Subgroups — C₂×#11754488 #14478992

Order 1920.

3840 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×#91815	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅×#217	C₂	1	4	yes	maximal, complemented
5	#11754488	C₂	1	16	yes	maximal, direct product factor
6	C₂×#91434	C₂	1	4	yes	maximal, complemented
7	C₂×Dic₃×D₂₀	C₂	1	4	yes	maximal, complemented
8	C₂×#65855	—	3	1	no	maximal, Hall
9	C₂⁴×C₃×D₅	C₂²	1	2	yes	—
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×D₂₀	C₄	1	16	yes	complemented
12	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
13	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
14	C₂²×C₃×D₂₀	C₂²	1	8	yes	—
15	C₂²×D₅×Dic₃	C₂²	1	8	yes	complemented
16	C₂×#6719	C₂²	1	2	yes	—
17	#91815	C₂²	1	8	yes	complemented
18	C₂×C₄⋊Dic₁₅	C₂²	1	2	yes	complemented
19	C₂×C₄×Dic₁₅	C₂²	1	2	yes	complemented
20	C₂×C₅×#217	C₂²	1	2	yes	—
21	C₅×#926	C₂²	1	8	yes	complemented
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
23	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
24	D₅×#217	C₂²	1	32	yes	complemented
25	C₂×#6665	C₂²	1	8	yes	complemented
26	#91434	C₂²	1	32	yes	complemented
27	Dic₃×D₂₀	C₂²	1	32	yes	complemented
28	C₂×#5798	—	5	1	no	maximal, Hall
29	C₂³×D₂₀	D₃	1	1	yes	characteristic
30	C₂×C₅×#117	—	3	1	no	—
31	C₂×#4072	—	3	1	no	—
32	#65855	—	3	16	no	—
33	C₂×#4039	—	3	4	no	—
34	C₂×D₅×C₂²⋊C₄	—	3	4	no	—
35	C₂×C₄×D₂₀	—	3	4	no	—
36	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
37	C₂³×C₃×D₅	—	4	8	no	—
38	C₂³×C₃×D₅	C₂×C₄	1	16	yes	complemented
39	C₂³×C₃×D₅	C₂³	1	4	yes	—
40	C₂³×C₃×D₅	C₂³	1	8	yes	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	complemented
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
45	C₂²×Dic₁₅	C₂³	1	4	yes	—
46	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
47	C₂×C₃×D₂₀	C₂×C₄	1	16	yes	complemented
48	C₂×C₃×D₂₀	C₂×C₄	1	16	yes	complemented
49	C₂×C₃×D₂₀	C₂×C₄	1	64	yes	complemented
50	C₂×C₃×D₂₀	C₂³	1	8	yes	—
51	C₂×C₃×D₂₀	C₂³	1	8	yes	—
52	C₂×D₅×Dic₃	—	4	16	no	—
53	C₂×D₅×Dic₃	C₂³	1	32	yes	complemented
54	#6719	C₂³	1	8	yes	—
55	C₄⋊Dic₁₅	C₂³	1	8	yes	complemented
56	C₄×Dic₁₅	C₂³	1	8	yes	complemented
57	C₅×#217	C₂³	1	8	yes	—
58	C₅×C₄⋊Dic₃	C₂³	1	8	yes	complemented
59	C₄×C₅×Dic₃	C₂³	1	8	yes	complemented
60	#6665	C₂³	1	32	yes	complemented
61	C₂³×C₃×D₄	—	5	1	no	—
62	C₂²×#217	—	5	4	no	—
63	#5798	—	5	16	no	—
64	C₂×D₄×Dic₃	—	5	4	no	—
65	C₂×D₄×Dic₃	—	5	4	no	—
66	C₂×#926	—	5	1	no	—
67	C₂×#926	D₅	1	1	yes	characteristic, complemented
68	C₂⁴×D₅	C₂×D₃	1	2	yes	—
69	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
70	C₂²×D₂₀	Dic₃	1	16	yes	complemented
71	C₂²×D₂₀	C₂×D₃	1	2	yes	—
72	C₂²×D₂₀	C₂×D₃	1	2	yes	—
73	C₂²×D₂₀	C₂×D₃	1	8	yes	—
74	C₂²×C₄×D₅	—	3	8	no	—
75	C₅×#117	—	3	8	no	—
76	C₂×C₅×C₄⋊C₄	—	3	2	no	—
77	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
78	C₂×C₄²×C₅	—	3	2	no	—
79	C₂×C₂²⋊Dic₅	—	3	2	no	—
80	C₂×#685	—	3	8	no	—
81	#4072	—	3	8	no	—
82	C₂×C₄⋊Dic₅	—	3	2	no	—
83	C₂×C₄×Dic₅	—	3	2	no	—
84	#4039	—	3	32	no	—
85	D₅×C₂²⋊C₄	—	3	32	no	—
86	C₄×D₂₀	—	3	32	no	—
87	C₂×#518	—	15	1	no	Sylow
88	C₂³×C₃×C₅	—	2	4	no	—
89	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
90	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
91	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
92	C₂²×C₃×D₅	—	2	16	no	—
93	C₂²×C₃×D₅	—	4	32	no	—
94	C₂²×C₃×D₅	—	4	16	no	—
95	C₂²×C₃×D₅	C₂²×C₄	1	16	yes	—
96	C₂²×C₃×D₅	C₂²×C₄	1	32	yes	complemented
97	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	16	yes	complemented
101	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
103	C₂×Dic₁₅	—	2	8	no	—
104	C₂×Dic₁₅	C₂⁴	1	8	yes	—
105	C₂×C₅×Dic₃	—	2	8	no	—
106	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
107	C₃×D₂₀	C₂²×C₄	1	32	yes	complemented
108	C₃×D₂₀	C₂²×C₄	1	32	yes	complemented
109	D₅×Dic₃	—	4	32	no	—
110	C₂⁵×C₃	—	5	2	no	—
111	C₂²×C₃×D₄	—	5	16	no	—
112	C₂²×C₃×D₄	—	5	2	no	—
113	C₂²×C₃×D₄	—	5	2	no	—
114	C₂²×C₃×D₄	—	5	8	no	—
115	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
116	C₂³×Dic₃	—	5	8	no	—
117	C₂×#217	—	5	2	no	—
118	C₂×#217	—	5	8	no	—
119	C₂×#217	—	5	32	no	—
120	C₂×#217	C₂×D₅	1	2	yes	—
121	D₄×Dic₃	—	5	32	no	—
122	D₄×Dic₃	—	5	32	no	—
123	#926	—	5	8	no	—
124	#926	C₂×D₅	1	8	yes	complemented
125	C₂×C₄⋊Dic₃	—	5	2	no	—
126	C₂×C₄⋊Dic₃	C₂×D₅	1	2	yes	complemented
127	C₂×C₄×Dic₃	—	5	2	no	—
128	C₂×C₄×Dic₃	C₂×D₅	1	2	yes	complemented
129	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
130	C₂³×D₅	—	4	8	no	—
131	C₂³×D₅	C₂×Dic₃	1	16	yes	complemented
132	C₂³×D₅	C₂²×D₃	1	4	yes	—
133	C₂³×D₅	C₂²×D₃	1	8	yes	—
134	C₂²×C₄×C₅	—	3	4	no	—
135	C₂²×C₄×C₅	C₂×Dic₃	1	8	yes	complemented
136	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
139	C₂²×Dic₅	—	3	4	no	—
140	C₂×D₂₀	C₂×Dic₃	1	16	yes	complemented
141	C₂×D₂₀	C₂×Dic₃	1	16	yes	complemented
142	C₂×D₂₀	C₂×Dic₃	1	64	yes	complemented
143	C₂×D₂₀	C₂²×D₃	1	8	yes	—
144	C₂×D₂₀	C₂²×D₃	1	8	yes	—
145	C₂×C₄×D₅	—	3	32	no	—
146	C₂×C₄×D₅	—	12	16	no	—
147	C₅×C₄⋊C₄	—	3	8	no	—
148	C₅×C₂²⋊C₄	—	3	8	no	—
149	C₄²×C₅	—	3	8	no	—
150	C₂²⋊Dic₅	—	3	8	no	—
151	#685	—	3	32	no	—
152	C₄⋊Dic₅	—	3	8	no	—
153	C₄×Dic₅	—	3	8	no	—
154	C₂³×D₄	—	5	1	no	—
155	#518	—	15	16	no	—
156	C₂×C₄×D₄	—	15	4	no	—
157	C₂×C₄×D₄	—	15	4	no	—
158	C₂×#117	—	3	1	no	—
159	C₂×#117	—	15	1	no	—
160	C₂²×C₂²⋊C₄	—	15	4	no	—
161	C₂²×C₃×C₅	—	2	8	no	—
162	C₂²×C₃×C₅	—	2	4	no	—
163	C₂²×C₃×C₅	C₂³×C₄	1	4	yes	—
164	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
165	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
166	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
167	C₂×C₃×D₅	—	2	32	no	—
168	C₂×C₃×D₅	—	2	16	no	—
169	C₂×C₃×D₅	—	4	32	no	—
170	C₂×C₃×D₅	C₂³×C₄	1	16	yes	—
171	C₃×C₄×C₅	C₂³×C₄	1	4	yes	—
172	C₃×C₄×C₅	C₂³×C₄	1	4	yes	—
173	Dic₁₅	—	2	8	no	—
174	C₅×Dic₃	—	2	8	no	—
175	C₂⁴×C₃	—	5	4	no	—
176	C₂⁴×C₃	—	5	16	no	—
177	C₂⁴×C₃	—	5	8	no	—
178	C₂⁴×C₃	—	20	8	no	—
179	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
180	C₂×C₃×D₄	—	5	16	no	—
181	C₂×C₃×D₄	—	5	16	no	—
182	C₂×C₃×D₄	—	5	64	no	—
183	C₂×C₃×D₄	—	5	8	no	—
184	C₂×C₃×D₄	—	5	8	no	—
185	C₂²×C₃×C₄	C₄×D₅	1	8	yes	complemented
186	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
189	C₂²×Dic₃	—	5	4	no	—
190	C₂²×Dic₃	—	5	32	no	—
191	C₂²×Dic₃	—	20	16	no	—
192	C₂²×Dic₃	C₂²×D₅	1	4	yes	—
193	#217	—	5	8	no	—
194	#217	—	5	32	no	—
195	#217	C₂²×D₅	1	8	yes	—
196	C₄⋊Dic₃	—	5	8	no	—
197	C₄⋊Dic₃	C₂²×D₅	1	8	yes	complemented
198	C₄×Dic₃	—	5	8	no	—
199	C₄×Dic₃	C₂²×D₅	1	8	yes	complemented
200	C₂³×C₅	—	2	4	no	—
201	C₂³×C₅	C₂²×Dic₃	1	4	yes	—
202	C₂³×C₅	C₂³×D₃	1	2	yes	—
203	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
204	C₂²×D₅	—	2	16	no	—
205	C₂²×D₅	—	4	32	no	—
206	C₂²×D₅	—	4	16	no	—
207	C₂²×D₅	C₂²×Dic₃	1	16	yes	—
208	C₂²×D₅	C₂²×Dic₃	1	32	yes	complemented
209	C₂²×D₅	C₂³×D₃	1	8	yes	—
210	C₂×C₄×C₅	—	3	8	no	—
211	C₂×C₄×C₅	—	6	8	no	—
212	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
213	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
214	C₂×C₄×C₅	C₂²×Dic₃	1	16	yes	complemented
215	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
216	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
217	C₂×Dic₅	—	3	8	no	—
218	C₂×Dic₅	—	6	8	no	—
219	D₂₀	C₂²×Dic₃	1	32	yes	complemented
220	D₂₀	C₂²×Dic₃	1	32	yes	complemented
221	C₄×D₅	—	12	32	no	—
222	C₂⁵	—	5	2	no	—
223	C₂²×D₄	—	5	16	no	—
224	C₂²×D₄	—	5	2	no	—
225	C₂²×D₄	—	5	2	no	—
226	C₂²×D₄	—	5	8	no	—
227	C₂³×C₄	—	15	8	no	—
228	C₂³×C₄	D₃×D₅	1	1	yes	characteristic
229	C₄×D₄	—	15	32	no	—
230	C₄×D₄	—	15	32	no	—
231	#117	—	3	8	no	—
232	#117	—	15	8	no	—
233	C₂×C₄⋊C₄	—	3	2	no	—
234	C₂×C₄⋊C₄	—	15	2	no	—
235	C₂×C₂²⋊C₄	—	3	2	no	—
236	C₂×C₂²⋊C₄	—	15	32	no	—
237	C₂×C₂²⋊C₄	—	15	8	no	—
238	C₂×C₂²⋊C₄	—	15	2	no	—
239	C₂×C₄²	—	3	2	no	—
240	C₂×C₄²	—	15	2	no	—
241	C₂×C₃×C₅	—	2	4	no	—
242	C₂×C₃×C₅	#518	1	4	yes	complemented
243	C₂×C₃×C₅	C₂⁴×C₄	1	1	yes	characteristic
244	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
245	C₃×D₅	—	2	16	no	—
246	C₂³×C₃	—	2	4	no	—
247	C₂³×C₃	—	5	16	no	—
248	C₂³×C₃	—	5	8	no	—
249	C₂³×C₃	—	5	32	no	—
250	C₂³×C₃	—	10	16	no	—
251	C₂³×C₃	—	20	32	no	—
252	C₂³×C₃	—	20	16	no	—
253	C₂³×C₃	C₂×C₄×D₅	1	4	yes	—
254	C₂³×C₃	C₂³×D₅	1	2	yes	—
255	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
256	C₃×D₄	—	5	32	no	—
257	C₃×D₄	—	5	32	no	—
258	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
259	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
260	C₂×C₃×C₄	C₂×C₄×D₅	1	16	yes	complemented
261	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
262	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
263	C₂×Dic₃	—	2	8	no	—
264	C₂×Dic₃	—	5	8	no	—
265	C₂×Dic₃	—	10	8	no	—
266	C₂×Dic₃	—	20	32	no	—
267	C₂×Dic₃	C₂³×D₅	1	8	yes	—
268	C₂²×C₅	—	2	4	no	—
269	C₂²×C₅	—	2	8	no	—
270	C₂²×C₅	#1004	1	4	yes	—
271	C₂²×C₅	C₂³×Dic₃	1	4	yes	—
272	C₂²×C₅	C₂³×Dic₃	1	2	yes	—
273	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
274	C₂×D₅	—	2	16	no	—
275	C₂×D₅	—	2	32	no	—
276	C₂×D₅	—	4	32	no	—
277	C₂×D₅	C₂³×Dic₃	1	16	yes	—
278	C₄×C₅	—	6	8	no	—
279	C₄×C₅	C₂³×Dic₃	1	4	yes	—
280	C₄×C₅	C₂³×Dic₃	1	4	yes	—
281	Dic₅	—	6	8	no	—
282	C₂⁴	—	5	4	no	—
283	C₂⁴	—	5	16	no	—
284	C₂⁴	—	5	8	no	—
285	C₂⁴	—	20	8	no	—
286	C₂⁴	C₂×D₃×D₅	1	1	yes	characteristic
287	C₂×D₄	—	5	16	no	—
288	C₂×D₄	—	5	16	no	—
289	C₂×D₄	—	5	64	no	—
290	C₂×D₄	—	5	8	no	—
291	C₂×D₄	—	5	8	no	—
292	C₂²×C₄	—	3	4	no	—
293	C₂²×C₄	—	15	32	no	—
294	C₂²×C₄	—	15	4	no	—
295	C₂²×C₄	—	60	16	no	—
296	C₂²×C₄	D₅×Dic₃	1	8	yes	complemented
297	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₃×D₅	1	4	yes	—
300	C₄⋊C₄	—	3	8	no	—
301	C₄⋊C₄	—	15	8	no	—
302	C₂²⋊C₄	—	3	8	no	—
303	C₂²⋊C₄	—	15	32	no	—
304	C₂²⋊C₄	—	15	8	no	—
305	C₄²	—	3	8	no	—
306	C₄²	—	15	8	no	—
307	C₃×C₅	C₂×#518	1	1	yes	characteristic, complemented, Hall
308	C₂²×C₃	—	2	8	no	—
309	C₂²×C₃	—	2	4	no	—
310	C₂²×C₃	—	5	16	no	—
311	C₂²×C₃	—	10	32	no	—
312	C₂²×C₃	—	10	16	no	—
313	C₂²×C₃	—	20	32	no	—
314	C₂²×C₃	C₂²×C₄×D₅	1	4	yes	—
315	C₂²×C₃	C₂²×C₄×D₅	1	2	yes	—
316	C₂²×C₃	#4149	1	4	yes	—
317	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
318	C₃×C₄	C₂²×C₄×D₅	1	4	yes	—
319	C₃×C₄	C₂²×C₄×D₅	1	4	yes	—
320	Dic₃	—	2	8	no	—
321	Dic₃	—	10	8	no	—
322	C₂×C₅	—	2	4	no	—
323	C₂×C₅	#5798	1	4	yes	complemented
324	C₂×C₅	C₂×#1004	1	2	yes	—
325	C₂×C₅	C₂⁴×Dic₃	1	1	yes	characteristic
326	D₅	—	2	16	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	5	16	no	—
329	C₂³	—	5	8	no	—
330	C₂³	—	5	32	no	—
331	C₂³	—	10	16	no	—
332	C₂³	—	20	16	no	—
333	C₂³	—	20	32	no	—
334	C₂³	C₂×D₅×Dic₃	1	4	yes	—
335	C₂³	C₂²×D₃×D₅	1	2	yes	—
336	C₂³	C₂²×D₃×D₅	1	1	yes	characteristic
337	D₄	—	5	32	no	—
338	D₄	—	5	32	no	—
339	C₂×C₄	—	3	8	no	—
340	C₂×C₄	—	6	8	no	—
341	C₂×C₄	—	15	8	no	—
342	C₂×C₄	—	30	8	no	—
343	C₂×C₄	—	60	32	no	—
344	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
345	C₂×C₄	C₂×D₅×Dic₃	1	4	yes	—
346	C₂×C₄	C₂×D₅×Dic₃	1	16	yes	complemented
347	C₂×C₄	C₂²×D₃×D₅	1	2	yes	—
348	C₂×C₄	C₂²×D₃×D₅	1	2	yes	—
349	C₂×C₃	—	2	4	no	—
350	C₂×C₃	—	10	16	no	—
351	C₂×C₃	#65855	1	4	yes	complemented
352	C₂×C₃	C₂³×C₄×D₅	1	1	yes	characteristic
353	C₂×C₃	C₂×#4149	1	2	yes	—
354	C₅	C₂×#5798	1	1	yes	characteristic, complemented, Sylow
355	C₂²	—	2	4	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	5	16	no	—
358	C₂²	—	10	16	no	—
359	C₂²	—	10	32	no	—
360	C₂²	—	20	32	no	—
361	C₂²	#92017	1	4	yes	—
362	C₂²	C₂²×D₅×Dic₃	1	4	yes	—
363	C₂²	C₂²×D₅×Dic₃	1	2	yes	—
364	C₂²	C₂³×D₃×D₅	1	1	yes	characteristic
365	C₄	—	6	8	no	—
366	C₄	—	30	8	no	—
367	C₄	C₂²×D₅×Dic₃	1	4	yes	—
368	C₄	C₂²×D₅×Dic₃	1	4	yes	—
369	C₃	C₂×#65855	1	1	yes	characteristic, complemented, Sylow
370	C₂	—	2	4	no	—
371	C₂	—	10	16	no	—
372	C₂	#11754488	1	4	yes	direct product factor
373	C₂	C₂×#92017	1	2	yes	—
374	C₂	C₂³×D₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂⁴×C₄
Frattini	C₂²	C₂³×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×D₂₀	C₂
cosocle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	C₂×#518
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#91815	C₂	semidirect
3. C₂×C₅×#926	C₂	semidirect
4. C₂×D₅×#217	C₂	semidirect
5. #11754488	C₂	direct (N × H)
6. C₂×#91434	C₂	semidirect
7. C₂×Dic₃×D₂₀	C₂	semidirect
11. C₂²×C₃×D₂₀	C₄	semidirect
15. C₂²×D₅×Dic₃	C₂²	semidirect
17. #91815	C₂²	semidirect
18. C₂×C₄⋊Dic₁₅	C₂²	semidirect
19. C₂×C₄×Dic₁₅	C₂²	semidirect
21. C₅×#926	C₂²	semidirect
22. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
23. C₂×C₄×C₅×Dic₃	C₂²	semidirect
24. D₅×#217	C₂²	semidirect
25. C₂×#6665	C₂²	semidirect
26. #91434	C₂²	semidirect
27. Dic₃×D₂₀	C₂²	semidirect
38. C₂³×C₃×D₅	C₂×C₄	semidirect
41. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
47. C₂×C₃×D₂₀	C₂×C₄	semidirect
48. C₂×C₃×D₂₀	C₂×C₄	semidirect
49. C₂×C₃×D₂₀	C₂×C₄	semidirect
53. C₂×D₅×Dic₃	C₂³	semidirect
55. C₄⋊Dic₁₅	C₂³	semidirect
56. C₄×Dic₁₅	C₂³	semidirect
58. C₅×C₄⋊Dic₃	C₂³	semidirect
59. C₄×C₅×Dic₃	C₂³	semidirect
60. #6665	C₂³	semidirect
67. C₂×#926	D₅	semidirect
70. C₂²×D₂₀	Dic₃	semidirect
96. C₂²×C₃×D₅	C₂²×C₄	semidirect
100. C₂×C₃×C₄×C₅	C₂²×C₄	semidirect
107. C₃×D₂₀	C₂²×C₄	semidirect
108. C₃×D₂₀	C₂²×C₄	semidirect
124. #926	C₂×D₅	semidirect
126. C₂×C₄⋊Dic₃	C₂×D₅	semidirect
128. C₂×C₄×Dic₃	C₂×D₅	semidirect
131. C₂³×D₅	C₂×Dic₃	semidirect
135. C₂²×C₄×C₅	C₂×Dic₃	semidirect
140. C₂×D₂₀	C₂×Dic₃	semidirect
141. C₂×D₂₀	C₂×Dic₃	semidirect
142. C₂×D₂₀	C₂×Dic₃	semidirect
185. C₂²×C₃×C₄	C₄×D₅	semidirect
197. C₄⋊Dic₃	C₂²×D₅	semidirect
199. C₄×Dic₃	C₂²×D₅	semidirect
208. C₂²×D₅	C₂²×Dic₃	semidirect
214. C₂×C₄×C₅	C₂²×Dic₃	semidirect
219. D₂₀	C₂²×Dic₃	semidirect
220. D₂₀	C₂²×Dic₃	semidirect
242. C₂×C₃×C₅	#518	semidirect
260. C₂×C₃×C₄	C₂×C₄×D₅	semidirect
296. C₂²×C₄	D₅×Dic₃	semidirect
307. C₃×C₅	C₂×#518	semidirect
323. C₂×C₅	#5798	semidirect
346. C₂×C₄	C₂×D₅×Dic₃	semidirect
351. C₂×C₃	#65855	semidirect
354. C₅	C₂×#5798	semidirect
369. C₃	C₂×#65855	semidirect
372. C₂	#11754488	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×D₂₀	2
C₂×#91815	2
C₂×C₅×#926	2
C₂×D₅×#217	2
#11754488	2
C₂×#91434	2
C₂×Dic₃×D₂₀	2
C₂×#65855	3
C₂×#5798	5

Subgroups — C2×#11754488 #14478992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11754488 #14478992