Subgroups — C₁₃×#24008 #15710347

Order 3328.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1779	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#525	—	2	4	no	—
19	C₁₃×#525	—	2	4	no	—
20	C₂×C₁₃×#123	—	2	1	no	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#120	—	2	1	no	—
26	C₂×C₄×D₄×C₁₃	—	2	1	no	—
27	C₂×C₄×D₄×C₁₃	—	2	1	no	—
28	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₁₃×#485	—	2	4	no	—
32	C₁₃×#482	—	2	4	no	—
33	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₁₃×#381	—	2	1	no	—
52	C₁₃×#380	C₂²	1	1	yes	characteristic
53	C₁₃×#380	C₂²	1	1	yes	characteristic
54	C₁₃×#380	C₂²	1	1	yes	characteristic
55	C₁₃×#380	C₂²	1	1	yes	characteristic
56	C₁₃×#379	—	2	1	no	—
57	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
59	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#340	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	4	1	no	—
69	C₂×C₁₃×#41	—	4	1	no	—
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	—	2	1	no	—
72	C₂²×D₄×C₁₃	—	2	1	no	—
73	C₂²×D₄×C₁₃	—	2	1	no	—
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₂³×C₄×C₁₃	—	2	2	no	—
77	C₂³×C₄×C₁₃	—	2	2	no	—
78	C₂³×C₄×C₁₃	—	2	2	no	—
79	C₂³×C₄×C₁₃	—	2	2	no	—
80	C₂³×C₄×C₁₃	—	4	1	no	—
81	C₂³×C₄×C₁₃	—	4	1	no	—
82	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#123	—	2	8	no	—
93	C₁₃×C₂²⋊Q₈	—	2	2	no	—
94	C₁₃×C₂²⋊Q₈	—	2	2	no	—
95	C₁₃×C₂²⋊Q₈	—	2	2	no	—
96	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
97	C₁₃×#121	—	2	2	no	—
98	C₁₃×#121	—	2	2	no	—
99	C₁₃×#121	—	2	2	no	—
100	C₁₃×#121	D₄	1	4	yes	—
101	C₁₃×#120	—	2	8	no	—
102	C₄×D₄×C₁₃	—	2	8	no	—
103	C₄×D₄×C₁₃	—	2	8	no	—
104	C₁₃×#117	—	2	2	no	—
105	C₁₃×#117	—	2	2	no	—
106	C₁₃×#117	—	2	2	no	—
107	C₁₃×#117	—	2	2	no	—
108	C₁₃×#117	—	4	1	no	—
109	C₁₃×#117	—	4	1	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
129	C₂×C₄²×C₁₃	—	2	1	no	—
130	C₂×C₄²×C₁₃	—	2	1	no	—
131	C₂×C₄²×C₁₃	—	2	1	no	—
132	C₁₃×#107	—	2	2	no	—
133	C₁₃×#107	—	2	2	no	—
134	C₁₃×#106	—	2	2	no	—
135	C₁₃×#106	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	—	2	2	no	—
138	C₁₃×#103	—	4	1	no	—
139	C₁₃×#103	—	4	1	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×#102	—	2	2	no	—
142	C₁₃×#102	—	4	1	no	—
143	C₁₃×#102	—	4	1	no	—
144	C₁₃×C₂²⋊C₈	—	2	2	no	—
145	C₁₃×C₂²⋊C₈	—	2	2	no	—
146	C₁₃×C₂²⋊C₈	—	2	2	no	—
147	C₁₃×C₂²⋊C₈	—	2	2	no	—
148	C₁₃×C₂²⋊C₈	—	4	1	no	—
149	C₁₃×C₂²⋊C₈	—	4	1	no	—
150	C₁₃×#95	—	2	1	no	—
151	C₁₃×#95	—	2	1	no	—
152	C₁₃×#95	—	2	1	no	—
153	C₁₃×#95	—	2	1	no	—
154	#24008	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂⁴×C₁₃	—	2	2	no	—
156	C₂⁴×C₁₃	—	2	2	no	—
157	C₂⁴×C₁₃	—	2	2	no	—
158	C₂⁴×C₁₃	—	2	1	no	—
159	C₂⁴×C₁₃	—	4	1	no	—
160	C₂⁴×C₁₃	—	4	1	no	—
161	C₂⁴×C₁₃	—	4	1	no	—
162	C₂⁴×C₁₃	—	4	1	no	—
163	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₁₃×#41	—	4	4	no	—
167	C₁₃×#41	—	4	4	no	—
168	C₁₃×#41	—	4	4	no	—
169	C₁₃×#41	—	4	4	no	—
170	C₂×Q₈×C₁₃	—	2	1	no	—
171	C₂×Q₈×C₁₃	—	2	1	no	—
172	C₂×Q₈×C₁₃	—	2	1	no	—
173	C₂×Q₈×C₁₃	—	2	1	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	4	2	no	—
185	C₂×D₄×C₁₃	—	4	2	no	—
186	C₂×D₄×C₁₃	—	4	2	no	—
187	C₂×D₄×C₁₃	—	4	2	no	—
188	C₂×D₄×C₁₃	—	4	2	no	—
189	C₂×D₄×C₁₃	—	4	2	no	—
190	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₁₃	—	2	1	no	—
192	C₂²×C₄×C₁₃	—	2	1	no	—
193	C₂²×C₄×C₁₃	—	2	1	no	—
194	C₂²×C₄×C₁₃	—	2	1	no	—
195	C₂²×C₄×C₁₃	—	2	1	no	—
196	C₂²×C₄×C₁₃	—	2	1	no	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	2	4	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	2	no	—
207	C₂²×C₄×C₁₃	—	2	2	no	—
208	C₂²×C₄×C₁₃	—	2	2	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	1	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	1	no	—
216	C₂²×C₄×C₁₃	—	2	1	no	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	4	1	no	—
220	C₂²×C₄×C₁₃	—	4	1	no	—
221	C₂²×C₄×C₁₃	—	4	1	no	—
222	C₂²×C₄×C₁₃	—	4	4	no	—
223	C₂²×C₄×C₁₃	—	4	4	no	—
224	C₂²×C₄×C₁₃	—	4	4	no	—
225	C₂²×C₄×C₁₃	—	4	4	no	—
226	C₂²×C₄×C₁₃	—	4	2	no	—
227	C₂²×C₄×C₁₃	—	4	2	no	—
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₁₃	#41	1	2	yes	—
234	C₂²×C₄×C₁₃	#41	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	1	no	—
238	C₂×C₈×C₁₃	—	2	1	no	—
239	C₂×C₈×C₁₃	—	2	1	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	—	2	1	no	—
242	C₂×C₈×C₁₃	—	2	1	no	—
243	C₂×C₈×C₁₃	—	2	1	no	—
244	C₂×C₈×C₁₃	—	2	1	no	—
245	C₂×C₈×C₁₃	—	2	1	no	—
246	C₂×C₈×C₁₃	—	2	1	no	—
247	C₂×C₈×C₁₃	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	4	no	—
249	C₁₃×C₄⋊C₄	—	2	4	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
261	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	4	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	4	2	no	—
268	C₁₃×C₂²⋊C₄	—	4	2	no	—
269	C₁₃×C₂²⋊C₄	—	4	2	no	—
270	C₁₃×C₂²⋊C₄	—	4	2	no	—
271	C₁₃×C₂²⋊C₄	—	4	2	no	—
272	C₁₃×C₂²⋊C₄	—	4	2	no	—
273	C₄²×C₁₃	—	2	4	no	—
274	C₄²×C₁₃	—	4	2	no	—
275	C₄²×C₁₃	—	4	2	no	—
276	C₂×#525	C₂×C₁₃	1	1	yes	characteristic
277	C₂×#485	C₂×C₁₃	1	1	yes	characteristic, complemented
278	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#2035	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1875	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1873	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1854	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
289	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#1779	C₂×C₁₃	1	1	yes	characteristic, complemented
291	C₂³×C₁₃	—	2	1	no	—
292	C₂³×C₁₃	—	2	1	no	—
293	C₂³×C₁₃	—	2	1	no	—
294	C₂³×C₁₃	—	2	1	no	—
295	C₂³×C₁₃	—	2	1	no	—
296	C₂³×C₁₃	—	2	1	no	—
297	C₂³×C₁₃	—	2	1	no	—
298	C₂³×C₁₃	—	2	1	no	—
299	C₂³×C₁₃	—	2	1	no	—
300	C₂³×C₁₃	—	2	1	no	—
301	C₂³×C₁₃	—	2	1	no	—
302	C₂³×C₁₃	—	2	1	no	—
303	C₂³×C₁₃	—	2	1	no	—
304	C₂³×C₁₃	—	2	1	no	—
305	C₂³×C₁₃	—	2	1	no	—
306	C₂³×C₁₃	—	2	1	no	—
307	C₂³×C₁₃	—	2	1	no	—
308	C₂³×C₁₃	—	2	1	no	—
309	C₂³×C₁₃	—	2	2	no	—
310	C₂³×C₁₃	—	4	4	no	—
311	C₂³×C₁₃	—	4	4	no	—
312	C₂³×C₁₃	—	4	4	no	—
313	C₂³×C₁₃	—	4	4	no	—
314	C₂³×C₁₃	—	4	4	no	—
315	C₂³×C₁₃	—	4	4	no	—
316	C₂³×C₁₃	—	4	4	no	—
317	C₂³×C₁₃	—	4	1	no	—
318	C₂³×C₁₃	—	4	1	no	—
319	C₂³×C₁₃	—	4	1	no	—
320	C₂³×C₁₃	—	4	1	no	—
321	C₂³×C₁₃	—	4	1	no	—
322	C₂³×C₁₃	—	4	1	no	—
323	C₂³×C₁₃	#120	1	2	yes	—
324	C₂³×C₁₃	#123	1	2	yes	—
325	C₂³×C₁₃	#135	1	2	yes	—
326	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	2	2	no	—
329	Q₈×C₁₃	—	4	1	no	—
330	Q₈×C₁₃	—	4	1	no	—
331	D₄×C₁₃	—	2	2	no	—
332	D₄×C₁₃	—	2	2	no	—
333	D₄×C₁₃	—	4	8	no	—
334	D₄×C₁₃	—	4	8	no	—
335	D₄×C₁₃	—	4	8	no	—
336	D₄×C₁₃	—	4	1	no	—
337	D₄×C₁₃	—	4	1	no	—
338	C₂×C₄×C₁₃	—	2	1	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	4	4	no	—
357	C₂×C₄×C₁₃	—	4	4	no	—
358	C₂×C₄×C₁₃	—	4	4	no	—
359	C₂×C₄×C₁₃	—	4	8	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	4	1	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	—	4	1	no	—
376	C₂×C₄×C₁₃	—	4	1	no	—
377	C₂×C₄×C₁₃	—	4	1	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	4	1	no	—
380	C₂×C₄×C₁₃	—	4	1	no	—
381	C₂×C₄×C₁₃	—	4	1	no	—
382	C₂×C₄×C₁₃	#120	1	2	yes	—
383	C₂×C₄×C₁₃	#123	1	2	yes	—
384	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
387	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
388	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
389	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
390	C₈×C₁₃	—	4	1	no	—
391	C₈×C₁₃	—	4	1	no	—
392	C₈×C₁₃	—	4	1	no	—
393	C₈×C₁₃	—	4	1	no	—
394	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
395	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
396	#525	—	2	4	no	—
397	#525	—	2	4	no	—
398	C₂×#123	—	2	1	no	—
399	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
402	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#120	—	2	1	no	—
404	C₂×C₄×D₄	—	2	1	no	—
405	C₂×C₄×D₄	—	2	1	no	—
406	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
409	#485	—	2	4	no	—
410	#482	—	2	4	no	—
411	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
412	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
417	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
418	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
422	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
429	#381	—	2	1	no	—
430	#380	C₂²×C₁₃	1	1	yes	characteristic
431	#380	C₂²×C₁₃	1	1	yes	characteristic
432	#380	C₂²×C₁₃	1	1	yes	characteristic
433	#380	C₂²×C₁₃	1	1	yes	characteristic
434	#379	—	2	1	no	—
435	C₄×C₂²⋊C₄	—	2	1	no	—
436	C₄×C₂²⋊C₄	—	2	1	no	—
437	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
440	#340	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	C₂²×C₁₃	—	2	2	no	—
442	C₂²×C₁₃	—	2	2	no	—
443	C₂²×C₁₃	—	2	2	no	—
444	C₂²×C₁₃	—	2	2	no	—
445	C₂²×C₁₃	—	2	2	no	—
446	C₂²×C₁₃	—	2	2	no	—
447	C₂²×C₁₃	—	2	2	no	—
448	C₂²×C₁₃	—	2	2	no	—
449	C₂²×C₁₃	—	2	2	no	—
450	C₂²×C₁₃	—	4	16	no	—
451	C₂²×C₁₃	—	4	1	no	—
452	C₂²×C₁₃	—	4	1	no	—
453	C₂²×C₁₃	—	4	1	no	—
454	C₂²×C₁₃	—	4	1	no	—
455	C₂²×C₁₃	—	4	1	no	—
456	C₂²×C₁₃	—	4	1	no	—
457	C₂²×C₁₃	—	4	1	no	—
458	C₂²×C₁₃	—	4	1	no	—
459	C₂²×C₁₃	—	4	1	no	—
460	C₂²×C₁₃	—	4	1	no	—
461	C₂²×C₁₃	—	4	1	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	—	4	2	no	—
464	C₂²×C₁₃	—	4	2	no	—
465	C₂²×C₁₃	—	4	2	no	—
466	C₂²×C₁₃	—	8	1	no	—
467	C₂²×C₁₃	—	8	1	no	—
468	C₂²×C₁₃	—	8	1	no	—
469	C₂²×C₁₃	—	8	1	no	—
470	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
471	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
472	C₂²×C₁₃	#534	1	1	yes	characteristic
473	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
474	C₂²×C₁₃	#575	1	1	yes	characteristic
475	C₂²×C₁₃	#575	1	1	yes	characteristic
476	C₂²×C₁₃	#575	1	1	yes	characteristic
477	C₄×C₁₃	—	2	2	no	—
478	C₄×C₁₃	—	2	2	no	—
479	C₄×C₁₃	—	4	1	no	—
480	C₄×C₁₃	—	4	2	no	—
481	C₄×C₁₃	—	4	2	no	—
482	C₄×C₁₃	—	4	2	no	—
483	C₄×C₁₃	—	8	1	no	—
484	C₄×C₁₃	—	8	1	no	—
485	C₄×C₁₃	—	8	1	no	—
486	C₄×C₁₃	—	8	1	no	—
487	C₄×C₁₃	#546	1	1	yes	characteristic
488	C₄×C₁₃	#546	1	1	yes	characteristic
489	C₄×C₁₃	#546	1	1	yes	characteristic
490	C₄×C₁₃	#546	1	1	yes	characteristic
491	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
492	C₂×#41	—	2	2	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	4	1	no	—
497	C₂×#41	—	4	1	no	—
498	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	2	no	—
505	C₂³×C₄	—	2	2	no	—
506	C₂³×C₄	—	2	2	no	—
507	C₂³×C₄	—	2	2	no	—
508	C₂³×C₄	—	4	1	no	—
509	C₂³×C₄	—	4	1	no	—
510	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
511	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
512	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
520	#123	—	2	8	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	2	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
525	#121	—	2	2	no	—
526	#121	—	2	2	no	—
527	#121	—	2	2	no	—
528	#121	D₄×C₁₃	1	4	yes	—
529	#120	—	2	8	no	—
530	C₄×D₄	—	2	8	no	—
531	C₄×D₄	—	2	8	no	—
532	#117	—	2	2	no	—
533	#117	—	2	2	no	—
534	#117	—	2	2	no	—
535	#117	—	2	2	no	—
536	#117	—	4	1	no	—
537	#117	—	4	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₂²⋊C₄	—	2	1	no	—
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	—	2	1	no	—
560	#107	—	2	2	no	—
561	#107	—	2	2	no	—
562	#106	—	2	2	no	—
563	#106	—	2	2	no	—
564	#103	—	2	2	no	—
565	#103	—	2	2	no	—
566	#103	—	4	1	no	—
567	#103	—	4	1	no	—
568	#102	—	2	2	no	—
569	#102	—	2	2	no	—
570	#102	—	4	1	no	—
571	#102	—	4	1	no	—
572	C₂²⋊C₈	—	2	2	no	—
573	C₂²⋊C₈	—	2	2	no	—
574	C₂²⋊C₈	—	2	2	no	—
575	C₂²⋊C₈	—	2	2	no	—
576	C₂²⋊C₈	—	4	1	no	—
577	C₂²⋊C₈	—	4	1	no	—
578	#95	—	2	1	no	—
579	#95	—	2	1	no	—
580	#95	—	2	1	no	—
581	#95	—	2	1	no	—
582	C₂×C₁₃	—	4	2	no	—
583	C₂×C₁₃	—	4	2	no	—
584	C₂×C₁₃	—	4	2	no	—
585	C₂×C₁₃	—	8	2	no	—
586	C₂×C₁₃	#2405	1	1	yes	characteristic
587	C₂×C₁₃	#3002	1	1	yes	characteristic
588	C₂×C₁₃	#3005	1	1	yes	characteristic
589	C₂×C₁₃	#3091	1	1	yes	characteristic
590	C₂×C₁₃	#3093	1	1	yes	characteristic
591	C₂×C₁₃	#3191	1	1	yes	characteristic
592	C₂×C₁₃	#3197	1	1	yes	characteristic
593	C₂⁴	—	2	2	no	—
594	C₂⁴	—	2	2	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	1	no	—
597	C₂⁴	—	4	1	no	—
598	C₂⁴	—	4	1	no	—
599	C₂⁴	—	4	1	no	—
600	C₂⁴	—	4	1	no	—
601	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
602	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
604	#41	—	4	4	no	—
605	#41	—	4	4	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	4	2	no	—
623	C₂×D₄	—	4	2	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	1	no	—
657	C₂²×C₄	—	4	1	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	—	4	1	no	—
660	C₂²×C₄	—	4	4	no	—
661	C₂²×C₄	—	4	4	no	—
662	C₂²×C₄	—	4	4	no	—
663	C₂²×C₄	—	4	4	no	—
664	C₂²×C₄	—	4	2	no	—
665	C₂²×C₄	—	4	2	no	—
666	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
667	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
668	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
669	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
670	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
671	C₂²×C₄	C₁₃×#41	1	2	yes	—
672	C₂²×C₄	C₁₃×#41	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
674	C₂×C₈	—	2	1	no	—
675	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
699	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₂²⋊C₄	—	4	2	no	—
709	C₂²⋊C₄	—	4	2	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₄²	—	2	4	no	—
712	C₄²	—	4	2	no	—
713	C₄²	—	4	2	no	—
714	C₁₃	#24008	1	1	yes	characteristic, direct product factor, Sylow
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	—	2	1	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	1	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	4	4	no	—
735	C₂³	—	4	4	no	—
736	C₂³	—	4	4	no	—
737	C₂³	—	4	4	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	C₁₃×#120	1	2	yes	—
748	C₂³	C₁₃×#123	1	2	yes	—
749	C₂³	C₁₃×#135	1	2	yes	—
750	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	4	1	no	—
754	Q₈	—	4	1	no	—
755	D₄	—	2	2	no	—
756	D₄	—	2	2	no	—
757	D₄	—	4	8	no	—
758	D₄	—	4	8	no	—
759	D₄	—	4	8	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	C₁₃×#120	1	2	yes	—
807	C₂×C₄	C₁₃×#123	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
810	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
811	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
812	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
813	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
814	C₈	—	4	1	no	—
815	C₈	—	4	1	no	—
816	C₈	—	4	1	no	—
817	C₈	—	4	1	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	4	16	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	8	1	no	—
844	C₂²	—	8	1	no	—
845	C₂²	—	8	1	no	—
846	C₂²	—	8	1	no	—
847	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
848	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
849	C₂²	C₁₃×#534	1	1	yes	characteristic
850	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
851	C₂²	C₁₃×#575	1	1	yes	characteristic
852	C₂²	C₁₃×#575	1	1	yes	characteristic
853	C₂²	C₁₃×#575	1	1	yes	characteristic
854	C₄	—	2	2	no	—
855	C₄	—	2	2	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	8	1	no	—
861	C₄	—	8	1	no	—
862	C₄	—	8	1	no	—
863	C₄	—	8	1	no	—
864	C₄	C₁₃×#546	1	1	yes	characteristic
865	C₄	C₁₃×#546	1	1	yes	characteristic
866	C₄	C₁₃×#546	1	1	yes	characteristic
867	C₄	C₁₃×#546	1	1	yes	characteristic
868	C₂	—	4	2	no	—
869	C₂	—	4	2	no	—
870	C₂	—	4	2	no	—
871	C₂	—	8	2	no	—
872	C₂	C₁₃×#2405	1	1	yes	characteristic
873	C₂	C₁₃×#3002	1	1	yes	characteristic
874	C₂	C₁₃×#3005	1	1	yes	characteristic
875	C₂	C₁₃×#3091	1	1	yes	characteristic
876	C₂	C₁₃×#3093	1	1	yes	characteristic
877	C₂	C₁₃×#3191	1	1	yes	characteristic
878	C₂	C₁₃×#3197	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#525	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#485	C₂	semidirect
3. C₂×C₁₃×#482	C₂	semidirect
4. C₁₃×#2280	C₂	semidirect
5. C₁₃×#2036	C₂	semidirect
6. C₁₃×#2035	C₂	semidirect
7. C₁₃×#2034	C₂	semidirect
8. C₁₃×#2033	C₂	semidirect
9. C₁₃×#1875	C₂	semidirect
10. C₁₃×#1873	C₂	semidirect
11. C₁₃×#1854	C₂	semidirect
12. C₁₃×#1854	C₂	semidirect
13. C₁₃×#1788	C₂	semidirect
14. C₁₃×#1788	C₂	semidirect
15. C₁₃×#1779	C₂	semidirect
33. C₂×C₁₃×#107	C₂²	semidirect
34. C₂×C₁₃×#107	C₂²	semidirect
35. C₂×C₁₃×#106	C₂²	semidirect
36. C₂×C₁₃×#106	C₂²	semidirect
37. C₂×C₁₃×#103	C₂²	semidirect
38. C₂×C₁₃×#103	C₂²	semidirect
39. C₂×C₁₃×#103	C₂²	semidirect
40. C₂×C₁₃×#103	C₂²	semidirect
41. C₂×C₁₃×#102	C₂²	semidirect
42. C₂×C₁₃×#102	C₂²	semidirect
43. C₂×C₁₃×#102	C₂²	semidirect
44. C₂×C₁₃×#102	C₂²	semidirect
59. C₁₃×#340	C₂²	semidirect
60. C₁₃×#340	C₂²	semidirect
61. C₁₃×#340	C₂²	semidirect
62. C₁₃×#340	C₂²	semidirect
154. #24008	C₁₃	direct (N × H)
277. C₂×#485	C₂×C₁₃	semidirect
278. C₂×#482	C₂×C₁₃	semidirect
279. #2280	C₂×C₁₃	semidirect
280. #2036	C₂×C₁₃	semidirect
281. #2035	C₂×C₁₃	semidirect
282. #2034	C₂×C₁₃	semidirect
283. #2033	C₂×C₁₃	semidirect
284. #1875	C₂×C₁₃	semidirect
285. #1873	C₂×C₁₃	semidirect
286. #1854	C₂×C₁₃	semidirect
287. #1854	C₂×C₁₃	semidirect
288. #1788	C₂×C₁₃	semidirect
289. #1788	C₂×C₁₃	semidirect
290. #1779	C₂×C₁₃	semidirect
411. C₂×#107	C₂²×C₁₃	semidirect
412. C₂×#107	C₂²×C₁₃	semidirect
413. C₂×#106	C₂²×C₁₃	semidirect
414. C₂×#106	C₂²×C₁₃	semidirect
415. C₂×#103	C₂²×C₁₃	semidirect
416. C₂×#103	C₂²×C₁₃	semidirect
417. C₂×#103	C₂²×C₁₃	semidirect
418. C₂×#103	C₂²×C₁₃	semidirect
419. C₂×#102	C₂²×C₁₃	semidirect
420. C₂×#102	C₂²×C₁₃	semidirect
421. C₂×#102	C₂²×C₁₃	semidirect
422. C₂×#102	C₂²×C₁₃	semidirect
437. #340	C₂²×C₁₃	semidirect
438. #340	C₂²×C₁₃	semidirect
439. #340	C₂²×C₁₃	semidirect
440. #340	C₂²×C₁₃	semidirect
714. C₁₃	#24008	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#525	2
C₂×C₁₃×#485	2
C₂×C₁₃×#482	2
C₁₃×#2280	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#1875	2
C₁₃×#1873	2
C₁₃×#1854	2
C₁₃×#1788	2
C₁₃×#1779	2
#24008	13

Subgroups — C13×#24008 #15710347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24008 #15710347