Subgroups — C₂×#20299343 #28404698

Order 14464.

1152 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299343	C₂	1	16	yes	maximal, direct product factor
2	C₂×#16813612	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16813609	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16813608	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16813605	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16813604	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16813603	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#16813603	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#16813601	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16813600	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16813599	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#16813599	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16813594	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16813594	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#16813593	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#121×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic
18	C₂²×Dic₂₂₆	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊D₁₁₃	C₂²	1	1	yes	characteristic
22	C₂³×Dic₁₁₃	C₂²	1	1	yes	characteristic
23	C₂³×Dic₁₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
25	#16813612	C₂²	1	8	yes	complemented
26	#16813609	C₂²	1	8	yes	complemented
27	#16813608	C₂²	1	8	yes	complemented
28	#16813605	C₂²	1	8	yes	complemented
29	#16813604	C₂²	1	8	yes	complemented
30	#16813603	C₂²	1	8	yes	complemented
31	#16813603	C₂²	1	8	yes	complemented
32	#16813601	C₂²	1	8	yes	complemented
33	#16813600	C₂²	1	8	yes	complemented
34	#16813599	C₂²	1	8	yes	complemented
35	#16813599	C₂²	1	8	yes	complemented
36	#16813594	C₂²	1	8	yes	complemented
37	#16813594	C₂²	1	8	yes	complemented
38	#16813593	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	C₂×#14268626	C₂²	1	1	yes	characteristic
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
51	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₁₁₃	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	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
62	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
63	#121×C₁₁₃	C₂²	1	8	yes	complemented
64	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
67	C₂³×D₁₁₃	C₂³	1	1	yes	characteristic
68	C₂×Dic₂₂₆	—	4	2	no	—
69	C₂×Dic₂₂₆	—	4	2	no	—
70	C₂×Dic₂₂₆	C₂³	1	4	yes	—
71	C₂×Dic₂₂₆	C₂³	1	4	yes	—
72	C₂×C₂²⋊D₁₁₃	—	4	2	no	—
73	C₂×C₂²⋊D₁₁₃	—	4	2	no	—
74	C₂×C₂²⋊D₁₁₃	—	4	2	no	—
75	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₁₁₃	C₂³	1	4	yes	—
78	C₂²×Dic₁₁₃	—	4	2	no	—
79	C₂²×Dic₁₁₃	—	4	2	no	—
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	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
84	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
85	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
86	C₂²×Dic₁₁₃	C₂³	1	1	yes	characteristic
87	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
88	C₂²×Dic₁₁₃	C₂³	1	4	yes	—
89	C₂×C₄×D₁₁₃	—	4	2	no	—
90	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
91	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
92	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
93	#14268626	C₂³	1	4	yes	—
94	#14268626	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	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
101	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
102	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
103	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
104	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
105	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
106	C₂²⋊Dic₁₁₃	C₂³	1	4	yes	—
107	#14268624	C₂³	1	4	yes	—
108	#14268624	C₂³	1	4	yes	—
109	#14268624	C₂³	1	4	yes	—
110	C₄×Dic₁₁₃	C₂³	1	4	yes	—
111	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
112	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
113	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₁₁₃	—	4	2	no	—
115	C₂×D₄×C₁₁₃	—	4	2	no	—
116	C₂×D₄×C₁₁₃	—	4	2	no	—
117	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
118	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
119	C₂×D₄×C₁₁₃	C₂³	1	4	yes	—
120	C₂²×C₄×C₁₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
124	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₁₁₃	C₂³	1	4	yes	—
126	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
127	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
128	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
129	C₂³×C₁₁₃	—	2	2	no	—
130	C₂³×C₁₁₃	—	2	2	no	—
131	C₂³×C₁₁₃	—	2	2	no	—
132	C₂³×C₁₁₃	—	2	2	no	—
133	C₂³×C₁₁₃	—	2	2	no	—
134	C₂³×C₁₁₃	—	2	2	no	—
135	C₂³×C₁₁₃	—	2	2	no	—
136	C₂³×C₁₁₃	—	2	2	no	—
137	C₂³×C₁₁₃	—	2	2	no	—
138	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
139	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
140	C₂³×C₁₁₃	C₂⁴	1	2	yes	—
141	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
142	C₂²×D₁₁₃	—	2	2	no	—
143	C₂²×D₁₁₃	—	2	2	no	—
144	C₂²×D₁₁₃	—	2	2	no	—
145	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
146	D₄×C₁₁₃	—	4	4	no	—
147	D₄×C₁₁₃	—	4	4	no	—
148	D₄×C₁₁₃	—	4	4	no	—
149	C₂×C₄×C₁₁₃	—	2	2	no	—
150	C₂×C₄×C₁₁₃	—	2	2	no	—
151	C₂×C₄×C₁₁₃	—	2	2	no	—
152	C₂×C₄×C₁₁₃	—	2	2	no	—
153	C₂×C₄×C₁₁₃	—	4	4	no	—
154	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
155	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
156	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
157	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
158	C₂²⋊D₁₁₃	—	4	4	no	—
159	C₂²⋊D₁₁₃	—	4	4	no	—
160	C₂²⋊D₁₁₃	—	4	4	no	—
161	C₂×Dic₁₁₃	—	2	2	no	—
162	C₂×Dic₁₁₃	—	2	2	no	—
163	C₂×Dic₁₁₃	—	2	2	no	—
164	C₂×Dic₁₁₃	—	2	2	no	—
165	C₂×Dic₁₁₃	—	2	2	no	—
166	C₂×Dic₁₁₃	—	2	2	no	—
167	C₂×Dic₁₁₃	—	2	2	no	—
168	C₂×Dic₁₁₃	—	4	4	no	—
169	C₂×Dic₁₁₃	—	4	4	no	—
170	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
171	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
172	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
173	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
174	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
175	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
176	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
177	C₄×D₁₁₃	—	4	4	no	—
178	Dic₂₂₆	—	4	4	no	—
179	Dic₂₂₆	—	4	4	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	2	no	—
187	C₂²×C₁₁₃	—	2	2	no	—
188	C₂²×C₁₁₃	—	2	2	no	—
189	C₂²×C₁₁₃	—	4	4	no	—
190	C₂²×C₁₁₃	—	4	4	no	—
191	C₂²×C₁₁₃	—	4	4	no	—
192	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
193	C₂²×C₁₁₃	H(5,𝔽₂)	1	2	yes	—
194	C₂²×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
195	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
196	C₂×D₁₁₃	—	2	2	no	—
197	C₂×D₁₁₃	—	2	2	no	—
198	C₂×D₁₁₃	—	2	2	no	—
199	C₂×D₁₁₃	—	4	4	no	—
200	C₄×C₁₁₃	—	2	2	no	—
201	C₄×C₁₁₃	—	2	2	no	—
202	C₄×C₁₁₃	—	2	2	no	—
203	C₄×C₁₁₃	—	2	2	no	—
204	Dic₁₁₃	—	2	2	no	—
205	Dic₁₁₃	—	2	2	no	—
206	Dic₁₁₃	—	2	2	no	—
207	Dic₁₁₃	—	2	2	no	—
208	Dic₁₁₃	—	2	2	no	—
209	Dic₁₁₃	—	2	2	no	—
210	Dic₁₁₃	—	2	2	no	—
211	C₂×C₁₁₃	—	4	2	no	—
212	C₂×C₁₁₃	—	4	2	no	—
213	C₂×C₁₁₃	—	4	2	no	—
214	C₂×C₁₁₃	#562	1	4	yes	complemented
215	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₁₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
218	D₁₁₃	—	4	2	no	—
219	C₂×#562	—	113	1	no	maximal, Sylow
220	C₁₁₃	C₂×#562	1	1	yes	characteristic, complemented, Sylow
221	#562	—	113	16	no	—
222	C₂×#125	—	113	1	no	—
223	C₂×#124	—	113	1	no	—
224	C₂×#124	—	113	1	no	—
225	C₂×#123	—	113	1	no	—
226	C₂×#123	—	113	1	no	—
227	C₂×#123	—	113	1	no	—
228	C₂×#123	—	113	1	no	—
229	C₂×C₂²⋊Q₈	—	113	1	no	—
230	C₂×C₂²⋊Q₈	—	113	1	no	—
231	C₂×C₂²⋊Q₈	—	113	1	no	—
232	C₂×C₂²⋊Q₈	—	113	1	no	—
233	C₂×#121	—	113	1	no	—
234	C₂×#121	—	113	1	no	—
235	C₂×#121	—	113	1	no	—
236	C₂×#121	D₁₁₃	1	1	yes	characteristic, complemented
237	C₂²×Q₈	—	113	1	no	—
238	C₂²×Q₈	—	113	1	no	—
239	C₂²×D₄	—	113	1	no	—
240	C₂²×D₄	—	113	1	no	—
241	C₂²×D₄	—	113	1	no	—
242	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
243	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
244	C₂²×D₄	C₂×D₁₁₃	1	1	yes	characteristic
245	C₂³×C₄	—	113	1	no	—
246	C₂³×C₄	—	113	1	no	—
247	C₂³×C₄	—	113	1	no	—
248	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic
249	#125	—	113	8	no	—
250	#124	—	113	8	no	—
251	#124	—	113	8	no	—
252	#123	—	113	8	no	—
253	#123	—	113	8	no	—
254	#123	—	113	8	no	—
255	#123	—	113	8	no	—
256	C₂²⋊Q₈	—	113	8	no	—
257	C₂²⋊Q₈	—	113	8	no	—
258	C₂²⋊Q₈	—	113	8	no	—
259	C₂²⋊Q₈	—	113	8	no	—
260	#121	—	113	8	no	—
261	#121	—	113	8	no	—
262	#121	—	113	8	no	—
263	#121	C₂×D₁₁₃	1	8	yes	complemented
264	C₂×C₄⋊C₄	—	113	1	no	—
265	C₂×C₄⋊C₄	—	113	1	no	—
266	C₂×C₄⋊C₄	—	113	1	no	—
267	C₂×C₄⋊C₄	—	113	1	no	—
268	C₂×C₄⋊C₄	—	113	1	no	—
269	C₂×C₄⋊C₄	—	113	1	no	—
270	C₂×C₄⋊C₄	—	113	1	no	—
271	C₂×C₄⋊C₄	—	113	1	no	—
272	C₂×C₄⋊C₄	—	113	1	no	—
273	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	—	113	1	no	—
275	C₂×C₂²⋊C₄	—	113	1	no	—
276	C₂×C₂²⋊C₄	—	113	1	no	—
277	C₂×C₂²⋊C₄	—	113	1	no	—
278	C₂×C₂²⋊C₄	—	113	1	no	—
279	C₂×C₂²⋊C₄	—	113	1	no	—
280	C₂×C₂²⋊C₄	—	113	1	no	—
281	C₂×C₂²⋊C₄	—	113	1	no	—
282	C₂×C₂²⋊C₄	—	113	1	no	—
283	C₂×C₂²⋊C₄	—	113	1	no	—
284	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
286	C₂×C₄²	—	113	1	no	—
287	C₂⁴	—	113	1	no	—
288	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
289	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
290	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
291	C₂×Q₈	—	113	4	no	—
292	C₂×Q₈	—	113	4	no	—
293	C₂×Q₈	—	452	2	no	—
294	C₂×Q₈	—	452	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	113	4	no	—
299	C₂×D₄	—	113	4	no	—
300	C₂×D₄	—	113	4	no	—
301	C₂×D₄	—	452	2	no	—
302	C₂×D₄	—	452	2	no	—
303	C₂×D₄	—	452	2	no	—
304	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
305	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
306	C₂×D₄	C₂²×D₁₁₃	1	4	yes	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	113	4	no	—
309	C₂²×C₄	—	113	4	no	—
310	C₂²×C₄	—	113	1	no	—
311	C₂²×C₄	—	113	1	no	—
312	C₂²×C₄	—	113	1	no	—
313	C₂²×C₄	—	113	1	no	—
314	C₂²×C₄	—	113	1	no	—
315	C₂²×C₄	—	113	1	no	—
316	C₂²×C₄	—	113	1	no	—
317	C₂²×C₄	—	113	4	no	—
318	C₂²×C₄	—	452	2	no	—
319	C₂²×C₄	—	452	2	no	—
320	C₂²×C₄	—	452	2	no	—
321	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₁₁₃	1	4	yes	—
326	C₄⋊C₄	—	113	4	no	—
327	C₄⋊C₄	—	113	4	no	—
328	C₄⋊C₄	—	113	4	no	—
329	C₄⋊C₄	—	113	4	no	—
330	C₄⋊C₄	—	113	4	no	—
331	C₄⋊C₄	—	113	4	no	—
332	C₄⋊C₄	—	113	4	no	—
333	C₄⋊C₄	—	113	4	no	—
334	C₄⋊C₄	—	113	4	no	—
335	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
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	—	113	4	no	—
341	C₂²⋊C₄	—	113	4	no	—
342	C₂²⋊C₄	—	113	4	no	—
343	C₂²⋊C₄	—	113	4	no	—
344	C₂²⋊C₄	—	113	4	no	—
345	C₂²⋊C₄	—	113	4	no	—
346	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
348	C₄²	—	113	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	113	2	no	—
359	C₂³	—	226	2	no	—
360	C₂³	—	226	2	no	—
361	C₂³	—	226	2	no	—
362	C₂³	C₂³×D₁₁₃	1	2	yes	—
363	C₂³	C₂³×D₁₁₃	1	2	yes	—
364	C₂³	C₂³×D₁₁₃	1	2	yes	—
365	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
366	Q₈	—	452	4	no	—
367	Q₈	—	452	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	4	no	—
371	D₄	—	452	4	no	—
372	D₄	—	452	4	no	—
373	D₄	—	452	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	113	2	no	—
380	C₂×C₄	—	113	2	no	—
381	C₂×C₄	—	113	2	no	—
382	C₂×C₄	—	113	2	no	—
383	C₂×C₄	—	113	2	no	—
384	C₂×C₄	—	113	2	no	—
385	C₂×C₄	—	113	2	no	—
386	C₂×C₄	—	452	4	no	—
387	C₂×C₄	—	452	4	no	—
388	C₂×C₄	—	452	4	no	—
389	C₂×C₄	—	226	2	no	—
390	C₂×C₄	—	226	2	no	—
391	C₂×C₄	—	226	2	no	—
392	C₂×C₄	—	226	2	no	—
393	C₂×C₄	—	226	2	no	—
394	C₂×C₄	—	226	2	no	—
395	C₂×C₄	—	226	2	no	—
396	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
397	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
398	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
399	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	452	4	no	—
413	C₂²	—	226	2	no	—
414	C₂²	—	226	2	no	—
415	C₂²	—	226	2	no	—
416	C₂²	#16813667	1	2	yes	—
417	C₂²	#16813667	1	2	yes	—
418	C₂²	#16813669	1	2	yes	—
419	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	226	2	no	—
425	C₄	—	226	2	no	—
426	C₄	—	226	2	no	—
427	C₄	—	226	2	no	—
428	C₄	—	226	2	no	—
429	C₄	—	226	2	no	—
430	C₄	—	226	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	4	2	no	—
433	C₂	—	4	2	no	—
434	C₂	—	452	2	no	—
435	C₂	#20299343	1	4	yes	direct product factor
436	C₂	C₂×#16813667	1	1	yes	characteristic
437	C₂	C₂×#16813667	1	1	yes	characteristic
438	C₂	C₂×#16813669	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×#562
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. #20299343	C₂	direct (N × H)
2. C₂×#16813612	C₂	semidirect
3. C₂×#16813609	C₂	semidirect
4. C₂×#16813608	C₂	semidirect
5. C₂×#16813605	C₂	semidirect
6. C₂×#16813604	C₂	semidirect
7. C₂×#16813603	C₂	semidirect
8. C₂×#16813603	C₂	semidirect
9. C₂×#16813601	C₂	semidirect
10. C₂×#16813600	C₂	semidirect
11. C₂×#16813599	C₂	semidirect
12. C₂×#16813599	C₂	semidirect
13. C₂×#16813594	C₂	semidirect
14. C₂×#16813594	C₂	semidirect
15. C₂×#16813593	C₂	semidirect
16. C₂×#121×C₁₁₃	C₂	semidirect
25. #16813612	C₂²	semidirect
26. #16813609	C₂²	semidirect
27. #16813608	C₂²	semidirect
28. #16813605	C₂²	semidirect
29. #16813604	C₂²	semidirect
30. #16813603	C₂²	semidirect
31. #16813603	C₂²	semidirect
32. #16813601	C₂²	semidirect
33. #16813600	C₂²	semidirect
34. #16813599	C₂²	semidirect
35. #16813599	C₂²	semidirect
36. #16813594	C₂²	semidirect
37. #16813594	C₂²	semidirect
38. #16813593	C₂²	semidirect
63. #121×C₁₁₃	C₂²	semidirect
214. C₂×C₁₁₃	#562	semidirect
220. C₁₁₃	C₂×#562	semidirect
236. C₂×#121	D₁₁₃	semidirect
263. #121	C₂×D₁₁₃	semidirect
435. C₂	#20299343	direct (N × H)

Maximal subgroups

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

subgroup	index
#20299343	2
C₂×#16813612	2
C₂×#16813609	2
C₂×#16813608	2
C₂×#16813605	2
C₂×#16813604	2
C₂×#16813603	2
C₂×#16813601	2
C₂×#16813600	2
C₂×#16813599	2
C₂×#16813594	2
C₂×#16813593	2
C₂×#121×C₁₁₃	2
C₂×#562	113

Subgroups — C2×#20299343 #28404698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20299343 #28404698