Subgroups — C₁₃×#25085 #15711424

Order 3328.

1134 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2432	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₁₃×#465	—	2	4	no	—
28	C₁₃×#463	—	2	4	no	—
29	C₁₃×#449	—	2	4	no	—
30	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₁₃×#416	—	2	4	no	—
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₃×#394	—	2	1	no	—
46	C₁₃×#394	—	2	1	no	—
47	C₁₃×#391	C₂²	1	1	yes	characteristic
48	C₁₃×#390	—	2	1	no	—
49	C₁₃×#390	C₂²	1	1	yes	characteristic
50	C₁₃×#390	C₂²	1	1	yes	characteristic
51	C₁₃×#389	C₂²	1	1	yes	characteristic
52	C₁₃×#388	—	2	1	no	—
53	C₁₃×#386	—	2	1	no	—
54	C₁₃×#385	—	2	1	no	—
55	C₁₃×#385	—	2	1	no	—
56	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
58	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	—	2	2	no	—
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	—	4	1	no	—
68	C₂×C₁₃×#41	—	4	1	no	—
69	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	—	2	1	no	—
76	C₂³×C₄×C₁₃	—	2	1	no	—
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×SD₁₆	—	2	2	no	—
79	C₂×C₁₃×SD₁₆	—	2	2	no	—
80	C₂×C₁₃×SD₁₆	—	2	2	no	—
81	C₂×C₁₃×SD₁₆	—	2	2	no	—
82	C₂×C₁₃×SD₁₆	—	4	1	no	—
83	C₂×C₁₃×SD₁₆	—	4	1	no	—
84	C₂×C₁₃×D₈	—	2	2	no	—
85	C₂×C₁₃×D₈	—	2	2	no	—
86	C₂×C₁₃×D₈	—	4	1	no	—
87	C₂²×C₈×C₁₃	—	2	2	no	—
88	C₂²×C₈×C₁₃	—	2	2	no	—
89	C₂²×C₈×C₁₃	—	4	1	no	—
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₄⋊Q₈	—	4	1	no	—
96	C₁₃×#124	—	2	2	no	—
97	C₁₃×#124	—	4	1	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	—	2	2	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	D₄	1	4	yes	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	4	1	no	—
104	C₁₃×#117	—	2	2	no	—
105	C₁₃×#117	—	4	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
125	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	—	2	1	no	—
127	C₂×C₄²×C₁₃	—	2	1	no	—
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₁₃×#106	—	2	2	no	—
131	C₁₃×C₄⋊C₈	—	2	2	no	—
132	C₁₃×C₄⋊C₈	—	4	1	no	—
133	C₁₃×#103	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	—	2	2	no	—
138	C₁₃×#103	—	4	1	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×#102	—	2	2	no	—
142	C₁₃×#102	D₄	1	4	yes	complemented
143	C₁₃×C₂²⋊C₈	—	2	2	no	—
144	C₁₃×#95	—	2	1	no	—
145	C₁₃×#95	—	2	1	no	—
146	C₁₃×#95	—	2	1	no	—
147	C₁₃×#95	—	2	1	no	—
148	C₁₃×#95	D₄	1	1	yes	characteristic
149	C₁₃×#95	D₄	1	1	yes	characteristic
150	#25085	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂⁴×C₁₃	—	2	1	no	—
152	C₂⁴×C₁₃	—	2	1	no	—
153	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₁₃×#41	—	2	8	no	—
155	C₁₃×#41	—	4	4	no	—
156	C₁₃×#41	—	4	4	no	—
157	C₁₃×#41	—	4	4	no	—
158	C₂×Q₈×C₁₃	—	2	1	no	—
159	C₂×Q₈×C₁₃	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	2	1	no	—
161	C₂×Q₈×C₁₃	—	2	1	no	—
162	C₂×Q₈×C₁₃	—	2	1	no	—
163	C₂×Q₈×C₁₃	—	2	1	no	—
164	C₂×Q₈×C₁₃	—	2	1	no	—
165	C₂×Q₈×C₁₃	—	2	1	no	—
166	C₂×Q₈×C₁₃	—	2	1	no	—
167	C₂×Q₈×C₁₃	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	#41	1	2	yes	—
170	C₂×D₄×C₁₃	—	2	4	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	2	1	no	—
174	C₂×D₄×C₁₃	—	2	1	no	—
175	C₂×D₄×C₁₃	—	2	1	no	—
176	C₂×D₄×C₁₃	—	2	1	no	—
177	C₂×D₄×C₁₃	—	2	1	no	—
178	C₂×D₄×C₁₃	—	2	1	no	—
179	C₂×D₄×C₁₃	—	2	1	no	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	4	2	no	—
182	C₂×D₄×C₁₃	—	4	2	no	—
183	C₂×D₄×C₁₃	—	4	2	no	—
184	C₂×D₄×C₁₃	—	8	1	no	—
185	C₂×D₄×C₁₃	—	8	1	no	—
186	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
187	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₃	—	2	1	no	—
189	C₂²×C₄×C₁₃	—	2	1	no	—
190	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	4	2	no	—
199	C₂²×C₄×C₁₃	—	4	2	no	—
200	C₂²×C₄×C₁₃	—	4	2	no	—
201	C₂²×C₄×C₁₃	—	4	2	no	—
202	C₂²×C₄×C₁₃	—	4	2	no	—
203	C₂²×C₄×C₁₃	—	8	1	no	—
204	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	#41	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₁₃×SD₁₆	—	4	4	no	—
213	C₁₃×SD₁₆	—	4	4	no	—
214	C₁₃×D₈	—	4	4	no	—
215	C₂×C₈×C₁₃	—	2	1	no	—
216	C₂×C₈×C₁₃	—	2	1	no	—
217	C₂×C₈×C₁₃	—	2	1	no	—
218	C₂×C₈×C₁₃	—	2	1	no	—
219	C₂×C₈×C₁₃	—	2	1	no	—
220	C₂×C₈×C₁₃	—	2	1	no	—
221	C₂×C₈×C₁₃	—	2	1	no	—
222	C₂×C₈×C₁₃	—	2	1	no	—
223	C₂×C₈×C₁₃	—	2	1	no	—
224	C₂×C₈×C₁₃	—	2	1	no	—
225	C₂×C₈×C₁₃	—	2	1	no	—
226	C₂×C₈×C₁₃	—	4	4	no	—
227	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
228	C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₁₃×C₄⋊C₄	—	2	1	no	—
230	C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₁₃×C₄⋊C₄	—	2	1	no	—
232	C₁₃×C₄⋊C₄	—	2	1	no	—
233	C₁₃×C₄⋊C₄	—	2	1	no	—
234	C₁₃×C₄⋊C₄	—	4	2	no	—
235	C₁₃×C₄⋊C₄	—	4	2	no	—
236	C₁₃×C₄⋊C₄	—	4	2	no	—
237	C₁₃×C₄⋊C₄	—	8	1	no	—
238	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
239	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	2	no	—
242	C₁₃×C₂²⋊C₄	—	4	1	no	—
243	C₁₃×C₂²⋊C₄	—	4	2	no	—
244	C₁₃×C₂²⋊C₄	—	4	2	no	—
245	C₁₃×C₂²⋊C₄	—	4	2	no	—
246	C₁₃×C₂²⋊C₄	—	4	2	no	—
247	C₁₃×C₂²⋊C₄	—	4	2	no	—
248	C₁₃×C₂²⋊C₄	—	4	2	no	—
249	C₁₃×C₂²⋊C₄	—	4	2	no	—
250	C₁₃×C₂²⋊C₄	—	4	2	no	—
251	C₁₃×C₂²⋊C₄	—	8	1	no	—
252	C₄²×C₁₃	—	2	1	no	—
253	C₄²×C₁₃	—	2	1	no	—
254	C₄²×C₁₃	—	2	1	no	—
255	C₄²×C₁₃	—	2	1	no	—
256	C₄²×C₁₃	—	4	2	no	—
257	C₄²×C₁₃	—	8	1	no	—
258	C₂×#465	C₂×C₁₃	1	1	yes	characteristic, complemented
259	C₂×#463	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂×#449	C₂×C₁₃	1	1	yes	characteristic
261	C₂×#416	C₂×C₁₃	1	1	yes	characteristic, complemented
262	#2432	C₂×C₁₃	1	1	yes	characteristic, complemented
263	#2363	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#2054	C₂×C₁₃	1	1	yes	characteristic, complemented
266	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#2013	C₂×C₁₃	1	1	yes	characteristic, complemented
268	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
269	#1926	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#1873	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#1850	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂³×C₁₃	—	2	1	no	—
274	C₂³×C₁₃	—	2	1	no	—
275	C₂³×C₁₃	—	2	1	no	—
276	C₂³×C₁₃	—	2	1	no	—
277	C₂³×C₁₃	—	2	1	no	—
278	C₂³×C₁₃	—	2	1	no	—
279	C₂³×C₁₃	—	2	2	no	—
280	C₂³×C₁₃	—	2	2	no	—
281	C₂³×C₁₃	—	4	1	no	—
282	C₂³×C₁₃	—	4	1	no	—
283	C₂³×C₁₃	—	4	1	no	—
284	C₂³×C₁₃	—	4	1	no	—
285	C₂³×C₁₃	—	4	1	no	—
286	C₂³×C₁₃	—	4	1	no	—
287	C₂³×C₁₃	—	4	1	no	—
288	C₂³×C₁₃	—	4	1	no	—
289	C₂³×C₁₃	—	4	1	no	—
290	C₂³×C₁₃	—	4	1	no	—
291	C₂³×C₁₃	—	4	1	no	—
292	C₂³×C₁₃	—	4	1	no	—
293	C₂³×C₁₃	#121	1	2	yes	—
294	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	Q₈×C₁₃	—	2	2	no	—
296	Q₈×C₁₃	—	2	2	no	—
297	Q₈×C₁₃	—	4	1	no	—
298	Q₈×C₁₃	—	4	1	no	—
299	Q₈×C₁₃	—	4	1	no	—
300	Q₈×C₁₃	—	4	1	no	—
301	Q₈×C₁₃	—	4	1	no	—
302	Q₈×C₁₃	—	4	1	no	—
303	D₄×C₁₃	—	2	2	no	—
304	D₄×C₁₃	—	2	2	no	—
305	D₄×C₁₃	—	2	2	no	—
306	D₄×C₁₃	—	2	2	no	—
307	D₄×C₁₃	—	4	8	no	—
308	D₄×C₁₃	—	4	1	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	8	4	no	—
313	C₂×C₄×C₁₃	—	2	1	no	—
314	C₂×C₄×C₁₃	—	2	1	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	2	no	—
318	C₂×C₄×C₁₃	—	2	2	no	—
319	C₂×C₄×C₁₃	—	2	2	no	—
320	C₂×C₄×C₁₃	—	2	2	no	—
321	C₂×C₄×C₁₃	—	2	2	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	2	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	2	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	1	no	—
330	C₂×C₄×C₁₃	—	2	1	no	—
331	C₂×C₄×C₁₃	—	2	1	no	—
332	C₂×C₄×C₁₃	—	2	1	no	—
333	C₂×C₄×C₁₃	—	4	8	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	4	1	no	—
337	C₂×C₄×C₁₃	—	4	1	no	—
338	C₂×C₄×C₁₃	—	4	1	no	—
339	C₂×C₄×C₁₃	—	4	1	no	—
340	C₂×C₄×C₁₃	—	4	1	no	—
341	C₂×C₄×C₁₃	—	4	1	no	—
342	C₂×C₄×C₁₃	—	4	1	no	—
343	C₂×C₄×C₁₃	—	4	1	no	—
344	C₂×C₄×C₁₃	—	4	1	no	—
345	C₂×C₄×C₁₃	—	4	1	no	—
346	C₂×C₄×C₁₃	—	4	1	no	—
347	C₂×C₄×C₁₃	—	4	1	no	—
348	C₂×C₄×C₁₃	—	4	1	no	—
349	C₂×C₄×C₁₃	—	8	4	no	—
350	C₂×C₄×C₁₃	#121	1	2	yes	—
351	C₂×C₄×C₁₃	#135	1	2	yes	—
352	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
355	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
357	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
358	C₈×C₁₃	—	2	2	no	—
359	C₈×C₁₃	—	4	1	no	—
360	C₈×C₁₃	—	4	1	no	—
361	C₈×C₁₃	—	4	1	no	—
362	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
363	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
364	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
365	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
366	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
367	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
368	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
370	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
373	#465	—	2	4	no	—
374	#463	—	2	4	no	—
375	#449	—	2	4	no	—
376	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
377	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
378	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
379	#416	—	2	4	no	—
380	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
381	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
382	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
383	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
386	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
388	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
389	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
391	#394	—	2	1	no	—
392	#394	—	2	1	no	—
393	#391	C₂²×C₁₃	1	1	yes	characteristic
394	#390	—	2	1	no	—
395	#390	C₂²×C₁₃	1	1	yes	characteristic
396	#390	C₂²×C₁₃	1	1	yes	characteristic
397	#389	C₂²×C₁₃	1	1	yes	characteristic
398	#388	—	2	1	no	—
399	#386	—	2	1	no	—
400	#385	—	2	1	no	—
401	#385	—	2	1	no	—
402	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₄×C₂²⋊C₄	—	2	1	no	—
404	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
405	#340	C₂²×C₁₃	1	1	yes	characteristic
406	#340	C₂²×C₁₃	1	1	yes	characteristic
407	#336	C₂²×C₁₃	1	1	yes	characteristic
408	#336	C₂²×C₁₃	1	1	yes	characteristic
409	C₂²×C₁₃	—	2	2	no	—
410	C₂²×C₁₃	—	2	2	no	—
411	C₂²×C₁₃	—	2	2	no	—
412	C₂²×C₁₃	—	4	1	no	—
413	C₂²×C₁₃	—	4	1	no	—
414	C₂²×C₁₃	—	4	1	no	—
415	C₂²×C₁₃	—	4	1	no	—
416	C₂²×C₁₃	—	4	2	no	—
417	C₂²×C₁₃	—	4	2	no	—
418	C₂²×C₁₃	—	4	2	no	—
419	C₂²×C₁₃	—	4	2	no	—
420	C₂²×C₁₃	—	4	2	no	—
421	C₂²×C₁₃	—	4	2	no	—
422	C₂²×C₁₃	—	8	1	no	—
423	C₂²×C₁₃	—	8	1	no	—
424	C₂²×C₁₃	—	8	1	no	—
425	C₂²×C₁₃	—	8	1	no	—
426	C₂²×C₁₃	—	8	1	no	—
427	C₂²×C₁₃	—	8	1	no	—
428	C₂²×C₁₃	—	8	1	no	—
429	C₂²×C₁₃	—	8	1	no	—
430	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
431	C₂²×C₁₃	D₄²	1	1	yes	characteristic
432	C₂²×C₁₃	#546	1	1	yes	characteristic
433	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
434	C₂²×C₁₃	#575	1	1	yes	characteristic
435	C₂²×C₁₃	#577	1	1	yes	characteristic
436	C₂²×C₁₃	#577	1	1	yes	characteristic
437	C₄×C₁₃	—	2	2	no	—
438	C₄×C₁₃	—	2	2	no	—
439	C₄×C₁₃	—	4	2	no	—
440	C₄×C₁₃	—	4	1	no	—
441	C₄×C₁₃	—	4	2	no	—
442	C₄×C₁₃	—	4	1	no	—
443	C₄×C₁₃	—	4	2	no	—
444	C₄×C₁₃	—	4	1	no	—
445	C₄×C₁₃	—	8	1	no	—
446	C₄×C₁₃	—	8	1	no	—
447	C₄×C₁₃	—	8	1	no	—
448	C₄×C₁₃	#525	1	1	yes	characteristic
449	C₄×C₁₃	#538	1	1	yes	characteristic
450	C₄×C₁₃	D₄²	1	1	yes	characteristic
451	C₄×C₁₃	#546	1	1	yes	characteristic
452	C₂×#41	—	2	2	no	—
453	C₂×#41	—	2	2	no	—
454	C₂×#41	—	2	2	no	—
455	C₂×#41	—	2	2	no	—
456	C₂×#41	—	4	1	no	—
457	C₂×#41	—	4	1	no	—
458	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
459	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	—	2	1	no	—
466	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×SD₁₆	—	2	2	no	—
468	C₂×SD₁₆	—	2	2	no	—
469	C₂×SD₁₆	—	2	2	no	—
470	C₂×SD₁₆	—	2	2	no	—
471	C₂×SD₁₆	—	4	1	no	—
472	C₂×SD₁₆	—	4	1	no	—
473	C₂×D₈	—	2	2	no	—
474	C₂×D₈	—	2	2	no	—
475	C₂×D₈	—	4	1	no	—
476	C₂²×C₈	—	2	2	no	—
477	C₂²×C₈	—	2	2	no	—
478	C₂²×C₈	—	4	1	no	—
479	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
483	C₄⋊Q₈	—	2	2	no	—
484	C₄⋊Q₈	—	4	1	no	—
485	#124	—	2	2	no	—
486	#124	—	4	1	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	#121	—	2	2	no	—
490	#121	D₄×C₁₃	1	4	yes	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	4	1	no	—
493	#117	—	2	2	no	—
494	#117	—	4	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
515	C₂×C₄²	—	2	1	no	—
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
519	#106	—	2	2	no	—
520	C₄⋊C₈	—	2	2	no	—
521	C₄⋊C₈	—	4	1	no	—
522	#103	—	2	2	no	—
523	#103	—	2	2	no	—
524	#103	—	2	2	no	—
525	#103	—	2	2	no	—
526	#103	—	2	2	no	—
527	#103	—	4	1	no	—
528	#102	—	2	2	no	—
529	#102	—	2	2	no	—
530	#102	—	2	2	no	—
531	#102	D₄×C₁₃	1	4	yes	complemented
532	C₂²⋊C₈	—	2	2	no	—
533	#95	—	2	1	no	—
534	#95	—	2	1	no	—
535	#95	—	2	1	no	—
536	#95	—	2	1	no	—
537	#95	D₄×C₁₃	1	1	yes	characteristic
538	#95	D₄×C₁₃	1	1	yes	characteristic
539	C₂×C₁₃	—	4	2	no	—
540	C₂×C₁₃	—	8	2	no	—
541	C₂×C₁₃	—	8	2	no	—
542	C₂×C₁₃	#2424	1	1	yes	characteristic
543	C₂×C₁₃	#3035	1	1	yes	characteristic
544	C₂×C₁₃	#3042	1	1	yes	characteristic
545	C₂×C₁₃	#3267	1	1	yes	characteristic
546	C₂×C₁₃	#3284	1	1	yes	characteristic
547	C₂×C₁₃	#3301	1	1	yes	characteristic
548	C₂×C₁₃	#3321	1	1	yes	characteristic
549	C₂⁴	—	2	1	no	—
550	C₂⁴	—	2	1	no	—
551	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
552	#41	—	2	8	no	—
553	#41	—	4	4	no	—
554	#41	—	4	4	no	—
555	#41	—	4	4	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	C₁₃×#41	1	2	yes	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	4	2	no	—
580	C₂×D₄	—	4	2	no	—
581	C₂×D₄	—	4	2	no	—
582	C₂×D₄	—	8	1	no	—
583	C₂×D₄	—	8	1	no	—
584	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
585	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	2	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	—	8	1	no	—
602	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
607	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂²×C₄	C₁₃×#41	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
610	SD₁₆	—	4	4	no	—
611	SD₁₆	—	4	4	no	—
612	D₈	—	4	4	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	4	4	no	—
625	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	8	1	no	—
636	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
637	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	4	1	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	2	no	—
647	C₂²⋊C₄	—	4	2	no	—
648	C₂²⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	8	1	no	—
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	4	2	no	—
655	C₄²	—	8	1	no	—
656	C₁₃	#25085	1	1	yes	characteristic, direct product factor, Sylow
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	C₁₃×#121	1	2	yes	—
678	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
679	Q₈	—	2	2	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	4	1	no	—
682	Q₈	—	4	1	no	—
683	Q₈	—	4	1	no	—
684	Q₈	—	4	1	no	—
685	Q₈	—	4	1	no	—
686	Q₈	—	4	1	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	2	no	—
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	4	8	no	—
692	D₄	—	4	1	no	—
693	D₄	—	4	1	no	—
694	D₄	—	4	1	no	—
695	D₄	—	4	1	no	—
696	D₄	—	8	4	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	4	8	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	8	4	no	—
734	C₂×C₄	C₁₃×#121	1	2	yes	—
735	C₂×C₄	C₁₃×#135	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
738	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
739	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
740	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
741	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
742	C₈	—	2	2	no	—
743	C₈	—	4	1	no	—
744	C₈	—	4	1	no	—
745	C₈	—	4	1	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	8	1	no	—
760	C₂²	—	8	1	no	—
761	C₂²	—	8	1	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	8	1	no	—
765	C₂²	—	8	1	no	—
766	C₂²	—	8	1	no	—
767	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
768	C₂²	D₄²×C₁₃	1	1	yes	characteristic
769	C₂²	C₁₃×#546	1	1	yes	characteristic
770	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
771	C₂²	C₁₃×#575	1	1	yes	characteristic
772	C₂²	C₁₃×#577	1	1	yes	characteristic
773	C₂²	C₁₃×#577	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	4	1	no	—
777	C₄	—	4	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	2	no	—
782	C₄	—	8	1	no	—
783	C₄	—	8	1	no	—
784	C₄	—	8	1	no	—
785	C₄	C₁₃×#525	1	1	yes	characteristic
786	C₄	C₁₃×#538	1	1	yes	characteristic
787	C₄	D₄²×C₁₃	1	1	yes	characteristic
788	C₄	C₁₃×#546	1	1	yes	characteristic
789	C₂	—	4	2	no	—
790	C₂	—	8	2	no	—
791	C₂	—	8	2	no	—
792	C₂	C₁₃×#2424	1	1	yes	characteristic
793	C₂	C₁₃×#3035	1	1	yes	characteristic
794	C₂	C₁₃×#3042	1	1	yes	characteristic
795	C₂	C₁₃×#3267	1	1	yes	characteristic
796	C₂	C₁₃×#3284	1	1	yes	characteristic
797	C₂	C₁₃×#3301	1	1	yes	characteristic
798	C₂	C₁₃×#3321	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#465	C₂	semidirect
2. C₂×C₁₃×#463	C₂	semidirect
4. C₂×C₁₃×#416	C₂	semidirect
5. C₁₃×#2432	C₂	semidirect
6. C₁₃×#2363	C₂	semidirect
7. C₁₃×#2066	C₂	semidirect
8. C₁₃×#2054	C₂	semidirect
9. C₁₃×#2042	C₂	semidirect
10. C₁₃×#2013	C₂	semidirect
11. C₁₃×#1981	C₂	semidirect
12. C₁₃×#1926	C₂	semidirect
13. C₁₃×#1877	C₂	semidirect
14. C₁₃×#1873	C₂	semidirect
15. C₁₃×#1850	C₂	semidirect
142. C₁₃×#102	D₄	semidirect
150. #25085	C₁₃	direct (N × H)
258. C₂×#465	C₂×C₁₃	semidirect
259. C₂×#463	C₂×C₁₃	semidirect
261. C₂×#416	C₂×C₁₃	semidirect
262. #2432	C₂×C₁₃	semidirect
263. #2363	C₂×C₁₃	semidirect
264. #2066	C₂×C₁₃	semidirect
265. #2054	C₂×C₁₃	semidirect
266. #2042	C₂×C₁₃	semidirect
267. #2013	C₂×C₁₃	semidirect
268. #1981	C₂×C₁₃	semidirect
269. #1926	C₂×C₁₃	semidirect
270. #1877	C₂×C₁₃	semidirect
271. #1873	C₂×C₁₃	semidirect
272. #1850	C₂×C₁₃	semidirect
531. #102	D₄×C₁₃	semidirect
656. C₁₃	#25085	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×#465	2
C₂×C₁₃×#463	2
C₂×C₁₃×#449	2
C₂×C₁₃×#416	2
C₁₃×#2432	2
C₁₃×#2363	2
C₁₃×#2066	2
C₁₃×#2054	2
C₁₃×#2042	2
C₁₃×#2013	2
C₁₃×#1981	2
C₁₃×#1926	2
C₁₃×#1877	2
C₁₃×#1873	2
C₁₃×#1850	2
#25085	13

Subgroups — C13×#25085 #15711424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25085 #15711424