Subgroups — C₂²×#65300 #12963139

Order 1280.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂³×#681	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁴×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#65300	C₂	1	24	yes	maximal, direct product factor
7	C₂²×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#3935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₅×D₄	C₄	1	1	yes	characteristic
10	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×D₄	C₄	1	12	yes	—
13	C₂×C₄×C₅×D₄	C₂²	1	12	yes	—
14	C₂²×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
15	C₂²×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
16	C₂²×C₅×C₂²⋊C₄	C₄	1	1	yes	characteristic
17	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂²×#681	—	2	8	no	—
19	C₂²×#681	C₂²	1	12	yes	complemented
20	C₂³×#168	—	2	8	no	—
21	C₂³×#168	C₂²	1	1	yes	characteristic
22	C₂³×#168	C₂²	1	1	yes	characteristic
23	C₂³×#168	C₂²	1	1	yes	characteristic
24	C₂³×#168	C₂²	1	1	yes	characteristic
25	C₂³×#168	C₂²	1	12	yes	complemented
26	C₂×C₂²⋊#168	C₂²	1	12	yes	complemented
27	C₂×C₂²⋊#168	C₂²	1	12	yes	complemented
28	#65300	C₂²	1	64	yes	direct product factor
29	C₂×C₄⋊#168	C₂²	1	12	yes	complemented
30	C₂×#3935	C₂²	1	12	yes	complemented
31	C₂²×#435	—	5	1	no	maximal, Sylow
32	C₂⁵×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂⁵×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₅×D₄	—	2	8	no	—
35	C₂²×C₅×D₄	C₂×C₄	1	12	yes	—
36	C₂³×C₄×C₅	—	2	4	no	—
37	C₂³×C₄×C₅	—	2	4	no	—
38	C₂³×C₄×C₅	—	2	4	no	—
39	C₂³×C₄×C₅	—	2	4	no	—
40	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₅	C₂×C₄	1	6	yes	—
45	C₂³×C₄×C₅	C₂×C₄	1	6	yes	—
46	C₂³×C₄×C₅	C₂³	1	6	yes	—
47	C₂³×C₄×C₅	C₂³	1	6	yes	—
48	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₄×C₅×D₄	C₂×C₄	1	48	yes	—
50	C₄×C₅×D₄	C₂³	1	16	yes	—
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	12	yes	—
52	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	12	yes	—
53	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	12	yes	—
54	C₂×C₄²×C₅	C₂×C₄	1	6	yes	—
55	C₂×C₄²×C₅	C₂³	1	6	yes	—
56	C₂×#681	—	2	48	no	—
57	C₂×#681	C₂³	1	16	yes	complemented
58	C₂²×#168	—	2	4	no	—
59	C₂²×#168	—	2	4	no	—
60	C₂²×#168	—	2	4	no	—
61	C₂²×#168	—	2	48	no	—
62	C₂²×#168	D₄	1	8	yes	complemented
63	C₂²×#168	C₂³	1	6	yes	—
64	C₂²×#168	C₂³	1	6	yes	—
65	C₂²×#168	C₂³	1	6	yes	—
66	C₂²×#168	C₂³	1	6	yes	—
67	C₂²×#168	C₂³	1	16	yes	complemented
68	C₂²⋊#168	C₂³	1	16	yes	complemented
69	C₂²⋊#168	C₂³	1	16	yes	complemented
70	C₄⋊#168	C₂³	1	16	yes	complemented
71	#3935	C₂³	1	16	yes	complemented
72	C₂³×M₁₆	—	5	1	no	—
73	C₂⁴×C₈	—	5	1	no	—
74	C₂²×C₄×D₄	D₅	1	1	yes	characteristic
75	C₂×#435	—	5	24	no	—
76	C₂²×C₄⋊C₈	—	5	1	no	—
77	C₂²×C₂²⋊C₈	—	5	1	no	—
78	C₂²×C₂²⋊C₈	—	5	1	no	—
79	C₂²×#97	—	5	1	no	—
80	C₂⁴×C₅	—	2	4	no	—
81	C₂⁴×C₅	—	2	4	no	—
82	C₂⁴×C₅	—	2	4	no	—
83	C₂⁴×C₅	—	2	4	no	—
84	C₂⁴×C₅	—	2	4	no	—
85	C₂⁴×C₅	M₁₆	1	8	yes	complemented
86	C₂⁴×C₅	C₂²×C₄	1	6	yes	—
87	C₂⁴×C₅	C₂²×C₄	1	6	yes	—
88	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₅×D₄	—	2	48	no	—
90	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
91	C₂²×C₄×C₅	—	2	4	no	—
92	C₂²×C₄×C₅	—	2	4	no	—
93	C₂²×C₄×C₅	—	2	4	no	—
94	C₂²×C₄×C₅	—	2	4	no	—
95	C₂²×C₄×C₅	—	2	24	no	—
96	C₂²×C₄×C₅	—	2	24	no	—
97	C₂²×C₄×C₅	—	2	12	no	—
98	C₂²×C₄×C₅	—	2	12	no	—
99	C₂²×C₄×C₅	—	2	12	no	—
100	C₂²×C₄×C₅	—	2	12	no	—
101	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
103	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
104	C₂²×C₄×C₅	C₂²×C₄	1	6	yes	—
105	C₂²×C₄×C₅	C₂²×C₄	1	12	yes	—
106	C₂²×C₄×C₅	C₂²×C₄	1	12	yes	—
107	C₂²×C₄×C₅	C₂²×C₄	1	3	yes	—
108	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₅	#41	1	4	yes	—
110	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
113	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
114	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
115	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
116	C₄²×C₅	C₂²×C₄	1	12	yes	—
117	C₄²×C₅	C₂⁴	1	4	yes	—
118	#681	—	2	32	no	—
119	C₂×#168	—	2	12	no	—
120	C₂×#168	—	2	12	no	—
121	C₂×#168	—	2	12	no	—
122	C₂×#168	—	2	32	no	—
123	C₂×#168	C₂×D₄	1	24	yes	complemented
124	C₂×#168	C₂⁴	1	4	yes	—
125	C₂×#168	C₂⁴	1	4	yes	—
126	C₂×#168	C₂⁴	1	4	yes	—
127	C₂×#168	C₂⁴	1	4	yes	—
128	C₂³×D₄	Dic₅	1	1	yes	characteristic
129	C₂⁴×C₄	C₂×D₅	1	1	yes	characteristic
130	C₂⁴×C₄	C₂×D₅	1	1	yes	characteristic
131	C₂²×M₁₆	—	5	12	no	—
132	C₂²×M₁₆	—	10	8	no	—
133	C₂³×C₈	—	5	1	no	—
134	C₂³×C₈	—	5	12	no	—
135	C₂³×C₈	—	5	1	no	—
136	C₂³×C₈	—	5	1	no	—
137	C₂³×C₈	—	5	1	no	—
138	C₂³×C₈	—	10	8	no	—
139	C₂×C₄×D₄	Dic₅	1	12	yes	—
140	C₂×C₄×D₄	C₂×D₅	1	12	yes	—
141	C₂²×C₄⋊C₄	Dic₅	1	1	yes	characteristic
142	C₂²×C₂²⋊C₄	Dic₅	1	1	yes	characteristic
143	C₂²×C₂²⋊C₄	Dic₅	1	1	yes	characteristic
144	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
145	#435	—	5	64	no	—
146	C₂×C₄⋊C₈	—	5	12	no	—
147	C₂×C₂²⋊C₈	—	5	12	no	—
148	C₂×C₂²⋊C₈	—	5	12	no	—
149	C₂×#97	—	5	12	no	—
150	C₂³×C₅	—	2	12	no	—
151	C₂³×C₅	—	2	12	no	—
152	C₂³×C₅	—	2	32	no	—
153	C₂³×C₅	—	2	12	no	—
154	C₂³×C₅	—	2	12	no	—
155	C₂³×C₅	—	2	12	no	—
156	C₂³×C₅	—	4	16	no	—
157	C₂³×C₅	C₄×D₄	1	4	yes	—
158	C₂³×C₅	C₂×M₁₆	1	4	yes	—
159	C₂³×C₅	C₂×M₁₆	1	24	yes	complemented
160	C₂³×C₅	#131	1	4	yes	—
161	C₂³×C₅	C₂³×C₄	1	4	yes	—
162	C₂³×C₅	C₂³×C₄	1	4	yes	—
163	C₂³×C₅	C₂³×C₄	1	3	yes	—
164	C₅×D₄	—	2	32	no	—
165	C₂×C₄×C₅	—	2	12	no	—
166	C₂×C₄×C₅	—	2	12	no	—
167	C₂×C₄×C₅	—	2	12	no	—
168	C₂×C₄×C₅	—	2	12	no	—
169	C₂×C₄×C₅	—	2	24	no	—
170	C₂×C₄×C₅	—	2	24	no	—
171	C₂×C₄×C₅	—	2	4	no	—
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	2	4	no	—
174	C₂×C₄×C₅	—	2	4	no	—
175	C₂×C₄×C₅	C₄×D₄	1	12	yes	—
176	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
177	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
178	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
179	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
180	C₂×C₄×C₅	C₂³×C₄	1	3	yes	—
181	C₂×C₄×C₅	C₂²×D₄	1	6	yes	—
182	C₂×C₄×C₅	C₂×#41	1	6	yes	—
183	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
184	#168	—	2	4	no	—
185	#168	—	2	4	no	—
186	#168	—	2	4	no	—
187	#168	C₂²×D₄	1	8	yes	complemented
188	C₂⁵	C₂×Dic₅	1	1	yes	characteristic
189	C₂⁵	C₂×Dic₅	1	1	yes	characteristic
190	C₂²×D₄	—	2	8	no	—
191	C₂²×D₄	C₂×Dic₅	1	12	yes	—
192	C₂³×C₄	—	2	4	no	—
193	C₂³×C₄	—	2	4	no	—
194	C₂³×C₄	—	2	4	no	—
195	C₂³×C₄	—	2	4	no	—
196	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
197	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
198	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
199	C₂³×C₄	C₂×Dic₅	1	1	yes	characteristic
200	C₂³×C₄	C₂×Dic₅	1	6	yes	—
201	C₂³×C₄	C₂×Dic₅	1	6	yes	—
202	C₂³×C₄	C₂²×D₅	1	6	yes	—
203	C₂³×C₄	C₂²×D₅	1	6	yes	—
204	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
205	C₂×M₁₆	—	5	16	no	—
206	C₂×M₁₆	—	10	48	no	—
207	C₂²×C₈	—	5	8	no	—
208	C₂²×C₈	—	5	6	no	—
209	C₂²×C₈	—	5	6	no	—
210	C₂²×C₈	—	5	16	no	—
211	C₂²×C₈	—	5	6	no	—
212	C₂²×C₈	—	5	6	no	—
213	C₂²×C₈	—	10	48	no	—
214	C₂²×C₈	—	10	4	no	—
215	C₂²×C₈	—	10	4	no	—
216	C₂²×C₈	—	10	4	no	—
217	C₄×D₄	C₂×Dic₅	1	48	yes	—
218	C₄×D₄	C₂²×D₅	1	16	yes	—
219	C₂×C₄⋊C₄	C₂×Dic₅	1	12	yes	—
220	C₂×C₂²⋊C₄	C₂×Dic₅	1	12	yes	—
221	C₂×C₂²⋊C₄	C₂×Dic₅	1	12	yes	—
222	C₂×C₄²	C₂×Dic₅	1	6	yes	—
223	C₂×C₄²	C₂²×D₅	1	6	yes	—
224	C₄⋊C₈	—	5	16	no	—
225	C₂²⋊C₈	—	5	16	no	—
226	C₂²⋊C₈	—	5	16	no	—
227	#97	—	5	16	no	—
228	C₂²×C₅	—	2	4	no	—
229	C₂²×C₅	—	2	48	no	—
230	C₂²×C₅	—	2	4	no	—
231	C₂²×C₅	—	2	4	no	—
232	C₂²×C₅	—	2	4	no	—
233	C₂²×C₅	—	2	4	no	—
234	C₂²×C₅	—	4	24	no	—
235	C₂²×C₅	#435	1	16	yes	complemented
236	C₂²×C₅	C₂×C₄×D₄	1	6	yes	—
237	C₂²×C₅	C₂²×M₁₆	1	6	yes	—
238	C₂²×C₅	C₂²×M₁₆	1	8	yes	complemented
239	C₂²×C₅	C₂×#131	1	6	yes	—
240	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
241	C₄×C₅	—	2	4	no	—
242	C₄×C₅	—	2	4	no	—
243	C₄×C₅	—	2	4	no	—
244	C₄×C₅	—	2	4	no	—
245	C₄×C₅	C₂×C₄×D₄	1	6	yes	—
246	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
247	C₄×C₅	C₂²×#41	1	1	yes	characteristic
248	C₂⁴	—	2	4	no	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	2	4	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	#681	1	8	yes	complemented
254	C₂⁴	C₂²×Dic₅	1	6	yes	—
255	C₂⁴	C₂²×Dic₅	1	6	yes	—
256	C₂⁴	C₂²×Dic₅	1	1	yes	characteristic
257	C₂×D₄	—	2	48	no	—
258	C₂×D₄	C₂²×Dic₅	1	16	yes	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	12	no	—
264	C₂²×C₄	—	2	12	no	—
265	C₂²×C₄	—	2	12	no	—
266	C₂²×C₄	—	2	12	no	—
267	C₂²×C₄	—	2	24	no	—
268	C₂²×C₄	—	2	24	no	—
269	C₂²×C₄	D₄×D₅	1	4	yes	—
270	C₂²×C₄	#711	1	4	yes	—
271	C₂²×C₄	C₂²×Dic₅	1	6	yes	—
272	C₂²×C₄	C₂²×Dic₅	1	6	yes	—
273	C₂²×C₄	C₂²×Dic₅	1	6	yes	—
274	C₂²×C₄	C₂²×Dic₅	1	6	yes	—
275	C₂²×C₄	C₂²×Dic₅	1	12	yes	—
276	C₂²×C₄	C₂²×Dic₅	1	12	yes	—
277	C₂²×C₄	C₂²×Dic₅	1	3	yes	—
278	C₂²×C₄	C₂³×D₅	1	4	yes	—
279	C₂²×C₄	C₂³×D₅	1	4	yes	—
280	C₂²×C₄	C₂³×D₅	1	3	yes	—
281	M₁₆	—	10	32	no	—
282	C₂×C₈	—	5	24	no	—
283	C₂×C₈	—	5	4	no	—
284	C₂×C₈	—	5	4	no	—
285	C₂×C₈	—	5	4	no	—
286	C₂×C₈	—	5	4	no	—
287	C₂×C₈	—	10	32	no	—
288	C₂×C₈	—	10	12	no	—
289	C₂×C₈	—	10	12	no	—
290	C₂×C₈	—	10	12	no	—
291	C₄⋊C₄	C₂²×Dic₅	1	16	yes	—
292	C₂²⋊C₄	C₂²×Dic₅	1	16	yes	—
293	C₂²⋊C₄	C₂²×Dic₅	1	16	yes	—
294	C₄²	C₂²×Dic₅	1	12	yes	—
295	C₄²	C₂³×D₅	1	4	yes	—
296	C₂×C₅	—	2	8	no	—
297	C₂×C₅	—	4	4	no	—
298	C₂×C₅	C₂×#435	1	12	yes	complemented
299	C₂×C₅	C₂²×C₄×D₄	1	1	yes	characteristic
300	C₂×C₅	C₂³×M₁₆	1	1	yes	characteristic
301	C₂×C₅	C₂²×#131	1	1	yes	characteristic
302	C₂³	—	2	32	no	—
303	C₂³	—	2	12	no	—
304	C₂³	—	2	12	no	—
305	C₂³	—	2	12	no	—
306	C₂³	—	2	12	no	—
307	C₂³	—	2	12	no	—
308	C₂³	—	4	16	no	—
309	C₂³	C₂×#681	1	4	yes	—
310	C₂³	C₂×#681	1	24	yes	complemented
311	C₂³	D₄×Dic₅	1	4	yes	—
312	C₂³	#4094	1	4	yes	—
313	C₂³	C₂³×Dic₅	1	4	yes	—
314	C₂³	C₂³×Dic₅	1	4	yes	—
315	C₂³	C₂³×Dic₅	1	3	yes	—
316	D₄	—	2	32	no	—
317	C₂×C₄	—	2	12	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	24	no	—
322	C₂×C₄	—	2	24	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	D₄×Dic₅	1	12	yes	—
328	C₂×C₄	C₂×D₄×D₅	1	6	yes	—
329	C₂×C₄	C₂×#711	1	6	yes	—
330	C₂×C₄	C₂³×Dic₅	1	4	yes	—
331	C₂×C₄	C₂³×Dic₅	1	4	yes	—
332	C₂×C₄	C₂³×Dic₅	1	4	yes	—
333	C₂×C₄	C₂³×Dic₅	1	4	yes	—
334	C₂×C₄	C₂³×Dic₅	1	3	yes	—
335	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
336	C₈	—	5	8	no	—
337	C₈	—	10	4	no	—
338	C₈	—	10	4	no	—
339	C₈	—	10	4	no	—
340	C₅	C₂²×#435	1	1	yes	characteristic, complemented, Sylow
341	C₂²	—	2	48	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	4	24	no	—
348	C₂²	#65300	1	16	yes	direct product factor
349	C₂²	C₂²×#681	1	6	yes	—
350	C₂²	C₂²×#681	1	8	yes	complemented
351	C₂²	C₂×D₄×Dic₅	1	6	yes	—
352	C₂²	C₂×#4094	1	6	yes	—
353	C₂²	C₂⁴×Dic₅	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	4	no	—
358	C₄	C₂×D₄×Dic₅	1	6	yes	—
359	C₄	C₂²×D₄×D₅	1	1	yes	characteristic
360	C₄	C₂²×#711	1	1	yes	characteristic
361	C₂	—	2	8	no	—
362	C₂	—	4	4	no	—
363	C₂	C₂×#65300	1	12	yes	direct product factor
364	C₂	C₂³×#681	1	1	yes	characteristic
365	C₂	C₂²×D₄×Dic₅	1	1	yes	characteristic
366	C₂	C₂²×#4094	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₅
Fitting	C₂²×C₄×C₅×D₄	C₂
socle	C₂⁴×C₅	C₂²×C₄
prime radical	C₂³×C₅×D₄	C₄
cosocle	C₂×C₄×C₅	C₂⁵
hypercenter	C₂²×C₄×D₄	D₅
hypocenter	C₅	C₂²×#435
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂³×#681	C₂	semidirect
3. C₂⁴×#168	C₂	semidirect
4. C₂²×C₂²⋊#168	C₂	semidirect
5. C₂²×C₂²⋊#168	C₂	semidirect
6. C₂×#65300	C₂	direct (N × H)
7. C₂²×C₄⋊#168	C₂	semidirect
8. C₂²×#3935	C₂	semidirect
19. C₂²×#681	C₂²	semidirect
25. C₂³×#168	C₂²	semidirect
26. C₂×C₂²⋊#168	C₂²	semidirect
27. C₂×C₂²⋊#168	C₂²	semidirect
28. #65300	C₂²	direct (N × H)
29. C₂×C₄⋊#168	C₂²	semidirect
30. C₂×#3935	C₂²	semidirect
57. C₂×#681	C₂³	semidirect
62. C₂²×#168	D₄	semidirect
67. C₂²×#168	C₂³	semidirect
68. C₂²⋊#168	C₂³	semidirect
69. C₂²⋊#168	C₂³	semidirect
70. C₄⋊#168	C₂³	semidirect
71. #3935	C₂³	semidirect
85. C₂⁴×C₅	M₁₆	semidirect
123. C₂×#168	C₂×D₄	semidirect
159. C₂³×C₅	C₂×M₁₆	semidirect
187. #168	C₂²×D₄	semidirect
235. C₂²×C₅	#435	semidirect
238. C₂²×C₅	C₂²×M₁₆	semidirect
253. C₂⁴	#681	semidirect
298. C₂×C₅	C₂×#435	semidirect
310. C₂³	C₂×#681	semidirect
340. C₅	C₂²×#435	semidirect
348. C₂²	#65300	direct (N × H)
350. C₂²	C₂²×#681	semidirect
363. C₂	C₂×#65300	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₅×D₄	2
C₂³×#681	2
C₂⁴×#168	2
C₂²×C₂²⋊#168	2
C₂×#65300	2
C₂²×C₄⋊#168	2
C₂²×#3935	2
C₂²×#435	5

Subgroups — C22×#65300 #12963139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#65300 #12963139