Subgroups — #15868379

Order 3328.

790 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115451	C₂	1	2	yes	maximal
2	#13115444	C₂	1	2	yes	maximal
3	#13115402	C₂	1	2	yes	maximal, complemented
4	#13115395	C₂	1	2	yes	maximal, complemented
5	#13114689	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114689	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114598	C₂	1	1	yes	maximal, characteristic
8	#13114598	C₂	1	1	yes	maximal, characteristic
9	#13114585	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88043	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
16	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
17	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
20	C₄×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₁₃×#376	C₄	1	1	yes	characteristic
24	C₁₃×#376	C₄	1	1	yes	characteristic
25	C₄³×C₁₃	C₂²	1	1	yes	characteristic
26	C₄³×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
28	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
29	C₂×C₄⋊#1055	C₂²	1	2	yes	—
30	C₂×C₄⋊#1055	C₂²	1	2	yes	—
31	C₂×#88043	C₂²	1	2	yes	—
32	C₂×#88043	C₂²	1	1	yes	characteristic
33	C₂×#88043	C₂²	1	1	yes	characteristic
34	C₂×#88043	C₂²	1	1	yes	characteristic
35	C₂×#88043	C₂²	1	1	yes	characteristic
36	C₂×C₄×#1055	C₂²	1	2	yes	—
37	#11718116	C₂²	1	2	yes	—
38	#11718116	C₂²	1	2	yes	—
39	#11718116	C₂²	1	2	yes	—
40	#11718116	C₂²	1	2	yes	—
41	#11718116	C₂²	1	2	yes	—
42	#11718116	C₂²	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₁₃×#117	—	2	4	no	—
47	C₁₃×#117	—	2	4	no	—
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	—	2	2	no	—
57	C₂×C₄²×C₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×#1055	C₂³	1	2	yes	—
75	C₂²×#1055	C₂³	1	2	yes	—
76	C₂²×#1055	C₂³	1	2	yes	—
77	C₂²×#1055	C₂³	1	2	yes	—
78	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
79	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
80	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
81	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
83	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
84	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
85	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
86	C₂²⋊#1055	—	2	4	no	—
87	C₂²⋊#1055	—	2	4	no	—
88	C₄⋊#1055	—	2	4	no	—
89	C₄⋊#1055	—	2	4	no	—
90	#88043	—	2	2	no	—
91	#88043	—	2	2	no	—
92	#88043	—	2	2	no	—
93	#88043	—	2	2	no	—
94	#88043	—	2	4	no	—
95	C₄×#1055	—	2	4	no	—
96	#21435	—	13	1	no	maximal, Sylow
97	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	4	1	no	—
107	C₂²×C₄×C₁₃	—	4	1	no	—
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	—
126	C₁₃×C₂²⋊C₄	—	2	2	no	—
127	C₁₃×C₂²⋊C₄	—	2	2	no	—
128	C₁₃×C₂²⋊C₄	—	2	2	no	—
129	C₁₃×C₂²⋊C₄	M₁₆	1	4	yes	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	2	2	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	C₄²×C₁₃	—	2	2	no	—
141	C₄²×C₁₃	—	2	2	no	—
142	C₄²×C₁₃	—	4	1	no	—
143	C₄²×C₁₃	—	4	1	no	—
144	C₄²×C₁₃	—	4	1	no	—
145	C₄²×C₁₃	—	4	1	no	—
146	C₄²×C₁₃	#41	1	2	yes	—
147	C₄²×C₁₃	#41	1	2	yes	—
148	C₂×#1055	—	2	2	no	—
149	C₂×#1055	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	2	2	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	—	2	2	no	—
156	C₂×#1055	—	2	2	no	—
157	C₂×#1055	—	2	2	no	—
158	C₂×#1055	#41	1	4	yes	—
159	C₂×#1055	#41	1	4	yes	—
160	C₄×#117	D₁₃	1	1	yes	characteristic
161	#1924	—	13	2	no	—
162	#1923	—	13	2	no	—
163	#1917	—	13	2	no	—
164	#1916	—	13	2	no	—
165	#1767	—	13	1	no	—
166	#1767	—	13	1	no	—
167	#1749	—	13	1	no	—
168	#1749	—	13	1	no	—
169	#1745	—	13	1	no	—
170	C₄×#97	—	13	1	no	—
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	—	2	1	no	—
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	—	2	1	no	—
175	C₂³×C₁₃	—	2	1	no	—
176	C₂³×C₁₃	—	2	1	no	—
177	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
178	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	1	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	4	4	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	#117	1	2	yes	—
216	C₂×C₄×C₁₃	#117	1	2	yes	—
217	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
218	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
219	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
220	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
221	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
222	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
225	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
226	#1055	—	2	4	no	—
227	#1055	—	2	4	no	—
228	#1055	—	4	2	no	—
229	#1055	—	4	2	no	—
230	C₂×#117	Dic₁₃	1	1	yes	characteristic
231	C₂×#117	Dic₁₃	1	1	yes	characteristic
232	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
233	C₂×C₄⋊C₈	—	13	2	no	—
234	C₂×C₄⋊C₈	—	13	2	no	—
235	C₂×C₂²⋊C₈	—	13	2	no	—
236	C₂×C₂²⋊C₈	—	13	2	no	—
237	C₂×#97	—	13	2	no	—
238	C₂×#97	—	13	1	no	—
239	C₂×#97	—	13	1	no	—
240	C₂×#97	—	13	1	no	—
241	C₂×#97	—	13	1	no	—
242	C₂×C₄×C₈	—	13	2	no	—
243	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
244	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
245	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
246	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
247	C₄×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
248	C₄×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
249	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
250	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
251	#376	Dic₁₃	1	1	yes	characteristic
252	#376	Dic₁₃	1	1	yes	characteristic
253	C₄³	C₂×D₁₃	1	1	yes	characteristic
254	C₄³	C₂×D₁₃	1	1	yes	characteristic
255	#336	—	13	2	no	—
256	#336	—	13	2	no	—
257	#336	—	13	2	no	—
258	#336	—	13	2	no	—
259	#336	—	13	2	no	—
260	#336	—	13	2	no	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	4	1	no	—
265	C₂²×C₁₃	—	4	1	no	—
266	C₂²×C₁₃	—	4	1	no	—
267	C₂²×C₁₃	—	4	1	no	—
268	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
269	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
270	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
271	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
272	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
273	C₂²×C₁₃	#568	1	1	yes	characteristic
274	C₂²×C₁₃	#568	1	1	yes	characteristic
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	2	2	no	—
277	C₄×C₁₃	—	2	2	no	—
278	C₄×C₁₃	—	2	2	no	—
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	2	2	no	—
281	C₄×C₁₃	—	2	2	no	—
282	C₄×C₁₃	—	4	1	no	—
283	C₄×C₁₃	—	4	1	no	—
284	C₄×C₁₃	—	4	1	no	—
285	C₄×C₁₃	—	4	1	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	4	1	no	—
288	C₄×C₁₃	#529	1	2	yes	—
289	C₄×C₁₃	#529	1	2	yes	—
290	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
291	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
292	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
293	C₂²×C₈	—	13	2	no	—
294	C₂²×C₈	—	13	2	no	—
295	C₂²×C₈	—	13	2	no	—
296	C₂²×C₈	—	13	2	no	—
297	#117	—	2	4	no	—
298	#117	—	2	4	no	—
299	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
310	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
311	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
312	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
313	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
314	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
315	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
316	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
317	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
318	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
319	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
320	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
321	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
322	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
324	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
325	C₄⋊C₈	—	26	4	no	—
326	C₄⋊C₈	—	26	4	no	—
327	C₂²⋊C₈	—	26	4	no	—
328	C₂²⋊C₈	—	26	4	no	—
329	#97	—	26	4	no	—
330	#97	—	26	2	no	—
331	#97	—	26	2	no	—
332	#97	—	26	2	no	—
333	#97	—	26	2	no	—
334	C₄×C₈	—	26	4	no	—
335	#95	C₂×Dic₁₃	1	1	yes	characteristic
336	#95	C₂×Dic₁₃	1	1	yes	characteristic
337	#95	C₂×Dic₁₃	1	1	yes	characteristic
338	#95	C₂×Dic₁₃	1	1	yes	characteristic
339	#95	C₂×Dic₁₃	1	1	yes	characteristic
340	#95	C₂×Dic₁₃	1	1	yes	characteristic
341	#95	C₂×Dic₁₃	1	1	yes	characteristic
342	#95	C₂×Dic₁₃	1	1	yes	characteristic
343	C₂×C₁₃	—	4	2	no	—
344	C₂×C₁₃	#2298	1	1	yes	characteristic
345	C₂×C₁₃	#2920	1	1	yes	characteristic
346	C₂×C₁₃	#2921	1	1	yes	characteristic
347	C₂×C₁₃	#2970	1	1	yes	characteristic
348	C₂×C₁₃	#2970	1	1	yes	characteristic
349	C₂×C₁₃	#2970	1	1	yes	characteristic
350	C₂×C₁₃	#2971	1	1	yes	characteristic
351	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
374	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
376	C₂×C₈	—	13	4	no	—
377	C₂×C₈	—	13	4	no	—
378	C₂×C₈	—	26	2	no	—
379	C₂×C₈	—	26	2	no	—
380	C₂×C₈	—	26	2	no	—
381	C₂×C₈	—	26	2	no	—
382	C₂×C₈	—	26	2	no	—
383	C₂×C₈	—	26	2	no	—
384	C₂×C₈	—	26	2	no	—
385	C₂×C₈	—	26	2	no	—
386	C₂×C₈	—	26	2	no	—
387	C₂×C₈	—	26	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	#6099	1	4	yes	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	#6099	1	4	yes	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	4	1	no	—
409	C₄²	—	4	1	no	—
410	C₄²	—	4	1	no	—
411	C₄²	—	4	1	no	—
412	C₄²	#6127	1	2	yes	—
413	C₄²	#6127	1	2	yes	—
414	C₁₃	#21435	1	1	yes	characteristic, complemented, Sylow
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	C₂×#6099	1	2	yes	—
422	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	C₂×#6099	1	2	yes	—
460	C₂×C₄	C₂×#6099	1	2	yes	—
461	C₂×C₄	C₂×#6099	1	2	yes	—
462	C₂×C₄	C₂×#6099	1	2	yes	—
463	C₂×C₄	C₂×#6099	1	2	yes	—
464	C₂×C₄	#88180	1	2	yes	—
465	C₂×C₄	#88180	1	2	yes	—
466	C₂×C₄	C₂×#6127	1	1	yes	characteristic
467	C₂×C₄	C₂×#6127	1	1	yes	characteristic
468	C₂×C₄	#41×D₁₃	1	2	yes	—
469	C₂×C₄	#41×D₁₃	1	2	yes	—
470	C₈	—	26	4	no	—
471	C₈	—	26	4	no	—
472	C₈	—	52	2	no	—
473	C₈	—	52	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	C₂²×#6099	1	1	yes	characteristic
482	C₂²	C₂²×#6099	1	1	yes	characteristic
483	C₂²	C₂×#88180	1	1	yes	characteristic
484	C₂²	#11719524	1	1	yes	characteristic
485	C₂²	#11719524	1	1	yes	characteristic
486	C₂²	#41×Dic₁₃	1	1	yes	characteristic
487	C₂²	#41×Dic₁₃	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	1	no	—
500	C₄	—	4	1	no	—
501	C₄	#11719233	1	2	yes	—
502	C₄	#11719233	1	2	yes	—
503	C₂	—	4	2	no	—
504	C₂	#13117334	1	1	yes	characteristic
505	C₂	#13123469	1	1	yes	characteristic
506	C₂	#13123474	1	1	yes	characteristic
507	C₂	#13123850	1	1	yes	characteristic
508	C₂	#13123850	1	1	yes	characteristic
509	C₂	#13123850	1	1	yes	characteristic
510	C₂	#13123856	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₄×C₁₃×#117	C₂
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#117	D₁₃
hypocenter	C₁₃	#21435
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
3. #13115402	C₂	semidirect
4. #13115395	C₂	semidirect
5. #13114689	C₂	semidirect
6. #13114689	C₂	semidirect
9. #13114585	C₂	semidirect
10. C₄×#88043	C₂	semidirect
414. C₁₃	#21435	semidirect

Maximal subgroups

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

subgroup	index
#13115451	2
#13115444	2
#13115402	2
#13115395	2
#13114689	2
#13114598	2
#13114585	2
C₄×#88043	2
C₄×C₁₃×#117	2
#21435	13