Subgroups — #15869940

Order 3328.

924 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718673	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6099	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115451	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115444	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115402	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115395	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115134	C₂	1	1	yes	maximal, characteristic
8	#13115021	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114904	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114711	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₄×#1055	C₂	1	1	yes	maximal, characteristic, complemented
12	#13114620	C₂	1	1	yes	maximal, characteristic, complemented
13	#13114620	C₂	1	1	yes	maximal, characteristic, complemented
14	#13114620	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#123	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₃×#123	C₄	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×#6099	C₂²	1	1	yes	characteristic
20	C₂²×#6099	C₂²	1	1	yes	characteristic
21	C₂²×#6099	C₂²	1	1	yes	characteristic
22	C₁₃×#388	C₄	1	1	yes	characteristic
23	C₁₃×#388	C₄	1	1	yes	characteristic
24	C₁₃×#387	C₄	1	1	yes	characteristic
25	C₁₃×#387	C₄	1	1	yes	characteristic
26	C₁₃×#386	C₄	1	1	yes	characteristic
27	C₁₃×#385	C₄	1	1	yes	characteristic
28	C₁₃×#381	C₄	1	1	yes	characteristic
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊#1055	C₂²	1	1	yes	characteristic
39	#11718673	—	2	4	no	—
40	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
43	C₄×#6099	—	2	4	no	—
44	C₂×#88043	C₂²	1	1	yes	characteristic
45	C₂×#88043	C₂²	1	1	yes	characteristic
46	C₂×#88043	C₂²	1	1	yes	characteristic
47	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
48	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
49	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
50	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
51	#11718116	C₂²	1	1	yes	characteristic
52	#11718116	C₂²	1	1	yes	characteristic
53	#11718116	C₂²	1	1	yes	characteristic
54	#11718116	C₂²	1	1	yes	characteristic
55	#11718116	C₂²	1	1	yes	characteristic
56	#11718116	C₂²	1	1	yes	characteristic
57	#11718116	C₂²	1	1	yes	characteristic
58	#11718116	C₂²	1	1	yes	characteristic
59	#11718116	C₂²	1	1	yes	characteristic
60	#11718116	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×#123	—	2	4	no	—
67	C₄×D₄×C₁₃	—	2	2	no	—
68	C₄×D₄×C₁₃	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×#6099	—	2	2	no	—
92	C₂×#6099	—	2	2	no	—
93	C₂×#6099	—	2	2	no	—
94	C₂×#6099	—	2	2	no	—
95	C₂×#6099	—	2	2	no	—
96	C₂×#6099	—	2	2	no	—
97	C₂×#6099	—	2	2	no	—
98	C₂×#6099	—	2	2	no	—
99	C₂×#6099	D₄	1	4	yes	—
100	C₂²×#1055	C₂³	1	1	yes	characteristic
101	C₂²×#1055	C₂³	1	1	yes	characteristic
102	C₂²×#1055	C₂³	1	1	yes	characteristic
103	C₂²×#1055	C₂³	1	1	yes	characteristic
104	C₂²×#1055	C₂³	1	1	yes	characteristic
105	C₂²×#1055	C₂³	1	1	yes	characteristic
106	C₂²×#1055	C₂³	1	1	yes	characteristic
107	C₂²×#1055	C₂³	1	1	yes	characteristic
108	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
109	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
110	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
113	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
114	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
115	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
116	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
117	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊#1055	—	2	2	no	—
119	C₂²⋊#1055	—	2	2	no	—
120	C₂²⋊#1055	—	2	2	no	—
121	C₂²⋊#1055	—	2	2	no	—
122	C₂²⋊#1055	—	2	2	no	—
123	C₄⋊#1055	—	2	2	no	—
124	C₄⋊#1055	—	2	2	no	—
125	C₄⋊#1055	—	2	2	no	—
126	#88043	—	2	2	no	—
127	#88043	—	2	2	no	—
128	#88043	—	2	2	no	—
129	C₄×#1055	—	2	2	no	—
130	C₄×#1055	—	2	2	no	—
131	C₄×#1055	—	2	2	no	—
132	C₄×#1055	—	2	2	no	—
133	#21565	—	13	1	no	maximal, Sylow
134	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	4	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	4	1	no	—
154	C₂²×C₄×C₁₃	—	4	1	no	—
155	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	#41	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	4	1	no	—
174	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	complemented
175	C₁₃×C₂²⋊C₄	—	2	2	no	—
176	C₁₃×C₂²⋊C₄	—	2	2	no	—
177	C₁₃×C₂²⋊C₄	—	2	2	no	—
178	C₁₃×C₂²⋊C₄	—	2	2	no	—
179	C₁₃×C₂²⋊C₄	—	2	2	no	—
180	C₁₃×C₂²⋊C₄	—	2	2	no	—
181	C₁₃×C₂²⋊C₄	—	4	1	no	—
182	C₁₃×C₂²⋊C₄	—	4	1	no	—
183	C₄²×C₁₃	—	2	2	no	—
184	C₄²×C₁₃	—	2	2	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	2	1	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	1	no	—
189	C₄²×C₁₃	—	2	1	no	—
190	C₄²×C₁₃	—	2	1	no	—
191	C₄²×C₁₃	—	2	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	#6099	—	2	8	no	—
196	#6099	—	2	8	no	—
197	#6099	—	4	4	no	—
198	C₂×#1055	—	2	1	no	—
199	C₂×#1055	—	2	1	no	—
200	C₂×#1055	—	2	1	no	—
201	C₂×#1055	—	2	1	no	—
202	C₂×#1055	—	2	1	no	—
203	C₂×#1055	—	2	1	no	—
204	C₂×#1055	—	2	1	no	—
205	C₂×#1055	—	2	1	no	—
206	C₂×#1055	—	2	1	no	—
207	C₂×#1055	—	2	1	no	—
208	C₂×#1055	—	2	1	no	—
209	C₂×#1055	—	2	1	no	—
210	C₂×#1055	—	2	1	no	—
211	C₂×#1055	—	2	1	no	—
212	C₂×#1055	—	2	1	no	—
213	C₂×#1055	—	2	1	no	—
214	C₂×#1055	—	2	1	no	—
215	C₂×#1055	—	2	1	no	—
216	C₂×#1055	C₂×D₄	1	2	yes	—
217	C₂×#1055	C₂×D₄	1	2	yes	—
218	C₂×#1055	#41	1	2	yes	—
219	C₂×#1055	#41	1	2	yes	—
220	C₂×#1055	#41	1	2	yes	—
221	C₂×#1055	#41	1	2	yes	—
222	C₂×#436	—	13	1	no	—
223	C₂×C₄×M₁₆	—	13	1	no	—
224	C₄×#123	D₁₃	1	1	yes	characteristic
225	#1924	—	13	1	no	—
226	#1923	—	13	1	no	—
227	#1917	—	13	1	no	—
228	#1916	—	13	1	no	—
229	#1870	—	13	1	no	—
230	#1851	—	13	1	no	—
231	#1817	—	13	1	no	—
232	#1771	—	13	1	no	—
233	C₈×C₄⋊C₄	—	13	1	no	—
234	#1753	—	13	1	no	—
235	#1753	—	13	1	no	—
236	#1753	—	13	1	no	—
237	C₂³×C₁₃	—	2	1	no	—
238	C₂³×C₁₃	—	2	1	no	—
239	C₂³×C₁₃	—	2	1	no	—
240	C₂³×C₁₃	—	2	1	no	—
241	C₂³×C₁₃	—	2	1	no	—
242	C₂³×C₁₃	—	2	1	no	—
243	C₂³×C₁₃	—	2	1	no	—
244	C₂³×C₁₃	—	2	1	no	—
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	2	1	no	—
247	C₂³×C₁₃	—	2	1	no	—
248	C₂³×C₁₃	—	2	1	no	—
249	C₂³×C₁₃	—	2	1	no	—
250	C₂³×C₁₃	C₄×D₄	1	2	yes	—
251	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
252	D₄×C₁₃	—	4	4	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	1	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	4	4	no	—
289	C₂×C₄×C₁₃	—	4	4	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
295	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
296	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
297	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
298	C₂×C₄×C₁₃	#131	1	2	yes	—
299	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
301	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
302	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
305	#1055	—	2	2	no	—
306	#1055	—	2	2	no	—
307	#1055	—	2	2	no	—
308	#1055	—	4	1	no	—
309	#1055	—	4	1	no	—
310	#1055	—	4	1	no	—
311	#1055	—	4	1	no	—
312	#1055	#123	1	4	yes	complemented
313	C₂²×M₁₆	—	13	1	no	—
314	C₂²×M₁₆	—	13	1	no	—
315	C₂²×M₁₆	—	13	1	no	—
316	C₂×#123	Dic₁₃	1	1	yes	characteristic
317	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
318	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
319	#436	—	26	4	no	—
320	C₂×C₄⋊C₈	—	13	1	no	—
321	C₂×C₄⋊C₈	—	13	1	no	—
322	C₂×C₄⋊C₈	—	13	1	no	—
323	C₂×C₂²⋊C₈	—	13	1	no	—
324	C₂×C₂²⋊C₈	—	13	1	no	—
325	C₂×C₂²⋊C₈	—	13	1	no	—
326	C₂×C₂²⋊C₈	—	13	1	no	—
327	C₂×C₂²⋊C₈	—	13	1	no	—
328	C₄×M₁₆	—	26	4	no	—
329	C₂×#97	—	13	1	no	—
330	C₂×#97	—	13	1	no	—
331	C₂×#97	—	13	1	no	—
332	C₂×C₄×C₈	—	13	1	no	—
333	C₂×C₄×C₈	—	13	1	no	—
334	C₂×C₄×C₈	—	13	1	no	—
335	C₂×C₄×C₈	—	13	1	no	—
336	#388	Dic₁₃	1	1	yes	characteristic
337	#388	Dic₁₃	1	1	yes	characteristic
338	#387	Dic₁₃	1	1	yes	characteristic
339	#387	Dic₁₃	1	1	yes	characteristic
340	#386	Dic₁₃	1	1	yes	characteristic
341	#385	Dic₁₃	1	1	yes	characteristic
342	#381	Dic₁₃	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
345	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
346	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
347	C₄×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
348	#336	—	13	1	no	—
349	#336	—	13	1	no	—
350	#336	—	13	1	no	—
351	#336	—	13	1	no	—
352	#336	—	13	1	no	—
353	#336	—	13	1	no	—
354	#336	—	13	1	no	—
355	#336	—	13	1	no	—
356	#336	—	13	1	no	—
357	#336	—	13	1	no	—
358	C₂²×C₁₃	—	2	2	no	—
359	C₂²×C₁₃	—	2	2	no	—
360	C₂²×C₁₃	—	2	2	no	—
361	C₂²×C₁₃	—	4	1	no	—
362	C₂²×C₁₃	—	4	1	no	—
363	C₂²×C₁₃	—	4	1	no	—
364	C₂²×C₁₃	—	4	1	no	—
365	C₂²×C₁₃	—	4	1	no	—
366	C₂²×C₁₃	—	4	1	no	—
367	C₂²×C₁₃	—	4	1	no	—
368	C₂²×C₁₃	—	4	1	no	—
369	C₂²×C₁₃	—	4	1	no	—
370	C₂²×C₁₃	—	4	1	no	—
371	C₂²×C₁₃	—	4	1	no	—
372	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
373	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
374	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
375	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
376	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
377	C₂²×C₁₃	#568	1	1	yes	characteristic
378	C₂²×C₁₃	#568	1	1	yes	characteristic
379	C₄×C₁₃	—	2	2	no	—
380	C₄×C₁₃	—	2	2	no	—
381	C₄×C₁₃	—	2	2	no	—
382	C₄×C₁₃	—	2	2	no	—
383	C₄×C₁₃	—	2	2	no	—
384	C₄×C₁₃	—	4	1	no	—
385	C₄×C₁₃	—	4	1	no	—
386	C₄×C₁₃	—	4	1	no	—
387	C₄×C₁₃	—	4	1	no	—
388	C₄×C₁₃	—	4	1	no	—
389	C₄×C₁₃	—	4	1	no	—
390	C₄×C₁₃	—	4	1	no	—
391	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
392	C₄×C₁₃	#525	1	1	yes	characteristic
393	C₄×C₁₃	#529	1	1	yes	characteristic
394	C₄×C₁₃	#529	1	1	yes	characteristic
395	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
396	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
397	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
398	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
399	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
400	C₂×M₁₆	—	13	4	no	—
401	C₂×M₁₆	—	26	2	no	—
402	C₂×M₁₆	—	26	2	no	—
403	C₂×M₁₆	—	26	2	no	—
404	C₂×M₁₆	—	26	2	no	—
405	C₂×M₁₆	—	26	2	no	—
406	C₂×M₁₆	—	26	2	no	—
407	C₂×M₁₆	—	26	2	no	—
408	C₂×M₁₆	—	26	2	no	—
409	C₂²×C₈	—	13	1	no	—
410	C₂²×C₈	—	13	1	no	—
411	C₂²×C₈	—	13	1	no	—
412	C₂²×C₈	—	13	1	no	—
413	C₂²×C₈	—	13	1	no	—
414	C₂²×C₈	—	13	1	no	—
415	C₂²×C₈	—	13	1	no	—
416	C₂²×C₈	—	13	1	no	—
417	#123	—	2	4	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
433	C₂×C₄²	—	2	2	no	—
434	C₂×C₄²	—	2	2	no	—
435	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
436	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
437	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
438	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
439	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
440	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
441	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
442	C₄⋊C₈	—	26	2	no	—
443	C₄⋊C₈	—	26	2	no	—
444	C₄⋊C₈	—	26	2	no	—
445	C₂²⋊C₈	—	26	2	no	—
446	C₂²⋊C₈	—	26	2	no	—
447	C₂²⋊C₈	—	26	2	no	—
448	C₂²⋊C₈	—	26	2	no	—
449	C₂²⋊C₈	—	26	2	no	—
450	#97	—	26	2	no	—
451	#97	—	26	2	no	—
452	#97	—	26	2	no	—
453	C₄×C₈	—	26	2	no	—
454	C₄×C₈	—	26	2	no	—
455	C₄×C₈	—	26	2	no	—
456	C₄×C₈	—	26	2	no	—
457	#95	C₂×Dic₁₃	1	1	yes	characteristic
458	#95	C₂×Dic₁₃	1	1	yes	characteristic
459	#95	C₂×Dic₁₃	1	1	yes	characteristic
460	#95	C₂×Dic₁₃	1	1	yes	characteristic
461	#95	C₂×Dic₁₃	1	1	yes	characteristic
462	#95	C₂×Dic₁₃	1	1	yes	characteristic
463	#95	C₂×Dic₁₃	1	1	yes	characteristic
464	#95	C₂×Dic₁₃	1	1	yes	characteristic
465	#95	C₂×Dic₁₃	1	1	yes	characteristic
466	#95	C₂×Dic₁₃	1	1	yes	characteristic
467	C₂×C₁₃	—	4	2	no	—
468	C₂×C₁₃	—	8	1	no	—
469	C₂×C₁₃	C₄×#123	1	1	yes	characteristic
470	C₂×C₁₃	#2933	1	1	yes	characteristic
471	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
472	C₂×C₁₃	#2965	1	1	yes	characteristic
473	C₂×C₁₃	#2967	1	1	yes	characteristic
474	C₂×C₁₃	#2969	1	1	yes	characteristic
475	C₂×C₁₃	#2971	1	1	yes	characteristic
476	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
477	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	D₄×D₁₃	1	2	yes	—
498	C₂²×C₄	#6129	1	2	yes	—
499	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
502	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
503	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
504	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
505	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
507	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
508	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
511	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
512	M₁₆	—	26	8	no	—
513	M₁₆	—	26	8	no	—
514	M₁₆	—	52	4	no	—
515	C₂×C₈	—	13	2	no	—
516	C₂×C₈	—	13	2	no	—
517	C₂×C₈	—	13	2	no	—
518	C₂×C₈	—	13	2	no	—
519	C₂×C₈	—	13	2	no	—
520	C₂×C₈	—	13	2	no	—
521	C₂×C₈	—	26	1	no	—
522	C₂×C₈	—	26	1	no	—
523	C₂×C₈	—	26	1	no	—
524	C₂×C₈	—	26	1	no	—
525	C₂×C₈	—	26	1	no	—
526	C₂×C₈	—	26	1	no	—
527	C₂×C₈	—	26	1	no	—
528	C₂×C₈	—	26	1	no	—
529	C₂×C₈	—	26	1	no	—
530	C₂×C₈	—	26	1	no	—
531	C₂×C₈	—	26	1	no	—
532	C₂×C₈	—	26	1	no	—
533	C₂×C₈	—	26	1	no	—
534	C₂×C₈	—	26	1	no	—
535	C₂×C₈	—	26	1	no	—
536	C₂×C₈	—	26	1	no	—
537	C₂×C₈	—	26	1	no	—
538	C₂×C₈	—	26	1	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	4	1	no	—
543	C₄⋊C₄	#6099	1	4	yes	complemented
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	2	2	no	—
546	C₂²⋊C₄	—	2	2	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	2	2	no	—
549	C₂²⋊C₄	—	2	2	no	—
550	C₂²⋊C₄	—	4	1	no	—
551	C₂²⋊C₄	—	4	1	no	—
552	C₄²	—	2	2	no	—
553	C₄²	—	2	2	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₁₃	#21565	1	1	yes	characteristic, complemented, Sylow
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	D₄×Dic₁₃	1	2	yes	—
579	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
580	D₄	—	4	4	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	4	4	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	C₂×#6099	1	2	yes	—
623	C₂×C₄	C₂×#6099	1	2	yes	—
624	C₂×C₄	C₂×#6099	1	2	yes	—
625	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
626	C₂×C₄	#88202	1	2	yes	—
627	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
628	C₂×C₄	C₂×#6129	1	1	yes	characteristic
629	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
630	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
631	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
632	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
633	C₈	—	13	4	no	—
634	C₈	—	26	2	no	—
635	C₈	—	26	2	no	—
636	C₈	—	26	2	no	—
637	C₈	—	52	1	no	—
638	C₈	—	52	1	no	—
639	C₈	—	52	1	no	—
640	C₈	—	52	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	C₂²×#6099	1	1	yes	characteristic
656	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
657	C₂²	C₂×#88202	1	1	yes	characteristic
658	C₂²	#11719524	1	1	yes	characteristic
659	C₂²	#11719524	1	1	yes	characteristic
660	C₂²	#41×Dic₁₃	1	1	yes	characteristic
661	C₂²	#41×Dic₁₃	1	1	yes	characteristic
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	#11719354	1	1	yes	characteristic
675	C₄	#11719354	1	1	yes	characteristic
676	C₄	D₁₃×#123	1	1	yes	characteristic
677	C₄	#11719361	1	1	yes	characteristic
678	C₂	—	4	2	no	—
679	C₂	—	8	1	no	—
680	C₂	#123×Dic₁₃	1	1	yes	characteristic
681	C₂	#13123563	1	1	yes	characteristic
682	C₂	D₄×#6099	1	1	yes	characteristic
683	C₂	#13123803	1	1	yes	characteristic
684	C₂	#13123823	1	1	yes	characteristic
685	C₂	#13123841	1	1	yes	characteristic
686	C₂	#13123856	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle	C₂³×C₁₃	C₂³×C₄
Fitting	C₄×C₁₃×#123	C₂
prime radical	C₂²×D₄×C₁₃	C₂×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#123	D₁₃
hypocenter	C₁₃	#21565
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#123

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#6099	C₂	semidirect
3. #13115451	C₂	semidirect
4. #13115444	C₂	semidirect
5. #13115402	C₂	semidirect
6. #13115395	C₂	semidirect
8. #13115021	C₂	semidirect
9. #13114904	C₂	semidirect
10. #13114711	C₂	semidirect
11. C₄⋊C₄×#1055	C₂	semidirect
12. #13114620	C₂	semidirect
13. #13114620	C₂	semidirect
14. #13114620	C₂	semidirect
174. C₁₃×C₄⋊C₄	M₁₆	semidirect
312. #1055	#123	semidirect
543. C₄⋊C₄	#6099	semidirect
564. C₁₃	#21565	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718673	2
C₂×C₄×#6099	2
#13115451	2
#13115444	2
#13115402	2
#13115395	2
#13115134	2
#13115021	2
#13114904	2
#13114711	2
C₄⋊C₄×#1055	2
#13114620	2
C₄×C₁₃×#123	2
#21565	13