Subgroups — C₂×#11747010 #14414868

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6649	C₂	1	2	yes	maximal, complemented
3	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90955	C₂	1	2	yes	maximal, complemented
6	#11747010	C₂	1	8	yes	maximal, direct product factor
7	C₂×#64977	—	3	1	no	maximal, Hall
8	C₂²×C₃×D₂₀	C₄	1	1	yes	characteristic
9	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊#168	C₂²	1	2	yes	—
12	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×#685	C₄	1	2	yes	—
15	C₂×C₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
16	C₃×C₄×D₂₀	C₄	1	4	yes	—
17	C₃×C₄×D₂₀	C₂²	1	4	yes	—
18	C₂×#6649	—	2	8	no	—
19	C₂×#6649	C₂²	1	8	yes	complemented
20	C₄⋊(C₃⋊#168)	C₂²	1	4	yes	complemented
21	C₄×C₅×C₃⋊C₈	C₂²	1	4	yes	complemented
22	#90955	C₂²	1	8	yes	complemented
23	C₂×#5012	—	5	1	no	maximal, Hall
24	C₂²×#676	—	3	2	no	—
25	C₂×C₄×D₂₀	D₃	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	—	3	1	no	—
27	C₂×#3952	—	3	2	no	—
28	C₂×C₄⋊#168	—	3	1	no	—
29	#64977	—	3	8	no	—
30	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
35	C₂×C₃×D₂₀	—	2	4	no	—
36	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	—
37	C₂×C₃×C₄×D₅	—	2	4	no	—
38	C₂×C₃×C₄×D₅	—	2	4	no	—
39	C₂×C₃×C₄×D₅	C₂×C₄	1	4	yes	—
40	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
41	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
42	C₃×C₄²×C₅	C₂³	1	2	yes	—
43	C₂×C₃⋊#168	—	2	4	no	—
44	C₂×C₃⋊#168	C₂³	1	4	yes	—
45	C₂×C₅×C₃⋊C₈	—	2	2	no	—
46	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
47	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
48	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
49	C₃×#685	C₂×C₄	1	8	yes	—
50	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
51	#6649	—	2	16	no	—
52	C₂×C₃×C₄×D₄	—	5	1	no	—
53	C₂²×#208	—	5	2	no	—
54	C₂×#830	—	5	2	no	—
55	#5012	—	5	8	no	—
56	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
57	C₂×C₄×C₃⋊C₈	D₅	1	1	yes	characteristic, complemented
58	C₂²×D₂₀	Dic₃	1	1	yes	characteristic
59	C₂²×C₄×D₅	C₂×D₃	1	2	yes	—
60	C₂²×C₅×C₈	—	3	1	no	—
61	C₂²×C₅×C₈	—	3	1	no	—
62	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
63	C₂×#685	Dic₃	1	2	yes	—
64	C₂×C₄⋊Dic₅	Dic₃	1	1	yes	characteristic
65	C₂²×#168	—	3	2	no	—
66	C₂×#676	—	3	8	no	—
67	C₂×#676	—	6	8	no	—
68	C₄×D₂₀	Dic₃	1	4	yes	—
69	C₄×D₂₀	C₂×D₃	1	4	yes	—
70	C₄×C₅×C₈	—	3	4	no	—
71	#3952	—	3	8	no	—
72	C₄⋊#168	—	3	4	no	—
73	C₂×#436	—	15	1	no	Sylow
74	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₃×D₅	—	2	4	no	—
76	C₂²×C₃×D₅	—	2	4	no	—
77	C₂²×C₃×D₅	—	2	4	no	—
78	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
81	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
82	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	#41	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
87	C₂×C₃×Dic₅	—	2	4	no	—
88	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
89	C₃×D₂₀	—	2	8	no	—
90	C₃×C₄×D₅	—	2	8	no	—
91	C₃×C₄×D₅	—	2	4	no	—
92	C₃×C₄×D₅	—	2	4	no	—
93	C₃⋊#168	—	2	4	no	—
94	C₅×C₃⋊C₈	—	2	2	no	—
95	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	complemented
96	C₂²×C₃×D₄	—	5	1	no	—
97	C₂³×C₃×C₄	—	5	2	no	—
98	C₃×C₄×D₄	—	5	4	no	—
99	C₃×C₄×D₄	—	5	4	no	—
100	C₂×C₃×C₄⋊C₄	—	5	1	no	—
101	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
102	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
103	C₂×#208	—	5	8	no	—
104	C₂×#208	—	10	8	no	—
105	C₂²×C₃⋊C₈	—	5	2	no	—
106	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
107	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
108	#830	—	5	8	no	—
109	C₄⋊(C₃⋊C₈)	—	5	4	no	—
110	C₄×C₃⋊C₈	C₂×D₅	1	4	yes	complemented
111	C₂³×D₅	C₂×Dic₃	1	2	yes	—
112	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
115	C₂²×Dic₅	C₂×Dic₃	1	2	yes	—
116	C₂×D₂₀	—	2	4	no	—
117	C₂×D₂₀	C₂×Dic₃	1	4	yes	—
118	C₂×C₄×D₅	—	2	4	no	—
119	C₂×C₄×D₅	—	2	4	no	—
120	C₂×C₄×D₅	C₂×Dic₃	1	4	yes	—
121	C₂×C₄×D₅	C₂²×D₃	1	4	yes	—
122	C₂×C₅×C₈	—	3	4	no	—
123	C₂×C₅×C₈	—	3	2	no	—
124	C₂×C₅×C₈	—	3	2	no	—
125	C₂×C₅×C₈	—	6	2	no	—
126	C₄²×C₅	C₂×Dic₃	1	2	yes	—
127	C₄²×C₅	C₂²×D₃	1	2	yes	—
128	#685	C₂×Dic₃	1	8	yes	—
129	C₄⋊Dic₅	C₂×Dic₃	1	4	yes	—
130	C₂×#168	—	3	4	no	—
131	C₂×#168	—	6	4	no	—
132	#676	—	6	16	no	—
133	C₂²×M₁₆	—	15	2	no	—
134	C₂×C₄×D₄	—	5	1	no	—
135	#436	—	15	8	no	—
136	C₂×C₄⋊C₈	—	15	1	no	—
137	C₂×C₂²⋊C₈	—	15	2	no	—
138	C₂×C₄×C₈	—	3	1	no	—
139	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
140	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
141	C₂²×C₃×C₅	#131	1	2	yes	—
142	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₃×D₅	—	2	4	no	—
144	C₂×C₃×D₅	—	2	4	no	—
145	C₂×C₃×D₅	—	2	4	no	—
146	C₂×C₃×D₅	—	4	8	no	—
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
149	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
150	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
152	C₃×Dic₅	—	2	4	no	—
153	C₂⁴×C₃	—	5	2	no	—
154	C₂×C₃×D₄	—	5	4	no	—
155	C₂×C₃×D₄	—	10	4	no	—
156	C₂²×C₃×C₄	—	5	2	no	—
157	C₂²×C₃×C₄	—	5	4	no	—
158	C₂²×C₃×C₄	—	5	4	no	—
159	C₂²×C₃×C₄	—	10	4	no	—
160	C₂²×C₃×C₄	—	10	4	no	—
161	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
164	C₃×C₄⋊C₄	—	5	4	no	—
165	C₃×C₂²⋊C₄	—	5	8	no	—
166	C₃×C₄²	C₄×D₅	1	2	yes	—
167	C₃×C₄²	C₂²×D₅	1	2	yes	—
168	#208	—	10	16	no	—
169	C₂×C₃⋊C₈	—	2	2	no	—
170	C₂×C₃⋊C₈	—	5	4	no	—
171	C₂×C₃⋊C₈	—	10	4	no	—
172	C₂×C₃⋊C₈	D₂₀	1	4	yes	complemented
173	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
174	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
175	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
176	C₂²×D₅	—	2	4	no	—
177	C₂²×D₅	—	2	4	no	—
178	C₂²×D₅	—	2	4	no	—
179	C₂²×D₅	C₂²×Dic₃	1	4	yes	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	#208	1	4	yes	complemented
182	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
183	C₂×C₄×C₅	#237	1	2	yes	—
184	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
185	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
186	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
187	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
188	C₂×Dic₅	—	2	4	no	—
189	C₂×Dic₅	C₂²×Dic₃	1	4	yes	—
190	D₂₀	—	2	8	no	—
191	C₄×D₅	—	2	8	no	—
192	C₄×D₅	—	2	4	no	—
193	C₄×D₅	—	2	4	no	—
194	C₅×C₈	—	3	4	no	—
195	C₅×C₈	—	6	2	no	—
196	#168	—	6	4	no	—
197	C₂²×D₄	—	5	1	no	—
198	C₂³×C₄	—	5	2	no	—
199	C₂×M₁₆	—	15	8	no	—
200	C₂×M₁₆	—	30	8	no	—
201	C₂²×C₈	—	3	1	no	—
202	C₂²×C₈	—	3	1	no	—
203	C₂²×C₈	—	15	2	no	—
204	C₄×D₄	—	5	4	no	—
205	C₄×D₄	—	5	4	no	—
206	C₂×C₄⋊C₄	—	5	1	no	—
207	C₂×C₂²⋊C₄	—	5	2	no	—
208	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
209	C₄⋊C₈	—	15	4	no	—
210	C₂²⋊C₈	—	15	8	no	—
211	C₄×C₈	—	3	4	no	—
212	C₂×C₃×C₅	#436	1	4	yes	complemented
213	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
215	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
216	C₃×D₅	—	4	4	no	—
217	C₂³×C₃	—	5	4	no	—
218	C₂³×C₃	—	10	4	no	—
219	C₂³×C₃	—	10	4	no	—
220	C₂³×C₃	—	10	4	no	—
221	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
222	C₃×D₄	—	10	8	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	5	4	no	—
225	C₂×C₃×C₄	—	10	4	no	—
226	C₂×C₃×C₄	—	10	4	no	—
227	C₂×C₃×C₄	—	10	4	no	—
228	C₂×C₃×C₄	—	10	8	no	—
229	C₂×C₃×C₄	#676	1	4	yes	complemented
230	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
231	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
233	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
234	C₂×C₃×C₄	#709	1	2	yes	—
235	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
236	C₃⋊C₈	—	2	2	no	—
237	C₃⋊C₈	—	10	4	no	—
238	C₃⋊C₈	C₂×D₂₀	1	4	yes	complemented
239	C₂²×C₅	C₂×#208	1	2	yes	—
240	C₂²×C₅	D₄×Dic₃	1	2	yes	—
241	C₂²×C₅	#948	1	2	yes	—
242	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
243	C₂×D₅	—	2	4	no	—
244	C₂×D₅	—	2	4	no	—
245	C₂×D₅	—	2	4	no	—
246	C₂×D₅	—	4	8	no	—
247	C₄×C₅	—	2	2	no	—
248	C₄×C₅	C₂×#208	1	4	yes	complemented
249	C₄×C₅	D₄×Dic₃	1	2	yes	—
250	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
251	C₄×C₅	C₂×#237	1	1	yes	characteristic
252	Dic₅	—	2	4	no	—
253	C₂⁴	—	5	2	no	—
254	C₂×D₄	—	5	4	no	—
255	C₂×D₄	—	10	4	no	—
256	C₂²×C₄	—	5	2	no	—
257	C₂²×C₄	—	5	4	no	—
258	C₂²×C₄	—	5	4	no	—
259	C₂²×C₄	—	10	4	no	—
260	C₂²×C₄	—	10	4	no	—
261	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
262	C₂²×C₄	D₅×Dic₃	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
264	M₁₆	—	30	16	no	—
265	C₂×C₈	—	3	4	no	—
266	C₂×C₈	—	3	2	no	—
267	C₂×C₈	—	3	2	no	—
268	C₂×C₈	—	6	2	no	—
269	C₂×C₈	—	15	4	no	—
270	C₂×C₈	—	30	4	no	—
271	C₄⋊C₄	—	5	4	no	—
272	C₂²⋊C₄	—	5	8	no	—
273	C₄²	D₅×Dic₃	1	2	yes	—
274	C₄²	C₂×D₃×D₅	1	2	yes	—
275	C₃×C₅	C₂×#436	1	1	yes	characteristic, complemented, Hall
276	C₂²×C₃	—	10	4	no	—
277	C₂²×C₃	—	10	4	no	—
278	C₂²×C₃	—	10	4	no	—
279	C₂²×C₃	—	20	8	no	—
280	C₂²×C₃	C₄×D₂₀	1	2	yes	—
281	C₂²×C₃	C₂×#676	1	2	yes	—
282	C₂²×C₃	#4047	1	2	yes	—
283	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	—	10	4	no	—
286	C₃×C₄	C₄×D₂₀	1	2	yes	—
287	C₃×C₄	C₂×#676	1	4	yes	complemented
288	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
289	C₃×C₄	C₂×#709	1	1	yes	characteristic
290	C₂×C₅	#5012	1	4	yes	complemented
291	C₂×C₅	C₂²×#208	1	1	yes	characteristic
292	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
293	C₂×C₅	C₂×#948	1	1	yes	characteristic
294	D₅	—	4	4	no	—
295	C₂³	—	5	4	no	—
296	C₂³	—	10	4	no	—
297	C₂³	—	10	4	no	—
298	C₂³	—	10	4	no	—
299	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
300	D₄	—	10	8	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	5	4	no	—
303	C₂×C₄	—	10	4	no	—
304	C₂×C₄	—	10	8	no	—
305	C₂×C₄	—	10	4	no	—
306	C₂×C₄	—	10	4	no	—
307	C₂×C₄	#6649	1	4	yes	complemented
308	C₂×C₄	#6765	1	2	yes	—
309	C₂×C₄	D₃×D₂₀	1	2	yes	—
310	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
311	C₂×C₄	C₂×D₅×Dic₃	1	1	yes	characteristic
312	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
313	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
314	C₈	—	3	4	no	—
315	C₈	—	6	2	no	—
316	C₈	—	30	4	no	—
317	C₂×C₃	—	20	4	no	—
318	C₂×C₃	#64977	1	4	yes	complemented
319	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
320	C₂×C₃	C₂²×#676	1	1	yes	characteristic
321	C₂×C₃	C₂×#4047	1	1	yes	characteristic
322	C₅	C₂×#5012	1	1	yes	characteristic, complemented, Sylow
323	C₂²	—	10	4	no	—
324	C₂²	—	10	4	no	—
325	C₂²	—	10	4	no	—
326	C₂²	—	20	8	no	—
327	C₂²	#91283	1	2	yes	—
328	C₂²	C₂×#6649	1	2	yes	—
329	C₂²	Dic₃×D₂₀	1	2	yes	—
330	C₂²	C₂²×D₅×Dic₃	1	1	yes	characteristic
331	C₄	—	2	2	no	—
332	C₄	—	10	4	no	—
333	C₄	C₂×#6649	1	4	yes	complemented
334	C₄	Dic₃×D₂₀	1	2	yes	—
335	C₄	C₂×#6765	1	1	yes	characteristic
336	C₄	C₂×D₃×D₂₀	1	1	yes	characteristic
337	C₃	C₂×#64977	1	1	yes	characteristic, complemented, Sylow
338	C₂	—	20	4	no	—
339	C₂	#11747010	1	4	yes	direct product factor
340	C₂	C₂×#91283	1	1	yes	characteristic
341	C₂	C₂²×#6649	1	1	yes	characteristic
342	C₂	C₂×Dic₃×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃×D₅
commutator	C₂²×C₃×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₃×D₂₀	C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₂×#436
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂²×#6649	C₂	semidirect
3. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
4. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
5. C₂×#90955	C₂	semidirect
6. #11747010	C₂	direct (N × H)
19. C₂×#6649	C₂²	semidirect
20. C₄⋊(C₃⋊#168)	C₂²	semidirect
21. C₄×C₅×C₃⋊C₈	C₂²	semidirect
22. #90955	C₂²	semidirect
46. C₂×C₅×C₃⋊C₈	D₄	semidirect
57. C₂×C₄×C₃⋊C₈	D₅	semidirect
80. C₂×C₃×C₄×C₅	M₁₆	semidirect
95. C₅×C₃⋊C₈	C₂×D₄	semidirect
110. C₄×C₃⋊C₈	C₂×D₅	semidirect
149. C₃×C₄×C₅	C₂×M₁₆	semidirect
172. C₂×C₃⋊C₈	D₂₀	semidirect
181. C₂×C₄×C₅	#208	semidirect
212. C₂×C₃×C₅	#436	semidirect
229. C₂×C₃×C₄	#676	semidirect
238. C₃⋊C₈	C₂×D₂₀	semidirect
248. C₄×C₅	C₂×#208	semidirect
275. C₃×C₅	C₂×#436	semidirect
287. C₃×C₄	C₂×#676	semidirect
290. C₂×C₅	#5012	semidirect
307. C₂×C₄	#6649	semidirect
318. C₂×C₃	#64977	semidirect
322. C₅	C₂×#5012	semidirect
333. C₄	C₂×#6649	semidirect
337. C₃	C₂×#64977	semidirect
339. C₂	#11747010	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×C₃×C₄×D₂₀	2
C₂²×#6649	2
C₂×C₄⋊(C₃⋊#168)	2
C₂×C₄×C₅×C₃⋊C₈	2
C₂×#90955	2
#11747010	2
C₂×#64977	3
C₂×#5012	5

Subgroups — C2×#11747010 #14414868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11747010 #14414868