Subgroups — #28404176

Order 14464.

1242 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299332	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299302	C₂	1	2	yes	maximal, complemented
3	#20299293	C₂	1	2	yes	maximal, complemented
4	#20299291	C₂	1	2	yes	maximal, complemented
5	#20299279	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299276	C₂	1	1	yes	maximal, characteristic, complemented
7	#20299275	C₂	1	2	yes	maximal, complemented
8	#20299237	C₂	1	2	yes	maximal, complemented
9	#20299235	C₂	1	2	yes	maximal, complemented
10	#20299230	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299144	C₂	1	1	yes	maximal, characteristic, complemented
12	#20299128	C₂	1	2	yes	maximal, complemented
13	#20299126	C₂	1	2	yes	maximal, complemented
14	#20299107	C₂	1	2	yes	maximal, complemented
15	#20299105	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#14268646	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊D₁₁₃	C₂	1	2	yes	maximal, complemented
18	C₄×D₄×D₁₁₃	C₂	1	2	yes	maximal, complemented
19	#525×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14268647	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14268646	C₂²	1	2	yes	—
22	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
23	C₂×D₄×D₁₁₃	C₂²	1	2	yes	—
24	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄×D₁₁₃	C₂²	1	2	yes	complemented
26	#16813620	C₂²	1	1	yes	characteristic, complemented
27	#16813618	C₂²	1	1	yes	characteristic
28	#16813617	C₂²	1	2	yes	complemented
29	#16813617	C₂²	1	2	yes	complemented
30	#16813615	C₂²	1	2	yes	complemented
31	#16813615	C₂²	1	2	yes	complemented
32	#16813612	C₂²	1	2	yes	complemented
33	#16813612	C₂²	1	2	yes	complemented
34	#16813611	C₂²	1	1	yes	characteristic, complemented
35	#16813609	C₂²	1	1	yes	characteristic, complemented
36	#16813608	C₂²	1	2	yes	complemented
37	#16813608	C₂²	1	2	yes	complemented
38	#16813607	C₂²	1	2	yes	complemented
39	#16813607	C₂²	1	2	yes	complemented
40	#16813606	C₂²	1	2	yes	complemented
41	#16813604	C₂²	1	2	yes	complemented
42	#16813604	C₂²	1	2	yes	complemented
43	#16813603	C₂²	1	1	yes	characteristic, complemented
44	#16813603	C₂²	1	2	yes	complemented
45	#16813603	C₂²	1	1	yes	characteristic, complemented
46	#16813600	C₂²	1	2	yes	complemented
47	#16813600	C₂²	1	2	yes	complemented
48	#16813599	C₂²	1	2	yes	complemented
49	#16813599	C₂²	1	2	yes	complemented
50	#16813598	C₂²	1	2	yes	complemented
51	#16813595	C₂²	1	2	yes	—
52	#16813595	C₂²	1	2	yes	complemented
53	#16813594	C₂²	1	2	yes	—
54	#16813594	C₂²	1	2	yes	complemented
55	#16813594	C₂²	1	2	yes	complemented
56	#16813594	C₂²	1	2	yes	complemented
57	#16813593	C₂²	1	2	yes	complemented
58	#16813592	C₂²	1	2	yes	—
59	#16813590	C₂²	1	1	yes	characteristic
60	#16813590	C₂²	1	1	yes	characteristic, complemented
61	#16813590	C₂²	1	2	yes	complemented
62	C₄×Dic₂₂₆	C₂²	1	2	yes	complemented
63	#16813587	C₂²	1	2	yes	complemented
64	C₄×D₄₅₂	C₂²	1	2	yes	complemented
65	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
66	D₄×Dic₁₁₃	C₂²	1	2	yes	complemented
67	#16813584	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
69	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
70	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
72	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
74	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
76	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
78	#16813582	C₂²	1	2	yes	—
79	#16813582	C₂²	1	2	yes	—
80	#16813582	C₂²	1	2	yes	complemented
81	#16813582	C₂²	1	2	yes	complemented
82	#16813581	C₂²	1	1	yes	characteristic, complemented
83	#16813580	C₂²	1	2	yes	complemented
84	#16813579	C₂²	1	2	yes	complemented
85	#16813578	C₂²	1	2	yes	complemented
86	#16813578	C₂²	1	2	yes	complemented
87	C₂×#14268626	C₂²	1	2	yes	complemented
88	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
89	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	complemented
90	C₂×#14268624	C₂²	1	2	yes	complemented
91	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
93	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	complemented
94	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
95	C₄²×D₁₁₃	C₂²	1	2	yes	complemented
96	C₂×#41×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
98	#123×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
99	#123×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
100	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	complemented
101	#121×C₁₁₃	C₂²	1	2	yes	complemented
102	#120×C₁₁₃	C₂²	1	1	yes	characteristic
103	#120×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
105	C₄×D₄×C₁₁₃	C₂²	1	2	yes	complemented
106	#117×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
108	C₂³×D₁₁₃	C₂³	1	2	yes	—
109	#14268647	—	4	2	no	—
110	#14268646	—	2	8	no	—
111	C₂×Dic₂₂₆	C₂³	1	2	yes	—
112	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
113	C₂×D₄₅₂	C₂³	1	2	yes	—
114	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊D₁₁₃	—	2	8	no	—
116	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
123	D₄×D₁₁₃	—	2	8	no	—
124	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
125	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
126	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
127	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
128	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₄×D₁₁₃	—	4	2	no	—
130	C₂×C₄×D₁₁₃	—	4	4	no	—
131	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
132	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
133	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
134	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
135	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
136	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
137	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
138	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
139	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
140	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
141	#14268626	C₂³	1	2	yes	—
142	#14268626	C₂³	1	2	yes	—
143	#14268626	C₂³	1	2	yes	—
144	#14268626	C₂³	1	2	yes	—
145	#14268626	C₂³	1	2	yes	—
146	#14268626	C₂³	1	2	yes	—
147	#14268626	C₂³	1	2	yes	—
148	#14268626	C₂³	1	2	yes	—
149	#14268626	C₂³	1	2	yes	—
150	#14268626	C₂³	1	2	yes	—
151	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
152	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
153	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
154	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
158	C₂²⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
159	#14268624	C₂³	1	2	yes	—
160	#14268624	C₂³	1	2	yes	—
161	#14268624	C₂³	1	2	yes	—
162	#14268624	C₂³	1	2	yes	—
163	#14268624	C₂³	1	2	yes	—
164	#14268624	C₂³	1	2	yes	—
165	#14268624	C₂³	1	2	yes	—
166	#14268624	C₂³	1	2	yes	—
167	#14268624	C₂³	1	2	yes	—
168	#14268624	C₂³	1	2	yes	—
169	C₄×Dic₁₁₃	C₂³	1	2	yes	—
170	C₄×Dic₁₁₃	C₂³	1	2	yes	—
171	C₄×Dic₁₁₃	C₂³	1	2	yes	—
172	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
173	C₄×Dic₁₁₃	C₂³	1	2	yes	—
174	C₄×Dic₁₁₃	C₂³	1	2	yes	—
175	C₄×Dic₁₁₃	C₂³	1	1	yes	characteristic
176	C₄×Dic₁₁₃	C₂³	1	2	yes	—
177	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
178	#41×C₁₁₃	—	4	2	no	—
179	C₂×Q₈×C₁₁₃	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
181	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
182	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
183	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
184	C₂×D₄×C₁₁₃	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₁₁₃	—	4	2	no	—
186	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
187	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
188	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
191	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
192	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
193	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
194	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
200	C₂²⋊C₄×C₁₁₃	C₂³	1	1	yes	characteristic
201	C₄²×C₁₁₃	C₂³	1	2	yes	—
202	C₂³×C₁₁₃	—	2	4	no	—
203	C₂³×C₁₁₃	—	4	1	no	—
204	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
205	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
206	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
207	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
208	C₂²×D₁₁₃	—	2	4	no	—
209	C₂²×D₁₁₃	—	2	4	no	—
210	C₂²×D₁₁₃	—	2	4	no	—
211	C₂²×D₁₁₃	—	4	1	no	—
212	C₂²×D₁₁₃	—	4	2	no	—
213	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
214	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
215	Q₈×C₁₁₃	—	4	1	no	—
216	D₄×C₁₁₃	—	2	4	no	—
217	D₄×C₁₁₃	—	2	4	no	—
218	D₄×C₁₁₃	—	4	1	no	—
219	D₄×C₁₁₃	—	4	1	no	—
220	D₄×C₁₁₃	—	4	1	no	—
221	C₂×C₄×C₁₁₃	—	2	2	no	—
222	C₂×C₄×C₁₁₃	—	2	4	no	—
223	C₂×C₄×C₁₁₃	—	2	2	no	—
224	C₂×C₄×C₁₁₃	—	2	2	no	—
225	C₂×C₄×C₁₁₃	—	4	1	no	—
226	C₂×C₄×C₁₁₃	—	4	2	no	—
227	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
228	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
229	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
230	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²⋊D₁₁₃	—	2	4	no	—
235	C₂²⋊D₁₁₃	—	2	4	no	—
236	C₂²⋊D₁₁₃	—	2	4	no	—
237	C₂²⋊D₁₁₃	—	2	4	no	—
238	C₂²⋊D₁₁₃	—	2	4	no	—
239	C₂²⋊D₁₁₃	—	4	2	no	—
240	C₂²⋊D₁₁₃	#41	1	8	yes	complemented
241	C₂×Dic₁₁₃	—	2	4	no	—
242	C₂×Dic₁₁₃	—	2	4	no	—
243	C₂×Dic₁₁₃	—	2	4	no	—
244	C₂×Dic₁₁₃	—	4	2	no	—
245	C₂×Dic₁₁₃	—	4	1	no	—
246	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
247	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
248	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
249	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
250	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
251	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
252	D₄₅₂	—	2	4	no	—
253	D₄₅₂	—	4	1	no	—
254	C₄×D₁₁₃	—	2	4	no	—
255	C₄×D₁₁₃	—	2	4	no	—
256	C₄×D₁₁₃	—	2	4	no	—
257	C₄×D₁₁₃	—	2	4	no	—
258	C₄×D₁₁₃	—	4	2	no	—
259	C₄×D₁₁₃	—	4	2	no	—
260	C₄×D₁₁₃	—	4	2	no	—
261	Dic₂₂₆	—	2	4	no	—
262	Dic₂₂₆	—	4	1	no	—
263	C₂²×C₁₁₃	—	2	2	no	—
264	C₂²×C₁₁₃	—	2	2	no	—
265	C₂²×C₁₁₃	—	2	2	no	—
266	C₂²×C₁₁₃	—	2	2	no	—
267	C₂²×C₁₁₃	—	2	2	no	—
268	C₂²×C₁₁₃	—	2	1	no	—
269	C₂²×C₁₁₃	—	2	1	no	—
270	C₂²×C₁₁₃	—	2	1	no	—
271	C₂²×C₁₁₃	—	4	4	no	—
272	C₂²×C₁₁₃	C₂×#41	1	4	yes	—
273	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
274	C₂×D₁₁₃	—	2	2	no	—
275	C₂×D₁₁₃	—	2	2	no	—
276	C₂×D₁₁₃	—	2	2	no	—
277	C₂×D₁₁₃	—	2	2	no	—
278	C₂×D₁₁₃	—	2	2	no	—
279	C₂×D₁₁₃	—	4	4	no	—
280	C₂×D₁₁₃	—	4	8	no	—
281	C₂×D₁₁₃	C₂×#41	1	4	yes	—
282	C₄×C₁₁₃	—	2	2	no	—
283	C₄×C₁₁₃	—	2	2	no	—
284	C₄×C₁₁₃	—	2	1	no	—
285	C₄×C₁₁₃	—	2	2	no	—
286	C₄×C₁₁₃	—	2	1	no	—
287	C₄×C₁₁₃	—	2	1	no	—
288	C₄×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
289	Dic₁₁₃	—	2	2	no	—
290	Dic₁₁₃	—	2	2	no	—
291	Dic₁₁₃	—	2	2	no	—
292	Dic₁₁₃	—	2	2	no	—
293	Dic₁₁₃	—	2	2	no	—
294	Dic₁₁₃	C₂×#41	1	4	yes	—
295	C₂×C₁₁₃	—	2	4	no	—
296	C₂×C₁₁₃	—	4	1	no	—
297	C₂×C₁₁₃	—	4	1	no	—
298	C₂×C₁₁₃	—	4	1	no	—
299	C₂×C₁₁₃	C₂²×#41	1	2	yes	—
300	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
301	D₁₁₃	—	2	4	no	—
302	D₁₁₃	—	4	2	no	—
303	#3481	—	113	1	no	maximal, Sylow
304	C₁₁₃	#3481	1	1	yes	characteristic, complemented, Sylow
305	#559	—	113	1	no	—
306	#554	—	113	2	no	—
307	#553	—	113	2	no	—
308	#553	—	113	2	no	—
309	#551	—	113	1	no	—
310	#551	—	113	2	no	—
311	#551	—	113	1	no	—
312	#546	—	113	2	no	—
313	#546	—	113	2	no	—
314	D₄²	—	113	1	no	—
315	#532	—	113	1	no	—
316	#529	—	113	2	no	—
317	#529	—	113	2	no	—
318	#525	—	113	1	no	—
319	#525	—	113	2	no	—
320	#525	D₁₁₃	1	1	yes	characteristic, complemented
321	C₄×#41	—	113	2	no	—
322	C₂×C₄×D₄	—	113	2	no	—
323	C₂×C₄×D₄	—	113	2	no	—
324	C₂×#41	—	113	2	no	—
325	C₂×#41	—	113	1	no	—
326	C₂×#41	C₂×D₁₁₃	1	1	yes	characteristic, complemented
327	C₂²×D₄	—	113	2	no	—
328	C₂²×D₄	—	113	2	no	—
329	C₂³×C₄	—	113	2	no	—
330	C₂³×C₄	—	113	1	no	—
331	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
332	C₄⋊Q₈	—	113	1	no	—
333	#127	—	113	1	no	—
334	#126	—	113	2	no	—
335	#126	—	113	2	no	—
336	#126	—	113	2	no	—
337	#126	—	113	2	no	—
338	#125	—	113	2	no	—
339	#125	—	113	2	no	—
340	#124	—	113	1	no	—
341	#124	—	113	1	no	—
342	#124	—	113	2	no	—
343	#124	—	113	2	no	—
344	#123	—	113	1	no	—
345	#123	—	113	1	no	—
346	#123	—	113	2	no	—
347	#123	—	113	2	no	—
348	#123	—	113	2	no	—
349	#123	—	113	2	no	—
350	#123	—	113	2	no	—
351	#123	—	113	2	no	—
352	#123	C₂×D₁₁₃	1	1	yes	characteristic, complemented
353	#123	C₂×D₁₁₃	1	1	yes	characteristic, complemented
354	C₂²⋊Q₈	—	113	2	no	—
355	C₂²⋊Q₈	—	113	2	no	—
356	C₂²⋊Q₈	—	113	2	no	—
357	C₂²⋊Q₈	—	113	2	no	—
358	C₂²⋊Q₈	—	113	2	no	—
359	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	complemented
360	#121	—	113	2	no	—
361	#121	—	113	2	no	—
362	#121	—	113	2	no	—
363	#121	—	113	2	no	—
364	#121	—	113	2	no	—
365	#121	—	113	2	no	—
366	#121	—	113	2	no	—
367	#121	C₂×D₁₁₃	1	2	yes	complemented
368	#120	—	113	1	no	—
369	#120	—	113	2	no	—
370	#120	—	113	1	no	—
371	#120	—	113	2	no	—
372	#120	C₂×D₁₁₃	1	1	yes	characteristic
373	#120	C₂×D₁₁₃	1	1	yes	characteristic, complemented
374	C₄×Q₈	—	113	2	no	—
375	C₄×Q₈	—	113	2	no	—
376	C₄×D₄	—	113	2	no	—
377	C₄×D₄	—	113	2	no	—
378	C₄×D₄	—	113	2	no	—
379	C₄×D₄	—	113	2	no	—
380	C₄×D₄	—	113	2	no	—
381	C₄×D₄	—	113	2	no	—
382	C₄×D₄	—	113	2	no	—
383	C₄×D₄	—	113	2	no	—
384	C₄×D₄	—	113	2	no	—
385	C₄×D₄	—	113	2	no	—
386	C₄×D₄	—	113	2	no	—
387	C₄×D₄	—	113	2	no	—
388	C₄×D₄	—	113	2	no	—
389	C₄×D₄	—	113	2	no	—
390	C₄×D₄	—	113	2	no	—
391	C₄×D₄	—	113	2	no	—
392	C₄×D₄	—	113	2	no	—
393	C₄×D₄	—	113	2	no	—
394	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
395	C₄×D₄	C₂×D₁₁₃	1	2	yes	complemented
396	#117	—	113	1	no	—
397	#117	—	113	2	no	—
398	#117	—	113	2	no	—
399	#117	—	113	2	no	—
400	#117	—	113	2	no	—
401	#117	C₂×D₁₁₃	1	1	yes	characteristic, complemented
402	C₂×C₄⋊C₄	—	113	2	no	—
403	C₂×C₄⋊C₄	—	113	2	no	—
404	C₂×C₂²⋊C₄	—	113	2	no	—
405	C₂×C₂²⋊C₄	—	113	2	no	—
406	C₂×C₂²⋊C₄	—	113	2	no	—
407	C₂×C₂²⋊C₄	—	113	2	no	—
408	C₂×C₄²	—	113	2	no	—
409	C₂×C₄²	—	113	1	no	—
410	C₂×C₄²	—	113	2	no	—
411	C₂⁴	—	113	1	no	—
412	C₂⁴	—	113	2	no	—
413	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
414	#41	—	4	2	no	—
415	#41	—	452	2	no	—
416	#41	—	226	8	no	—
417	C₂×Q₈	—	113	1	no	—
418	C₂×Q₈	—	113	2	no	—
419	C₂×Q₈	C₂²×D₁₁₃	1	1	yes	characteristic
420	C₂×D₄	—	113	2	no	—
421	C₂×D₄	—	113	2	no	—
422	C₂×D₄	—	113	2	no	—
423	C₂×D₄	—	113	2	no	—
424	C₂×D₄	—	113	2	no	—
425	C₂×D₄	—	113	2	no	—
426	C₂×D₄	—	113	2	no	—
427	C₂×D₄	—	113	1	no	—
428	C₂×D₄	—	113	2	no	—
429	C₂×D₄	—	226	8	no	—
430	C₂×D₄	—	226	8	no	—
431	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
432	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
433	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
434	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
435	C₂×D₄	C₂²×D₁₁₃	1	1	yes	characteristic
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	113	2	no	—
438	C₂²×C₄	—	113	1	no	—
439	C₂²×C₄	—	113	2	no	—
440	C₂²×C₄	—	113	2	no	—
441	C₂²×C₄	—	113	2	no	—
442	C₂²×C₄	—	113	2	no	—
443	C₂²×C₄	—	113	2	no	—
444	C₂²×C₄	—	113	2	no	—
445	C₂²×C₄	—	113	2	no	—
446	C₂²×C₄	—	113	2	no	—
447	C₂²×C₄	—	113	2	no	—
448	C₂²×C₄	—	113	2	no	—
449	C₂²×C₄	—	452	4	no	—
450	C₂²×C₄	—	452	2	no	—
451	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
452	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
455	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
456	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
457	C₄⋊C₄	—	113	2	no	—
458	C₄⋊C₄	—	113	2	no	—
459	C₄⋊C₄	—	113	2	no	—
460	C₄⋊C₄	—	113	2	no	—
461	C₄⋊C₄	—	113	2	no	—
462	C₄⋊C₄	—	113	2	no	—
463	C₄⋊C₄	—	113	2	no	—
464	C₄⋊C₄	—	113	2	no	—
465	C₄⋊C₄	—	113	2	no	—
466	C₄⋊C₄	—	113	2	no	—
467	C₄⋊C₄	—	113	2	no	—
468	C₄⋊C₄	—	113	2	no	—
469	C₄⋊C₄	—	113	2	no	—
470	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
471	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
472	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
473	C₂²⋊C₄	—	113	2	no	—
474	C₂²⋊C₄	—	113	2	no	—
475	C₂²⋊C₄	—	113	2	no	—
476	C₂²⋊C₄	—	113	2	no	—
477	C₂²⋊C₄	—	113	2	no	—
478	C₂²⋊C₄	—	113	2	no	—
479	C₂²⋊C₄	—	113	1	no	—
480	C₂²⋊C₄	—	113	1	no	—
481	C₂²⋊C₄	—	113	2	no	—
482	C₂²⋊C₄	—	113	2	no	—
483	C₂²⋊C₄	—	113	2	no	—
484	C₂²⋊C₄	—	113	2	no	—
485	C₂²⋊C₄	—	113	2	no	—
486	C₂²⋊C₄	—	113	2	no	—
487	C₂²⋊C₄	—	113	2	no	—
488	C₂²⋊C₄	—	113	2	no	—
489	C₂²⋊C₄	—	113	2	no	—
490	C₂²⋊C₄	—	113	2	no	—
491	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
494	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
495	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
496	C₂²⋊C₄	C₂²×D₁₁₃	1	1	yes	characteristic
497	C₄²	—	113	1	no	—
498	C₄²	—	113	2	no	—
499	C₄²	—	113	2	no	—
500	C₄²	—	113	2	no	—
501	C₄²	—	113	2	no	—
502	C₄²	—	113	1	no	—
503	C₄²	—	113	2	no	—
504	C₄²	—	113	2	no	—
505	C₄²	C₂²×D₁₁₃	1	2	yes	—
506	C₂³	—	2	4	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	113	2	no	—
509	C₂³	—	113	2	no	—
510	C₂³	—	452	2	no	—
511	C₂³	—	452	1	no	—
512	C₂³	—	226	4	no	—
513	C₂³	—	226	4	no	—
514	C₂³	—	226	4	no	—
515	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
516	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
517	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
518	C₂³	C₂³×D₁₁₃	1	2	yes	—
519	Q₈	—	4	1	no	—
520	Q₈	—	452	1	no	—
521	Q₈	—	226	4	no	—
522	D₄	—	2	4	no	—
523	D₄	—	2	4	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	113	8	no	—
528	D₄	—	452	1	no	—
529	D₄	—	452	2	no	—
530	D₄	—	226	4	no	—
531	D₄	—	226	4	no	—
532	D₄	—	226	4	no	—
533	D₄	—	226	4	no	—
534	D₄	—	226	4	no	—
535	D₄	—	226	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	113	2	no	—
543	C₂×C₄	—	113	2	no	—
544	C₂×C₄	—	113	2	no	—
545	C₂×C₄	—	113	2	no	—
546	C₂×C₄	—	113	2	no	—
547	C₂×C₄	—	113	2	no	—
548	C₂×C₄	—	452	2	no	—
549	C₂×C₄	—	452	2	no	—
550	C₂×C₄	—	452	2	no	—
551	C₂×C₄	—	452	1	no	—
552	C₂×C₄	—	452	2	no	—
553	C₂×C₄	—	226	4	no	—
554	C₂×C₄	—	226	4	no	—
555	C₂×C₄	—	226	4	no	—
556	C₂×C₄	—	226	4	no	—
557	C₂×C₄	—	226	4	no	—
558	C₂×C₄	—	226	4	no	—
559	C₂×C₄	—	226	4	no	—
560	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
561	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
563	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
564	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
566	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	113	4	no	—
577	C₂²	—	452	8	no	—
578	C₂²	—	452	4	no	—
579	C₂²	—	226	2	no	—
580	C₂²	—	226	2	no	—
581	C₂²	—	226	2	no	—
582	C₂²	—	226	2	no	—
583	C₂²	—	226	2	no	—
584	C₂²	#41×D₁₁₃	1	4	yes	—
585	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	113	4	no	—
593	C₄	—	226	2	no	—
594	C₄	—	226	2	no	—
595	C₄	—	226	2	no	—
596	C₄	—	226	2	no	—
597	C₄	—	226	2	no	—
598	C₄	#16813667	1	2	yes	—
599	C₂	—	2	4	no	—
600	C₂	—	4	1	no	—
601	C₂	—	4	1	no	—
602	C₂	—	4	1	no	—
603	C₂	—	452	2	no	—
604	C₂	—	226	4	no	—
605	C₂	C₂×#41×D₁₁₃	1	2	yes	—
606	C₂	C₂×#16813667	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	#525×C₁₁₃	C₂
hypercenter	#525	D₁₁₃
hypocenter	C₁₁₃	#3481
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #20299332	C₂	semidirect
2. #20299302	C₂	semidirect
3. #20299293	C₂	semidirect
4. #20299291	C₂	semidirect
5. #20299279	C₂	semidirect
6. #20299276	C₂	semidirect
7. #20299275	C₂	semidirect
8. #20299237	C₂	semidirect
9. #20299235	C₂	semidirect
10. #20299230	C₂	semidirect
11. #20299144	C₂	semidirect
12. #20299128	C₂	semidirect
13. #20299126	C₂	semidirect
14. #20299107	C₂	semidirect
15. #20299105	C₂	semidirect
16. C₄×#14268646	C₂	semidirect
17. C₂×C₄×C₂²⋊D₁₁₃	C₂	semidirect
18. C₄×D₄×D₁₁₃	C₂	semidirect
19. #525×C₁₁₃	C₂	semidirect
20. C₂×#14268647	C₂²	semidirect
24. C₂²×C₄×D₁₁₃	C₂²	semidirect
25. C₂²×C₄×D₁₁₃	C₂²	semidirect
26. #16813620	C₂²	semidirect
28. #16813617	C₂²	semidirect
29. #16813617	C₂²	semidirect
30. #16813615	C₂²	semidirect
31. #16813615	C₂²	semidirect
32. #16813612	C₂²	semidirect
33. #16813612	C₂²	semidirect
34. #16813611	C₂²	semidirect
35. #16813609	C₂²	semidirect
36. #16813608	C₂²	semidirect
37. #16813608	C₂²	semidirect
38. #16813607	C₂²	semidirect
39. #16813607	C₂²	semidirect
40. #16813606	C₂²	semidirect
41. #16813604	C₂²	semidirect
42. #16813604	C₂²	semidirect
43. #16813603	C₂²	semidirect
44. #16813603	C₂²	semidirect
45. #16813603	C₂²	semidirect
46. #16813600	C₂²	semidirect
47. #16813600	C₂²	semidirect
48. #16813599	C₂²	semidirect
49. #16813599	C₂²	semidirect
50. #16813598	C₂²	semidirect
52. #16813595	C₂²	semidirect
54. #16813594	C₂²	semidirect
55. #16813594	C₂²	semidirect
56. #16813594	C₂²	semidirect
57. #16813593	C₂²	semidirect
60. #16813590	C₂²	semidirect
61. #16813590	C₂²	semidirect
62. C₄×Dic₂₂₆	C₂²	semidirect
63. #16813587	C₂²	semidirect
64. C₄×D₄₅₂	C₂²	semidirect
65. D₄×Dic₁₁₃	C₂²	semidirect
66. D₄×Dic₁₁₃	C₂²	semidirect
67. #16813584	C₂²	semidirect
70. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
71. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
72. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
73. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
74. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
75. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
76. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
77. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
80. #16813582	C₂²	semidirect
81. #16813582	C₂²	semidirect
82. #16813581	C₂²	semidirect
83. #16813580	C₂²	semidirect
84. #16813579	C₂²	semidirect
85. #16813578	C₂²	semidirect
86. #16813578	C₂²	semidirect
87. C₂×#14268626	C₂²	semidirect
88. C₄⋊C₄×D₁₁₃	C₂²	semidirect
89. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
90. C₂×#14268624	C₂²	semidirect
91. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
92. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
93. C₂×C₄×Dic₁₁₃	C₂²	semidirect
94. C₂×C₄×Dic₁₁₃	C₂²	semidirect
95. C₄²×D₁₁₃	C₂²	semidirect
96. C₂×#41×C₁₁₃	C₂²	semidirect
97. C₂³×C₄×C₁₁₃	C₂²	semidirect
98. #123×C₁₁₃	C₂²	semidirect
99. #123×C₁₁₃	C₂²	semidirect
100. C₂²⋊Q₈×C₁₁₃	C₂²	semidirect
101. #121×C₁₁₃	C₂²	semidirect
103. #120×C₁₁₃	C₂²	semidirect
104. C₄×D₄×C₁₁₃	C₂²	semidirect
105. C₄×D₄×C₁₁₃	C₂²	semidirect
106. #117×C₁₁₃	C₂²	semidirect
240. C₂²⋊D₁₁₃	#41	semidirect
304. C₁₁₃	#3481	semidirect
320. #525	D₁₁₃	semidirect
326. C₂×#41	C₂×D₁₁₃	semidirect
331. C₂³×C₄	C₂×D₁₁₃	semidirect
352. #123	C₂×D₁₁₃	semidirect
353. #123	C₂×D₁₁₃	semidirect
359. C₂²⋊Q₈	C₂×D₁₁₃	semidirect
367. #121	C₂×D₁₁₃	semidirect
373. #120	C₂×D₁₁₃	semidirect
394. C₄×D₄	C₂×D₁₁₃	semidirect
395. C₄×D₄	C₂×D₁₁₃	semidirect
401. #117	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#20299332	2
#20299302	2
#20299293	2
#20299291	2
#20299279	2
#20299276	2
#20299275	2
#20299237	2
#20299235	2
#20299230	2
#20299144	2
#20299128	2
#20299126	2
#20299107	2
#20299105	2
C₄×#14268646	2
C₂×C₄×C₂²⋊D₁₁₃	2
C₄×D₄×D₁₁₃	2
#525×C₁₁₃	2
#3481	113