Subgroups — #28404261

Order 14464.

1328 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299279	C₂	1	4	yes	maximal, complemented
2	#20299274	C₂	1	4	yes	maximal, complemented
3	#20299242	C₂	1	4	yes	maximal, complemented
4	#20299235	C₂	1	4	yes	maximal, complemented
5	#20299224	C₂	1	1	yes	maximal, characteristic, complemented
6	#20299183	C₂	1	4	yes	maximal, complemented
7	#20299157	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299104	C₂	1	4	yes	maximal, complemented
9	C₂×#16813591	C₂	1	1	yes	maximal, characteristic, complemented
10	#20299073	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299071	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₂²⋊Dic₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#120×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14268646	C₂²	1	4	yes	complemented
15	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊D₁₁₃	C₂²	1	2	yes	complemented
17	C₂³×Dic₁₁₃	C₂²	1	2	yes	complemented
18	#16813615	C₂²	1	4	yes	complemented
19	#16813615	C₂²	1	4	yes	complemented
20	#16813609	C₂²	1	4	yes	complemented
21	#16813608	C₂²	1	4	yes	complemented
22	#16813606	C₂²	1	4	yes	complemented
23	#16813605	C₂²	1	2	yes	complemented
24	#16813604	C₂²	1	4	yes	complemented
25	#16813603	C₂²	1	4	yes	complemented
26	#16813603	C₂²	1	2	yes	complemented
27	#16813603	C₂²	1	4	yes	complemented
28	#16813601	C₂²	1	4	yes	complemented
29	#16813599	C₂²	1	4	yes	complemented
30	#16813599	C₂²	1	4	yes	complemented
31	#16813599	C₂²	1	4	yes	complemented
32	#16813594	C₂²	1	4	yes	complemented
33	#16813594	C₂²	1	4	yes	complemented
34	#16813594	C₂²	1	4	yes	complemented
35	#16813593	C₂²	1	4	yes	complemented
36	#16813591	C₂²	1	4	yes	—
37	#16813591	C₂²	1	2	yes	complemented
38	#16813591	C₂²	1	2	yes	complemented
39	#16813591	C₂²	1	2	yes	complemented
40	#16813590	C₂²	1	2	yes	complemented
41	D₄×Dic₁₁₃	C₂²	1	4	yes	complemented
42	D₄×Dic₁₁₃	C₂²	1	4	yes	complemented
43	D₄×Dic₁₁₃	C₂²	1	4	yes	complemented
44	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	complemented
45	#16813582	C₂²	1	4	yes	complemented
46	#16813582	C₂²	1	4	yes	complemented
47	#16813581	C₂²	1	2	yes	complemented
48	#16813578	C₂²	1	4	yes	complemented
49	#16813578	C₂²	1	2	yes	complemented
50	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₁₁₃	C₂²	1	4	yes	complemented
54	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	complemented
55	C₂×C₂²⋊Dic₁₁₃	C₂²	1	4	yes	complemented
56	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	complemented
57	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	complemented
58	C₂²⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
59	C₂⁵×C₁₁₃	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₁₁₃	C₂²	1	2	yes	complemented
62	#120×C₁₁₃	C₂²	1	4	yes	—
63	#120×C₁₁₃	C₂²	1	2	yes	complemented
64	#120×C₁₁₃	C₂²	1	2	yes	complemented
65	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	complemented
67	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
68	#14268646	—	4	8	no	—
69	C₂×Dic₂₂₆	C₂³	1	4	yes	complemented
70	C₂×C₂²⋊D₁₁₃	—	2	4	no	—
71	C₂×C₂²⋊D₁₁₃	—	4	4	no	—
72	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
73	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
74	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
75	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	complemented
77	C₂²×Dic₁₁₃	—	4	4	no	—
78	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
80	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
81	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
82	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
83	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
84	C₂²×Dic₁₁₃	C₂³	1	4	yes	complemented
85	C₂×C₄×D₁₁₃	C₂³	1	4	yes	complemented
86	C₄⋊Dic₁₁₃	C₂³	1	4	yes	complemented
87	C₄⋊Dic₁₁₃	C₂³	1	4	yes	complemented
88	#14268626	C₂³	1	4	yes	complemented
89	#14268626	C₂³	1	4	yes	complemented
90	#14268626	C₂³	1	4	yes	complemented
91	#14268626	C₂³	1	4	yes	complemented
92	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
93	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
94	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
95	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
96	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
97	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
98	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
99	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
100	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
101	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
102	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	complemented
103	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	complemented
104	#14268624	C₂³	1	4	yes	complemented
105	#14268624	C₂³	1	4	yes	complemented
106	C₄×Dic₁₁₃	C₂³	1	4	yes	complemented
107	C₄×Dic₁₁₃	C₂³	1	4	yes	complemented
108	C₂⁴×C₁₁₃	—	2	4	no	—
109	C₂⁴×C₁₁₃	—	4	4	no	—
110	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
111	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
112	C₂⁴×C₁₁₃	C₂³	1	2	yes	—
113	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
114	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
115	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₁₁₃	—	2	4	no	—
117	C₂×D₄×C₁₁₃	—	4	4	no	—
118	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
119	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
120	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
121	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
122	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
124	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
125	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
126	C₂²⋊C₄×C₁₁₃	C₂³	1	2	yes	—
127	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
128	C₂³×C₁₁₃	—	2	2	no	—
129	C₂³×C₁₁₃	—	2	4	no	—
130	C₂³×C₁₁₃	—	2	4	no	—
131	C₂³×C₁₁₃	—	2	4	no	—
132	C₂³×C₁₁₃	—	2	2	no	—
133	C₂³×C₁₁₃	—	2	4	no	—
134	C₂³×C₁₁₃	—	2	4	no	—
135	C₂³×C₁₁₃	—	2	2	no	—
136	C₂³×C₁₁₃	—	4	2	no	—
137	C₂³×C₁₁₃	—	4	2	no	—
138	C₂³×C₁₁₃	—	4	2	no	—
139	C₂³×C₁₁₃	—	4	2	no	—
140	C₂³×C₁₁₃	—	4	2	no	—
141	C₂³×C₁₁₃	—	4	16	no	—
142	C₂³×C₁₁₃	#41	1	4	yes	complemented
143	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
144	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
145	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
146	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
147	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
148	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
149	C₂²×D₁₁₃	—	2	2	no	—
150	C₂²×D₁₁₃	—	4	2	no	—
151	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
152	D₄×C₁₁₃	—	2	4	no	—
153	D₄×C₁₁₃	—	2	4	no	—
154	D₄×C₁₁₃	—	2	8	no	—
155	D₄×C₁₁₃	—	4	4	no	—
156	C₂×C₄×C₁₁₃	—	2	2	no	—
157	C₂×C₄×C₁₁₃	—	4	2	no	—
158	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
159	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
160	C₂²⋊D₁₁₃	—	2	4	no	—
161	C₂²⋊D₁₁₃	—	2	4	no	—
162	C₂²⋊D₁₁₃	—	2	8	no	—
163	C₂²⋊D₁₁₃	—	4	4	no	—
164	C₂²⋊D₁₁₃	—	4	4	no	—
165	C₂×Dic₁₁₃	—	2	2	no	—
166	C₂×Dic₁₁₃	—	2	8	no	—
167	C₂×Dic₁₁₃	—	4	2	no	—
168	C₂×Dic₁₁₃	—	4	4	no	—
169	C₂×Dic₁₁₃	—	4	2	no	—
170	C₂×Dic₁₁₃	—	4	2	no	—
171	C₂×Dic₁₁₃	—	4	4	no	—
172	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
173	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
174	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
175	C₂×Dic₁₁₃	C₂⁴	1	4	yes	—
176	C₄×D₁₁₃	—	4	4	no	—
177	Dic₂₂₆	—	4	4	no	—
178	C₂²×C₁₁₃	—	2	8	no	—
179	C₂²×C₁₁₃	—	2	2	no	—
180	C₂²×C₁₁₃	—	2	2	no	—
181	C₂²×C₁₁₃	—	2	2	no	—
182	C₂²×C₁₁₃	—	2	2	no	—
183	C₂²×C₁₁₃	—	2	2	no	—
184	C₂²×C₁₁₃	—	2	2	no	—
185	C₂²×C₁₁₃	—	2	2	no	—
186	C₂²×C₁₁₃	—	2	4	no	—
187	C₂²×C₁₁₃	—	2	2	no	—
188	C₂²×C₁₁₃	—	2	2	no	—
189	C₂²×C₁₁₃	—	4	4	no	—
190	C₂²×C₁₁₃	—	4	8	no	—
191	C₂²×C₁₁₃	—	4	8	no	—
192	C₂²×C₁₁₃	—	4	4	no	—
193	C₂²×C₁₁₃	—	8	2	no	—
194	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
195	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
196	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
197	C₂²×C₁₁₃	H(5,𝔽₂)	1	4	yes	—
198	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
199	C₂×D₁₁₃	—	2	2	no	—
200	C₂×D₁₁₃	—	2	4	no	—
201	C₂×D₁₁₃	—	8	2	no	—
202	C₄×C₁₁₃	—	2	2	no	—
203	C₄×C₁₁₃	—	2	4	no	—
204	Dic₁₁₃	—	2	2	no	—
205	Dic₁₁₃	—	2	4	no	—
206	Dic₁₁₃	—	2	4	no	—
207	Dic₁₁₃	—	2	4	no	—
208	C₂×C₁₁₃	—	2	2	no	—
209	C₂×C₁₁₃	—	2	2	no	—
210	C₂×C₁₁₃	—	2	4	no	—
211	C₂×C₁₁₃	—	2	2	no	—
212	C₂×C₁₁₃	—	4	2	no	—
213	C₂×C₁₁₃	—	4	2	no	—
214	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
215	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
216	D₁₁₃	—	4	2	no	—
217	#3490	—	113	1	no	maximal, Sylow
218	C₁₁₃	#3490	1	1	yes	characteristic, complemented, Sylow
219	#551	—	113	4	no	—
220	#551	—	113	4	no	—
221	#546	—	113	4	no	—
222	#546	—	113	4	no	—
223	#543	—	113	1	no	—
224	#538	—	113	4	no	—
225	#534	—	113	1	no	—
226	#525	—	113	4	no	—
227	C₂×#120	—	113	1	no	—
228	C₂×#120	D₁₁₃	1	1	yes	characteristic, complemented
229	#518	—	113	1	no	—
230	#518	—	113	1	no	—
231	C₂²×C₂²⋊C₄	—	113	1	no	—
232	C₂⁵	C₂×D₁₁₃	1	1	yes	characteristic
233	C₂×#41	—	113	4	no	—
234	C₂²×D₄	—	113	2	no	—
235	C₂²×D₄	—	113	1	no	—
236	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
237	C₂²×D₄	C₂×D₁₁₃	1	2	yes	complemented
238	C₂³×C₄	—	113	2	no	—
239	#126	—	113	4	no	—
240	#126	—	113	4	no	—
241	#124	—	113	4	no	—
242	#124	—	113	4	no	—
243	#123	—	113	4	no	—
244	#123	—	113	2	no	—
245	#123	—	113	4	no	—
246	#123	—	113	2	no	—
247	#123	—	113	4	no	—
248	#123	—	113	4	no	—
249	C₂²⋊Q₈	—	113	4	no	—
250	C₂²⋊Q₈	—	113	4	no	—
251	C₂²⋊Q₈	—	113	4	no	—
252	C₂²⋊Q₈	—	113	4	no	—
253	#121	—	113	4	no	—
254	#121	—	113	4	no	—
255	#121	—	113	4	no	—
256	#121	—	113	4	no	—
257	#120	—	113	2	no	—
258	#120	—	113	4	no	—
259	#120	—	113	2	no	—
260	#120	—	113	2	no	—
261	#120	—	113	2	no	—
262	#120	C₂×D₁₁₃	1	4	yes	—
263	#120	C₂×D₁₁₃	1	2	yes	complemented
264	#120	C₂×D₁₁₃	1	2	yes	complemented
265	C₄×D₄	—	113	4	no	—
266	C₄×D₄	—	113	4	no	—
267	C₄×D₄	—	113	4	no	—
268	C₄×D₄	—	113	4	no	—
269	C₄×D₄	—	113	4	no	—
270	C₄×D₄	—	113	4	no	—
271	#117	—	113	2	no	—
272	#117	—	113	2	no	—
273	#117	—	113	4	no	—
274	C₂×C₂²⋊C₄	—	113	1	no	—
275	C₂×C₂²⋊C₄	—	113	1	no	—
276	C₂×C₂²⋊C₄	—	113	2	no	—
277	C₂×C₂²⋊C₄	—	113	4	no	—
278	C₂×C₂²⋊C₄	—	113	4	no	—
279	C₂×C₂²⋊C₄	—	113	1	no	—
280	C₂×C₂²⋊C₄	—	113	2	no	—
281	C₂×C₂²⋊C₄	—	113	2	no	—
282	C₂×C₂²⋊C₄	—	113	2	no	—
283	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	complemented
285	C₂⁴	—	2	4	no	—
286	C₂⁴	—	4	4	no	—
287	C₂⁴	—	113	1	no	—
288	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
289	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
290	C₂⁴	C₂²×D₁₁₃	1	2	yes	—
291	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
292	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
293	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
294	#41	—	452	8	no	—
295	C₂×Q₈	—	113	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	113	4	no	—
299	C₂×D₄	—	113	4	no	—
300	C₂×D₄	—	113	2	no	—
301	C₂×D₄	—	113	2	no	—
302	C₂×D₄	—	113	4	no	—
303	C₂×D₄	—	452	4	no	—
304	C₂×D₄	—	226	4	no	—
305	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
306	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
307	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
308	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
309	C₂²×C₄	—	113	2	no	—
310	C₂²×C₄	—	113	4	no	—
311	C₂²×C₄	—	113	2	no	—
312	C₂²×C₄	—	113	2	no	—
313	C₂²×C₄	—	113	4	no	—
314	C₂²×C₄	—	113	1	no	—
315	C₂²×C₄	—	113	4	no	—
316	C₂²×C₄	—	113	4	no	—
317	C₂²×C₄	—	452	4	no	—
318	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
320	C₄⋊C₄	—	113	4	no	—
321	C₄⋊C₄	—	113	4	no	—
322	C₄⋊C₄	—	113	4	no	—
323	C₄⋊C₄	—	113	4	no	—
324	C₄⋊C₄	—	113	4	no	—
325	C₄⋊C₄	—	113	4	no	—
326	C₂²⋊C₄	—	113	2	no	—
327	C₂²⋊C₄	—	113	2	no	—
328	C₂²⋊C₄	—	113	2	no	—
329	C₂²⋊C₄	—	113	2	no	—
330	C₂²⋊C₄	—	113	4	no	—
331	C₂²⋊C₄	—	113	4	no	—
332	C₂²⋊C₄	—	113	2	no	—
333	C₂²⋊C₄	—	113	4	no	—
334	C₂²⋊C₄	—	113	2	no	—
335	C₂²⋊C₄	—	113	4	no	—
336	C₂²⋊C₄	—	113	4	no	—
337	C₂²⋊C₄	—	113	4	no	—
338	C₂²⋊C₄	—	113	4	no	—
339	C₂²⋊C₄	—	113	4	no	—
340	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
341	C₂²⋊C₄	C₂²×D₁₁₃	1	2	yes	—
342	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
343	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
344	C₄²	—	113	4	no	—
345	C₄²	—	113	4	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	16	no	—
360	C₂³	—	113	2	no	—
361	C₂³	—	452	2	no	—
362	C₂³	—	226	2	no	—
363	C₂³	#14268646	1	4	yes	complemented
364	C₂³	C₂³×D₁₁₃	1	2	yes	—
365	C₂³	C₂³×D₁₁₃	1	2	yes	—
366	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
367	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
368	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
369	C₂³	C₂³×D₁₁₃	1	2	yes	—
370	Q₈	—	452	4	no	—
371	D₄	—	2	4	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	8	no	—
374	D₄	—	4	4	no	—
375	D₄	—	452	4	no	—
376	D₄	—	452	4	no	—
377	D₄	—	226	4	no	—
378	D₄	—	226	4	no	—
379	D₄	—	226	8	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	113	2	no	—
383	C₂×C₄	—	113	4	no	—
384	C₂×C₄	—	113	4	no	—
385	C₂×C₄	—	113	4	no	—
386	C₂×C₄	—	452	4	no	—
387	C₂×C₄	—	452	2	no	—
388	C₂×C₄	—	452	4	no	—
389	C₂×C₄	—	452	2	no	—
390	C₂×C₄	—	452	2	no	—
391	C₂×C₄	—	452	4	no	—
392	C₂×C₄	—	226	2	no	—
393	C₂×C₄	—	226	8	no	—
394	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
395	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
396	C₂²	—	2	8	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	8	no	—
409	C₂²	—	4	8	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	904	2	no	—
413	C₂²	—	226	2	no	—
414	C₂²	—	226	4	no	—
415	C₂²	C₂×#14268646	1	2	yes	—
416	C₂²	C₂×#14268646	1	2	yes	—
417	C₂²	C₂×#14268646	1	2	yes	—
418	C₂²	#16813667	1	4	yes	—
419	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	4	no	—
422	C₄	—	226	2	no	—
423	C₄	—	226	4	no	—
424	C₄	—	226	4	no	—
425	C₄	—	226	4	no	—
426	C₂	—	2	2	no	—
427	C₂	—	2	4	no	—
428	C₂	—	2	2	no	—
429	C₂	—	2	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	452	2	no	—
433	C₂	C₂²×#14268646	1	1	yes	characteristic
434	C₂	C₂×#16813667	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	C₂×#120×C₁₁₃	C₂
hypercenter	C₂×#120	D₁₁₃
hypocenter	C₁₁₃	#3490
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. #20299279	C₂	semidirect
2. #20299274	C₂	semidirect
3. #20299242	C₂	semidirect
4. #20299235	C₂	semidirect
5. #20299224	C₂	semidirect
6. #20299183	C₂	semidirect
7. #20299157	C₂	semidirect
8. #20299104	C₂	semidirect
9. C₂×#16813591	C₂	semidirect
10. #20299073	C₂	semidirect
11. #20299071	C₂	semidirect
12. C₂²×C₂²⋊Dic₁₁₃	C₂	semidirect
13. C₂×#120×C₁₁₃	C₂	semidirect
14. C₂×#14268646	C₂²	semidirect
16. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
17. C₂³×Dic₁₁₃	C₂²	semidirect
18. #16813615	C₂²	semidirect
19. #16813615	C₂²	semidirect
20. #16813609	C₂²	semidirect
21. #16813608	C₂²	semidirect
22. #16813606	C₂²	semidirect
23. #16813605	C₂²	semidirect
24. #16813604	C₂²	semidirect
25. #16813603	C₂²	semidirect
26. #16813603	C₂²	semidirect
27. #16813603	C₂²	semidirect
28. #16813601	C₂²	semidirect
29. #16813599	C₂²	semidirect
30. #16813599	C₂²	semidirect
31. #16813599	C₂²	semidirect
32. #16813594	C₂²	semidirect
33. #16813594	C₂²	semidirect
34. #16813594	C₂²	semidirect
35. #16813593	C₂²	semidirect
37. #16813591	C₂²	semidirect
38. #16813591	C₂²	semidirect
39. #16813591	C₂²	semidirect
40. #16813590	C₂²	semidirect
41. D₄×Dic₁₁₃	C₂²	semidirect
42. D₄×Dic₁₁₃	C₂²	semidirect
43. D₄×Dic₁₁₃	C₂²	semidirect
44. C₄×C₂²⋊D₁₁₃	C₂²	semidirect
45. #16813582	C₂²	semidirect
46. #16813582	C₂²	semidirect
47. #16813581	C₂²	semidirect
48. #16813578	C₂²	semidirect
49. #16813578	C₂²	semidirect
53. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
54. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
55. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
56. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
57. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
58. C₂²⋊C₄×D₁₁₃	C₂²	semidirect
61. C₂²×D₄×C₁₁₃	C₂²	semidirect
63. #120×C₁₁₃	C₂²	semidirect
64. #120×C₁₁₃	C₂²	semidirect
66. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
69. C₂×Dic₂₂₆	C₂³	semidirect
76. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
84. C₂²×Dic₁₁₃	C₂³	semidirect
85. C₂×C₄×D₁₁₃	C₂³	semidirect
86. C₄⋊Dic₁₁₃	C₂³	semidirect
87. C₄⋊Dic₁₁₃	C₂³	semidirect
88. #14268626	C₂³	semidirect
89. #14268626	C₂³	semidirect
90. #14268626	C₂³	semidirect
91. #14268626	C₂³	semidirect
102. C₂²⋊Dic₁₁₃	C₂³	semidirect
103. C₂²⋊Dic₁₁₃	C₂³	semidirect
104. #14268624	C₂³	semidirect
105. #14268624	C₂³	semidirect
106. C₄×Dic₁₁₃	C₂³	semidirect
107. C₄×Dic₁₁₃	C₂³	semidirect
142. C₂³×C₁₁₃	#41	semidirect
218. C₁₁₃	#3490	semidirect
228. C₂×#120	D₁₁₃	semidirect
237. C₂²×D₄	C₂×D₁₁₃	semidirect
263. #120	C₂×D₁₁₃	semidirect
264. #120	C₂×D₁₁₃	semidirect
284. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
363. C₂³	#14268646	semidirect

Maximal subgroups

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

subgroup	index
#20299279	2
#20299274	2
#20299242	2
#20299235	2
#20299224	2
#20299183	2
#20299157	2
#20299104	2
C₂×#16813591	2
#20299073	2
#20299071	2
C₂²×C₂²⋊Dic₁₁₃	2
C₂×#120×C₁₁₃	2
#3490	113