Subgroups — #28404246

Order 14464.

1522 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813669	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14268647	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₂₂₆	C₂	1	2	yes	maximal, complemented
4	#20299257	C₂	1	2	yes	maximal, complemented
5	#20299253	C₂	1	2	yes	maximal, complemented
6	#20299246	C₂	1	4	yes	maximal, complemented
7	#20299244	C₂	1	2	yes	maximal, complemented
8	#20299235	C₂	1	4	yes	maximal, complemented
9	#20299177	C₂	1	2	yes	maximal, complemented
10	#20299176	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299174	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299171	C₂	1	2	yes	maximal, complemented
13	#20299108	C₂	1	2	yes	maximal, complemented
14	C₂×#16813601	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²⋊Q₈×D₁₁₃	C₂	1	2	yes	maximal, complemented
16	#20299078	C₂	1	1	yes	maximal, characteristic, complemented
17	#525×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#16813669	—	2	8	no	—
19	C₂×#14268647	—	2	8	no	—
20	C₂×#14268647	C₂²	1	2	yes	—
21	C₂×#14268647	C₂²	1	1	yes	characteristic
22	C₂×#14268647	C₂²	1	2	yes	—
23	C₂×#14268647	C₂²	1	1	yes	characteristic
24	C₂×#14268647	C₂²	1	1	yes	characteristic
25	C₂×#14268647	C₂²	1	1	yes	characteristic
26	C₂×#14268647	C₂²	1	2	yes	complemented
27	C₂×#14268646	C₂²	1	2	yes	complemented
28	C₂×#14268646	C₂²	1	4	yes	complemented
29	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic
30	C₂²×Dic₂₂₆	C₂²	1	2	yes	complemented
31	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
32	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	complemented
33	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
35	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	—
36	#16813622	C₂²	1	2	yes	complemented
37	#16813621	C₂²	1	4	yes	complemented
38	#16813610	C₂²	1	2	yes	complemented
39	#16813608	C₂²	1	4	yes	complemented
40	#16813607	C₂²	1	4	yes	complemented
41	#16813606	C₂²	1	4	yes	complemented
42	#16813604	C₂²	1	4	yes	complemented
43	#16813604	C₂²	1	4	yes	complemented
44	#16813602	C₂²	1	2	yes	complemented
45	#16813602	C₂²	1	2	yes	complemented
46	#16813601	C₂²	1	2	yes	—
47	#16813601	C₂²	1	2	yes	—
48	#16813601	C₂²	1	2	yes	complemented
49	#16813601	C₂²	1	2	yes	complemented
50	#16813601	C₂²	1	2	yes	complemented
51	#16813600	C₂²	1	4	yes	complemented
52	#16813599	C₂²	1	4	yes	—
53	#16813599	C₂²	1	4	yes	complemented
54	#16813598	C₂²	1	2	yes	complemented
55	#16813596	C₂²	1	2	yes	complemented
56	#16813595	C₂²	1	4	yes	complemented
57	#16813594	C₂²	1	4	yes	complemented
58	#16813594	C₂²	1	4	yes	complemented
59	#16813593	C₂²	1	2	yes	complemented
60	#16813593	C₂²	1	4	yes	complemented
61	#16813590	C₂²	1	4	yes	—
62	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
63	C₄×D₄₅₂	C₂²	1	2	yes	complemented
64	D₄×Dic₁₁₃	C₂²	1	4	yes	—
65	#16813582	C₂²	1	4	yes	complemented
66	#16813582	C₂²	1	4	yes	complemented
67	#16813580	C₂²	1	2	yes	complemented
68	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
69	C₂×#14268626	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₁₁₃	C₂²	1	4	yes	complemented
72	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₁₁₃	C₂²	1	4	yes	—
74	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
75	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
76	#123×C₁₁₃	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
78	C₂²⋊Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
79	#121×C₁₁₃	C₂²	1	1	yes	characteristic
80	#121×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
81	#120×C₁₁₃	C₂²	1	2	yes	—
82	C₄×D₄×C₁₁₃	C₂²	1	2	yes	—
83	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
84	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
85	C₂³×D₁₁₃	C₂³	1	2	yes	—
86	#14268647	—	2	4	no	—
87	#14268647	—	2	8	no	—
88	#14268647	—	2	4	no	—
89	#14268647	—	2	8	no	—
90	#14268647	—	2	8	no	—
91	#14268647	—	2	4	no	—
92	#14268647	D₄	1	8	yes	complemented
93	#14268646	—	2	16	no	—
94	#14268646	—	2	8	no	—
95	C₂×Dic₂₂₆	—	2	4	no	—
96	C₂×Dic₂₂₆	—	2	4	no	—
97	C₂×Dic₂₂₆	—	2	8	no	—
98	C₂×Dic₂₂₆	C₂³	1	4	yes	—
99	C₂×Dic₂₂₆	C₂³	1	2	yes	—
100	C₂×Dic₂₂₆	C₂³	1	2	yes	—
101	C₂×Dic₂₂₆	C₂³	1	2	yes	—
102	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
103	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
104	Q₈×D₁₁₃	—	2	8	no	—
105	C₂×D₄₅₂	—	2	4	no	—
106	C₂×D₄₅₂	C₂³	1	2	yes	—
107	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
108	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
110	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
111	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
112	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
113	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
114	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
115	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
116	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
117	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
118	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
119	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
120	C₂×C₄×D₁₁₃	—	2	8	no	—
121	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
122	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
123	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
124	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
125	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
126	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
127	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
128	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
129	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
130	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
131	#14268626	C₂³	1	4	yes	—
132	#14268626	C₂³	1	4	yes	—
133	#14268626	C₂³	1	4	yes	—
134	#14268626	C₂³	1	4	yes	—
135	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
136	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
137	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
138	#14268624	C₂³	1	4	yes	—
139	#14268624	C₂³	1	4	yes	—
140	#14268624	C₂³	1	4	yes	—
141	#14268624	C₂³	1	4	yes	—
142	C₄×Dic₁₁₃	C₂³	1	4	yes	—
143	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
144	#41×C₁₁₃	—	2	4	no	—
145	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
146	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
147	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
148	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
149	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
150	C₂²×C₄×C₁₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
152	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
153	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
154	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
155	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
156	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
157	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
159	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
167	C₄²×C₁₁₃	C₂³	1	2	yes	—
168	C₂³×C₁₁₃	—	2	2	no	—
169	C₂³×C₁₁₃	—	2	2	no	—
170	C₂³×C₁₁₃	—	4	1	no	—
171	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
172	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
173	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
174	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
175	C₂²×D₁₁₃	—	2	4	no	—
176	C₂²×D₁₁₃	—	2	4	no	—
177	C₂²×D₁₁₃	—	4	2	no	—
178	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
179	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
180	Q₈×C₁₁₃	—	2	2	no	—
181	D₄×C₁₁₃	—	2	4	no	—
182	D₄×C₁₁₃	—	2	4	no	—
183	D₄×C₁₁₃	—	2	2	no	—
184	D₄×C₁₁₃	—	4	2	no	—
185	C₂×C₄×C₁₁₃	—	2	2	no	—
186	C₂×C₄×C₁₁₃	—	2	2	no	—
187	C₂×C₄×C₁₁₃	—	2	2	no	—
188	C₂×C₄×C₁₁₃	—	2	2	no	—
189	C₂×C₄×C₁₁₃	—	2	2	no	—
190	C₂×C₄×C₁₁₃	—	2	4	no	—
191	C₂×C₄×C₁₁₃	C₂×D₄	1	4	yes	—
192	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
193	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
194	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
196	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
197	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
199	C₂²⋊D₁₁₃	—	2	4	no	—
200	C₂²⋊D₁₁₃	—	2	4	no	—
201	C₂²⋊D₁₁₃	—	2	8	no	—
202	C₂²⋊D₁₁₃	—	2	4	no	—
203	C₂²⋊D₁₁₃	—	4	4	no	—
204	C₂²⋊D₁₁₃	C₂×D₄	1	8	yes	—
205	C₂×Dic₁₁₃	—	2	4	no	—
206	C₂×Dic₁₁₃	—	2	4	no	—
207	C₂×Dic₁₁₃	—	2	8	no	—
208	C₂×Dic₁₁₃	—	4	2	no	—
209	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
210	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
211	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
212	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
213	D₄₅₂	—	2	4	no	—
214	D₄₅₂	—	2	2	no	—
215	D₄₅₂	C₂×D₄	1	4	yes	—
216	C₄×D₁₁₃	—	2	4	no	—
217	C₄×D₁₁₃	—	2	8	no	—
218	C₄×D₁₁₃	—	2	4	no	—
219	C₄×D₁₁₃	—	2	4	no	—
220	C₄×D₁₁₃	—	4	4	no	—
221	C₄×D₁₁₃	C₂×D₄	1	8	yes	—
222	Dic₂₂₆	—	2	4	no	—
223	Dic₂₂₆	—	2	4	no	—
224	Dic₂₂₆	—	2	2	no	—
225	Dic₂₂₆	—	2	8	no	—
226	Dic₂₂₆	—	2	4	no	—
227	Dic₂₂₆	C₂×D₄	1	4	yes	—
228	C₂²×C₁₁₃	—	2	1	no	—
229	C₂²×C₁₁₃	—	2	1	no	—
230	C₂²×C₁₁₃	—	2	1	no	—
231	C₂²×C₁₁₃	—	2	1	no	—
232	C₂²×C₁₁₃	—	2	2	no	—
233	C₂²×C₁₁₃	—	2	1	no	—
234	C₂²×C₁₁₃	—	2	2	no	—
235	C₂²×C₁₁₃	—	2	1	no	—
236	C₂²×C₁₁₃	—	2	2	no	—
237	C₂²×C₁₁₃	—	2	1	no	—
238	C₂²×C₁₁₃	—	4	4	no	—
239	C₂²×C₁₁₃	C₂²×D₄	1	2	yes	—
240	C₂²×C₁₁₃	2₋¹⁺⁴	1	2	yes	complemented
241	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
242	C₂×D₁₁₃	—	2	2	no	—
243	C₂×D₁₁₃	—	2	2	no	—
244	C₂×D₁₁₃	—	2	2	no	—
245	C₂×D₁₁₃	—	2	2	no	—
246	C₂×D₁₁₃	—	2	2	no	—
247	C₂×D₁₁₃	—	4	8	no	—
248	C₂×D₁₁₃	C₂²×D₄	1	4	yes	—
249	C₄×C₁₁₃	—	2	2	no	—
250	C₄×C₁₁₃	—	2	1	no	—
251	C₄×C₁₁₃	—	2	1	no	—
252	C₄×C₁₁₃	—	2	2	no	—
253	C₄×C₁₁₃	—	2	2	no	—
254	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
255	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
256	Dic₁₁₃	—	2	4	no	—
257	Dic₁₁₃	—	2	2	no	—
258	Dic₁₁₃	—	2	4	no	—
259	Dic₁₁₃	C₂²×D₄	1	4	yes	—
260	C₂×C₁₁₃	—	2	2	no	—
261	C₂×C₁₁₃	—	2	2	no	—
262	C₂×C₁₁₃	—	4	2	no	—
263	C₂×C₁₁₃	—	4	1	no	—
264	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
265	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
266	C₂×C₁₁₃	#585	1	1	yes	characteristic
267	D₁₁₃	—	2	4	no	—
268	D₁₁₃	—	4	2	no	—
269	#3489	—	113	1	no	maximal, Sylow
270	C₁₁₃	#3489	1	1	yes	characteristic, complemented, Sylow
271	C₂×2₋¹⁺⁴	—	113	1	no	—
272	C₂²×#41	—	113	1	no	—
273	D₄×Q₈	—	113	2	no	—
274	#548	—	113	2	no	—
275	#547	—	113	4	no	—
276	#547	—	113	2	no	—
277	#546	—	113	4	no	—
278	#546	—	113	2	no	—
279	#537	—	113	1	no	—
280	#537	—	113	2	no	—
281	#536	—	113	2	no	—
282	#536	—	113	1	no	—
283	#525	—	113	2	no	—
284	#525	D₁₁₃	1	1	yes	characteristic, complemented
285	C₂×C₂²⋊Q₈	—	113	1	no	—
286	C₂×C₂²⋊Q₈	—	113	2	no	—
287	#520	—	113	1	no	—
288	2₋¹⁺⁴	—	226	8	no	—
289	C₂×#41	—	113	2	no	—
290	C₂×#41	—	113	4	no	—
291	C₂×#41	—	113	1	no	—
292	C₂×#41	—	113	2	no	—
293	C₂×#41	—	113	1	no	—
294	C₂×#41	—	113	2	no	—
295	C₂×#41	—	113	1	no	—
296	C₂×#41	—	113	2	no	—
297	C₂×#41	—	113	1	no	—
298	C₂×#41	—	226	8	no	—
299	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic, complemented
300	C₂²×Q₈	—	113	2	no	—
301	C₂²×Q₈	—	113	1	no	—
302	C₂²×Q₈	—	113	2	no	—
303	C₂²×Q₈	—	113	1	no	—
304	C₂²×D₄	—	113	2	no	—
305	C₂²×D₄	—	113	1	no	—
306	C₂³×C₄	—	113	2	no	—
307	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic
308	C₄⋊Q₈	—	113	4	no	—
309	C₄⋊Q₈	—	113	2	no	—
310	#124	—	113	4	no	—
311	#124	—	113	2	no	—
312	#123	—	113	4	no	—
313	#123	—	113	4	no	—
314	#123	—	113	4	no	—
315	#123	—	113	4	no	—
316	#123	C₂×D₁₁₃	1	2	yes	complemented
317	C₂²⋊Q₈	—	113	2	no	—
318	C₂²⋊Q₈	—	113	2	no	—
319	C₂²⋊Q₈	—	113	2	no	—
320	C₂²⋊Q₈	—	113	2	no	—
321	C₂²⋊Q₈	—	113	2	no	—
322	C₂²⋊Q₈	—	113	2	no	—
323	C₂²⋊Q₈	—	113	2	no	—
324	C₂²⋊Q₈	—	113	4	no	—
325	C₂²⋊Q₈	—	113	2	no	—
326	C₂²⋊Q₈	—	113	4	no	—
327	C₂²⋊Q₈	—	113	4	no	—
328	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic
329	C₂²⋊Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
330	#121	—	113	2	no	—
331	#121	—	113	4	no	—
332	#121	—	113	4	no	—
333	#121	—	113	4	no	—
334	#121	—	113	2	no	—
335	#121	—	113	4	no	—
336	#121	C₂×D₁₁₃	1	1	yes	characteristic
337	#121	C₂×D₁₁₃	1	1	yes	characteristic, complemented
338	#120	—	113	4	no	—
339	#120	C₂×D₁₁₃	1	2	yes	—
340	C₄×Q₈	—	113	2	no	—
341	C₄×D₄	—	113	4	no	—
342	C₄×D₄	—	113	4	no	—
343	C₄×D₄	—	113	4	no	—
344	C₄×D₄	—	113	2	no	—
345	C₄×D₄	C₂×D₁₁₃	1	2	yes	—
346	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
347	#117	—	113	2	no	—
348	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
349	C₂×C₄⋊C₄	—	113	1	no	—
350	C₂×C₄⋊C₄	—	113	2	no	—
351	C₂×C₄⋊C₄	—	113	2	no	—
352	C₂×C₄⋊C₄	—	113	4	no	—
353	C₂×C₂²⋊C₄	—	113	2	no	—
354	C₂×C₂²⋊C₄	—	113	4	no	—
355	C₂⁴	—	113	2	no	—
356	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
357	#41	—	2	4	no	—
358	#41	—	113	8	no	—
359	#41	—	226	8	no	—
360	#41	—	226	8	no	—
361	#41	—	226	4	no	—
362	#41	—	226	8	no	—
363	#41	—	226	4	no	—
364	#41	—	226	8	no	—
365	#41	—	226	16	no	—
366	#41	—	226	4	no	—
367	C₂×Q₈	—	113	1	no	—
368	C₂×Q₈	—	113	2	no	—
369	C₂×Q₈	—	113	4	no	—
370	C₂×Q₈	—	113	2	no	—
371	C₂×Q₈	—	113	2	no	—
372	C₂×Q₈	—	113	1	no	—
373	C₂×Q₈	—	226	4	no	—
374	C₂×Q₈	—	226	8	no	—
375	C₂×Q₈	—	226	8	no	—
376	C₂×Q₈	—	226	4	no	—
377	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
378	C₂×D₄	—	113	2	no	—
379	C₂×D₄	—	113	4	no	—
380	C₂×D₄	—	113	4	no	—
381	C₂×D₄	—	113	2	no	—
382	C₂×D₄	—	113	2	no	—
383	C₂×D₄	—	113	2	no	—
384	C₂×D₄	—	113	1	no	—
385	C₂×D₄	—	113	2	no	—
386	C₂×D₄	—	113	1	no	—
387	C₂×D₄	—	226	4	no	—
388	C₂×D₄	—	226	8	no	—
389	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
390	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
391	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
392	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	113	2	no	—
395	C₂²×C₄	—	113	2	no	—
396	C₂²×C₄	—	113	2	no	—
397	C₂²×C₄	—	113	4	no	—
398	C₂²×C₄	—	113	2	no	—
399	C₂²×C₄	—	113	4	no	—
400	C₂²×C₄	—	113	4	no	—
401	C₂²×C₄	—	113	2	no	—
402	C₂²×C₄	—	113	2	no	—
403	C₂²×C₄	—	113	2	no	—
404	C₂²×C₄	—	226	8	no	—
405	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
407	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
408	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
410	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
412	C₄⋊C₄	—	113	2	no	—
413	C₄⋊C₄	—	113	4	no	—
414	C₄⋊C₄	—	113	4	no	—
415	C₄⋊C₄	—	113	2	no	—
416	C₄⋊C₄	—	113	4	no	—
417	C₄⋊C₄	—	113	4	no	—
418	C₄⋊C₄	—	113	4	no	—
419	C₄⋊C₄	—	113	4	no	—
420	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
421	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
422	C₄⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
423	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
424	C₂²⋊C₄	—	113	4	no	—
425	C₂²⋊C₄	—	113	4	no	—
426	C₂²⋊C₄	—	113	4	no	—
427	C₂²⋊C₄	—	113	4	no	—
428	C₂²⋊C₄	—	113	4	no	—
429	C₂²⋊C₄	—	113	4	no	—
430	C₂²⋊C₄	—	113	4	no	—
431	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
432	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
433	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
434	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
435	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
436	C₄²	—	113	4	no	—
437	C₄²	C₂²×D₁₁₃	1	2	yes	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	113	2	no	—
442	C₂³	—	113	2	no	—
443	C₂³	—	452	2	no	—
444	C₂³	—	226	4	no	—
445	C₂³	—	226	4	no	—
446	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
447	C₂³	C₂³×D₁₁₃	1	2	yes	—
448	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
449	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
450	Q₈	—	2	2	no	—
451	Q₈	—	113	4	no	—
452	Q₈	—	226	8	no	—
453	Q₈	—	226	4	no	—
454	Q₈	—	226	4	no	—
455	Q₈	—	226	4	no	—
456	Q₈	—	226	2	no	—
457	D₄	—	2	4	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	113	8	no	—
462	D₄	—	113	4	no	—
463	D₄	—	452	4	no	—
464	D₄	—	226	4	no	—
465	D₄	—	226	4	no	—
466	D₄	—	226	4	no	—
467	D₄	—	226	8	no	—
468	D₄	—	226	4	no	—
469	D₄	—	226	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	113	2	no	—
477	C₂×C₄	—	113	8	no	—
478	C₂×C₄	—	113	4	no	—
479	C₂×C₄	—	113	4	no	—
480	C₂×C₄	—	113	2	no	—
481	C₂×C₄	—	452	4	no	—
482	C₂×C₄	—	452	2	no	—
483	C₂×C₄	—	226	4	no	—
484	C₂×C₄	—	226	4	no	—
485	C₂×C₄	—	226	8	no	—
486	C₂×C₄	—	226	4	no	—
487	C₂×C₄	—	226	8	no	—
488	C₂×C₄	—	226	4	no	—
489	C₂×C₄	—	226	4	no	—
490	C₂×C₄	D₄×D₁₁₃	1	4	yes	—
491	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
492	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
493	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
494	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
495	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
496	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
497	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	113	4	no	—
510	C₂²	—	452	8	no	—
511	C₂²	—	226	2	no	—
512	C₂²	—	226	2	no	—
513	C₂²	—	226	2	no	—
514	C₂²	—	226	2	no	—
515	C₂²	—	226	2	no	—
516	C₂²	C₂×D₄×D₁₁₃	1	2	yes	—
517	C₂²	#16813669	1	2	yes	complemented
518	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	113	4	no	—
525	C₄	—	226	2	no	—
526	C₄	—	226	4	no	—
527	C₄	—	226	4	no	—
528	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
529	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
530	C₂	—	2	2	no	—
531	C₂	—	2	2	no	—
532	C₂	—	4	1	no	—
533	C₂	—	4	2	no	—
534	C₂	—	452	2	no	—
535	C₂	—	226	4	no	—
536	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic
537	C₂	C₂×#16813669	1	1	yes	characteristic
538	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	#525×C₁₁₃	C₂
hypercenter	#525	D₁₁₃
hypocenter	C₁₁₃	#3489
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂×#16813669	C₂	semidirect
2. C₂²×#14268647	C₂	semidirect
3. D₄×Dic₂₂₆	C₂	semidirect
4. #20299257	C₂	semidirect
5. #20299253	C₂	semidirect
6. #20299246	C₂	semidirect
7. #20299244	C₂	semidirect
8. #20299235	C₂	semidirect
9. #20299177	C₂	semidirect
10. #20299176	C₂	semidirect
11. #20299174	C₂	semidirect
12. #20299171	C₂	semidirect
13. #20299108	C₂	semidirect
14. C₂×#16813601	C₂	semidirect
15. C₂²⋊Q₈×D₁₁₃	C₂	semidirect
16. #20299078	C₂	semidirect
17. #525×C₁₁₃	C₂	semidirect
26. C₂×#14268647	C₂²	semidirect
27. C₂×#14268646	C₂²	semidirect
28. C₂×#14268646	C₂²	semidirect
30. C₂²×Dic₂₂₆	C₂²	semidirect
31. C₂²×Dic₂₂₆	C₂²	semidirect
32. C₂×Q₈×D₁₁₃	C₂²	semidirect
36. #16813622	C₂²	semidirect
37. #16813621	C₂²	semidirect
38. #16813610	C₂²	semidirect
39. #16813608	C₂²	semidirect
40. #16813607	C₂²	semidirect
41. #16813606	C₂²	semidirect
42. #16813604	C₂²	semidirect
43. #16813604	C₂²	semidirect
44. #16813602	C₂²	semidirect
45. #16813602	C₂²	semidirect
48. #16813601	C₂²	semidirect
49. #16813601	C₂²	semidirect
50. #16813601	C₂²	semidirect
51. #16813600	C₂²	semidirect
53. #16813599	C₂²	semidirect
54. #16813598	C₂²	semidirect
55. #16813596	C₂²	semidirect
56. #16813595	C₂²	semidirect
57. #16813594	C₂²	semidirect
58. #16813594	C₂²	semidirect
59. #16813593	C₂²	semidirect
60. #16813593	C₂²	semidirect
62. C₄×Dic₂₂₆	C₂²	semidirect
63. C₄×D₄₅₂	C₂²	semidirect
65. #16813582	C₂²	semidirect
66. #16813582	C₂²	semidirect
67. #16813580	C₂²	semidirect
68. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
69. C₂×#14268626	C₂²	semidirect
70. C₄⋊C₄×D₁₁₃	C₂²	semidirect
71. C₄⋊C₄×D₁₁₃	C₂²	semidirect
74. C₂×#41×C₁₁₃	C₂²	semidirect
76. #123×C₁₁₃	C₂²	semidirect
78. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
80. #121×C₁₁₃	C₂²	semidirect
83. C₄×D₄×C₁₁₃	C₂²	semidirect
84. #117×C₁₁₃	C₂²	semidirect
92. #14268647	D₄	semidirect
240. C₂²×C₁₁₃	2₋¹⁺⁴	semidirect
270. C₁₁₃	#3489	semidirect
284. #525	D₁₁₃	semidirect
299. C₂×#41	C₂×D₁₁₃	semidirect
316. #123	C₂×D₁₁₃	semidirect
329. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
337. #121	C₂×D₁₁₃	semidirect
346. C₄×D₄	C₂×D₁₁₃	semidirect
348. #117	C₂×D₁₁₃	semidirect
517. C₂²	#16813669	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813669	2
C₂²×#14268647	2
D₄×Dic₂₂₆	2
#20299257	2
#20299253	2
#20299246	2
#20299244	2
#20299235	2
#20299177	2
#20299176	2
#20299174	2
#20299171	2
#20299108	2
C₂×#16813601	2
C₂²⋊Q₈×D₁₁₃	2
#20299078	2
#525×C₁₁₃	2
#3489	113