Subgroups — C₂×#20299336 #28404689

Order 14464.

1344 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299336	C₂	1	16	yes	maximal, direct product factor
2	C₂×#16813618	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16813617	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16813615	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16813607	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16813606	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16813605	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16813596	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16813595	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16813594	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16813594	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16813593	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16813592	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16813590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16813590	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#121×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁴×D₁₁₃	C₂²	1	1	yes	characteristic
18	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
19	C₂²×D₄₅₂	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂³×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
29	#16813618	C₂²	1	8	yes	complemented
30	#16813617	C₂²	1	8	yes	complemented
31	#16813615	C₂²	1	8	yes	complemented
32	#16813607	C₂²	1	8	yes	complemented
33	#16813606	C₂²	1	8	yes	complemented
34	#16813605	C₂²	1	8	yes	complemented
35	#16813596	C₂²	1	8	yes	complemented
36	#16813595	C₂²	1	8	yes	complemented
37	#16813594	C₂²	1	8	yes	complemented
38	#16813594	C₂²	1	8	yes	complemented
39	#16813593	C₂²	1	8	yes	complemented
40	#16813592	C₂²	1	8	yes	complemented
41	#16813590	C₂²	1	8	yes	complemented
42	#16813590	C₂²	1	8	yes	complemented
43	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#14268626	C₂²	1	1	yes	characteristic, complemented
46	C₂×#14268626	C₂²	1	1	yes	characteristic, complemented
47	C₂×#14268626	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
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, complemented
58	C₂×C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
62	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
63	#121×C₁₁₃	C₂²	1	8	yes	complemented
64	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
67	C₂³×D₁₁₃	—	4	2	no	—
68	C₂³×D₁₁₃	—	4	2	no	—
69	C₂³×D₁₁₃	—	4	2	no	—
70	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
71	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
72	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
73	C₂³×D₁₁₃	C₂³	1	4	yes	—
74	C₂×D₄₅₂	—	4	2	no	—
75	C₂×D₄₅₂	—	4	2	no	—
76	C₂×D₄₅₂	C₂³	1	4	yes	—
77	C₂×D₄₅₂	C₂³	1	4	yes	—
78	C₂×C₂²⋊D₁₁₃	—	4	2	no	—
79	C₂×C₂²⋊D₁₁₃	—	4	2	no	—
80	C₂×C₂²⋊D₁₁₃	—	4	2	no	—
81	C₂×C₂²⋊D₁₁₃	—	4	2	no	—
82	C₂×C₂²⋊D₁₁₃	—	4	2	no	—
83	C₂×C₂²⋊D₁₁₃	—	4	2	no	—
84	C₂×C₂²⋊D₁₁₃	—	4	2	no	—
85	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	complemented
91	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	complemented
92	C₂²×Dic₁₁₃	—	4	2	no	—
93	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
94	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
95	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
96	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
97	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
98	C₂²×Dic₁₁₃	C₂³	1	4	yes	complemented
99	C₂×C₄×D₁₁₃	—	4	2	no	—
100	C₂×C₄×D₁₁₃	C₂³	1	4	yes	complemented
101	C₄⋊Dic₁₁₃	C₂³	1	4	yes	complemented
102	C₄⋊Dic₁₁₃	C₂³	1	4	yes	complemented
103	#14268626	C₂³	1	4	yes	complemented
104	#14268626	C₂³	1	4	yes	complemented
105	#14268626	C₂³	1	4	yes	complemented
106	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
107	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
108	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	complemented
109	#14268624	C₂³	1	4	yes	—
110	#14268624	C₂³	1	4	yes	—
111	#14268624	C₂³	1	4	yes	—
112	#14268624	C₂³	1	4	yes	—
113	#14268624	C₂³	1	4	yes	—
114	#14268624	C₂³	1	4	yes	—
115	#14268624	C₂³	1	4	yes	complemented
116	C₄×Dic₁₁₃	C₂³	1	4	yes	complemented
117	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
118	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
119	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
120	C₂×D₄×C₁₁₃	—	4	2	no	—
121	C₂×D₄×C₁₁₃	—	4	2	no	—
122	C₂×D₄×C₁₁₃	—	4	2	no	—
123	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
124	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
125	C₂×D₄×C₁₁₃	C₂³	1	4	yes	complemented
126	C₂²×C₄×C₁₁₃	—	4	2	no	—
127	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	complemented
132	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	complemented
133	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
134	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	complemented
135	C₂³×C₁₁₃	—	2	2	no	—
136	C₂³×C₁₁₃	—	2	2	no	—
137	C₂³×C₁₁₃	—	2	2	no	—
138	C₂³×C₁₁₃	—	2	2	no	—
139	C₂³×C₁₁₃	—	2	2	no	—
140	C₂³×C₁₁₃	—	2	2	no	—
141	C₂³×C₁₁₃	—	2	2	no	—
142	C₂³×C₁₁₃	—	2	2	no	—
143	C₂³×C₁₁₃	—	2	2	no	—
144	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
145	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
146	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
147	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
148	C₂²×D₁₁₃	—	2	2	no	—
149	C₂²×D₁₁₃	—	2	2	no	—
150	C₂²×D₁₁₃	—	2	2	no	—
151	C₂²×D₁₁₃	—	2	2	no	—
152	C₂²×D₁₁₃	—	2	2	no	—
153	C₂²×D₁₁₃	—	2	2	no	—
154	C₂²×D₁₁₃	—	2	2	no	—
155	C₂²×D₁₁₃	—	2	2	no	—
156	C₂²×D₁₁₃	—	2	2	no	—
157	C₂²×D₁₁₃	—	4	4	no	—
158	C₂²×D₁₁₃	—	4	4	no	—
159	C₂²×D₁₁₃	—	4	4	no	—
160	C₂²×D₁₁₃	—	4	16	no	—
161	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
162	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
163	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
164	D₄×C₁₁₃	—	4	4	no	—
165	D₄×C₁₁₃	—	4	4	no	—
166	D₄×C₁₁₃	—	4	4	no	—
167	C₂×C₄×C₁₁₃	—	2	2	no	—
168	C₂×C₄×C₁₁₃	—	2	2	no	—
169	C₂×C₄×C₁₁₃	—	2	2	no	—
170	C₂×C₄×C₁₁₃	—	2	2	no	—
171	C₂×C₄×C₁₁₃	—	4	4	no	—
172	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
173	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
176	C₂²⋊D₁₁₃	—	4	4	no	—
177	C₂²⋊D₁₁₃	—	4	4	no	—
178	C₂²⋊D₁₁₃	—	4	4	no	—
179	C₂²⋊D₁₁₃	—	4	4	no	—
180	C₂²⋊D₁₁₃	—	4	4	no	—
181	C₂²⋊D₁₁₃	—	4	4	no	—
182	C₂²⋊D₁₁₃	—	4	4	no	—
183	C₂×Dic₁₁₃	—	2	2	no	—
184	C₂×Dic₁₁₃	—	2	2	no	—
185	C₂×Dic₁₁₃	—	2	2	no	—
186	C₂×Dic₁₁₃	—	2	2	no	—
187	C₂×Dic₁₁₃	—	2	2	no	—
188	C₂×Dic₁₁₃	—	4	4	no	—
189	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
190	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
191	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
192	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
193	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
194	D₄₅₂	—	4	4	no	—
195	D₄₅₂	—	4	4	no	—
196	C₄×D₁₁₃	—	4	4	no	—
197	C₂²×C₁₁₃	—	2	2	no	—
198	C₂²×C₁₁₃	—	2	2	no	—
199	C₂²×C₁₁₃	—	2	2	no	—
200	C₂²×C₁₁₃	—	2	2	no	—
201	C₂²×C₁₁₃	—	2	2	no	—
202	C₂²×C₁₁₃	—	2	2	no	—
203	C₂²×C₁₁₃	—	2	2	no	—
204	C₂²×C₁₁₃	—	2	2	no	—
205	C₂²×C₁₁₃	—	2	2	no	—
206	C₂²×C₁₁₃	—	4	4	no	—
207	C₂²×C₁₁₃	—	4	4	no	—
208	C₂²×C₁₁₃	—	4	4	no	—
209	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
210	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
211	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
212	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
213	C₂×D₁₁₃	—	2	2	no	—
214	C₂×D₁₁₃	—	2	2	no	—
215	C₂×D₁₁₃	—	2	2	no	—
216	C₂×D₁₁₃	—	2	2	no	—
217	C₂×D₁₁₃	—	2	2	no	—
218	C₂×D₁₁₃	—	2	2	no	—
219	C₂×D₁₁₃	—	2	2	no	—
220	C₂×D₁₁₃	—	2	2	no	—
221	C₂×D₁₁₃	—	2	2	no	—
222	C₂×D₁₁₃	—	4	16	no	—
223	C₂×D₁₁₃	—	4	4	no	—
224	C₂×D₁₁₃	—	4	4	no	—
225	C₂×D₁₁₃	—	4	4	no	—
226	C₄×C₁₁₃	—	2	2	no	—
227	C₄×C₁₁₃	—	2	2	no	—
228	C₄×C₁₁₃	—	2	2	no	—
229	C₄×C₁₁₃	—	2	2	no	—
230	Dic₁₁₃	—	2	2	no	—
231	Dic₁₁₃	—	2	2	no	—
232	Dic₁₁₃	—	2	2	no	—
233	Dic₁₁₃	—	2	2	no	—
234	Dic₁₁₃	—	2	2	no	—
235	C₂×C₁₁₃	—	4	2	no	—
236	C₂×C₁₁₃	—	4	2	no	—
237	C₂×C₁₁₃	—	4	2	no	—
238	C₂×C₁₁₃	#560	1	4	yes	complemented
239	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	D₁₁₃	—	4	2	no	—
243	D₁₁₃	—	4	2	no	—
244	D₁₁₃	—	4	2	no	—
245	C₂×#560	—	113	1	no	maximal, Sylow
246	C₁₁₃	C₂×#560	1	1	yes	characteristic, complemented, Sylow
247	#560	—	113	16	no	—
248	C₂×#127	—	113	1	no	—
249	C₂×#126	—	113	1	no	—
250	C₂×#126	—	113	1	no	—
251	C₂×#123	—	113	1	no	—
252	C₂×#123	—	113	1	no	—
253	C₂×#123	—	113	1	no	—
254	C₂×#121	—	113	1	no	—
255	C₂×#121	—	113	1	no	—
256	C₂×#121	—	113	1	no	—
257	C₂×#121	—	113	1	no	—
258	C₂×#121	—	113	1	no	—
259	C₂×#121	D₁₁₃	1	1	yes	characteristic, complemented
260	C₂×#120	—	113	1	no	—
261	C₂×#120	—	113	1	no	—
262	C₂×#120	—	113	1	no	—
263	C₂⁵	—	113	1	no	—
264	C₂²×D₄	—	113	1	no	—
265	C₂²×D₄	—	113	1	no	—
266	C₂²×D₄	—	113	1	no	—
267	C₂²×D₄	—	113	1	no	—
268	C₂²×D₄	—	113	1	no	—
269	C₂²×D₄	—	113	1	no	—
270	C₂²×D₄	—	113	1	no	—
271	C₂²×D₄	—	113	1	no	—
272	C₂²×D₄	—	113	1	no	—
273	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
274	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
275	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
276	C₂³×C₄	—	113	1	no	—
277	C₂³×C₄	—	113	1	no	—
278	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
279	#127	—	113	8	no	—
280	#126	—	113	8	no	—
281	#126	—	113	8	no	—
282	#123	—	113	8	no	—
283	#123	—	113	8	no	—
284	#123	—	113	8	no	—
285	#121	—	113	8	no	—
286	#121	—	113	8	no	—
287	#121	—	113	8	no	—
288	#121	—	113	8	no	—
289	#121	—	113	8	no	—
290	#121	C₂×D₁₁₃	1	8	yes	complemented
291	#120	—	113	8	no	—
292	#120	—	113	8	no	—
293	#120	—	113	8	no	—
294	C₂×C₄⋊C₄	—	113	1	no	—
295	C₂×C₄⋊C₄	—	113	1	no	—
296	C₂×C₄⋊C₄	—	113	1	no	—
297	C₂×C₄⋊C₄	—	113	1	no	—
298	C₂×C₄⋊C₄	—	113	1	no	—
299	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
300	C₂×C₂²⋊C₄	—	113	1	no	—
301	C₂×C₂²⋊C₄	—	113	1	no	—
302	C₂×C₂²⋊C₄	—	113	1	no	—
303	C₂×C₂²⋊C₄	—	113	1	no	—
304	C₂×C₂²⋊C₄	—	113	1	no	—
305	C₂×C₂²⋊C₄	—	113	1	no	—
306	C₂×C₂²⋊C₄	—	113	1	no	—
307	C₂×C₂²⋊C₄	—	113	1	no	—
308	C₂×C₂²⋊C₄	—	113	1	no	—
309	C₂×C₂²⋊C₄	—	113	1	no	—
310	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic, complemented
312	C₂×C₄²	—	113	1	no	—
313	C₂⁴	—	113	4	no	—
314	C₂⁴	—	113	1	no	—
315	C₂⁴	—	113	1	no	—
316	C₂⁴	—	113	1	no	—
317	C₂⁴	—	452	2	no	—
318	C₂⁴	—	452	2	no	—
319	C₂⁴	—	452	2	no	—
320	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
321	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
322	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	113	4	no	—
327	C₂×D₄	—	113	4	no	—
328	C₂×D₄	—	113	4	no	—
329	C₂×D₄	—	113	4	no	—
330	C₂×D₄	—	113	4	no	—
331	C₂×D₄	—	113	4	no	—
332	C₂×D₄	—	113	4	no	—
333	C₂×D₄	—	113	4	no	—
334	C₂×D₄	—	113	4	no	—
335	C₂×D₄	—	452	2	no	—
336	C₂×D₄	—	452	2	no	—
337	C₂×D₄	—	452	2	no	—
338	C₂×D₄	—	452	2	no	—
339	C₂×D₄	—	452	2	no	—
340	C₂×D₄	—	452	2	no	—
341	C₂×D₄	—	452	2	no	—
342	C₂×D₄	—	452	2	no	—
343	C₂×D₄	—	452	2	no	—
344	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
345	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
346	C₂×D₄	C₂²×D₁₁₃	1	4	yes	complemented
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	113	4	no	—
349	C₂²×C₄	—	113	1	no	—
350	C₂²×C₄	—	113	1	no	—
351	C₂²×C₄	—	113	1	no	—
352	C₂²×C₄	—	113	1	no	—
353	C₂²×C₄	—	113	1	no	—
354	C₂²×C₄	—	113	4	no	—
355	C₂²×C₄	—	452	2	no	—
356	C₂²×C₄	—	452	2	no	—
357	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
359	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	complemented
362	C₄⋊C₄	—	113	4	no	—
363	C₄⋊C₄	—	113	4	no	—
364	C₄⋊C₄	—	113	4	no	—
365	C₄⋊C₄	—	113	4	no	—
366	C₄⋊C₄	—	113	4	no	—
367	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	complemented
368	C₂²⋊C₄	—	113	4	no	—
369	C₂²⋊C₄	—	113	4	no	—
370	C₂²⋊C₄	—	113	4	no	—
371	C₂²⋊C₄	—	113	4	no	—
372	C₂²⋊C₄	—	113	4	no	—
373	C₂²⋊C₄	—	113	4	no	—
374	C₂²⋊C₄	—	113	4	no	—
375	C₂²⋊C₄	—	113	4	no	—
376	C₂²⋊C₄	—	113	4	no	—
377	C₂²⋊C₄	—	113	4	no	—
378	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
379	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	complemented
380	C₄²	—	113	4	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	113	2	no	—
391	C₂³	—	113	2	no	—
392	C₂³	—	113	2	no	—
393	C₂³	—	452	4	no	—
394	C₂³	—	452	4	no	—
395	C₂³	—	452	4	no	—
396	C₂³	—	452	16	no	—
397	C₂³	—	226	2	no	—
398	C₂³	—	226	2	no	—
399	C₂³	—	226	2	no	—
400	C₂³	—	226	2	no	—
401	C₂³	—	226	2	no	—
402	C₂³	—	226	2	no	—
403	C₂³	—	226	2	no	—
404	C₂³	—	226	2	no	—
405	C₂³	—	226	2	no	—
406	C₂³	C₂³×D₁₁₃	1	2	yes	—
407	C₂³	C₂³×D₁₁₃	1	2	yes	—
408	C₂³	C₂³×D₁₁₃	1	2	yes	—
409	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
410	D₄	—	4	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	452	4	no	—
414	D₄	—	452	4	no	—
415	D₄	—	452	4	no	—
416	D₄	—	452	4	no	—
417	D₄	—	452	4	no	—
418	D₄	—	452	4	no	—
419	D₄	—	452	4	no	—
420	D₄	—	452	4	no	—
421	D₄	—	452	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	113	2	no	—
428	C₂×C₄	—	113	2	no	—
429	C₂×C₄	—	113	2	no	—
430	C₂×C₄	—	113	2	no	—
431	C₂×C₄	—	113	2	no	—
432	C₂×C₄	—	452	4	no	—
433	C₂×C₄	—	452	4	no	—
434	C₂×C₄	—	226	2	no	—
435	C₂×C₄	—	226	2	no	—
436	C₂×C₄	—	226	2	no	—
437	C₂×C₄	—	226	2	no	—
438	C₂×C₄	—	226	2	no	—
439	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
440	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
441	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
442	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	452	16	no	—
456	C₂²	—	452	4	no	—
457	C₂²	—	452	4	no	—
458	C₂²	—	452	4	no	—
459	C₂²	—	226	2	no	—
460	C₂²	—	226	2	no	—
461	C₂²	—	226	2	no	—
462	C₂²	—	226	2	no	—
463	C₂²	—	226	2	no	—
464	C₂²	—	226	2	no	—
465	C₂²	—	226	2	no	—
466	C₂²	—	226	2	no	—
467	C₂²	—	226	2	no	—
468	C₂²	#16813667	1	2	yes	—
469	C₂²	#16813667	1	2	yes	—
470	C₂²	#16813668	1	2	yes	—
471	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	226	2	no	—
477	C₄	—	226	2	no	—
478	C₄	—	226	2	no	—
479	C₄	—	226	2	no	—
480	C₄	—	226	2	no	—
481	C₂	—	4	2	no	—
482	C₂	—	4	2	no	—
483	C₂	—	4	2	no	—
484	C₂	—	452	2	no	—
485	C₂	—	452	2	no	—
486	C₂	—	452	2	no	—
487	C₂	#20299336	1	4	yes	direct product factor
488	C₂	C₂×#16813667	1	1	yes	characteristic
489	C₂	C₂×#16813667	1	1	yes	characteristic
490	C₂	C₂×#16813668	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₁₃
commutator, cosocle	C₂²×C₁₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₁₃
Fitting	C₂×#121×C₁₁₃	C₂
socle	C₂³×C₁₁₃	C₂⁴
hypercenter	C₂×#121	D₁₁₃
hypocenter	C₁₁₃	C₂×#560
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. #20299336	C₂	direct (N × H)
2. C₂×#16813618	C₂	semidirect
3. C₂×#16813617	C₂	semidirect
4. C₂×#16813615	C₂	semidirect
5. C₂×#16813607	C₂	semidirect
6. C₂×#16813606	C₂	semidirect
7. C₂×#16813605	C₂	semidirect
8. C₂×#16813596	C₂	semidirect
9. C₂×#16813595	C₂	semidirect
10. C₂×#16813594	C₂	semidirect
11. C₂×#16813594	C₂	semidirect
12. C₂×#16813593	C₂	semidirect
13. C₂×#16813592	C₂	semidirect
14. C₂×#16813590	C₂	semidirect
15. C₂×#16813590	C₂	semidirect
16. C₂×#121×C₁₁₃	C₂	semidirect
25. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
26. C₂²×C₂²⋊D₁₁₃	C₂²	semidirect
27. C₂³×Dic₁₁₃	C₂²	semidirect
28. C₂²×C₄×D₁₁₃	C₂²	semidirect
29. #16813618	C₂²	semidirect
30. #16813617	C₂²	semidirect
31. #16813615	C₂²	semidirect
32. #16813607	C₂²	semidirect
33. #16813606	C₂²	semidirect
34. #16813605	C₂²	semidirect
35. #16813596	C₂²	semidirect
36. #16813595	C₂²	semidirect
37. #16813594	C₂²	semidirect
38. #16813594	C₂²	semidirect
39. #16813593	C₂²	semidirect
40. #16813592	C₂²	semidirect
41. #16813590	C₂²	semidirect
42. #16813590	C₂²	semidirect
43. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
44. C₂×C₄⋊Dic₁₁₃	C₂²	semidirect
45. C₂×#14268626	C₂²	semidirect
46. C₂×#14268626	C₂²	semidirect
47. C₂×#14268626	C₂²	semidirect
50. C₂×C₂²⋊Dic₁₁₃	C₂²	semidirect
57. C₂×#14268624	C₂²	semidirect
58. C₂×C₄×Dic₁₁₃	C₂²	semidirect
61. C₂²×D₄×C₁₁₃	C₂²	semidirect
62. C₂³×C₄×C₁₁₃	C₂²	semidirect
63. #121×C₁₁₃	C₂²	semidirect
64. C₂×C₄⋊C₄×C₁₁₃	C₂²	semidirect
66. C₂×C₂²⋊C₄×C₁₁₃	C₂²	semidirect
90. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
91. C₂×C₂²⋊D₁₁₃	C₂³	semidirect
98. C₂²×Dic₁₁₃	C₂³	semidirect
100. C₂×C₄×D₁₁₃	C₂³	semidirect
101. C₄⋊Dic₁₁₃	C₂³	semidirect
102. C₄⋊Dic₁₁₃	C₂³	semidirect
103. #14268626	C₂³	semidirect
104. #14268626	C₂³	semidirect
105. #14268626	C₂³	semidirect
108. C₂²⋊Dic₁₁₃	C₂³	semidirect
115. #14268624	C₂³	semidirect
116. C₄×Dic₁₁₃	C₂³	semidirect
125. C₂×D₄×C₁₁₃	C₂³	semidirect
131. C₂²×C₄×C₁₁₃	C₂³	semidirect
132. C₄⋊C₄×C₁₁₃	C₂³	semidirect
134. C₂²⋊C₄×C₁₁₃	C₂³	semidirect
238. C₂×C₁₁₃	#560	semidirect
246. C₁₁₃	C₂×#560	semidirect
259. C₂×#121	D₁₁₃	semidirect
275. C₂²×D₄	C₂×D₁₁₃	semidirect
278. C₂³×C₄	C₂×D₁₁₃	semidirect
290. #121	C₂×D₁₁₃	semidirect
299. C₂×C₄⋊C₄	C₂×D₁₁₃	semidirect
311. C₂×C₂²⋊C₄	C₂×D₁₁₃	semidirect
346. C₂×D₄	C₂²×D₁₁₃	semidirect
361. C₂²×C₄	C₂²×D₁₁₃	semidirect
367. C₄⋊C₄	C₂²×D₁₁₃	semidirect
379. C₂²⋊C₄	C₂²×D₁₁₃	semidirect
487. C₂	#20299336	direct (N × H)

Maximal subgroups

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

subgroup	index
#20299336	2
C₂×#16813618	2
C₂×#16813617	2
C₂×#16813615	2
C₂×#16813607	2
C₂×#16813606	2
C₂×#16813605	2
C₂×#16813596	2
C₂×#16813595	2
C₂×#16813594	2
C₂×#16813593	2
C₂×#16813592	2
C₂×#16813590	2
C₂×#121×C₁₁₃	2
C₂×#560	113

Subgroups — C2×#20299336 #28404689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20299336 #28404689