃×#462	C₂²	1	2	yes	—
91	C₁₃×#462	C₂²	1	1	yes	characteristic
92	C₁₃×#462	C₂²	1	1	yes	characteristic
93	C₁₃×#462	C₂²	1	2	yes	—
94	C₁₃×#451	C₂²	1	2	yes	—
95	C₁₃×#451	C₂²	1	2	yes	—
96	C₁₃×#451	C₂²	1	2	yes	—
97	C₁₃×#446	C₂²	1	2	yes	—
98	C₁₃×#441	C₂²	1	2	yes	—
99	C₁₃×#441	C₂²	1	2	yes	—
100	C₁₃×#441	C₂²	1	2	yes	—
101	C₁₃×#441	C₂²	1	2	yes	—
102	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
103	C₄×C₁₃×Q₁₆	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	C₁₃×#427	C₂²	1	2	yes	—
111	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
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×#419	C₂²	1	2	yes	—
116	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
117	C₂×C₁₃×#103	C₂²	1	2	yes	—
118	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
119	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
121	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
126	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	—	2	1	no	—
130	C₁₃×C₄⋊Q₈	—	2	2	no	—
131	C₁₃×C₄⋊Q₈	—	2	1	no	—
132	C₁₃×C₄⋊Q₈	—	2	2	no	—
133	C₁₃×C₄⋊Q₈	—	2	2	no	—
134	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
135	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
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	1	yes	characteristic
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#126	—	2	2	no	—
146	C₁₃×#126	—	2	2	no	—
147	C₁₃×#126	—	2	2	no	—
148	C₁₃×#126	D₄	1	2	yes	—
149	C₁₃×#125	—	2	1	no	—
150	C₁₃×#125	—	2	2	no	—
151	C₁₃×#125	—	2	2	no	—
152	C₁₃×#125	—	2	2	no	—
153	C₁₃×#125	—	2	2	no	—
154	C₁₃×#125	—	2	2	no	—
155	C₁₃×#125	—	2	2	no	—
156	C₁₃×#125	—	2	2	no	—
157	C₁₃×#125	—	2	2	no	—
158	C₁₃×#125	—	2	2	no	—
159	C₁₃×#125	—	2	2	no	—
160	C₁₃×#125	—	2	2	no	—
161	C₁₃×#125	—	2	2	no	—
162	C₁₃×#125	—	2	2	no	—
163	C₁₃×#125	—	2	1	no	—
164	C₁₃×#125	—	2	1	no	—
165	C₁₃×#125	—	2	1	no	—
166	C₁₃×#125	—	2	1	no	—
167	C₁₃×#125	D₄	1	1	yes	characteristic
168	C₁₃×#125	C₂³	1	2	yes	—
169	C₁₃×#125	C₂³	1	2	yes	—
170	C₁₃×#125	C₂³	1	2	yes	—
171	C₁₃×#125	C₂³	1	2	yes	—
172	C₁₃×#124	—	2	1	no	—
173	C₁₃×#124	D₄	1	1	yes	characteristic
174	C₁₃×#123	—	2	2	no	—
175	C₁₃×#123	—	2	2	no	—
176	C₁₃×#123	—	2	2	no	—
177	C₁₃×#123	D₄	1	2	yes	—
178	C₁₃×C₂²⋊Q₈	—	2	1	no	—
179	C₁₃×C₂²⋊Q₈	—	2	1	no	—
180	C₁₃×C₂²⋊Q₈	—	2	2	no	—
181	C₁₃×C₂²⋊Q₈	—	2	2	no	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
188	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₁₃×#121	D₄	1	1	yes	characteristic
195	C₄×Q₈×C₁₃	—	2	1	no	—
196	C₄×Q₈×C₁₃	—	2	2	no	—
197	C₄×Q₈×C₁₃	—	2	2	no	—
198	C₄×Q₈×C₁₃	—	2	1	no	—
199	C₄×Q₈×C₁₃	—	2	1	no	—
200	C₄×Q₈×C₁₃	—	2	2	no	—
201	C₄×Q₈×C₁₃	—	2	1	no	—
202	C₄×Q₈×C₁₃	—	2	1	no	—
203	C₄×Q₈×C₁₃	—	2	1	no	—
204	C₄×Q₈×C₁₃	—	2	1	no	—
205	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
206	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
213	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
214	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
215	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₁₃	—	2	2	no	—
217	C₄×D₄×C₁₃	—	2	1	no	—
218	C₄×D₄×C₁₃	—	2	2	no	—
219	C₄×D₄×C₁₃	C₂³	1	2	yes	—
220	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
221	C₁₃×#117	—	2	1	no	—
222	C₁₃×#117	—	2	1	no	—
223	C₁₃×#117	—	2	2	no	—
224	C₁₃×#117	—	2	2	no	—
225	C₁₃×#117	—	2	2	no	—
226	C₁₃×#117	—	2	2	no	—
227	C₁₃×#117	—	2	2	no	—
228	C₁₃×#117	C₂³	1	2	yes	—
229	C₁₃×#117	C₂³	1	2	yes	—
230	C₁₃×#117	C₂³	1	2	yes	—
231	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
235	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×#106	C₂³	1	2	yes	—
247	C₁₃×#106	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×#103	C₂³	1	2	yes	—
265	C₁₃×#103	C₂³	1	2	yes	—
266	C₁₃×#103	C₂³	1	2	yes	—
267	C₁₃×#103	C₂³	1	2	yes	—
268	C₁₃×#103	C₂³	1	2	yes	—
269	C₁₃×#103	C₂³	1	2	yes	—
270	C₁₃×#103	C₂³	1	2	yes	—
271	C₁₃×#103	C₂³	1	2	yes	—
272	C₁₃×#103	C₂³	1	2	yes	—
273	C₁₃×#103	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	#62168	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂×Q₈×C₁₃	—	2	1	no	—
282	C₂×Q₈×C₁₃	—	2	2	no	—
283	C₂×Q₈×C₁₃	—	2	1	no	—
284	C₂×Q₈×C₁₃	—	2	1	no	—
285	C₂×Q₈×C₁₃	—	2	2	no	—
286	C₂×Q₈×C₁₃	—	2	2	no	—
287	C₂×Q₈×C₁₃	—	2	4	no	—
288	C₂×Q₈×C₁₃	—	4	1	no	—
289	C₂×Q₈×C₁₃	—	4	2	no	—
290	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
292	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
293	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
294	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
295	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
296	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	—	2	1	no	—
298	C₂²×C₄×C₁₃	—	2	1	no	—
299	C₂²×C₄×C₁₃	—	2	1	no	—
300	C₂²×C₄×C₁₃	—	2	2	no	—
301	C₂²×C₄×C₁₃	—	2	1	no	—
302	C₂²×C₄×C₁₃	—	2	2	no	—
303	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
307	C₁₃×Q₁₆	—	2	4	no	—
308	C₁₃×Q₁₆	—	4	2	no	—
309	C₁₃×Q₁₆	—	4	2	no	—
310	C₁₃×Q₁₆	—	4	2	no	—
311	C₁₃×M₁₆	—	4	2	no	—
312	C₂×C₈×C₁₃	—	4	1	no	—
313	C₂×C₈×C₁₃	—	4	2	no	—
314	C₂×C₈×C₁₃	—	4	1	no	—
315	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
316	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
317	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
319	C₁₃×C₄⋊C₄	—	2	1	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	1	no	—
322	C₁₃×C₄⋊C₄	—	2	1	no	—
323	C₁₃×C₄⋊C₄	—	2	1	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	1	no	—
328	C₁₃×C₄⋊C₄	—	2	1	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	1	no	—
331	C₁₃×C₄⋊C₄	—	2	2	no	—
332	C₁₃×C₄⋊C₄	—	2	2	no	—
333	C₁₃×C₄⋊C₄	—	2	2	no	—
334	C₁₃×C₄⋊C₄	—	2	1	no	—
335	C₁₃×C₄⋊C₄	—	2	1	no	—
336	C₁₃×C₄⋊C₄	—	2	2	no	—
337	C₁₃×C₄⋊C₄	—	2	2	no	—
338	C₁₃×C₄⋊C₄	—	2	2	no	—
339	C₁₃×C₄⋊C₄	—	2	2	no	—
340	C₁₃×C₄⋊C₄	—	2	1	no	—
341	C₁₃×C₄⋊C₄	—	2	1	no	—
342	C₁₃×C₄⋊C₄	—	2	2	no	—
343	C₁₃×C₄⋊C₄	—	2	1	no	—
344	C₁₃×C₄⋊C₄	—	2	2	no	—
345	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
353	C₁₃×C₄⋊C₄	—	2	2	no	—
354	C₁₃×C₄⋊C₄	—	2	2	no	—
355	C₁₃×C₄⋊C₄	—	2	2	no	—
356	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
357	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
358	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
359	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
360	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
361	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
365	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
366	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
367	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₁₃×C₂²⋊C₄	—	2	2	no	—
369	C₁₃×C₂²⋊C₄	—	2	2	no	—
370	C₁₃×C₂²⋊C₄	—	2	2	no	—
371	C₁₃×C₂²⋊C₄	—	2	2	no	—
372	C₁₃×C₂²⋊C₄	—	2	2	no	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
377	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
378	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
379	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
380	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
381	C₄²×C₁₃	—	2	1	no	—
382	C₄²×C₁₃	—	2	1	no	—
383	C₄²×C₁₃	—	2	1	no	—
384	C₄²×C₁₃	—	2	1	no	—
385	C₄²×C₁₃	—	2	2	no	—
386	C₄²×C₁₃	—	2	2	no	—
387	C₄²×C₁₃	—	2	2	no	—
388	C₄²×C₁₃	—	2	2	no	—
389	C₄²×C₁₃	—	2	2	no	—
390	C₄²×C₁₃	—	2	2	no	—
391	C₄²×C₁₃	—	2	2	no	—
392	C₄²×C₁₃	—	2	2	no	—
393	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₁₃	C₂⁴	1	2	yes	—
396	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
397	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
398	#3563	C₂×C₁₃	1	1	yes	characteristic
399	#3523	C₂×C₁₃	1	1	yes	characteristic
400	#3390	C₂×C₁₃	1	2	yes	complemented
401	#3374	C₂×C₁₃	1	2	yes	complemented
402	#3349	C₂×C₁₃	1	2	yes	complemented
403	#3344	C₂×C₁₃	1	2	yes	complemented
404	#3336	C₂×C₁₃	1	2	yes	complemented
405	#3312	C₂×C₁₃	1	2	yes	complemented
406	#3312	C₂×C₁₃	1	2	yes	complemented
407	#3299	C₂×C₁₃	1	2	yes	complemented
408	#3261	C₂×C₁₃	1	2	yes	complemented
409	#3249	C₂×C₁₃	1	1	yes	characteristic, complemented
410	#3242	C₂×C₁₃	1	2	yes	complemented
411	#3236	C₂×C₁₃	1	1	yes	characteristic, complemented
412	#3127	C₂×C₁₃	1	2	yes	complemented
413	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
414	#3082	C₂×C₁₃	1	2	yes	complemented
415	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
416	#2992	C₂×C₁₃	1	1	yes	characteristic
417	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
418	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
419	Q₈×C₁₃	—	2	1	no	—
420	Q₈×C₁₃	—	2	2	no	—
421	Q₈×C₁₃	—	2	1	no	—
422	Q₈×C₁₃	—	2	2	no	—
423	Q₈×C₁₃	—	2	2	no	—
424	Q₈×C₁₃	—	2	2	no	—
425	Q₈×C₁₃	—	2	1	no	—
426	Q₈×C₁₃	—	4	1	no	—
427	Q₈×C₁₃	—	4	2	no	—
428	Q₈×C₁₃	—	4	4	no	—
429	Q₈×C₁₃	—	4	2	no	—
430	Q₈×C₁₃	—	8	1	no	—
431	Q₈×C₁₃	—	8	2	no	—
432	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
433	D₄×C₁₃	—	2	4	no	—
434	D₄×C₁₃	—	4	1	no	—
435	C₂×C₄×C₁₃	—	2	2	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	1	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	2	1	no	—
440	C₂×C₄×C₁₃	—	2	2	no	—
441	C₂×C₄×C₁₃	—	2	1	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	1	no	—
445	C₂×C₄×C₁₃	—	2	2	no	—
446	C₂×C₄×C₁₃	—	2	1	no	—
447	C₂×C₄×C₁₃	—	2	2	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	4	1	no	—
451	C₂×C₄×C₁₃	—	4	2	no	—
452	C₂×C₄×C₁₃	—	4	4	no	—
453	C₂×C₄×C₁₃	—	4	2	no	—
454	C₂×C₄×C₁₃	—	4	2	no	—
455	C₂×C₄×C₁₃	—	8	1	no	—
456	C₂×C₄×C₁₃	—	8	2	no	—
457	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
466	C₈×C₁₃	—	2	2	no	—
467	C₈×C₁₃	—	2	2	no	—
468	C₈×C₁₃	—	2	2	no	—
469	C₈×C₁₃	—	2	2	no	—
470	#564	—	2	1	no	—
471	#563	—	2	1	no	—
472	#557	—	2	1	no	—
473	#557	C₂²×C₁₃	1	1	yes	characteristic
474	#557	C₂²×C₁₃	1	2	yes	—
475	#557	C₂²×C₁₃	1	1	yes	characteristic
476	#556	—	2	1	no	—
477	#556	C₂²×C₁₃	1	1	yes	characteristic
478	#554	C₂²×C₁₃	1	2	yes	—
479	#552	—	2	2	no	—
480	#552	—	2	2	no	—
481	#552	C₂²×C₁₃	1	2	yes	—
482	#552	C₂²×C₁₃	1	2	yes	—
483	#552	C₂²×C₁₃	1	2	yes	—
484	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
485	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
486	#544	—	2	1	no	—
487	#544	C₂²×C₁₃	1	2	yes	—
488	#541	—	2	2	no	—
489	#541	—	2	2	no	—
490	#541	C₂²×C₁₃	1	2	yes	—
491	#541	C₂²×C₁₃	1	2	yes	—
492	#539	—	2	1	no	—
493	#533	—	2	1	no	—
494	#533	C₂²×C₁₃	1	1	yes	characteristic
495	#533	C₂²×C₁₃	1	1	yes	characteristic
496	#529	—	2	1	no	—
497	#529	C₂²×C₁₃	1	1	yes	characteristic
498	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
499	#519	C₂²×C₁₃	1	2	yes	—
500	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
501	#501	C₂²×C₁₃	1	2	yes	—
502	#501	C₂²×C₁₃	1	2	yes	—
503	#499	C₂²×C₁₃	1	2	yes	—
504	#491	C₂²×C₁₃	1	2	yes	—
505	#491	C₂²×C₁₃	1	2	yes	—
506	#487	C₂²×C₁₃	1	2	yes	—
507	#485	C₂²×C₁₃	1	2	yes	—
508	#485	C₂²×C₁₃	1	2	yes	—
509	#485	C₂²×C₁₃	1	2	yes	—
510	#485	C₂²×C₁₃	1	2	yes	—
511	#484	C₂²×C₁₃	1	2	yes	—
512	#484	C₂²×C₁₃	1	2	yes	—
513	#483	C₂²×C₁₃	1	2	yes	—
514	#483	C₂²×C₁₃	1	2	yes	—
515	#483	C₂²×C₁₃	1	2	yes	—
516	#479	C₂²×C₁₃	1	2	yes	—
517	#479	C₂²×C₁₃	1	2	yes	—
518	#479	C₂²×C₁₃	1	2	yes	—
519	#479	C₂²×C₁₃	1	2	yes	—
520	#479	C₂²×C₁₃	1	2	yes	—
521	#479	C₂²×C₁₃	1	2	yes	—
522	#479	C₂²×C₁₃	1	2	yes	—
523	#479	C₂²×C₁₃	1	2	yes	—
524	#479	C₂²×C₁₃	1	2	yes	—
525	#479	C₂²×C₁₃	1	2	yes	—
526	#477	C₂²×C₁₃	1	2	yes	—
527	#477	C₂²×C₁₃	1	2	yes	—
528	#477	C₂²×C₁₃	1	2	yes	—
529	#475	C₂²×C₁₃	1	1	yes	characteristic
530	#475	C₂²×C₁₃	1	2	yes	—
531	#475	C₂²×C₁₃	1	1	yes	characteristic
532	#470	C₂²×C₁₃	1	2	yes	—
533	#470	C₂²×C₁₃	1	2	yes	—
534	#467	C₂²×C₁₃	1	2	yes	—
535	#467	C₂²×C₁₃	1	2	yes	—
536	#467	C₂²×C₁₃	1	2	yes	—
537	#467	C₂²×C₁₃	1	2	yes	—
538	#462	C₂²×C₁₃	1	1	yes	characteristic
539	#462	C₂²×C₁₃	1	1	yes	characteristic
540	#462	C₂²×C₁₃	1	2	yes	—
541	#462	C₂²×C₁₃	1	2	yes	—
542	#462	C₂²×C₁₃	1	2	yes	—
543	#462	C₂²×C₁₃	1	2	yes	—
544	#451	C₂²×C₁₃	1	2	yes	—
545	#451	C₂²×C₁₃	1	2	yes	—
546	#451	C₂²×C₁₃	1	2	yes	—
547	#446	C₂²×C₁₃	1	2	yes	—
548	#441	C₂²×C₁₃	1	2	yes	—
549	#441	C₂²×C₁₃	1	2	yes	—
550	#441	C₂²×C₁₃	1	2	yes	—
551	#441	C₂²×C₁₃	1	2	yes	—
552	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
553	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
554	#435	C₂²×C₁₃	1	2	yes	—
555	#435	C₂²×C₁₃	1	2	yes	—
556	C₈×D₄	C₂²×C₁₃	1	2	yes	—
557	#433	C₂²×C₁₃	1	2	yes	—
558	#432	C₂²×C₁₃	1	1	yes	characteristic
559	#428	C₂²×C₁₃	1	2	yes	—
560	#427	C₂²×C₁₃	1	2	yes	—
561	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
562	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
563	#424	C₂²×C₁₃	1	2	yes	—
564	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
565	#419	C₂²×C₁₃	1	2	yes	—
566	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
567	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
568	C₂×#103	C₂²×C₁₃	1	2	yes	—
569	C₂²×C₁₃	—	2	1	no	—
570	C₂²×C₁₃	—	2	1	no	—
571	C₂²×C₁₃	—	2	2	no	—
572	C₂²×C₁₃	—	2	2	no	—
573	C₂²×C₁₃	—	2	2	no	—
574	C₂²×C₁₃	#578	1	2	yes	—
575	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
576	C₄×C₁₃	—	2	1	no	—
577	C₄×C₁₃	—	2	1	no	—
578	C₄×C₁₃	—	2	2	no	—
579	C₄×C₁₃	—	2	1	no	—
580	C₄×C₁₃	—	2	2	no	—
581	C₄×C₁₃	—	2	2	no	—
582	C₄×C₁₃	—	2	1	no	—
583	C₄×C₁₃	—	2	1	no	—
584	C₄×C₁₃	—	2	2	no	—
585	C₄×C₁₃	—	4	2	no	—
586	C₄×C₁₃	—	4	2	no	—
587	C₄×C₁₃	—	4	2	no	—
588	C₄×C₁₃	—	4	1	no	—
589	C₄×C₁₃	—	4	2	no	—
590	C₄×C₁₃	—	4	2	no	—
591	C₄×C₁₃	—	4	1	no	—
592	C₄×C₁₃	—	4	1	no	—
593	C₄×C₁₃	—	4	2	no	—
594	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
595	C₄×C₁₃	#585	1	1	yes	characteristic
596	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
598	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
599	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
600	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
601	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
602	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
603	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
604	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
605	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
606	C₄⋊Q₈	—	2	1	no	—
607	C₄⋊Q₈	—	2	2	no	—
608	C₄⋊Q₈	—	2	1	no	—
609	C₄⋊Q₈	—	2	2	no	—
610	C₄⋊Q₈	—	2	2	no	—
611	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
612	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
613	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
614	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
615	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
616	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
617	#126	—	2	2	no	—
618	#126	—	2	2	no	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#126	—	2	2	no	—
624	#126	—	2	2	no	—
625	#126	D₄×C₁₃	1	2	yes	—
626	#125	—	2	1	no	—
627	#125	—	2	2	no	—
628	#125	—	2	2	no	—
629	#125	—	2	2	no	—
630	#125	—	2	2	no	—
631	#125	—	2	2	no	—
632	#125	—	2	2	no	—
633	#125	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	2	no	—
636	#125	—	2	2	no	—
637	#125	—	2	2	no	—
638	#125	—	2	2	no	—
639	#125	—	2	2	no	—
640	#125	—	2	1	no	—
641	#125	—	2	1	no	—
642	#125	—	2	1	no	—
643	#125	—	2	1	no	—
644	#125	D₄×C₁₃	1	1	yes	characteristic
645	#125	C₂³×C₁₃	1	2	yes	—
646	#125	C₂³×C₁₃	1	2	yes	—
647	#125	C₂³×C₁₃	1	2	yes	—
648	#125	C₂³×C₁₃	1	2	yes	—
649	#124	—	2	1	no	—
650	#124	D₄×C₁₃	1	1	yes	characteristic
651	#123	—	2	2	no	—
652	#123	—	2	2	no	—
653	#123	—	2	2	no	—
654	#123	D₄×C₁₃	1	2	yes	—
655	C₂²⋊Q₈	—	2	1	no	—
656	C₂²⋊Q₈	—	2	1	no	—
657	C₂²⋊Q₈	—	2	2	no	—
658	C₂²⋊Q₈	—	2	2	no	—
659	C₂²⋊Q₈	—	2	2	no	—
660	C₂²⋊Q₈	—	2	2	no	—
661	C₂²⋊Q₈	—	2	2	no	—
662	C₂²⋊Q₈	—	2	2	no	—
663	C₂²⋊Q₈	—	2	2	no	—
664	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
665	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
666	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
667	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
668	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
669	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
670	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
671	#121	D₄×C₁₃	1	1	yes	characteristic
672	C₄×Q₈	—	2	1	no	—
673	C₄×Q₈	—	2	2	no	—
674	C₄×Q₈	—	2	2	no	—
675	C₄×Q₈	—	2	1	no	—
676	C₄×Q₈	—	2	1	no	—
677	C₄×Q₈	—	2	2	no	—
678	C₄×Q₈	—	2	1	no	—
679	C₄×Q₈	—	2	1	no	—
680	C₄×Q₈	—	2	1	no	—
681	C₄×Q₈	—	2	1	no	—
682	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
683	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
684	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
685	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
686	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
687	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
688	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
689	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
690	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
691	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
692	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	1	no	—
695	C₄×D₄	—	2	2	no	—
696	C₄×D₄	C₂³×C₁₃	1	2	yes	—
697	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
698	#117	—	2	1	no	—
699	#117	—	2	1	no	—
700	#117	—	2	2	no	—
701	#117	—	2	2	no	—
702	#117	—	2	2	no	—
703	#117	—	2	2	no	—
704	#117	—	2	2	no	—
705	#117	C₂³×C₁₃	1	2	yes	—
706	#117	C₂³×C₁₃	1	2	yes	—
707	#117	C₂³×C₁₃	1	2	yes	—
708	C₂×C₄⋊C₄	—	2	1	no	—
709	C₂×C₄⋊C₄	—	2	1	no	—
710	C₂×C₄⋊C₄	—	2	1	no	—
711	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
715	C₂×C₄²	—	2	1	no	—
716	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
717	#107	C₂³×C₁₃	1	2	yes	—
718	#107	C₂³×C₁₃	1	2	yes	—
719	#107	C₂³×C₁₃	1	2	yes	—
720	#107	C₂³×C₁₃	1	2	yes	—
721	#107	C₂³×C₁₃	1	2	yes	—
722	#107	C₂³×C₁₃	1	2	yes	—
723	#106	C₂³×C₁₃	1	2	yes	—
724	#106	C₂³×C₁₃	1	2	yes	—
725	#106	C₂³×C₁₃	1	2	yes	—
726	#106	C₂³×C₁₃	1	2	yes	—
727	#106	C₂³×C₁₃	1	2	yes	—
728	#106	C₂³×C₁₃	1	2	yes	—
729	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
730	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
731	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
732	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
733	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
734	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
735	#103	C₂³×C₁₃	1	2	yes	—
736	#103	C₂³×C₁₃	1	2	yes	—
737	#103	C₂³×C₁₃	1	2	yes	—
738	#103	C₂³×C₁₃	1	2	yes	—
739	#103	C₂³×C₁₃	1	2	yes	—
740	#103	C₂³×C₁₃	1	2	yes	—
741	#103	C₂³×C₁₃	1	2	yes	—
742	#103	C₂³×C₁₃	1	2	yes	—
743	#103	C₂³×C₁₃	1	2	yes	—
744	#103	C₂³×C₁₃	1	2	yes	—
745	#103	C₂³×C₁₃	1	2	yes	—
746	#103	C₂³×C₁₃	1	2	yes	—
747	#103	C₂³×C₁₃	1	2	yes	—
748	#103	C₂³×C₁₃	1	2	yes	—
749	#103	C₂³×C₁₃	1	2	yes	—
750	#103	C₂³×C₁₃	1	2	yes	—
751	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
752	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
753	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
754	#97	C₂³×C₁₃	1	2	yes	—
755	#97	C₂³×C₁₃	1	2	yes	—
756	C₄×C₈	C₂³×C₁₃	1	2	yes	—
757	C₂×C₁₃	—	2	2	no	—
758	C₂×C₁₃	—	4	2	no	—
759	C₂×C₁₃	#3489	1	1	yes	characteristic
760	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
761	C₂×C₁₃	#3586	1	1	yes	characteristic
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	1	no	—
765	C₂×Q₈	—	2	1	no	—
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	—	2	4	no	—
769	C₂×Q₈	—	4	1	no	—
770	C₂×Q₈	—	4	2	no	—
771	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
772	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
773	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
774	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
775	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
776	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
777	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
778	C₂²×C₄	—	2	1	no	—
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	1	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
788	Q₁₆	—	2	4	no	—
789	Q₁₆	—	4	2	no	—
790	Q₁₆	—	4	2	no	—
791	Q₁₆	—	4	2	no	—
792	M₁₆	—	4	2	no	—
793	C₂×C₈	—	4	1	no	—
794	C₂×C₈	—	4	2	no	—
795	C₂×C₈	—	4	1	no	—
796	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
797	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
798	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
799	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
800	C₄⋊C₄	—	2	1	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	1	no	—
803	C₄⋊C₄	—	2	1	no	—
804	C₄⋊C₄	—	2	1	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	2	1	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	1	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	1	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
838	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
839	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
840	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
841	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
842	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
843	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
844	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
845	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
846	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
847	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
848	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
858	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
859	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
860	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
861	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
862	C₄²	—	2	1	no	—
863	C₄²	—	2	1	no	—
864	C₄²	—	2	1	no	—
865	C₄²	—	2	1	no	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	2	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
875	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
876	C₄²	C₂⁴×C₁₃	1	2	yes	—
877	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
878	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
879	C₁₃	#62168	1	1	yes	characteristic, direct product factor, Sylow
880	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
881	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
882	Q₈	—	2	1	no	—
883	Q₈	—	2	2	no	—
884	Q₈	—	2	1	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	2	2	no	—
887	Q₈	—	2	2	no	—
888	Q₈	—	2	1	no	—
889	Q₈	—	4	1	no	—
890	Q₈	—	4	2	no	—
891	Q₈	—	4	4	no	—
892	Q₈	—	4	2	no	—
893	Q₈	—	8	1	no	—
894	Q₈	—	8	2	no	—
895	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
896	D₄	—	2	4	no	—
897	D₄	—	4	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	4	2	no	—
917	C₂×C₄	—	4	2	no	—
918	C₂×C₄	—	8	1	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
921	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
922	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
923	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
928	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
929	C₈	—	2	2	no	—
930	C₈	—	2	2	no	—
931	C₈	—	2	2	no	—
932	C₈	—	2	2	no	—
933	C₂²	—	2	1	no	—
934	C₂²	—	2	1	no	—
935	C₂²	—	2	2	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	2	no	—
938	C₂²	C₁₃×#578	1	2	yes	—
939	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	1	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	2	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	2	no	—
957	C₄	—	4	2	no	—
958	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
959	C₄	C₁₃×#585	1	1	yes	characteristic
960	C₂	—	2	2	no	—
961	C₂	—	4	2	no	—
962	C₂	C₁₃×#3489	1	1	yes	characteristic
963	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
964	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	C₁₃×#121	D₄
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
3. C₁₃×#3390	C₂	semidirect
4. C₁₃×#3374	C₂	semidirect
5. C₁₃×#3349	C₂	semidirect
6. C₁₃×#3344	C₂	semidirect
7. C₁₃×#3336	C₂	semidirect
8. C₁₃×#3312	C₂	semidirect
9. C₁₃×#3312	C₂	semidirect
10. C₁₃×#3299	C₂	semidirect
11. C₁₃×#3261	C₂	semidirect
12. C₁₃×#3249	C₂	semidirect
13. C₁₃×#3242	C₂	semidirect
14. C₁₃×#3236	C₂	semidirect
15. C₁₃×#3127	C₂	semidirect
16. C₁₃×#3113	C₂	semidirect
17. C₁₃×#3082	C₂	semidirect
18. C₂×C₁₃×#479	C₂	semidirect
280. #62168	C₁₃	direct (N × H)
400. #3390	C₂×C₁₃	semidirect
401. #3374	C₂×C₁₃	semidirect
402. #3349	C₂×C₁₃	semidirect
403. #3344	C₂×C₁₃	semidirect
404. #3336	C₂×C₁₃	semidirect
405. #3312	C₂×C₁₃	semidirect
406. #3312	C₂×C₁₃	semidirect
407. #3299	C₂×C₁₃	semidirect
408. #3261	C₂×C₁₃	semidirect
409. #3249	C₂×C₁₃	semidirect
410. #3242	C₂×C₁₃	semidirect
411. #3236	C₂×C₁₃	semidirect
412. #3127	C₂×C₁₃	semidirect
413. #3113	C₂×C₁₃	semidirect
414. #3082	C₂×C₁₃	semidirect
415. C₂×#479	C₂×C₁₃	semidirect
879. C₁₃	#62168	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×#3563	2
C₁₃×#3523	2
C₁₃×#3390	2
C₁₃×#3374	2
C₁₃×#3349	2
C₁₃×#3344	2
C₁₃×#3336	2
C₁₃×#3312	2
C₁₃×#3299	2
C₁₃×#3261	2
C₁₃×#3249	2
C₁₃×#3242	2
C₁₃×#3236	2
C₁₃×#3127	2
C₁₃×#3113	2
C₁₃×#3082	2
C₂×C₁₃×#479	2
C₁₃×#2992	2
#62168	13

Subgroups — C13×#62168 #15748507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62168 #15748507