Subgroups — C₁₃×#24028 #15710367

Order 3328.

1250 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3489	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2040	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2039	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2038	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2038	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1901	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1871	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1859	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1793	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1793	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1789	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₁₃	—	2	1	no	—
20	C₁₃×#548	—	2	1	no	—
21	C₁₃×#547	—	2	1	no	—
22	C₁₃×#547	—	2	2	no	—
23	C₁₃×#546	—	2	1	no	—
24	C₁₃×#546	—	2	2	no	—
25	C₁₃×#537	—	2	1	no	—
26	C₁₃×#537	C₂²	1	1	yes	characteristic
27	C₁₃×#536	—	2	1	no	—
28	C₁₃×#536	C₂²	1	1	yes	characteristic
29	C₁₃×#525	—	2	1	no	—
30	C₁₃×#525	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₃×#520	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
35	C₁₃×#485	—	2	1	no	—
36	C₁₃×#485	—	2	1	no	—
37	C₁₃×#482	—	2	1	no	—
38	C₁₃×#482	—	2	1	no	—
39	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#419	—	2	1	no	—
48	C₁₃×#418	—	2	1	no	—
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₁₃×#417	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic
52	C₁₃×#417	C₂²	1	1	yes	characteristic
53	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#416	—	2	1	no	—
56	C₁₃×#416	—	2	1	no	—
57	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#407	C₂²	1	1	yes	characteristic
60	C₁₃×#397	—	2	2	no	—
61	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#387	—	2	2	no	—
64	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
67	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×2₋¹⁺⁴	—	2	2	no	—
72	C₁₃×2₋¹⁺⁴	—	2	2	no	—
73	C₁₃×2₋¹⁺⁴	—	4	1	no	—
74	C₁₃×2₋¹⁺⁴	—	4	1	no	—
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	—	2	1	no	—
77	C₂×C₁₃×#41	—	2	1	no	—
78	C₂×C₁₃×#41	—	2	2	no	—
79	C₂×C₁₃×#41	—	2	1	no	—
80	C₂×C₁₃×#41	—	2	2	no	—
81	C₂×C₁₃×#41	—	2	2	no	—
82	C₂×C₁₃×#41	—	4	1	no	—
83	C₂×C₁₃×#41	—	4	1	no	—
84	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
85	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
86	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₁₃	—	2	1	no	—
90	C₂²×Q₈×C₁₃	—	2	1	no	—
91	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
92	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	—	2	1	no	—
94	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	—	2	1	no	—
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×M₁₆	—	2	1	no	—
98	C₂×C₁₃×M₁₆	—	4	1	no	—
99	C₂×C₁₃×M₁₆	—	4	1	no	—
100	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	—	2	1	no	—
105	C₁₃×C₄⋊Q₈	—	2	2	no	—
106	C₁₃×C₄⋊Q₈	—	2	1	no	—
107	C₁₃×#124	—	2	2	no	—
108	C₁₃×#124	—	2	1	no	—
109	C₁₃×#123	—	2	2	no	—
110	C₁₃×#123	—	2	2	no	—
111	C₁₃×#123	—	2	2	no	—
112	C₁₃×#123	—	2	1	no	—
113	C₁₃×#123	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	2	no	—
115	C₁₃×C₂²⋊Q₈	—	2	2	no	—
116	C₁₃×C₂²⋊Q₈	—	2	2	no	—
117	C₁₃×C₂²⋊Q₈	—	2	1	no	—
118	C₁₃×C₂²⋊Q₈	—	2	1	no	—
119	C₁₃×C₂²⋊Q₈	—	2	1	no	—
120	C₁₃×C₂²⋊Q₈	—	2	1	no	—
121	C₁₃×C₂²⋊Q₈	—	2	1	no	—
122	C₁₃×C₂²⋊Q₈	—	2	1	no	—
123	C₁₃×C₂²⋊Q₈	—	2	1	no	—
124	C₁₃×C₂²⋊Q₈	—	2	1	no	—
125	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
126	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₁₃×#121	—	2	2	no	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	2	no	—
130	C₁₃×#121	—	2	1	no	—
131	C₁₃×#121	—	2	1	no	—
132	C₁₃×#121	—	2	2	no	—
133	C₁₃×#121	D₄	1	1	yes	characteristic
134	C₁₃×#121	D₄	1	1	yes	characteristic
135	C₁₃×#120	—	2	2	no	—
136	C₁₃×#120	—	2	1	no	—
137	C₄×Q₈×C₁₃	—	2	1	no	—
138	C₄×D₄×C₁₃	—	2	2	no	—
139	C₄×D₄×C₁₃	—	2	2	no	—
140	C₄×D₄×C₁₃	—	2	1	no	—
141	C₄×D₄×C₁₃	—	2	2	no	—
142	C₄×D₄×C₁₃	—	2	1	no	—
143	C₄×D₄×C₁₃	—	2	1	no	—
144	C₁₃×#117	—	2	1	no	—
145	C₁₃×#117	—	2	1	no	—
146	C₁₃×#117	—	2	1	no	—
147	C₁₃×#117	—	2	1	no	—
148	C₁₃×#117	—	2	1	no	—
149	C₁₃×#117	C₂³	1	1	yes	characteristic
150	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
161	C₂×C₄²×C₁₃	—	2	1	no	—
162	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₁₃×#107	—	2	1	no	—
165	C₁₃×#107	—	2	1	no	—
166	C₁₃×#106	—	2	1	no	—
167	C₁₃×#106	—	2	1	no	—
168	C₁₃×#104	—	2	2	no	—
169	C₁₃×#104	—	2	2	no	—
170	C₁₃×#104	—	4	1	no	—
171	C₁₃×#104	—	4	1	no	—
172	C₁₃×#104	—	4	1	no	—
173	C₁₃×#104	—	4	1	no	—
174	C₁₃×#103	—	2	1	no	—
175	C₁₃×#103	—	2	1	no	—
176	C₁₃×#103	—	2	1	no	—
177	C₁₃×#103	—	2	1	no	—
178	C₁₃×#103	—	2	1	no	—
179	C₁₃×#103	—	2	1	no	—
180	C₁₃×#102	—	2	1	no	—
181	C₁₃×#102	—	2	1	no	—
182	C₁₃×#102	—	2	1	no	—
183	C₁₃×#102	—	2	1	no	—
184	C₁₃×#102	—	2	1	no	—
185	C₁₃×#102	—	2	1	no	—
186	C₁₃×#101	—	4	1	no	—
187	C₁₃×#101	—	4	1	no	—
188	C₁₃×C₂²⋊C₈	—	2	1	no	—
189	C₁₃×C₂²⋊C₈	—	2	1	no	—
190	C₁₃×#95	—	2	1	no	—
191	C₁₃×#95	—	2	2	no	—
192	C₁₃×#95	—	2	2	no	—
193	C₁₃×#95	—	2	2	no	—
194	#24028	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂⁴×C₁₃	—	2	1	no	—
196	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₁₃×#41	—	2	1	no	—
198	C₁₃×#41	—	2	1	no	—
199	C₁₃×#41	—	2	2	no	—
200	C₁₃×#41	—	2	2	no	—
201	C₁₃×#41	—	2	1	no	—
202	C₁₃×#41	—	2	1	no	—
203	C₁₃×#41	—	2	1	no	—
204	C₁₃×#41	—	2	1	no	—
205	C₁₃×#41	—	2	1	no	—
206	C₁₃×#41	—	2	1	no	—
207	C₁₃×#41	—	2	1	no	—
208	C₁₃×#41	—	2	1	no	—
209	C₁₃×#41	—	4	2	no	—
210	C₁₃×#41	—	4	2	no	—
211	C₁₃×#41	—	4	1	no	—
212	C₁₃×#41	—	4	1	no	—
213	C₁₃×#41	—	4	2	no	—
214	C₁₃×#41	—	4	2	no	—
215	C₁₃×#41	—	4	2	no	—
216	C₁₃×#41	—	4	2	no	—
217	C₁₃×#41	—	4	4	no	—
218	C₁₃×#41	—	4	4	no	—
219	C₁₃×#41	—	4	2	no	—
220	C₁₃×#41	—	4	2	no	—
221	C₁₃×#41	#41	1	2	yes	—
222	C₁₃×#41	#41	1	2	yes	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	—	2	1	no	—
225	C₂×Q₈×C₁₃	—	2	1	no	—
226	C₂×Q₈×C₁₃	—	2	1	no	—
227	C₂×Q₈×C₁₃	—	2	1	no	—
228	C₂×Q₈×C₁₃	—	2	1	no	—
229	C₂×Q₈×C₁₃	—	2	1	no	—
230	C₂×Q₈×C₁₃	—	2	1	no	—
231	C₂×Q₈×C₁₃	—	2	2	no	—
232	C₂×Q₈×C₁₃	—	4	1	no	—
233	C₂×Q₈×C₁₃	—	4	2	no	—
234	C₂×Q₈×C₁₃	—	4	2	no	—
235	C₂×Q₈×C₁₃	—	4	2	no	—
236	C₂×Q₈×C₁₃	—	4	2	no	—
237	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
240	C₂×D₄×C₁₃	—	2	1	no	—
241	C₂×D₄×C₁₃	—	2	2	no	—
242	C₂×D₄×C₁₃	—	2	2	no	—
243	C₂×D₄×C₁₃	—	2	1	no	—
244	C₂×D₄×C₁₃	—	2	1	no	—
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	4	1	no	—
252	C₂×D₄×C₁₃	—	4	2	no	—
253	C₂×D₄×C₁₃	—	4	2	no	—
254	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	1	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	1	no	—
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	2	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	1	no	—
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	1	no	—
274	C₂²×C₄×C₁₃	—	4	2	no	—
275	C₂²×C₄×C₁₃	—	4	2	no	—
276	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₁₃×M₁₆	—	2	1	no	—
285	C₁₃×M₁₆	—	2	1	no	—
286	C₁₃×M₁₆	—	2	1	no	—
287	C₁₃×M₁₆	—	2	1	no	—
288	C₁₃×M₁₆	—	2	1	no	—
289	C₁₃×M₁₆	—	2	1	no	—
290	C₁₃×M₁₆	—	2	1	no	—
291	C₁₃×M₁₆	—	2	1	no	—
292	C₁₃×M₁₆	—	4	2	no	—
293	C₂×C₈×C₁₃	—	2	1	no	—
294	C₂×C₈×C₁₃	—	2	1	no	—
295	C₂×C₈×C₁₃	—	2	1	no	—
296	C₂×C₈×C₁₃	—	2	1	no	—
297	C₂×C₈×C₁₃	—	4	2	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	—	2	1	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	—	2	1	no	—
312	C₁₃×C₄⋊C₄	—	4	4	no	—
313	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
314	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	2	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	1	no	—
324	C₁₃×C₂²⋊C₄	—	2	1	no	—
325	C₁₃×C₂²⋊C₄	—	2	1	no	—
326	C₁₃×C₂²⋊C₄	—	2	1	no	—
327	C₁₃×C₂²⋊C₄	—	4	2	no	—
328	C₁₃×C₂²⋊C₄	—	4	1	no	—
329	C₁₃×C₂²⋊C₄	—	4	1	no	—
330	C₄²×C₁₃	—	2	2	no	—
331	C₄²×C₁₃	—	2	1	no	—
332	C₄²×C₁₃	—	2	1	no	—
333	C₄²×C₁₃	—	2	1	no	—
334	C₄²×C₁₃	—	2	1	no	—
335	C₄²×C₁₃	—	2	1	no	—
336	C₄²×C₁₃	—	4	1	no	—
337	C₄²×C₁₃	—	4	1	no	—
338	#3489	C₂×C₁₃	1	1	yes	characteristic
339	#3093	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#2896	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#2499	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#2040	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#2039	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#2038	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#2038	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#1901	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#1871	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#1859	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#1793	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#1793	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#1789	C₂×C₁₃	1	1	yes	characteristic, complemented
353	C₂³×C₁₃	—	2	1	no	—
354	C₂³×C₁₃	—	2	1	no	—
355	C₂³×C₁₃	—	2	1	no	—
356	C₂³×C₁₃	—	2	1	no	—
357	C₂³×C₁₃	—	2	1	no	—
358	C₂³×C₁₃	—	4	1	no	—
359	C₂³×C₁₃	—	4	1	no	—
360	C₂³×C₁₃	—	4	2	no	—
361	C₂³×C₁₃	—	4	2	no	—
362	C₂³×C₁₃	—	8	1	no	—
363	C₂³×C₁₃	#120	1	1	yes	characteristic
364	C₂³×C₁₃	#120	1	1	yes	characteristic
365	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	Q₈×C₁₃	—	2	1	no	—
367	Q₈×C₁₃	—	2	1	no	—
368	Q₈×C₁₃	—	2	1	no	—
369	Q₈×C₁₃	—	2	1	no	—
370	Q₈×C₁₃	—	2	1	no	—
371	Q₈×C₁₃	—	4	2	no	—
372	Q₈×C₁₃	—	4	4	no	—
373	Q₈×C₁₃	—	4	1	no	—
374	Q₈×C₁₃	—	4	1	no	—
375	Q₈×C₁₃	—	4	1	no	—
376	Q₈×C₁₃	—	4	1	no	—
377	Q₈×C₁₃	#123	1	2	yes	—
378	D₄×C₁₃	—	2	2	no	—
379	D₄×C₁₃	—	2	2	no	—
380	D₄×C₁₃	—	2	1	no	—
381	D₄×C₁₃	—	2	1	no	—
382	D₄×C₁₃	—	2	1	no	—
383	D₄×C₁₃	—	2	1	no	—
384	D₄×C₁₃	—	2	1	no	—
385	D₄×C₁₃	—	4	2	no	—
386	D₄×C₁₃	—	4	2	no	—
387	D₄×C₁₃	—	4	2	no	—
388	D₄×C₁₃	—	4	2	no	—
389	D₄×C₁₃	—	4	4	no	—
390	D₄×C₁₃	—	4	1	no	—
391	D₄×C₁₃	—	4	1	no	—
392	D₄×C₁₃	—	4	1	no	—
393	D₄×C₁₃	—	4	1	no	—
394	D₄×C₁₃	—	8	1	no	—
395	D₄×C₁₃	—	8	2	no	—
396	D₄×C₁₃	#123	1	2	yes	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	1	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	2	2	no	—
410	C₂×C₄×C₁₃	—	2	2	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	2	no	—
419	C₂×C₄×C₁₃	—	4	2	no	—
420	C₂×C₄×C₁₃	—	4	2	no	—
421	C₂×C₄×C₁₃	—	4	2	no	—
422	C₂×C₄×C₁₃	—	4	4	no	—
423	C₂×C₄×C₁₃	—	4	1	no	—
424	C₂×C₄×C₁₃	—	4	4	no	—
425	C₂×C₄×C₁₃	—	4	1	no	—
426	C₂×C₄×C₁₃	—	4	1	no	—
427	C₂×C₄×C₁₃	—	4	1	no	—
428	C₂×C₄×C₁₃	—	4	1	no	—
429	C₂×C₄×C₁₃	—	4	1	no	—
430	C₂×C₄×C₁₃	—	4	2	no	—
431	C₂×C₄×C₁₃	—	4	1	no	—
432	C₂×C₄×C₁₃	—	4	2	no	—
433	C₂×C₄×C₁₃	—	4	1	no	—
434	C₂×C₄×C₁₃	—	4	2	no	—
435	C₂×C₄×C₁₃	—	4	1	no	—
436	C₂×C₄×C₁₃	—	4	1	no	—
437	C₂×C₄×C₁₃	—	4	1	no	—
438	C₂×C₄×C₁₃	—	8	2	no	—
439	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
440	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
441	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
444	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
445	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
446	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
447	C₈×C₁₃	—	4	1	no	—
448	C₈×C₁₃	—	4	1	no	—
449	C₈×C₁₃	—	4	1	no	—
450	C₈×C₁₃	—	4	1	no	—
451	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	1	yes	characteristic
452	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
453	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
454	D₄×Q₈	—	2	1	no	—
455	#548	—	2	1	no	—
456	#547	—	2	1	no	—
457	#547	—	2	2	no	—
458	#546	—	2	1	no	—
459	#546	—	2	2	no	—
460	#537	—	2	1	no	—
461	#537	C₂²×C₁₃	1	1	yes	characteristic
462	#536	—	2	1	no	—
463	#536	C₂²×C₁₃	1	1	yes	characteristic
464	#525	—	2	1	no	—
465	#525	C₂²×C₁₃	1	1	yes	characteristic
466	C₂×C₂²⋊Q₈	—	2	1	no	—
467	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
468	#520	C₂²×C₁₃	1	1	yes	characteristic
469	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
470	#485	—	2	1	no	—
471	#485	—	2	1	no	—
472	#482	—	2	1	no	—
473	#482	—	2	1	no	—
474	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
476	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
477	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
478	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
479	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
480	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
481	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	#419	—	2	1	no	—
483	#418	—	2	1	no	—
484	#417	C₂²×C₁₃	1	1	yes	characteristic
485	#417	C₂²×C₁₃	1	1	yes	characteristic
486	#417	C₂²×C₁₃	1	1	yes	characteristic
487	#417	C₂²×C₁₃	1	1	yes	characteristic
488	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
489	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	#416	—	2	1	no	—
491	#416	—	2	1	no	—
492	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	#407	C₂²×C₁₃	1	1	yes	characteristic
495	#397	—	2	2	no	—
496	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
497	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	#387	—	2	2	no	—
499	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
500	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
501	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
502	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
503	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
504	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
505	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
506	C₂²×C₁₃	—	2	1	no	—
507	C₂²×C₁₃	—	2	1	no	—
508	C₂²×C₁₃	—	2	1	no	—
509	C₂²×C₁₃	—	2	1	no	—
510	C₂²×C₁₃	—	2	2	no	—
511	C₂²×C₁₃	—	2	1	no	—
512	C₂²×C₁₃	—	2	1	no	—
513	C₂²×C₁₃	—	2	1	no	—
514	C₂²×C₁₃	—	2	1	no	—
515	C₂²×C₁₃	—	4	1	no	—
516	C₂²×C₁₃	—	4	1	no	—
517	C₂²×C₁₃	—	4	1	no	—
518	C₂²×C₁₃	—	4	1	no	—
519	C₂²×C₁₃	—	4	1	no	—
520	C₂²×C₁₃	—	4	1	no	—
521	C₂²×C₁₃	—	4	1	no	—
522	C₂²×C₁₃	—	4	1	no	—
523	C₂²×C₁₃	—	8	1	no	—
524	C₂²×C₁₃	—	8	1	no	—
525	C₂²×C₁₃	—	8	4	no	—
526	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
527	C₂²×C₁₃	#546	1	1	yes	characteristic
528	C₂²×C₁₃	#546	1	1	yes	characteristic
529	C₄×C₁₃	—	2	1	no	—
530	C₄×C₁₃	—	2	1	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	4	2	no	—
533	C₄×C₁₃	—	4	2	no	—
534	C₄×C₁₃	—	4	1	no	—
535	C₄×C₁₃	—	4	1	no	—
536	C₄×C₁₃	—	4	2	no	—
537	C₄×C₁₃	—	4	1	no	—
538	C₄×C₁₃	—	4	1	no	—
539	C₄×C₁₃	—	8	1	no	—
540	C₄×C₁₃	—	8	1	no	—
541	C₄×C₁₃	—	8	1	no	—
542	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
543	C₄×C₁₃	#534	1	1	yes	characteristic
544	C₄×C₁₃	#546	1	1	yes	characteristic
545	C₄×C₁₃	#546	1	1	yes	characteristic
546	2₋¹⁺⁴	—	2	2	no	—
547	2₋¹⁺⁴	—	2	2	no	—
548	2₋¹⁺⁴	—	4	1	no	—
549	2₋¹⁺⁴	—	4	1	no	—
550	C₂×#41	—	2	1	no	—
551	C₂×#41	—	2	1	no	—
552	C₂×#41	—	2	1	no	—
553	C₂×#41	—	2	2	no	—
554	C₂×#41	—	2	1	no	—
555	C₂×#41	—	2	2	no	—
556	C₂×#41	—	2	2	no	—
557	C₂×#41	—	4	1	no	—
558	C₂×#41	—	4	1	no	—
559	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
560	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
561	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
562	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
563	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
564	C₂²×Q₈	—	2	1	no	—
565	C₂²×Q₈	—	2	1	no	—
566	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
567	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
568	C₂²×D₄	—	2	1	no	—
569	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
570	C₂³×C₄	—	2	1	no	—
571	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×M₁₆	—	2	1	no	—
573	C₂×M₁₆	—	4	1	no	—
574	C₂×M₁₆	—	4	1	no	—
575	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
576	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
579	C₂²×C₈	—	2	1	no	—
580	C₄⋊Q₈	—	2	2	no	—
581	C₄⋊Q₈	—	2	1	no	—
582	#124	—	2	2	no	—
583	#124	—	2	1	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	1	no	—
588	#123	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	1	no	—
598	C₂²⋊Q₈	—	2	1	no	—
599	C₂²⋊Q₈	—	2	1	no	—
600	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
601	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
602	#121	—	2	2	no	—
603	#121	—	2	2	no	—
604	#121	—	2	2	no	—
605	#121	—	2	1	no	—
606	#121	—	2	1	no	—
607	#121	—	2	2	no	—
608	#121	D₄×C₁₃	1	1	yes	characteristic
609	#121	D₄×C₁₃	1	1	yes	characteristic
610	#120	—	2	2	no	—
611	#120	—	2	1	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	#117	—	2	1	no	—
620	#117	—	2	1	no	—
621	#117	—	2	1	no	—
622	#117	—	2	1	no	—
623	#117	—	2	1	no	—
624	#117	C₂³×C₁₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	—	2	2	no	—
626	C₂×C₄⋊C₄	—	2	1	no	—
627	C₂×C₄⋊C₄	—	2	2	no	—
628	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	—	2	2	no	—
633	C₂×C₂²⋊C₄	—	2	1	no	—
634	C₂×C₂²⋊C₄	—	2	1	no	—
635	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
639	#107	—	2	1	no	—
640	#107	—	2	1	no	—
641	#106	—	2	1	no	—
642	#106	—	2	1	no	—
643	#104	—	2	2	no	—
644	#104	—	2	2	no	—
645	#104	—	4	1	no	—
646	#104	—	4	1	no	—
647	#104	—	4	1	no	—
648	#104	—	4	1	no	—
649	#103	—	2	1	no	—
650	#103	—	2	1	no	—
651	#103	—	2	1	no	—
652	#103	—	2	1	no	—
653	#103	—	2	1	no	—
654	#103	—	2	1	no	—
655	#102	—	2	1	no	—
656	#102	—	2	1	no	—
657	#102	—	2	1	no	—
658	#102	—	2	1	no	—
659	#102	—	2	1	no	—
660	#102	—	2	1	no	—
661	#101	—	4	1	no	—
662	#101	—	4	1	no	—
663	C₂²⋊C₈	—	2	1	no	—
664	C₂²⋊C₈	—	2	1	no	—
665	#95	—	2	1	no	—
666	#95	—	2	2	no	—
667	#95	—	2	2	no	—
668	#95	—	2	2	no	—
669	C₂×C₁₃	—	2	1	no	—
670	C₂×C₁₃	—	2	1	no	—
671	C₂×C₁₃	—	4	1	no	—
672	C₂×C₁₃	—	4	1	no	—
673	C₂×C₁₃	—	4	2	no	—
674	C₂×C₁₃	—	8	1	no	—
675	C₂×C₁₃	—	8	1	no	—
676	C₂×C₁₃	#2405	1	1	yes	characteristic
677	C₂×C₁₃	#3018	1	1	yes	characteristic
678	C₂×C₁₃	#3020	1	1	yes	characteristic
679	C₂⁴	—	2	1	no	—
680	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
681	#41	—	2	1	no	—
682	#41	—	2	1	no	—
683	#41	—	2	2	no	—
684	#41	—	2	2	no	—
685	#41	—	2	1	no	—
686	#41	—	2	1	no	—
687	#41	—	2	1	no	—
688	#41	—	2	1	no	—
689	#41	—	2	1	no	—
690	#41	—	2	1	no	—
691	#41	—	2	1	no	—
692	#41	—	2	1	no	—
693	#41	—	4	2	no	—
694	#41	—	4	2	no	—
695	#41	—	4	1	no	—
696	#41	—	4	1	no	—
697	#41	—	4	2	no	—
698	#41	—	4	2	no	—
699	#41	—	4	2	no	—
700	#41	—	4	2	no	—
701	#41	—	4	4	no	—
702	#41	—	4	4	no	—
703	#41	—	4	2	no	—
704	#41	—	4	2	no	—
705	#41	C₁₃×#41	1	2	yes	—
706	#41	C₁₃×#41	1	2	yes	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	2	1	no	—
709	C₂×Q₈	—	2	1	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	2	1	no	—
713	C₂×Q₈	—	2	1	no	—
714	C₂×Q₈	—	2	1	no	—
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	4	1	no	—
717	C₂×Q₈	—	4	2	no	—
718	C₂×Q₈	—	4	2	no	—
719	C₂×Q₈	—	4	2	no	—
720	C₂×Q₈	—	4	2	no	—
721	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
722	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
723	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	2	1	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	1	no	—
734	C₂×D₄	—	2	1	no	—
735	C₂×D₄	—	4	1	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
739	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	1	no	—
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	4	2	no	—
759	C₂²×C₄	—	4	2	no	—
760	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
761	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
764	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
768	M₁₆	—	2	1	no	—
769	M₁₆	—	2	1	no	—
770	M₁₆	—	2	1	no	—
771	M₁₆	—	2	1	no	—
772	M₁₆	—	2	1	no	—
773	M₁₆	—	2	1	no	—
774	M₁₆	—	2	1	no	—
775	M₁₆	—	2	1	no	—
776	M₁₆	—	4	2	no	—
777	C₂×C₈	—	2	1	no	—
778	C₂×C₈	—	2	1	no	—
779	C₂×C₈	—	2	1	no	—
780	C₂×C₈	—	2	1	no	—
781	C₂×C₈	—	4	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	—	2	1	no	—
795	C₄⋊C₄	—	2	1	no	—
796	C₄⋊C₄	—	4	4	no	—
797	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
798	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	1	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	1	no	—
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	4	2	no	—
812	C₂²⋊C₄	—	4	1	no	—
813	C₂²⋊C₄	—	4	1	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	1	no	—
816	C₄²	—	2	1	no	—
817	C₄²	—	2	1	no	—
818	C₄²	—	2	1	no	—
819	C₄²	—	2	1	no	—
820	C₄²	—	4	1	no	—
821	C₄²	—	4	1	no	—
822	C₁₃	#24028	1	1	yes	characteristic, direct product factor, Sylow
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	1	no	—
830	C₂³	—	4	2	no	—
831	C₂³	—	4	2	no	—
832	C₂³	—	8	1	no	—
833	C₂³	C₁₃×#120	1	1	yes	characteristic
834	C₂³	C₁₃×#120	1	1	yes	characteristic
835	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
836	Q₈	—	2	1	no	—
837	Q₈	—	2	1	no	—
838	Q₈	—	2	1	no	—
839	Q₈	—	2	1	no	—
840	Q₈	—	2	1	no	—
841	Q₈	—	4	2	no	—
842	Q₈	—	4	4	no	—
843	Q₈	—	4	1	no	—
844	Q₈	—	4	1	no	—
845	Q₈	—	4	1	no	—
846	Q₈	—	4	1	no	—
847	Q₈	C₁₃×#123	1	2	yes	—
848	D₄	—	2	2	no	—
849	D₄	—	2	2	no	—
850	D₄	—	2	1	no	—
851	D₄	—	2	1	no	—
852	D₄	—	2	1	no	—
853	D₄	—	2	1	no	—
854	D₄	—	2	1	no	—
855	D₄	—	4	2	no	—
856	D₄	—	4	2	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	2	no	—
859	D₄	—	4	4	no	—
860	D₄	—	4	1	no	—
861	D₄	—	4	1	no	—
862	D₄	—	4	1	no	—
863	D₄	—	4	1	no	—
864	D₄	—	8	1	no	—
865	D₄	—	8	2	no	—
866	D₄	C₁₃×#123	1	2	yes	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	1	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	1	no	—
896	C₂×C₄	—	4	1	no	—
897	C₂×C₄	—	4	1	no	—
898	C₂×C₄	—	4	1	no	—
899	C₂×C₄	—	4	1	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	1	no	—
902	C₂×C₄	—	4	2	no	—
903	C₂×C₄	—	4	1	no	—
904	C₂×C₄	—	4	2	no	—
905	C₂×C₄	—	4	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
910	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
911	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
913	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
914	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
915	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
916	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
917	C₈	—	4	1	no	—
918	C₈	—	4	1	no	—
919	C₈	—	4	1	no	—
920	C₈	—	4	1	no	—
921	C₂²	—	2	1	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	1	no	—
932	C₂²	—	4	1	no	—
933	C₂²	—	4	1	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	8	1	no	—
939	C₂²	—	8	1	no	—
940	C₂²	—	8	4	no	—
941	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
942	C₂²	C₁₃×#546	1	1	yes	characteristic
943	C₂²	C₁₃×#546	1	1	yes	characteristic
944	C₄	—	2	1	no	—
945	C₄	—	2	1	no	—
946	C₄	—	2	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	1	no	—
954	C₄	—	8	1	no	—
955	C₄	—	8	1	no	—
956	C₄	—	8	1	no	—
957	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
958	C₄	C₁₃×#534	1	1	yes	characteristic
959	C₄	C₁₃×#546	1	1	yes	characteristic
960	C₄	C₁₃×#546	1	1	yes	characteristic
961	C₂	—	2	1	no	—
962	C₂	—	2	1	no	—
963	C₂	—	4	1	no	—
964	C₂	—	4	1	no	—
965	C₂	—	4	2	no	—
966	C₂	—	8	1	no	—
967	C₂	—	8	1	no	—
968	C₂	C₁₃×#2405	1	1	yes	characteristic
969	C₂	C₁₃×#3018	1	1	yes	characteristic
970	C₂	C₁₃×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3489	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3093	C₂	semidirect
3. C₁₃×#2896	C₂	semidirect
4. C₁₃×#2499	C₂	semidirect
5. C₁₃×#2040	C₂	semidirect
6. C₁₃×#2039	C₂	semidirect
7. C₁₃×#2038	C₂	semidirect
8. C₁₃×#2038	C₂	semidirect
9. C₁₃×#1901	C₂	semidirect
10. C₁₃×#1871	C₂	semidirect
11. C₁₃×#1860	C₂	semidirect
12. C₁₃×#1859	C₂	semidirect
13. C₁₃×#1793	C₂	semidirect
14. C₁₃×#1793	C₂	semidirect
15. C₁₃×#1789	C₂	semidirect
39. C₁₃×#428	C₂²	semidirect
40. C₁₃×#428	C₂²	semidirect
45. C₂×C₁₃×#104	C₂²	semidirect
46. C₂×C₁₃×#104	C₂²	semidirect
53. C₁₃×#417	C₂²	semidirect
54. C₁₃×#417	C₂²	semidirect
57. C₂×C₁₃×#101	C₂²	semidirect
58. C₂×C₁₃×#101	C₂²	semidirect
61. C₁₃×#391	C₂²	semidirect
62. C₁₃×#391	C₂²	semidirect
64. C₁₃×#384	C₂²	semidirect
65. C₁₃×#382	C₂²	semidirect
67. C₁₃×#343	C₂²	semidirect
68. C₁₃×#343	C₂²	semidirect
69. C₁₃×#339	C₂²	semidirect
70. C₁₃×#339	C₂²	semidirect
194. #24028	C₁₃	direct (N × H)
339. #3093	C₂×C₁₃	semidirect
340. #2896	C₂×C₁₃	semidirect
341. #2499	C₂×C₁₃	semidirect
342. #2040	C₂×C₁₃	semidirect
343. #2039	C₂×C₁₃	semidirect
344. #2038	C₂×C₁₃	semidirect
345. #2038	C₂×C₁₃	semidirect
346. #1901	C₂×C₁₃	semidirect
347. #1871	C₂×C₁₃	semidirect
348. #1860	C₂×C₁₃	semidirect
349. #1859	C₂×C₁₃	semidirect
350. #1793	C₂×C₁₃	semidirect
351. #1793	C₂×C₁₃	semidirect
352. #1789	C₂×C₁₃	semidirect
474. #428	C₂²×C₁₃	semidirect
475. #428	C₂²×C₁₃	semidirect
480. C₂×#104	C₂²×C₁₃	semidirect
481. C₂×#104	C₂²×C₁₃	semidirect
488. #417	C₂²×C₁₃	semidirect
489. #417	C₂²×C₁₃	semidirect
492. C₂×#101	C₂²×C₁₃	semidirect
493. C₂×#101	C₂²×C₁₃	semidirect
496. #391	C₂²×C₁₃	semidirect
497. #391	C₂²×C₁₃	semidirect
499. #384	C₂²×C₁₃	semidirect
500. #382	C₂²×C₁₃	semidirect
502. #343	C₂²×C₁₃	semidirect
503. #343	C₂²×C₁₃	semidirect
504. #339	C₂²×C₁₃	semidirect
505. #339	C₂²×C₁₃	semidirect
822. C₁₃	#24028	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×#3489	2
C₁₃×#3093	2
C₁₃×#2896	2
C₁₃×#2499	2
C₁₃×#2040	2
C₁₃×#2039	2
C₁₃×#2038	2
C₁₃×#1901	2
C₁₃×#1871	2
C₁₃×#1860	2
C₁₃×#1859	2
C₁₃×#1793	2
C₁₃×#1789	2
#24028	13

Subgroups — C13×#24028 #15710367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24028 #15710367