Subgroups — C₂×#20299196 #28403926

Order 14464.

1144 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299196	C₂	1	16	yes	maximal, direct product factor
2	C₂×#16813617	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16813616	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16813612	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16813607	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16813607	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16813607	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16813607	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16813602	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16813600	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16813600	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16813597	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄×D₄₅₂	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16813584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄⋊C₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#125×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic
18	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
19	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
20	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
26	#16813617	C₂²	1	8	yes	complemented
27	#16813616	C₂²	1	8	yes	complemented
28	#16813612	C₂²	1	8	yes	complemented
29	#16813607	C₂²	1	8	yes	complemented
30	#16813607	C₂²	1	8	yes	complemented
31	#16813607	C₂²	1	8	yes	complemented
32	#16813607	C₂²	1	8	yes	complemented
33	#16813602	C₂²	1	8	yes	complemented
34	#16813600	C₂²	1	8	yes	complemented
35	#16813600	C₂²	1	8	yes	complemented
36	#16813597	C₂²	1	8	yes	—
37	C₄×D₄₅₂	C₂²	1	8	yes	complemented
38	#16813584	C₂²	1	8	yes	complemented
39	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
41	C₂×#14268626	C₂²	1	1	yes	characteristic
42	C₂×#14268626	C₂²	1	1	yes	characteristic
43	C₂×#14268626	C₂²	1	1	yes	characteristic
44	C₂×#14268626	C₂²	1	1	yes	characteristic
45	C₂×#14268626	C₂²	1	1	yes	characteristic
46	C₂×#14268626	C₂²	1	1	yes	characteristic
47	C₄⋊C₄×D₁₁₃	C₂²	1	8	yes	complemented
48	C₂×#14268624	C₂²	1	1	yes	characteristic
49	C₂×#14268624	C₂²	1	1	yes	characteristic
50	C₂×#14268624	C₂²	1	1	yes	characteristic
51	C₂×#14268624	C₂²	1	1	yes	characteristic
52	C₂×#14268624	C₂²	1	1	yes	characteristic
53	C₂×#14268624	C₂²	1	1	yes	characteristic
54	C₂×#14268624	C₂²	1	1	yes	characteristic
55	C₂×#14268624	C₂²	1	1	yes	characteristic
56	C₂×#14268624	C₂²	1	1	yes	characteristic
57	C₂×#14268624	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
59	#125×C₁₁₃	C₂²	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
67	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
68	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
69	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
70	C₂×Dic₂₂₆	—	4	2	no	—
71	C₂×Dic₂₂₆	C₂³	1	4	yes	—
72	C₂×D₄₅₂	—	2	4	no	—
73	C₂×D₄₅₂	—	2	4	no	—
74	C₂×D₄₅₂	—	4	2	no	—
75	C₂×D₄₅₂	C₂³	1	4	yes	—
76	C₂×D₄₅₂	C₂³	1	4	yes	—
77	C₂×D₄₅₂	C₂³	1	4	yes	—
78	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
79	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
80	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
81	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₄×D₁₁₃	—	2	4	no	—
84	C₂×C₄×D₁₁₃	—	4	2	no	—
85	C₂×C₄×D₁₁₃	—	4	2	no	—
86	C₂×C₄×D₁₁₃	—	4	2	no	—
87	C₂×C₄×D₁₁₃	—	4	2	no	—
88	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
89	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
90	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
91	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
92	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
93	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
94	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
95	#14268626	C₂³	1	4	yes	—
96	#14268626	C₂³	1	4	yes	—
97	#14268626	C₂³	1	4	yes	—
98	#14268626	C₂³	1	4	yes	—
99	#14268626	C₂³	1	4	yes	—
100	#14268626	C₂³	1	4	yes	—
101	#14268624	C₂³	1	4	yes	—
102	#14268624	C₂³	1	4	yes	—
103	#14268624	C₂³	1	4	yes	—
104	#14268624	C₂³	1	4	yes	—
105	#14268624	C₂³	1	4	yes	—
106	#14268624	C₂³	1	4	yes	—
107	#14268624	C₂³	1	4	yes	—
108	#14268624	C₂³	1	4	yes	—
109	#14268624	C₂³	1	4	yes	—
110	#14268624	C₂³	1	4	yes	—
111	C₄×Dic₁₁₃	C₂³	1	4	yes	—
112	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
119	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
120	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
121	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
122	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
123	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
124	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
125	C₄²×C₁₁₃	C₂³	1	4	yes	—
126	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
127	C₂²×D₁₁₃	—	2	2	no	—
128	C₂²×D₁₁₃	—	2	2	no	—
129	C₂²×D₁₁₃	—	2	2	no	—
130	C₂²×D₁₁₃	—	2	2	no	—
131	C₂²×D₁₁₃	—	2	2	no	—
132	C₂²×D₁₁₃	—	2	2	no	—
133	C₂²×D₁₁₃	—	2	2	no	—
134	C₂²×D₁₁₃	—	2	2	no	—
135	C₂²×D₁₁₃	#41	1	4	yes	—
136	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
137	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
138	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
139	C₂×C₄×C₁₁₃	—	2	2	no	—
140	C₂×C₄×C₁₁₃	—	2	2	no	—
141	C₂×C₄×C₁₁₃	—	2	2	no	—
142	C₂×C₄×C₁₁₃	—	2	2	no	—
143	C₂×C₄×C₁₁₃	—	2	2	no	—
144	C₂×C₄×C₁₁₃	—	2	2	no	—
145	C₂×C₄×C₁₁₃	—	2	2	no	—
146	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
147	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
148	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
149	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
150	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
151	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
152	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
153	C₂×Dic₁₁₃	—	2	2	no	—
154	C₂×Dic₁₁₃	—	2	2	no	—
155	C₂×Dic₁₁₃	—	2	2	no	—
156	C₂×Dic₁₁₃	—	2	2	no	—
157	C₂×Dic₁₁₃	—	2	2	no	—
158	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
159	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
160	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
161	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
162	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
163	D₄₅₂	—	2	8	no	—
164	D₄₅₂	—	2	8	no	—
165	D₄₅₂	—	4	4	no	—
166	C₄×D₁₁₃	—	2	8	no	—
167	C₄×D₁₁₃	—	4	4	no	—
168	C₄×D₁₁₃	—	4	4	no	—
169	C₄×D₁₁₃	—	4	4	no	—
170	C₄×D₁₁₃	—	4	4	no	—
171	Dic₂₂₆	—	4	4	no	—
172	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
173	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
174	C₂²×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
175	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
176	C₂×D₁₁₃	—	2	8	no	—
177	C₂×D₁₁₃	—	2	2	no	—
178	C₂×D₁₁₃	—	2	2	no	—
179	C₂×D₁₁₃	—	2	2	no	—
180	C₂×D₁₁₃	—	2	2	no	—
181	C₂×D₁₁₃	—	2	2	no	—
182	C₂×D₁₁₃	—	2	2	no	—
183	C₂×D₁₁₃	—	2	2	no	—
184	C₂×D₁₁₃	—	2	2	no	—
185	C₂×D₁₁₃	—	4	4	no	—
186	C₂×D₁₁₃	—	4	4	no	—
187	C₂×D₁₁₃	C₂×#41	1	4	yes	—
188	C₄×C₁₁₃	—	2	2	no	—
189	C₄×C₁₁₃	—	2	2	no	—
190	C₄×C₁₁₃	—	2	2	no	—
191	C₄×C₁₁₃	—	2	2	no	—
192	C₄×C₁₁₃	—	2	2	no	—
193	C₄×C₁₁₃	—	2	2	no	—
194	C₄×C₁₁₃	—	2	2	no	—
195	Dic₁₁₃	—	2	2	no	—
196	Dic₁₁₃	—	2	2	no	—
197	Dic₁₁₃	—	2	2	no	—
198	Dic₁₁₃	—	2	2	no	—
199	Dic₁₁₃	—	2	2	no	—
200	C₂×C₁₁₃	#539	1	4	yes	complemented
201	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
202	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
204	D₁₁₃	—	2	4	no	—
205	D₁₁₃	—	4	2	no	—
206	D₁₁₃	—	4	2	no	—
207	C₂×#539	—	113	1	no	maximal, Sylow
208	C₁₁₃	C₂×#539	1	1	yes	characteristic, complemented, Sylow
209	#539	—	113	16	no	—
210	C₂×#126	—	113	1	no	—
211	C₂×#126	—	113	1	no	—
212	C₂×#125	—	113	1	no	—
213	C₂×#125	D₁₁₃	1	1	yes	characteristic, complemented
214	C₂×#123	—	113	1	no	—
215	C₂×#123	—	113	1	no	—
216	C₂×#123	—	113	1	no	—
217	C₂×#123	—	113	1	no	—
218	C₂×C₂²⋊Q₈	—	113	1	no	—
219	C₂×C₂²⋊Q₈	—	113	1	no	—
220	C₂×C₂²⋊Q₈	—	113	1	no	—
221	C₂×#121	—	113	1	no	—
222	C₂×C₄×D₄	—	113	1	no	—
223	C₂×C₄×D₄	—	113	1	no	—
224	C₂²×C₄⋊C₄	—	113	1	no	—
225	C₂²×Q₈	—	113	1	no	—
226	C₂²×D₄	—	113	1	no	—
227	C₂²×D₄	—	113	1	no	—
228	C₂²×D₄	—	113	1	no	—
229	C₂³×C₄	—	113	1	no	—
230	C₂³×C₄	—	113	1	no	—
231	C₂³×C₄	—	113	1	no	—
232	C₂³×C₄	—	113	1	no	—
233	C₂³×C₄	—	113	1	no	—
234	#126	—	113	8	no	—
235	#126	—	113	8	no	—
236	#125	—	113	8	no	—
237	#125	C₂×D₁₁₃	1	8	yes	complemented
238	#123	—	113	8	no	—
239	#123	—	113	8	no	—
240	#123	—	113	8	no	—
241	#123	—	113	8	no	—
242	C₂²⋊Q₈	—	113	8	no	—
243	C₂²⋊Q₈	—	113	8	no	—
244	C₂²⋊Q₈	—	113	8	no	—
245	#121	—	113	8	no	—
246	C₄×D₄	—	113	8	no	—
247	C₄×D₄	—	113	8	no	—
248	C₂×C₄⋊C₄	—	113	1	no	—
249	C₂×C₄⋊C₄	—	113	1	no	—
250	C₂×C₄⋊C₄	—	113	1	no	—
251	C₂×C₄⋊C₄	—	113	1	no	—
252	C₂×C₄⋊C₄	—	113	1	no	—
253	C₂×C₄⋊C₄	—	113	1	no	—
254	C₂×C₄⋊C₄	—	113	1	no	—
255	C₂×C₄⋊C₄	—	113	1	no	—
256	C₂×C₄⋊C₄	—	113	8	no	—
257	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	113	1	no	—
264	C₂×C₂²⋊C₄	—	113	1	no	—
265	C₂×C₂²⋊C₄	—	113	1	no	—
266	C₂×C₂²⋊C₄	—	113	1	no	—
267	C₂×C₂²⋊C₄	—	113	1	no	—
268	C₂×C₂²⋊C₄	—	113	1	no	—
269	C₂×C₂²⋊C₄	—	113	1	no	—
270	C₂×C₂²⋊C₄	—	113	1	no	—
271	C₂×C₂²⋊C₄	—	113	1	no	—
272	C₂×C₂²⋊C₄	—	113	1	no	—
273	C₂×C₄²	—	113	1	no	—
274	C₂×C₄²	C₂×D₁₁₃	1	1	yes	characteristic
275	C₂⁴	—	113	1	no	—
276	C₂⁴	—	113	1	no	—
277	C₂⁴	—	113	1	no	—
278	C₂×Q₈	—	113	4	no	—
279	C₂×Q₈	—	452	2	no	—
280	C₂×D₄	—	113	4	no	—
281	C₂×D₄	—	113	4	no	—
282	C₂×D₄	—	113	4	no	—
283	C₂×D₄	—	452	2	no	—
284	C₂×D₄	—	226	4	no	—
285	C₂×D₄	—	226	4	no	—
286	C₂²×C₄	—	113	1	no	—
287	C₂²×C₄	—	113	1	no	—
288	C₂²×C₄	—	113	1	no	—
289	C₂²×C₄	—	113	1	no	—
290	C₂²×C₄	—	113	1	no	—
291	C₂²×C₄	—	113	4	no	—
292	C₂²×C₄	—	113	4	no	—
293	C₂²×C₄	—	113	4	no	—
294	C₂²×C₄	—	113	4	no	—
295	C₂²×C₄	—	113	4	no	—
296	C₂²×C₄	—	452	2	no	—
297	C₂²×C₄	—	452	2	no	—
298	C₂²×C₄	—	452	2	no	—
299	C₂²×C₄	—	452	2	no	—
300	C₂²×C₄	—	226	4	no	—
301	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
308	C₄⋊C₄	—	113	4	no	—
309	C₄⋊C₄	—	113	4	no	—
310	C₄⋊C₄	—	113	4	no	—
311	C₄⋊C₄	—	113	4	no	—
312	C₄⋊C₄	—	113	4	no	—
313	C₄⋊C₄	—	113	4	no	—
314	C₄⋊C₄	—	113	4	no	—
315	C₄⋊C₄	—	113	4	no	—
316	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
317	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
318	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
319	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
320	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
321	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
322	C₂²⋊C₄	—	113	4	no	—
323	C₂²⋊C₄	—	113	4	no	—
324	C₂²⋊C₄	—	113	4	no	—
325	C₂²⋊C₄	—	113	4	no	—
326	C₂²⋊C₄	—	113	4	no	—
327	C₂²⋊C₄	—	113	4	no	—
328	C₂²⋊C₄	—	113	4	no	—
329	C₂²⋊C₄	—	113	4	no	—
330	C₂²⋊C₄	—	113	4	no	—
331	C₂²⋊C₄	—	113	4	no	—
332	C₄²	—	113	4	no	—
333	C₄²	C₂²×D₁₁₃	1	4	yes	—
334	C₂³	—	113	4	no	—
335	C₂³	—	113	2	no	—
336	C₂³	—	113	2	no	—
337	C₂³	—	113	2	no	—
338	C₂³	—	226	2	no	—
339	C₂³	—	226	2	no	—
340	C₂³	—	226	2	no	—
341	C₂³	—	226	2	no	—
342	C₂³	—	226	2	no	—
343	C₂³	—	226	2	no	—
344	C₂³	—	226	2	no	—
345	C₂³	—	226	2	no	—
346	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
347	Q₈	—	452	4	no	—
348	D₄	—	452	4	no	—
349	D₄	—	226	8	no	—
350	D₄	—	226	8	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	113	2	no	—
359	C₂×C₄	—	113	2	no	—
360	C₂×C₄	—	113	2	no	—
361	C₂×C₄	—	113	2	no	—
362	C₂×C₄	—	113	2	no	—
363	C₂×C₄	—	452	4	no	—
364	C₂×C₄	—	452	4	no	—
365	C₂×C₄	—	452	4	no	—
366	C₂×C₄	—	452	4	no	—
367	C₂×C₄	—	226	8	no	—
368	C₂×C₄	—	226	2	no	—
369	C₂×C₄	—	226	2	no	—
370	C₂×C₄	—	226	2	no	—
371	C₂×C₄	—	226	2	no	—
372	C₂×C₄	—	226	2	no	—
373	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
374	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
375	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
376	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
377	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
378	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
379	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
380	C₂²	—	113	4	no	—
381	C₂²	—	452	4	no	—
382	C₂²	—	452	4	no	—
383	C₂²	—	226	2	no	—
384	C₂²	—	226	2	no	—
385	C₂²	—	226	2	no	—
386	C₂²	—	226	2	no	—
387	C₂²	—	226	2	no	—
388	C₂²	—	226	2	no	—
389	C₂²	—	226	2	no	—
390	C₂²	—	226	2	no	—
391	C₂²	—	226	8	no	—
392	C₂²	#41×D₁₁₃	1	2	yes	—
393	C₂²	#16813668	1	2	yes	—
394	C₂²	#16813670	1	2	yes	—
395	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	226	2	no	—
404	C₄	—	226	2	no	—
405	C₄	—	226	2	no	—
406	C₄	—	226	2	no	—
407	C₄	—	226	2	no	—
408	C₂	—	452	2	no	—
409	C₂	—	452	2	no	—
410	C₂	—	226	4	no	—
411	C₂	#20299196	1	4	yes	direct product factor
412	C₂	C₂×#41×D₁₁₃	1	1	yes	characteristic
413	C₂	C₂×#16813668	1	1	yes	characteristic
414	C₂	C₂×#16813670	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₁₃
commutator, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	C₂×#125×C₁₁₃	C₂
socle	C₂³×C₁₁₃	C₂⁴
prime radical	C₂×#16813597	C₂
hypercenter	C₂×#125	D₁₁₃
hypocenter	C₁₁₃	C₂×#539
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
1. #20299196	C₂	direct (N × H)
2. C₂×#16813617	C₂	semidirect
3. C₂×#16813616	C₂	semidirect
4. C₂×#16813612	C₂	semidirect
5. C₂×#16813607	C₂	semidirect
6. C₂×#16813607	C₂	semidirect
7. C₂×#16813607	C₂	semidirect
8. C₂×#16813607	C₂	semidirect
9. C₂×#16813602	C₂	semidirect
10. C₂×#16813600	C₂	semidirect
11. C₂×#16813600	C₂	semidirect
13. C₂×C₄×D₄₅₂	C₂	semidirect
14. C₂×#16813584	C₂	semidirect
15. C₂×C₄⋊C₄×D₁₁₃	C₂	semidirect
16. C₂×#125×C₁₁₃	C₂	semidirect
26. #16813617	C₂²	semidirect
27. #16813616	C₂²	semidirect
28. #16813612	C₂²	semidirect
29. #16813607	C₂²	semidirect
30. #16813607	C₂²	semidirect
31. #16813607	C₂²	semidirect
32. #16813607	C₂²	semidirect
33. #16813602	C₂²	semidirect
34. #16813600	C₂²	semidirect
35. #16813600	C₂²	semidirect
37. C₄×D₄₅₂	C₂²	semidirect
38. #16813584	C₂²	semidirect
47. C₄⋊C₄×D₁₁₃	C₂²	semidirect
59. #125×C₁₁₃	C₂²	semidirect
200. C₂×C₁₁₃	#539	semidirect
208. C₁₁₃	C₂×#539	semidirect
213. C₂×#125	D₁₁₃	semidirect
237. #125	C₂×D₁₁₃	semidirect
411. C₂	#20299196	direct (N × H)

Maximal subgroups

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

subgroup	index
#20299196	2
C₂×#16813617	2
C₂×#16813616	2
C₂×#16813612	2
C₂×#16813607	2
C₂×#16813602	2
C₂×#16813600	2
C₂×#16813597	2
C₂×C₄×D₄₅₂	2
C₂×#16813584	2
C₂×C₄⋊C₄×D₁₁₃	2
C₂×#125×C₁₁₃	2
C₂×#539	113

Subgroups — C2×#20299196 #28403926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20299196 #28403926