Subgroups — C₂×#20289489 #28297926

Order 13568.

10858 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811459	C₂	1	2	yes	maximal, complemented
2	#20289489	C₂	1	32	yes	maximal, direct product factor
3	C₂×#16811440	C₂	1	4	yes	maximal, complemented
4	C₂×#16811435	C₂	1	8	yes	maximal, complemented
5	C₂×#16811428	C₂	1	4	yes	maximal, complemented
6	C₂×#16811423	C₂	1	6	yes	maximal, complemented
7	C₂²×#13133239	C₂	1	6	yes	maximal, complemented
8	C₂²×#131×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811459	—	2	16	no	—
10	#16811459	C₂²	1	32	yes	complemented
11	C₂×#13133265	—	2	2	no	—
12	C₂×#13133264	C₂²	1	8	yes	complemented
13	C₂×#13133263	C₂²	1	8	yes	complemented
14	C₂×#13133262	—	2	6	no	—
15	C₂²×#11719945	C₂²	1	12	yes	complemented
16	C₂×#41×D₅₃	—	2	8	no	—
17	#16811440	C₂²	1	64	yes	complemented
18	#16811435	C₂²	1	128	yes	complemented
19	#16811428	C₂²	1	64	yes	complemented
20	#16811423	C₂²	1	96	yes	complemented
21	C₂×#13133250	C₂²	1	24	yes	complemented
22	C₂×#13133245	C₂²	1	24	yes	complemented
23	C₂×#13133239	C₂²	1	4	yes	complemented
24	C₂×#13133239	C₂²	1	12	yes	complemented
25	C₂×#13133239	C₂²	1	12	yes	complemented
26	C₂×#13133239	C₂²	1	12	yes	complemented
27	C₂×#13133239	C₂²	1	96	yes	complemented
28	C₂²×Dic₂₁₂	C₂²	1	6	yes	complemented
29	C₂²×#11719913	C₂²	1	12	yes	complemented
30	C₂²×D₄₂₄	C₂²	1	6	yes	complemented
31	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#131×C₅₃	C₂²	1	4	yes	complemented
33	C₂×#131×C₅₃	C₂²	1	4	yes	complemented
34	C₂×#131×C₅₃	C₂²	1	16	yes	complemented
35	C₂²×M₁₆×C₅₃	C₂²	1	3	yes	complemented
36	C₂³×C₈×C₅₃	C₂²	1	3	yes	complemented
37	#13133265	—	2	32	no	—
38	#13133264	—	2	32	no	—
39	#13133264	C₂³	1	64	yes	complemented
40	#13133263	—	2	32	no	—
41	#13133263	C₂³	1	64	yes	complemented
42	#13133262	—	2	96	no	—
43	C₂×#11719949	—	2	8	no	—
44	C₂×#11719945	—	2	12	no	—
45	C₂×#11719945	—	2	12	no	—
46	C₂×#11719945	—	2	48	no	—
47	C₂×#11719945	C₂³	1	8	yes	—
48	C₂×#11719945	C₂³	1	24	yes	—
49	C₂×#11719945	C₂³	1	96	yes	complemented
50	C₂×#11719947	—	2	24	no	—
51	#41×D₅₃	—	2	128	no	—
52	C₂²×Dic₁₀₆	C₂³	1	12	yes	—
53	C₂×Q₈×D₅₃	—	2	8	no	—
54	C₂²×D₂₁₂	C₂³	1	12	yes	—
55	C₂²×C₂²⋊D₅₃	—	2	12	no	—
56	C₂×D₄×D₅₃	—	2	24	no	—
57	C₂²×C₄×D₅₃	—	2	12	no	—
58	#13133250	C₂³	1	192	yes	complemented
59	#13133245	C₂³	1	192	yes	complemented
60	#13133239	C₂³	1	32	yes	complemented
61	#13133239	C₂³	1	96	yes	complemented
62	#13133239	C₂³	1	96	yes	complemented
63	#13133239	C₂³	1	96	yes	complemented
64	C₂×Dic₂₁₂	C₂³	1	4	yes	—
65	C₂×Dic₂₁₂	C₂³	1	12	yes	—
66	C₂×Dic₂₁₂	C₂³	1	48	yes	complemented
67	C₂×#11719913	C₂³	1	8	yes	—
68	C₂×#11719913	C₂³	1	24	yes	—
69	C₂×#11719913	C₂³	1	96	yes	complemented
70	C₂×D₄₂₄	C₂³	1	4	yes	—
71	C₂×D₄₂₄	C₂³	1	12	yes	—
72	C₂×D₄₂₄	C₂³	1	48	yes	complemented
73	C₂×#41×C₅₃	D₄	1	4	yes	—
74	C₂×#41×C₅₃	D₄	1	8	yes	—
75	C₂×#41×C₅₃	C₂³	1	4	yes	—
76	C₂×#41×C₅₃	C₂³	1	8	yes	—
77	C₂²×Q₈×C₅₃	D₄	1	1	yes	characteristic
78	C₂²×D₄×C₅₃	D₄	1	3	yes	—
79	C₂³×C₄×C₅₃	C₂³	1	3	yes	—
80	#131×C₅₃	C₂³	1	32	yes	complemented
81	#131×C₅₃	C₂³	1	32	yes	complemented
82	C₂×M₁₆×C₅₃	C₂³	1	12	yes	—
83	C₂×M₁₆×C₅₃	C₂³	1	24	yes	complemented
84	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₅₃	C₂³	1	3	yes	—
86	C₂²×C₈×C₅₃	C₂³	1	6	yes	—
87	C₂²×C₈×C₅₃	C₂³	1	6	yes	—
88	C₂²×C₈×C₅₃	C₂³	1	24	yes	complemented
89	C₂⁴×C₅₃	C₂×D₄	1	3	yes	—
90	C₂³×D₅₃	—	2	12	no	—
91	#41×C₅₃	C₂×D₄	1	32	yes	—
92	#41×C₅₃	C₂×D₄	1	16	yes	—
93	#41×C₅₃	C₂⁴	1	16	yes	—
94	C₂×Q₈×C₅₃	C₂×D₄	1	4	yes	—
95	C₂×Q₈×C₅₃	C₂×D₄	1	8	yes	—
96	C₂×D₄×C₅₃	C₂×D₄	1	12	yes	—
97	C₂×D₄×C₅₃	C₂×D₄	1	24	yes	—
98	C₂²×C₄×C₅₃	C₂×D₄	1	3	yes	—
99	C₂²×C₄×C₅₃	C₂×D₄	1	6	yes	—
100	C₂²×C₄×C₅₃	C₂×D₄	1	12	yes	—
101	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
102	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
103	C₂²×C₄×C₅₃	C₂⁴	1	12	yes	—
104	C₂×C₂²⋊D₅₃	—	2	24	no	—
105	C₂×C₂²⋊D₅₃	—	2	8	no	—
106	C₂×C₂²⋊D₅₃	—	2	96	no	—
107	C₂²×Dic₅₃	—	2	12	no	—
108	#11719949	—	2	64	no	—
109	Q₈×D₅₃	—	2	64	no	—
110	#11719947	—	2	192	no	—
111	D₄×D₅₃	—	2	192	no	—
112	#11719945	—	2	96	no	—
113	#11719945	—	2	16	no	—
114	#11719945	—	2	48	no	—
115	#11719945	—	2	96	no	—
116	#11719945	C₂⁴	1	32	yes	—
117	#11719945	C₂⁴	1	96	yes	—
118	C₂×D₂₁₂	—	2	12	no	—
119	C₂×D₂₁₂	—	2	24	no	—
120	C₂×D₂₁₂	C₂⁴	1	8	yes	—
121	C₂×D₂₁₂	C₂⁴	1	48	yes	—
122	C₂×C₄×D₅₃	—	2	8	no	—
123	C₂×C₄×D₅₃	—	2	24	no	—
124	C₂×C₄×D₅₃	—	2	96	no	—
125	C₂×Dic₁₀₆	—	2	12	no	—
126	C₂×Dic₁₀₆	—	2	24	no	—
127	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
128	C₂×Dic₁₀₆	C₂⁴	1	48	yes	—
129	M₁₆×C₅₃	C₂⁴	1	48	yes	—
130	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
131	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₅₃	C₂⁴	1	6	yes	—
133	C₂×C₈×C₅₃	C₂⁴	1	4	yes	—
134	C₂×C₈×C₅₃	C₂⁴	1	12	yes	—
135	C₂×C₈×C₅₃	C₂⁴	1	24	yes	—
136	C₂×C₈×C₅₃	C₂⁴	1	24	yes	—
137	Dic₂₁₂	C₂⁴	1	16	yes	—
138	Dic₂₁₂	C₂⁴	1	48	yes	—
139	D₄₂₄	C₂⁴	1	16	yes	—
140	D₄₂₄	C₂⁴	1	48	yes	—
141	#11719913	C₂⁴	1	32	yes	—
142	#11719913	C₂⁴	1	96	yes	—
143	C₂³×C₅₃	—	4	6	no	—
144	C₂³×C₅₃	C₂²×D₄	1	6	yes	—
145	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
146	C₂³×C₅₃	C₂²×D₄	1	12	yes	—
147	C₂²×D₅₃	—	2	8	no	—
148	C₂²×D₅₃	—	2	48	no	—
149	C₂²×D₅₃	—	8	24	no	—
150	Q₈×C₅₃	C₂²×D₄	1	16	yes	—
151	D₄×C₅₃	C₂²×D₄	1	48	yes	—
152	C₂×C₄×C₅₃	C₂²×D₄	1	6	yes	—
153	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	—
154	C₂×C₄×C₅₃	C₂²×D₄	1	24	yes	—
155	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	—
157	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
159	C₂×C₄×C₅₃	C₂⁵	1	12	yes	—
160	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
161	C₂²⋊D₅₃	—	2	32	no	—
162	C₂²⋊D₅₃	—	2	96	no	—
163	C₂×Dic₅₃	—	2	8	no	—
164	C₂×Dic₅₃	—	2	48	no	—
165	D₂₁₂	—	2	8	no	—
166	D₂₁₂	—	2	48	no	—
167	D₂₁₂	C₂⁵	1	16	yes	—
168	C₄×D₅₃	—	2	32	no	—
169	C₄×D₅₃	—	2	96	no	—
170	Dic₁₀₆	—	2	8	no	—
171	Dic₁₀₆	—	2	48	no	—
172	Dic₁₀₆	C₂⁵	1	16	yes	—
173	C₈×C₅₃	C₂⁵	1	2	yes	—
174	C₈×C₅₃	C₂⁵	1	12	yes	—
175	C₈×C₅₃	C₂⁵	1	2	yes	—
176	C₂×#3584	—	53	1	no	maximal, Sylow
177	C₂²×C₅₃	—	2	12	no	—
178	C₂²×C₅₃	—	2	2	no	—
179	C₂²×C₅₃	—	4	12	no	—
180	C₂²×C₅₃	C₂³×D₄	1	12	yes	—
181	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
182	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
183	C₂×D₅₃	—	2	16	no	—
184	C₂×D₅₃	—	4	16	no	—
185	C₂×D₅₃	—	8	48	no	—
186	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
187	C₄×C₅₃	C₂³×D₄	1	12	yes	—
188	C₄×C₅₃	C₂³×D₄	1	2	yes	—
189	C₄×C₅₃	C₂⁶	1	1	yes	characteristic
190	Dic₅₃	—	2	16	no	—
191	C₂×#585	—	53	2	no	—
192	#3584	—	53	32	no	—
193	C₂×#578	—	53	4	no	—
194	C₂×#577	—	53	8	no	—
195	C₂×#576	—	53	4	no	—
196	C₂×#575	—	53	6	no	—
197	C₂²×#135	—	53	6	no	—
198	C₂²×#131	D₅₃	1	1	yes	characteristic, complemented
199	C₂×C₅₃	—	2	12	no	—
200	C₂×C₅₃	—	2	2	no	—
201	C₂×C₅₃	#3584	1	2	yes	complemented
202	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
203	D₅₃	—	4	16	no	—
204	#585	—	53	32	no	—
205	#585	—	106	16	no	—
206	C₂×2₋¹⁺⁴	—	53	8	no	—
207	C₂×2₋¹⁺⁴	—	106	2	no	—
208	C₂×H(5,𝔽₂)	—	53	8	no	—
209	C₂×H(5,𝔽₂)	—	106	6	no	—
210	C₂²×#41	—	53	12	no	—
211	C₂²×#41	—	106	8	no	—
212	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic
213	#578	—	53	64	no	—
214	#577	—	53	128	no	—
215	#576	—	53	64	no	—
216	#575	—	53	96	no	—
217	C₂×#137	—	53	24	no	—
218	C₂×AGL(1,ℤ/8)	—	53	24	no	—
219	C₂×#135	—	53	4	no	—
220	C₂×#135	—	53	12	no	—
221	C₂×#135	—	53	12	no	—
222	C₂×#135	—	53	12	no	—
223	C₂×#135	—	53	96	no	—
224	C₂²×Q₁₆	—	53	6	no	—
225	C₂²×SD₁₆	—	53	12	no	—
226	C₂²×D₈	—	53	6	no	—
227	C₂×#131	C₂×D₅₃	1	4	yes	complemented
228	C₂×#131	C₂×D₅₃	1	4	yes	complemented
229	C₂×#131	C₂×D₅₃	1	16	yes	complemented
230	C₂²×M₁₆	C₂×D₅₃	1	3	yes	complemented
231	C₂³×C₈	C₂×D₅₃	1	3	yes	complemented
232	C₅₃	C₂×#3584	1	1	yes	characteristic, complemented, Sylow
233	2₋¹⁺⁴	—	53	64	no	—
234	2₋¹⁺⁴	—	106	32	no	—
235	2₋¹⁺⁴	—	106	32	no	—
236	H(5,𝔽₂)	—	53	64	no	—
237	H(5,𝔽₂)	—	106	32	no	—
238	H(5,𝔽₂)	—	106	96	no	—
239	C₂×#41	—	53	8	no	—
240	C₂×#41	—	53	24	no	—
241	C₂×#41	—	53	96	no	—
242	C₂×#41	—	106	128	no	—
243	C₂×#41	—	106	8	no	—
244	C₂×#41	—	106	24	no	—
245	C₂×#41	—	106	12	no	—
246	C₂×#41	—	106	12	no	—
247	C₂×#41	—	106	48	no	—
248	C₂×#41	D₂₁₂	1	4	yes	—
249	C₂×#41	D₂₁₂	1	8	yes	—
250	C₂×#41	C₂²×D₅₃	1	4	yes	—
251	C₂×#41	C₂²×D₅₃	1	8	yes	—
252	C₂²×Q₈	—	53	12	no	—
253	C₂²×Q₈	—	106	8	no	—
254	C₂²×Q₈	D₂₁₂	1	1	yes	characteristic
255	C₂²×D₄	—	53	12	no	—
256	C₂²×D₄	—	106	12	no	—
257	C₂²×D₄	—	106	24	no	—
258	C₂²×D₄	D₂₁₂	1	3	yes	—
259	C₂³×C₄	—	106	12	no	—
260	C₂³×C₄	C₂²×D₅₃	1	3	yes	—
261	#137	—	53	192	no	—
262	AGL(1,ℤ/8)	—	53	192	no	—
263	#135	—	53	32	no	—
264	#135	—	53	96	no	—
265	#135	—	53	96	no	—
266	#135	—	53	96	no	—
267	C₂×Q₁₆	—	53	4	no	—
268	C₂×Q₁₆	—	53	12	no	—
269	C₂×Q₁₆	—	53	48	no	—
270	C₂×SD₁₆	—	53	8	no	—
271	C₂×SD₁₆	—	53	24	no	—
272	C₂×SD₁₆	—	53	96	no	—
273	C₂×D₈	—	53	4	no	—
274	C₂×D₈	—	53	12	no	—
275	C₂×D₈	—	53	48	no	—
276	#131	C₂²×D₅₃	1	32	yes	complemented
277	#131	C₂²×D₅₃	1	32	yes	complemented
278	C₂×M₁₆	C₂²×D₅₃	1	12	yes	—
279	C₂×M₁₆	C₂²×D₅₃	1	24	yes	complemented
280	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₅₃	1	3	yes	—
282	C₂²×C₈	C₂²×D₅₃	1	6	yes	—
283	C₂²×C₈	C₂²×D₅₃	1	6	yes	—
284	C₂²×C₈	C₂²×D₅₃	1	24	yes	complemented
285	C₂⁴	—	106	12	no	—
286	C₂⁴	C₂×D₂₁₂	1	3	yes	—
287	#41	—	53	32	no	—
288	#41	—	53	96	no	—
289	#41	—	106	64	no	—
290	#41	—	106	192	no	—
291	#41	—	106	96	no	—
292	#41	—	106	16	no	—
293	#41	—	106	48	no	—
294	#41	—	106	96	no	—
295	#41	C₂×D₂₁₂	1	32	yes	—
296	#41	C₂×D₂₁₂	1	16	yes	—
297	#41	C₂³×D₅₃	1	16	yes	—
298	C₂×Q₈	—	53	8	no	—
299	C₂×Q₈	—	53	48	no	—
300	C₂×Q₈	—	106	64	no	—
301	C₂×Q₈	—	106	12	no	—
302	C₂×Q₈	—	106	24	no	—
303	C₂×Q₈	C₂×D₂₁₂	1	4	yes	—
304	C₂×Q₈	C₂×D₂₁₂	1	8	yes	—
305	C₂×D₄	—	53	8	no	—
306	C₂×D₄	—	53	48	no	—
307	C₂×D₄	—	106	24	no	—
308	C₂×D₄	—	106	8	no	—
309	C₂×D₄	—	106	96	no	—
310	C₂×D₄	—	106	192	no	—
311	C₂×D₄	—	106	12	no	—
312	C₂×D₄	—	106	24	no	—
313	C₂×D₄	C₂×D₂₁₂	1	12	yes	—
314	C₂×D₄	C₂×D₂₁₂	1	24	yes	—
315	C₂²×C₄	—	106	12	no	—
316	C₂²×C₄	—	106	24	no	—
317	C₂²×C₄	—	106	96	no	—
318	C₂²×C₄	—	106	8	no	—
319	C₂²×C₄	C₂×D₂₁₂	1	3	yes	—
320	C₂²×C₄	C₂×D₂₁₂	1	12	yes	—
321	C₂²×C₄	C₂×D₂₁₂	1	6	yes	—
322	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
323	C₂²×C₄	C₂³×D₅₃	1	12	yes	—
324	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
325	Q₁₆	—	53	16	no	—
326	Q₁₆	—	53	48	no	—
327	SD₁₆	—	53	32	no	—
328	SD₁₆	—	53	96	no	—
329	D₈	—	53	16	no	—
330	D₈	—	53	48	no	—
331	M₁₆	C₂³×D₅₃	1	48	yes	—
332	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
333	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
334	C₂×C₈	C₂³×D₅₃	1	6	yes	—
335	C₂×C₈	C₂³×D₅₃	1	4	yes	—
336	C₂×C₈	C₂³×D₅₃	1	12	yes	—
337	C₂×C₈	C₂³×D₅₃	1	24	yes	—
338	C₂×C₈	C₂³×D₅₃	1	24	yes	—
339	C₂³	—	4	6	no	—
340	C₂³	—	106	48	no	—
341	C₂³	—	106	8	no	—
342	C₂³	—	424	24	no	—
343	C₂³	C₂²×D₂₁₂	1	6	yes	—
344	C₂³	C₂²×D₂₁₂	1	1	yes	characteristic
345	C₂³	C₂²×D₂₁₂	1	12	yes	—
346	Q₈	—	53	16	no	—
347	Q₈	—	106	48	no	—
348	Q₈	—	106	8	no	—
349	Q₈	C₂²×D₂₁₂	1	16	yes	—
350	D₄	—	53	16	no	—
351	D₄	—	106	96	no	—
352	D₄	—	106	32	no	—
353	D₄	—	106	48	no	—
354	D₄	—	106	8	no	—
355	D₄	C₂²×D₂₁₂	1	48	yes	—
356	C₂×C₄	—	106	8	no	—
357	C₂×C₄	—	106	48	no	—
358	C₂×C₄	—	106	32	no	—
359	C₂×C₄	—	106	96	no	—
360	C₂×C₄	C₂²×D₂₁₂	1	6	yes	—
361	C₂×C₄	C₂²×D₂₁₂	1	24	yes	—
362	C₂×C₄	C₂²×D₂₁₂	1	2	yes	—
363	C₂×C₄	C₂²×D₂₁₂	1	12	yes	—
364	C₂×C₄	C₂²×D₂₁₂	1	12	yes	—
365	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
366	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
367	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
368	C₂×C₄	C₂⁴×D₅₃	1	12	yes	—
369	C₈	C₂⁴×D₅₃	1	2	yes	—
370	C₈	C₂⁴×D₅₃	1	2	yes	—
371	C₈	C₂⁴×D₅₃	1	12	yes	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	12	no	—
374	C₂²	—	4	12	no	—
375	C₂²	—	106	16	no	—
376	C₂²	—	424	48	no	—
377	C₂²	—	212	16	no	—
378	C₂²	C₂³×D₂₁₂	1	12	yes	—
379	C₂²	C₂³×D₂₁₂	1	2	yes	—
380	C₂²	C₂³×D₂₁₂	1	1	yes	characteristic
381	C₄	—	106	16	no	—
382	C₄	C₂³×D₂₁₂	1	2	yes	—
383	C₄	C₂³×D₂₁₂	1	12	yes	—
384	C₄	C₂³×D₂₁₂	1	1	yes	characteristic
385	C₄	C₂⁵×D₅₃	1	1	yes	characteristic
386	C₂	—	2	2	no	—
387	C₂	—	2	12	no	—
388	C₂	—	212	16	no	—
389	C₂	#20289489	1	2	yes	direct product factor
390	C₂	C₂⁴×D₂₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₁₂
commutator, cosocle	C₄×C₅₃	C₂⁶
Frattini	C₄	C₂⁵×D₅₃
Fitting	C₂²×#131×C₅₃	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	C₂²×#131	D₅₃
hypocenter	C₅₃	C₂×#3584
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41 ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
1. C₂×#16811459	C₂	semidirect
2. #20289489	C₂	direct (N × H)
3. C₂×#16811440	C₂	semidirect
4. C₂×#16811435	C₂	semidirect
5. C₂×#16811428	C₂	semidirect
6. C₂×#16811423	C₂	semidirect
7. C₂²×#13133239	C₂	semidirect
8. C₂²×#131×C₅₃	C₂	semidirect
10. #16811459	C₂²	semidirect
12. C₂×#13133264	C₂²	semidirect
13. C₂×#13133263	C₂²	semidirect
15. C₂²×#11719945	C₂²	semidirect
17. #16811440	C₂²	semidirect
18. #16811435	C₂²	semidirect
19. #16811428	C₂²	semidirect
20. #16811423	C₂²	semidirect
21. C₂×#13133250	C₂²	semidirect
22. C₂×#13133245	C₂²	semidirect
23. C₂×#13133239	C₂²	semidirect
24. C₂×#13133239	C₂²	semidirect
25. C₂×#13133239	C₂²	semidirect
26. C₂×#13133239	C₂²	semidirect
27. C₂×#13133239	C₂²	semidirect
28. C₂²×Dic₂₁₂	C₂²	semidirect
29. C₂²×#11719913	C₂²	semidirect
30. C₂²×D₄₂₄	C₂²	semidirect
32. C₂×#131×C₅₃	C₂²	semidirect
33. C₂×#131×C₅₃	C₂²	semidirect
34. C₂×#131×C₅₃	C₂²	semidirect
35. C₂²×M₁₆×C₅₃	C₂²	semidirect
36. C₂³×C₈×C₅₃	C₂²	semidirect
39. #13133264	C₂³	semidirect
41. #13133263	C₂³	semidirect
49. C₂×#11719945	C₂³	semidirect
58. #13133250	C₂³	semidirect
59. #13133245	C₂³	semidirect
60. #13133239	C₂³	semidirect
61. #13133239	C₂³	semidirect
62. #13133239	C₂³	semidirect
63. #13133239	C₂³	semidirect
66. C₂×Dic₂₁₂	C₂³	semidirect
69. C₂×#11719913	C₂³	semidirect
72. C₂×D₄₂₄	C₂³	semidirect
80. #131×C₅₃	C₂³	semidirect
81. #131×C₅₃	C₂³	semidirect
83. C₂×M₁₆×C₅₃	C₂³	semidirect
88. C₂²×C₈×C₅₃	C₂³	semidirect
198. C₂²×#131	D₅₃	semidirect
201. C₂×C₅₃	#3584	semidirect
227. C₂×#131	C₂×D₅₃	semidirect
228. C₂×#131	C₂×D₅₃	semidirect
229. C₂×#131	C₂×D₅₃	semidirect
230. C₂²×M₁₆	C₂×D₅₃	semidirect
231. C₂³×C₈	C₂×D₅₃	semidirect
232. C₅₃	C₂×#3584	semidirect
276. #131	C₂²×D₅₃	semidirect
277. #131	C₂²×D₅₃	semidirect
279. C₂×M₁₆	C₂²×D₅₃	semidirect
284. C₂²×C₈	C₂²×D₅₃	semidirect
389. C₂	#20289489	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16811459	2
#20289489	2
C₂×#16811440	2
C₂×#16811435	2
C₂×#16811428	2
C₂×#16811423	2
C₂²×#13133239	2
C₂²×#131×C₅₃	2
C₂×#3584	53

Subgroups — C2×#20289489 #28297926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20289489 #28297926