Subgroups — C₂×H(5,𝔽₂)×#6157 #28330808

Order 13568.

12378 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(5,𝔽₂)×#6157	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811692	C₂	1	6	yes	maximal, complemented
3	C₂×#16811690	C₂	1	9	yes	maximal, complemented
4	C₂×#41×#6157	C₂	1	6	yes	maximal, complemented
5	C₂²×D₄×#6157	C₂	1	9	yes	maximal, complemented
6	C₂×H(5,𝔽₂)×D₅₃	C₂	1	1	yes	maximal, characteristic
7	C₂⁴×#6157	C₂²	1	6	yes	complemented
8	#16811692	C₂²	1	96	yes	complemented
9	#16811690	C₂²	1	144	yes	complemented
10	#41×#6157	C₂²	1	96	yes	complemented
11	C₂×Q₈×#6157	C₂²	1	2	yes	complemented
12	C₂×Q₈×#6157	C₂²	1	6	yes	complemented
13	C₂×D₄×#6157	C₂²	1	18	yes	complemented
14	C₂×D₄×#6157	C₂²	1	36	yes	complemented
15	C₂×D₄×#6157	C₂²	1	18	yes	complemented
16	C₂×D₄×#6157	C₂²	1	144	yes	complemented
17	C₂×#13133296	C₂²	1	18	yes	complemented
18	C₂²×C₄⋊#6157	C₂²	1	9	yes	complemented
19	C₂²×C₂²⋊#6157	C₂²	1	18	yes	complemented
20	C₂²×C₄×#6157	C₂²	1	9	yes	complemented
21	C₂×#13133263	C₄	1	6	yes	complemented
22	C₂×#13133262	C₄	1	9	yes	complemented
23	H(5,𝔽₂)×D₅₃	C₄	1	16	yes	complemented
24	H(5,𝔽₂)×D₅₃	C₂²	1	16	yes	—
25	C₂×#41×D₅₃	C₂²	1	6	yes	—
26	C₂²×D₄×D₅₃	C₂²	1	9	yes	—
27	C₂×H(5,𝔽₂)×C₅₃	C₄	1	1	yes	characteristic, complemented
28	C₂³×#6157	—	4	24	no	—
29	C₂³×#6157	C₂³	1	9	yes	—
30	C₂³×#6157	C₂³	1	9	yes	—
31	C₂³×#6157	C₂³	1	18	yes	—
32	C₂³×#6157	C₂³	1	48	yes	complemented
33	Q₈×#6157	C₂³	1	16	yes	complemented
34	Q₈×#6157	C₂³	1	48	yes	complemented
35	D₄×#6157	C₂³	1	144	yes	complemented
36	D₄×#6157	C₂³	1	288	yes	complemented
37	D₄×#6157	C₂³	1	144	yes	complemented
38	#13133296	C₂³	1	144	yes	complemented
39	C₂×C₄⋊#6157	C₂³	1	18	yes	—
40	C₂×C₄⋊#6157	C₂³	1	6	yes	—
41	C₂×C₄⋊#6157	C₂³	1	72	yes	complemented
42	C₂×C₂²⋊#6157	C₂³	1	36	yes	—
43	C₂×C₂²⋊#6157	C₂³	1	144	yes	complemented
44	C₂×C₄×#6157	C₂³	1	6	yes	—
45	C₂×C₄×#6157	C₂³	1	18	yes	—
46	C₂×C₄×#6157	C₂³	1	72	yes	complemented
47	C₂⁴×D₅₃	C₂³	1	6	yes	—
48	#13133263	C₂×C₄	1	96	yes	complemented
49	#13133262	C₂×C₄	1	144	yes	complemented
50	C₂×#11719949	C₂×C₄	1	6	yes	complemented
51	C₂×#11719945	C₂×C₄	1	18	yes	complemented
52	C₂×#11719947	C₂×C₄	1	18	yes	complemented
53	#41×D₅₃	C₂×C₄	1	48	yes	complemented
54	#41×D₅₃	C₂³	1	48	yes	—
55	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
56	C₂²×D₂₁₂	C₂×C₄	1	9	yes	complemented
57	C₂²×C₂²⋊D₅₃	C₂×C₄	1	18	yes	complemented
58	C₂×D₄×D₅₃	C₂×C₄	1	72	yes	complemented
59	C₂×D₄×D₅₃	C₂×C₄	1	36	yes	complemented
60	C₂×D₄×D₅₃	C₂³	1	18	yes	—
61	C₂×D₄×D₅₃	C₂³	1	72	yes	—
62	C₂²×C₄×D₅₃	C₂³	1	9	yes	—
63	H(5,𝔽₂)×C₅₃	C₂×C₄	1	16	yes	complemented
64	C₂×#41×C₅₃	C₂×C₄	1	6	yes	complemented
65	C₂²×D₄×C₅₃	C₂×C₄	1	9	yes	complemented
66	C₂⁴×C₅₃	C₂²×C₄	1	6	yes	complemented
67	C₂³×D₅₃	—	4	12	no	—
68	C₂³×D₅₃	—	4	12	no	—
69	C₂³×D₅₃	C₂²×C₄	1	24	yes	complemented
70	C₂³×D₅₃	C₂²×C₄	1	18	yes	complemented
71	C₂³×D₅₃	C₂⁴	1	9	yes	—
72	C₂³×D₅₃	C₂⁴	1	24	yes	—
73	C₂²×#6157	—	2	36	no	—
74	C₂²×#6157	—	4	96	no	—
75	C₂²×#6157	—	4	36	no	—
76	C₂²×#6157	—	4	18	no	—
77	C₂²×#6157	C₂⁴	1	6	yes	—
78	C₂²×#6157	C₂⁴	1	9	yes	—
79	C₂²×#6157	C₂⁴	1	36	yes	—
80	C₂²×#6157	C₂⁴	1	36	yes	—
81	C₂²×#6157	C₂⁴	1	72	yes	—
82	C₂²×#6157	C₂⁴	1	1	yes	characteristic
83	#41×C₅₃	C₂²×C₄	1	48	yes	complemented
84	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	complemented
85	C₂×D₄×C₅₃	C₂²×C₄	1	18	yes	complemented
86	C₂×D₄×C₅₃	C₂²×C₄	1	72	yes	complemented
87	C₂²×C₄×C₅₃	C₂²×C₄	1	9	yes	complemented
88	C₂×C₂²⋊D₅₃	C₂²×C₄	1	36	yes	complemented
89	C₂×C₂²⋊D₅₃	C₂²×C₄	1	144	yes	complemented
90	C₂²×Dic₅₃	C₂²×C₄	1	9	yes	complemented
91	#11719949	C₂²×C₄	1	48	yes	complemented
92	Q₈×D₅₃	C₂²×C₄	1	8	yes	complemented
93	Q₈×D₅₃	C₂⁴	1	8	yes	—
94	#11719947	C₂²×C₄	1	144	yes	complemented
95	D₄×D₅₃	C₂²×C₄	1	72	yes	complemented
96	D₄×D₅₃	C₂²×C₄	1	288	yes	complemented
97	D₄×D₅₃	C₂⁴	1	72	yes	—
98	#11719945	C₂²×C₄	1	144	yes	complemented
99	C₂×D₂₁₂	C₂²×C₄	1	18	yes	complemented
100	C₂×D₂₁₂	C₂²×C₄	1	72	yes	complemented
101	C₂×C₄×D₅₃	C₂²×C₄	1	36	yes	complemented
102	C₂×C₄×D₅₃	C₂²×C₄	1	18	yes	complemented
103	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
104	C₂×C₄×D₅₃	C₂⁴	1	36	yes	—
105	C₂×Dic₁₀₆	C₂²×C₄	1	6	yes	complemented
106	C₂²⋊#6157	C₂⁴	1	144	yes	—
107	C₄⋊#6157	C₂⁴	1	72	yes	—
108	C₄⋊#6157	C₂⁴	1	24	yes	—
109	C₄×#6157	C₂⁴	1	24	yes	—
110	C₄×#6157	C₂⁴	1	72	yes	—
111	C₂³×C₅₃	—	4	12	no	—
112	C₂³×C₅₃	C₂³×C₄	1	9	yes	—
113	C₂³×C₅₃	C₂³×C₄	1	24	yes	complemented
114	C₂²×D₅₃	—	2	18	no	—
115	C₂²×D₅₃	—	2	18	no	—
116	C₂²×D₅₃	—	4	24	no	—
117	C₂²×D₅₃	—	4	48	no	—
118	C₂²×D₅₃	—	4	24	no	—
119	C₂²×D₅₃	—	4	36	no	—
120	C₂²×D₅₃	C₂³×C₄	1	9	yes	—
121	C₂²×D₅₃	C₂³×C₄	1	18	yes	—
122	C₂²×D₅₃	C₂³×C₄	1	72	yes	complemented
123	C₂²×D₅₃	C₂⁵	1	18	yes	—
124	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
125	C₂×#6157	—	2	18	no	—
126	C₂×#6157	—	2	12	no	—
127	C₂×#6157	—	2	72	no	—
128	C₂×#6157	—	4	72	no	—
129	C₂×#6157	—	4	36	no	—
130	C₂×#6157	H(5,𝔽₂)	1	4	yes	direct product factor
131	C₂×#6157	C₂⁵	1	12	yes	—
132	C₂×#6157	C₂⁵	1	18	yes	—
133	C₂×#6157	C₂⁵	1	2	yes	—
134	Q₈×C₅₃	C₂³×C₄	1	8	yes	complemented
135	D₄×C₅₃	C₂³×C₄	1	72	yes	complemented
136	C₂×C₄×C₅₃	C₂³×C₄	1	6	yes	—
137	C₂×C₄×C₅₃	C₂³×C₄	1	36	yes	complemented
138	C₂²⋊D₅₃	C₂³×C₄	1	144	yes	complemented
139	C₂×Dic₅₃	C₂³×C₄	1	6	yes	—
140	C₂×Dic₅₃	C₂³×C₄	1	36	yes	complemented
141	D₂₁₂	C₂³×C₄	1	72	yes	complemented
142	C₄×D₅₃	C₂³×C₄	1	12	yes	—
143	C₄×D₅₃	C₂³×C₄	1	72	yes	complemented
144	C₄×D₅₃	C₂⁵	1	12	yes	—
145	Dic₁₀₆	C₂³×C₄	1	24	yes	complemented
146	C₂×C₄×H(5,𝔽₂)	—	53	1	no	maximal, Sylow
147	C₂²×C₅₃	—	2	18	no	—
148	C₂²×C₅₃	—	4	24	no	—
149	C₂²×C₅₃	C₂⁴×C₄	1	18	yes	—
150	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
151	C₂×D₅₃	—	2	18	no	—
152	C₂×D₅₃	—	2	18	no	—
153	C₂×D₅₃	—	2	18	no	—
154	C₂×D₅₃	—	2	36	no	—
155	C₂×D₅₃	—	4	72	no	—
156	C₂×D₅₃	C₂⁴×C₄	1	18	yes	—
157	C₂×D₅₃	C₂⁴×C₄	1	1	yes	characteristic
158	C₂×D₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
159	C₂×D₅₃	#585	1	2	yes	—
160	C₂×D₅₃	C₂⁶	1	1	yes	characteristic
161	#6157	—	2	18	no	—
162	#6157	—	2	12	no	—
163	#6157	C₂×H(5,𝔽₂)	1	4	yes	direct product factor
164	C₄×C₅₃	C₂⁴×C₄	1	12	yes	—
165	Dic₅₃	C₂⁴×C₄	1	12	yes	—
166	C₂²×H(5,𝔽₂)	—	53	1	no	—
167	C₄×H(5,𝔽₂)	—	53	32	no	—
168	C₂×#520	—	53	6	no	—
169	C₂×#518	—	53	9	no	—
170	C₂×C₄×#41	—	53	6	no	—
171	C₂²×C₄×D₄	—	53	9	no	—
172	C₂×C₅₃	—	2	18	no	—
173	C₂×C₅₃	C₄×H(5,𝔽₂)	1	2	yes	complemented
174	C₂×C₅₃	C₂⁵×C₄	1	1	yes	characteristic
175	D₅₃	—	2	18	no	—
176	D₅₃	C₄×H(5,𝔽₂)	1	2	yes	complemented
177	D₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
178	D₅₃	C₂×#585	1	1	yes	characteristic
179	C₂×H(5,𝔽₂)	—	53	16	no	—
180	C₂×H(5,𝔽₂)	—	53	16	no	—
181	C₂×H(5,𝔽₂)	—	53	6	no	—
182	C₂×H(5,𝔽₂)	—	53	9	no	—
183	C₂×H(5,𝔽₂)	#6157	1	1	yes	characteristic, direct product factor
184	C₂²×#41	—	53	6	no	—
185	C₂³×D₄	—	53	9	no	—
186	C₂⁴×C₄	—	53	6	no	—
187	#520	—	53	96	no	—
188	#518	—	53	144	no	—
189	C₄×#41	—	53	96	no	—
190	C₂×C₄×Q₈	—	53	2	no	—
191	C₂×C₄×Q₈	—	53	6	no	—
192	C₂×C₄×D₄	—	53	18	no	—
193	C₂×C₄×D₄	—	53	36	no	—
194	C₂×C₄×D₄	—	53	144	no	—
195	C₂×C₄×D₄	—	53	18	no	—
196	C₂×#117	—	53	18	no	—
197	C₂²×C₄⋊C₄	—	53	9	no	—
198	C₂²×C₂²⋊C₄	—	53	18	no	—
199	C₂²×C₄²	—	53	9	no	—
200	C₅₃	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
201	C₂⁵	—	53	6	no	—
202	H(5,𝔽₂)	—	53	96	no	—
203	H(5,𝔽₂)	—	53	144	no	—
204	H(5,𝔽₂)	C₂×#6157	1	16	yes	direct product factor
205	C₂×#41	—	53	48	no	—
206	C₂×#41	—	53	48	no	—
207	C₂×#41	—	53	6	no	—
208	C₂×#41	—	53	18	no	—
209	C₂×#41	—	53	18	no	—
210	C₂×#41	C₂×#6157	1	6	yes	complemented
211	C₂²×Q₈	—	53	2	no	—
212	C₂²×D₄	—	53	18	no	—
213	C₂²×D₄	—	53	18	no	—
214	C₂²×D₄	—	53	72	no	—
215	C₂²×D₄	—	53	36	no	—
216	C₂²×D₄	—	53	72	no	—
217	C₂²×D₄	—	53	9	no	—
218	C₂²×D₄	C₂×#6157	1	9	yes	complemented
219	C₂³×C₄	—	53	9	no	—
220	C₂³×C₄	—	53	9	no	—
221	C₂³×C₄	—	53	9	no	—
222	C₂³×C₄	—	53	18	no	—
223	C₂³×C₄	—	53	48	no	—
224	C₂³×C₄	—	212	24	no	—
225	C₄×Q₈	—	53	16	no	—
226	C₄×Q₈	—	53	48	no	—
227	C₄×D₄	—	53	144	no	—
228	C₄×D₄	—	53	288	no	—
229	C₄×D₄	—	53	144	no	—
230	#117	—	53	144	no	—
231	C₂×C₄⋊C₄	—	53	18	no	—
232	C₂×C₄⋊C₄	—	53	72	no	—
233	C₂×C₄⋊C₄	—	53	6	no	—
234	C₂×C₂²⋊C₄	—	53	36	no	—
235	C₂×C₂²⋊C₄	—	53	144	no	—
236	C₂×C₄²	—	53	18	no	—
237	C₂×C₄²	—	53	6	no	—
238	C₂×C₄²	—	53	72	no	—
239	C₂⁴	—	53	9	no	—
240	C₂⁴	—	53	18	no	—
241	C₂⁴	—	53	24	no	—
242	C₂⁴	—	53	24	no	—
243	C₂⁴	—	212	12	no	—
244	C₂⁴	—	212	12	no	—
245	C₂⁴	C₂²×#6157	1	6	yes	complemented
246	#41	—	53	48	no	—
247	#41	—	53	144	no	—
248	#41	—	53	144	no	—
249	#41	C₂²×#6157	1	48	yes	complemented
250	C₂×Q₈	—	53	8	no	—
251	C₂×Q₈	—	53	8	no	—
252	C₂×Q₈	—	53	6	no	—
253	C₂×Q₈	C₂²×#6157	1	2	yes	complemented
254	C₂×D₄	—	53	36	no	—
255	C₂×D₄	—	53	144	no	—
256	C₂×D₄	—	53	72	no	—
257	C₂×D₄	—	53	288	no	—
258	C₂×D₄	—	53	72	no	—
259	C₂×D₄	—	53	18	no	—
260	C₂×D₄	—	53	72	no	—
261	C₂×D₄	C₂²×#6157	1	18	yes	complemented
262	C₂×D₄	C₂²×#6157	1	72	yes	complemented
263	C₂²×C₄	—	53	1	no	—
264	C₂²×C₄	—	53	9	no	—
265	C₂²×C₄	—	53	18	no	—
266	C₂²×C₄	—	53	6	no	—
267	C₂²×C₄	—	53	36	no	—
268	C₂²×C₄	—	53	36	no	—
269	C₂²×C₄	—	53	6	no	—
270	C₂²×C₄	—	53	9	no	—
271	C₂²×C₄	—	53	36	no	—
272	C₂²×C₄	—	53	36	no	—
273	C₂²×C₄	—	53	72	no	—
274	C₂²×C₄	—	106	36	no	—
275	C₂²×C₄	—	212	96	no	—
276	C₂²×C₄	—	212	18	no	—
277	C₂²×C₄	—	212	36	no	—
278	C₂²×C₄	C₂²×#6157	1	9	yes	complemented
279	C₄⋊C₄	—	53	72	no	—
280	C₄⋊C₄	—	53	24	no	—
281	C₂²⋊C₄	—	53	144	no	—
282	C₄²	—	53	24	no	—
283	C₄²	—	53	72	no	—
284	C₂³	—	4	12	no	—
285	C₂³	—	53	1	no	—
286	C₂³	—	53	18	no	—
287	C₂³	—	53	18	no	—
288	C₂³	—	53	9	no	—
289	C₂³	—	53	72	no	—
290	C₂³	—	106	18	no	—
291	C₂³	—	106	18	no	—
292	C₂³	—	212	36	no	—
293	C₂³	—	212	24	no	—
294	C₂³	—	212	24	no	—
295	C₂³	—	212	48	no	—
296	C₂³	C₂³×#6157	1	9	yes	—
297	C₂³	C₂³×#6157	1	24	yes	complemented
298	Q₈	—	53	24	no	—
299	Q₈	C₂³×#6157	1	8	yes	complemented
300	D₄	—	53	144	no	—
301	D₄	—	53	72	no	—
302	D₄	C₂³×#6157	1	72	yes	complemented
303	C₂×C₄	—	53	4	no	—
304	C₂×C₄	—	53	2	no	—
305	C₂×C₄	—	53	36	no	—
306	C₂×C₄	—	53	6	no	—
307	C₂×C₄	—	53	12	no	—
308	C₂×C₄	—	53	72	no	—
309	C₂×C₄	—	53	12	no	—
310	C₂×C₄	—	53	12	no	—
311	C₂×C₄	—	53	18	no	—
312	C₂×C₄	—	106	72	no	—
313	C₂×C₄	—	106	18	no	—
314	C₂×C₄	—	106	12	no	—
315	C₂×C₄	—	212	36	no	—
316	C₂×C₄	—	212	72	no	—
317	C₂×C₄	C₂³×#6157	1	6	yes	—
318	C₂×C₄	C₂³×#6157	1	36	yes	complemented
319	C₂²	—	2	18	no	—
320	C₂²	—	4	24	no	—
321	C₂²	—	53	2	no	—
322	C₂²	—	53	2	no	—
323	C₂²	—	53	1	no	—
324	C₂²	—	53	1	no	—
325	C₂²	—	53	18	no	—
326	C₂²	—	106	18	no	—
327	C₂²	—	106	18	no	—
328	C₂²	—	106	36	no	—
329	C₂²	—	106	18	no	—
330	C₂²	—	212	72	no	—
331	C₂²	C₂⁴×#6157	1	18	yes	—
332	C₂²	C₂⁴×#6157	1	1	yes	characteristic
333	C₄	—	53	4	no	—
334	C₄	—	53	12	no	—
335	C₄	—	106	18	no	—
336	C₄	—	106	12	no	—
337	C₄	C₂⁴×#6157	1	12	yes	—
338	C₂	—	2	18	no	—
339	C₂	—	53	1	no	—
340	C₂	—	53	1	no	—
341	C₂	—	53	2	no	—
342	C₂	—	106	18	no	—
343	C₂	H(5,𝔽₂)×#6157	1	2	yes	direct product factor
344	C₂	C₂⁵×#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂⁴×#6157
commutator	C₂×C₅₃	C₂⁵×C₄
Frattini	C₂	C₂⁵×#6157
Fitting	C₂×H(5,𝔽₂)×C₅₃	C₄
socle	C₂²×C₅₃	C₂⁴×C₄
prime radical	C₂×H(5,𝔽₂)×D₅₃	C₂
cosocle	C₂×D₅₃	C₂⁶
hypercenter	C₂×H(5,𝔽₂)	#6157
hypocenter	C₅₃	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. H(5,𝔽₂)×#6157	C₂	direct (N × H)
2. C₂×#16811692	C₂	semidirect
3. C₂×#16811690	C₂	semidirect
4. C₂×#41×#6157	C₂	semidirect
5. C₂²×D₄×#6157	C₂	semidirect
7. C₂⁴×#6157	C₂²	semidirect
8. #16811692	C₂²	semidirect
9. #16811690	C₂²	semidirect
10. #41×#6157	C₂²	semidirect
11. C₂×Q₈×#6157	C₂²	semidirect
12. C₂×Q₈×#6157	C₂²	semidirect
13. C₂×D₄×#6157	C₂²	semidirect
14. C₂×D₄×#6157	C₂²	semidirect
15. C₂×D₄×#6157	C₂²	semidirect
16. C₂×D₄×#6157	C₂²	semidirect
17. C₂×#13133296	C₂²	semidirect
18. C₂²×C₄⋊#6157	C₂²	semidirect
19. C₂²×C₂²⋊#6157	C₂²	semidirect
20. C₂²×C₄×#6157	C₂²	semidirect
21. C₂×#13133263	C₄	semidirect
22. C₂×#13133262	C₄	semidirect
23. H(5,𝔽₂)×D₅₃	C₄	semidirect
27. C₂×H(5,𝔽₂)×C₅₃	C₄	semidirect
32. C₂³×#6157	C₂³	semidirect
33. Q₈×#6157	C₂³	semidirect
34. Q₈×#6157	C₂³	semidirect
35. D₄×#6157	C₂³	semidirect
36. D₄×#6157	C₂³	semidirect
37. D₄×#6157	C₂³	semidirect
38. #13133296	C₂³	semidirect
41. C₂×C₄⋊#6157	C₂³	semidirect
43. C₂×C₂²⋊#6157	C₂³	semidirect
46. C₂×C₄×#6157	C₂³	semidirect
48. #13133263	C₂×C₄	semidirect
49. #13133262	C₂×C₄	semidirect
50. C₂×#11719949	C₂×C₄	semidirect
51. C₂×#11719945	C₂×C₄	semidirect
52. C₂×#11719947	C₂×C₄	semidirect
53. #41×D₅₃	C₂×C₄	semidirect
56. C₂²×D₂₁₂	C₂×C₄	semidirect
57. C₂²×C₂²⋊D₅₃	C₂×C₄	semidirect
58. C₂×D₄×D₅₃	C₂×C₄	semidirect
59. C₂×D₄×D₅₃	C₂×C₄	semidirect
63. H(5,𝔽₂)×C₅₃	C₂×C₄	semidirect
64. C₂×#41×C₅₃	C₂×C₄	semidirect
65. C₂²×D₄×C₅₃	C₂×C₄	semidirect
66. C₂⁴×C₅₃	C₂²×C₄	semidirect
69. C₂³×D₅₃	C₂²×C₄	semidirect
70. C₂³×D₅₃	C₂²×C₄	semidirect
83. #41×C₅₃	C₂²×C₄	semidirect
84. C₂×Q₈×C₅₃	C₂²×C₄	semidirect
85. C₂×D₄×C₅₃	C₂²×C₄	semidirect
86. C₂×D₄×C₅₃	C₂²×C₄	semidirect
87. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
88. C₂×C₂²⋊D₅₃	C₂²×C₄	semidirect
89. C₂×C₂²⋊D₅₃	C₂²×C₄	semidirect
90. C₂²×Dic₅₃	C₂²×C₄	semidirect
91. #11719949	C₂²×C₄	semidirect
92. Q₈×D₅₃	C₂²×C₄	semidirect
94. #11719947	C₂²×C₄	semidirect
95. D₄×D₅₃	C₂²×C₄	semidirect
96. D₄×D₅₃	C₂²×C₄	semidirect
98. #11719945	C₂²×C₄	semidirect
99. C₂×D₂₁₂	C₂²×C₄	semidirect
100. C₂×D₂₁₂	C₂²×C₄	semidirect
101. C₂×C₄×D₅₃	C₂²×C₄	semidirect
102. C₂×C₄×D₅₃	C₂²×C₄	semidirect
105. C₂×Dic₁₀₆	C₂²×C₄	semidirect
113. C₂³×C₅₃	C₂³×C₄	semidirect
122. C₂²×D₅₃	C₂³×C₄	semidirect
130. C₂×#6157	H(5,𝔽₂)	direct (N × H)
134. Q₈×C₅₃	C₂³×C₄	semidirect
135. D₄×C₅₃	C₂³×C₄	semidirect
137. C₂×C₄×C₅₃	C₂³×C₄	semidirect
138. C₂²⋊D₅₃	C₂³×C₄	semidirect
140. C₂×Dic₅₃	C₂³×C₄	semidirect
141. D₂₁₂	C₂³×C₄	semidirect
143. C₄×D₅₃	C₂³×C₄	semidirect
145. Dic₁₀₆	C₂³×C₄	semidirect
163. #6157	C₂×H(5,𝔽₂)	direct (N × H)
173. C₂×C₅₃	C₄×H(5,𝔽₂)	semidirect
176. D₅₃	C₄×H(5,𝔽₂)	semidirect
183. C₂×H(5,𝔽₂)	#6157	direct (N × H)
200. C₅₃	C₂×C₄×H(5,𝔽₂)	semidirect
204. H(5,𝔽₂)	C₂×#6157	direct (N × H)
210. C₂×#41	C₂×#6157	semidirect
218. C₂²×D₄	C₂×#6157	semidirect
245. C₂⁴	C₂²×#6157	semidirect
249. #41	C₂²×#6157	semidirect
253. C₂×Q₈	C₂²×#6157	semidirect
261. C₂×D₄	C₂²×#6157	semidirect
262. C₂×D₄	C₂²×#6157	semidirect
278. C₂²×C₄	C₂²×#6157	semidirect
297. C₂³	C₂³×#6157	semidirect
299. Q₈	C₂³×#6157	semidirect
302. D₄	C₂³×#6157	semidirect
318. C₂×C₄	C₂³×#6157	semidirect
343. C₂	H(5,𝔽₂)×#6157	direct (N × H)

Maximal subgroups

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

subgroup	index
H(5,𝔽₂)×#6157	2
C₂×#16811692	2
C₂×#16811690	2
C₂×#41×#6157	2
C₂²×D₄×#6157	2
C₂×H(5,𝔽₂)×D₅₃	2
C₂×C₄×H(5,𝔽₂)	53

Subgroups — C2×H(5,𝔽2)×#6157 #28330808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×H(5,𝔽₂)×#6157 #28330808