Subgroups — C₂×C₃×#66051 #14482413

Order 1920.

5072 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄×D₅	C₂	1	4	yes	maximal, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4084	C₂	1	4	yes	maximal, complemented
4	C₂×C₃×#4083	C₂	1	4	yes	maximal, complemented
5	C₃×#66051	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃×C₄×D₂₀	C₂	1	2	yes	maximal, complemented
7	C₂×#66051	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₃×D₅	C₂²	1	4	yes	complemented
9	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
11	C₂²×C₃×C₂²⋊D₅	C₂²	1	8	yes	complemented
12	C₂×C₃×D₄×D₅	—	2	32	no	—
13	C₂×C₃×D₄×D₅	C₂²	1	32	yes	complemented
14	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
15	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	complemented
16	C₃×C₅×#127	C₂²	1	8	yes	complemented
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	complemented
19	C₃×#4084	C₂²	1	32	yes	complemented
20	C₃×#4083	C₂²	1	32	yes	complemented
21	C₂×C₃×#685	C₂²	1	4	yes	complemented
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
23	C₃×C₄×D₂₀	C₂²	1	16	yes	complemented
24	C₂×C₃×D₄²	—	5	1	no	maximal, Hall
25	C₂²×D₄×D₅	C₂×C₃	1	4	yes	complemented
26	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#4084	C₂×C₃	1	4	yes	complemented
28	C₂×#4083	C₂×C₃	1	4	yes	complemented
29	#66051	C₂×C₃	1	16	yes	direct product factor
30	C₂×C₄×D₂₀	C₂×C₃	1	2	yes	complemented
31	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
32	C₂³×C₃×D₅	—	2	32	no	—
33	C₂³×C₃×D₅	—	4	8	no	—
34	C₂³×C₃×D₅	C₂³	1	4	yes	—
35	C₂³×C₃×D₅	C₂³	1	16	yes	complemented
36	C₂×C₃×C₅×D₄	—	2	16	no	—
37	C₂×C₃×C₅×D₄	—	4	4	no	—
38	C₂×C₃×C₅×D₄	C₂³	1	16	yes	complemented
39	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂×C₃×C₂²⋊D₅	—	2	32	no	—
43	C₂×C₃×C₂²⋊D₅	C₂³	1	32	yes	complemented
44	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
45	C₃×D₄×D₅	—	2	128	no	—
46	C₂×C₃×D₂₀	D₄	1	16	yes	complemented
47	C₂×C₃×D₂₀	C₂³	1	8	yes	—
48	C₂×C₃×C₄×D₅	—	2	16	no	—
49	C₂×C₃×C₄×D₅	C₂³	1	16	yes	complemented
50	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
51	C₃×C₂²⋊Dic₅	C₂³	1	16	yes	complemented
52	C₃×#685	C₂³	1	16	yes	complemented
53	C₃×C₄⋊Dic₅	C₂³	1	8	yes	complemented
54	C₂³×C₃×D₄	—	5	4	no	—
55	C₃×D₄²	—	5	16	no	—
56	C₂×C₃×#127	D₅	1	1	yes	characteristic, complemented
57	C₂×C₃×#121	—	5	4	no	—
58	C₂×C₃×#120	—	5	4	no	—
59	C₂×C₃×C₄×D₄	—	5	2	no	—
60	C₂⁴×D₅	C₂²×C₃	1	4	yes	complemented
61	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	complemented
62	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
63	C₂²×C₂²⋊D₅	C₂²×C₃	1	8	yes	complemented
64	C₂×D₄×D₅	—	2	32	no	—
65	C₂×D₄×D₅	C₂²×C₃	1	32	yes	complemented
66	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
67	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	complemented
68	C₅×#127	C₂²×C₃	1	8	yes	complemented
69	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
70	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	complemented
71	#4084	C₂²×C₃	1	32	yes	complemented
72	#4083	C₂²×C₃	1	32	yes	complemented
73	C₂×#685	C₂²×C₃	1	4	yes	complemented
74	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	complemented
75	C₄×D₂₀	C₂²×C₃	1	16	yes	complemented
76	C₂×D₄²	—	5	1	no	Sylow
77	C₂³×C₃×C₅	—	2	16	no	—
78	C₂³×C₃×C₅	—	2	8	no	—
79	C₂³×C₃×C₅	C₂⁴	1	8	yes	—
80	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
81	C₂²×C₃×D₅	—	2	8	no	—
82	C₂²×C₃×D₅	—	2	8	no	—
83	C₂²×C₃×D₅	—	2	64	no	—
84	C₂²×C₃×D₅	—	4	16	no	—
85	C₂²×C₃×D₅	—	4	64	no	—
86	C₂²×C₃×D₅	C₂×D₄	1	16	yes	complemented
87	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
88	C₃×C₅×D₄	—	2	32	no	—
89	C₃×C₅×D₄	—	4	8	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	complemented
92	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
94	C₃×C₂²⋊D₅	—	2	64	no	—
95	C₂×C₃×Dic₅	—	2	8	no	—
96	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
97	C₃×D₂₀	C₂×D₄	1	32	yes	complemented
98	C₃×C₄×D₅	—	2	32	no	—
99	C₂⁵×C₃	—	5	4	no	—
100	C₂²×C₃×D₄	—	5	8	no	—
101	C₂²×C₃×D₄	—	5	32	no	—
102	C₂²×C₃×D₄	—	5	2	no	—
103	C₂²×C₃×D₄	—	10	32	no	—
104	C₂²×C₃×D₄	C₂×D₅	1	4	yes	complemented
105	C₂²×C₃×D₄	C₂×D₅	1	2	yes	complemented
106	C₂³×C₃×C₄	—	5	4	no	—
107	C₃×#127	C₂×D₅	1	8	yes	complemented
108	C₃×#121	—	5	32	no	—
109	C₃×#120	—	5	32	no	—
110	C₃×C₄×D₄	—	5	16	no	—
111	C₂×C₃×C₄⋊C₄	—	5	2	no	—
112	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
113	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
114	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
115	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
116	C₂³×D₅	—	2	32	no	—
117	C₂³×D₅	—	4	8	no	—
118	C₂³×D₅	C₂³×C₃	1	4	yes	—
119	C₂³×D₅	C₂³×C₃	1	16	yes	complemented
120	C₂×C₅×D₄	—	2	16	no	—
121	C₂×C₅×D₄	—	4	4	no	—
122	C₂×C₅×D₄	C₂³×C₃	1	16	yes	complemented
123	C₂×C₅×D₄	C₂³×C₃	1	8	yes	complemented
124	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
126	C₂×C₂²⋊D₅	—	2	32	no	—
127	C₂×C₂²⋊D₅	C₂³×C₃	1	32	yes	complemented
128	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
129	D₄×D₅	—	2	128	no	—
130	C₂×D₂₀	C₃×D₄	1	16	yes	complemented
131	C₂×D₂₀	C₂³×C₃	1	8	yes	—
132	C₂×C₄×D₅	—	2	16	no	—
133	C₂×C₄×D₅	C₂³×C₃	1	16	yes	complemented
134	C₄²×C₅	C₂³×C₃	1	4	yes	complemented
135	C₂²⋊Dic₅	C₂³×C₃	1	16	yes	complemented
136	#685	C₂³×C₃	1	16	yes	complemented
137	C₄⋊Dic₅	C₂³×C₃	1	8	yes	complemented
138	C₂³×D₄	—	5	4	no	—
139	D₄²	—	5	16	no	—
140	C₂×#127	C₃×D₅	1	1	yes	characteristic, complemented
141	C₂×#121	—	5	4	no	—
142	C₂×#120	—	5	4	no	—
143	C₂×C₄×D₄	—	5	2	no	—
144	C₂²×C₃×C₅	—	2	16	no	—
145	C₂²×C₃×C₅	—	2	8	no	—
146	C₂²×C₃×C₅	—	4	16	no	—
147	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
148	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
149	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
150	C₂×C₃×D₅	—	2	32	no	—
151	C₂×C₃×D₅	—	2	8	no	—
152	C₂×C₃×D₅	—	2	8	no	—
153	C₂×C₃×D₅	—	4	64	no	—
154	C₂×C₃×D₅	C₂²×D₄	1	16	yes	complemented
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	C₂²×D₄	1	8	yes	complemented
157	C₃×Dic₅	—	2	8	no	—
158	C₂⁴×C₃	—	5	4	no	—
159	C₂⁴×C₃	—	5	16	no	—
160	C₂⁴×C₃	—	10	32	no	—
161	C₂⁴×C₃	—	20	8	no	—
162	C₂⁴×C₃	C₂²×D₅	1	4	yes	—
163	C₂×C₃×D₄	—	2	16	no	—
164	C₂×C₃×D₄	—	4	4	no	—
165	C₂×C₃×D₄	—	5	32	no	—
166	C₂×C₃×D₄	—	5	16	no	—
167	C₂×C₃×D₄	—	5	8	no	—
168	C₂×C₃×D₄	—	10	128	no	—
169	C₂×C₃×D₄	—	10	32	no	—
170	C₂×C₃×D₄	C₂²×D₅	1	16	yes	complemented
171	C₂×C₃×D₄	C₂²×D₅	1	8	yes	complemented
172	C₂²×C₃×C₄	—	5	4	no	—
173	C₂²×C₃×C₄	—	5	16	no	—
174	C₂²×C₃×C₄	—	10	16	no	—
175	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
177	C₃×C₄⋊C₄	—	5	8	no	—
178	C₃×C₂²⋊C₄	—	5	16	no	—
179	C₃×C₂²⋊C₄	—	5	16	no	—
180	C₃×C₄²	C₂²×D₅	1	4	yes	complemented
181	C₂³×C₅	—	2	16	no	—
182	C₂³×C₅	—	2	8	no	—
183	C₂³×C₅	C₂⁴×C₃	1	8	yes	—
184	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
185	C₂²×D₅	—	2	8	no	—
186	C₂²×D₅	—	2	8	no	—
187	C₂²×D₅	—	2	64	no	—
188	C₂²×D₅	—	4	16	no	—
189	C₂²×D₅	—	4	64	no	—
190	C₂²×D₅	C₂×C₃×D₄	1	16	yes	complemented
191	C₂²×D₅	C₂⁴×C₃	1	8	yes	—
192	C₅×D₄	—	2	32	no	—
193	C₅×D₄	—	4	8	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	complemented
196	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
197	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
198	C₂²⋊D₅	—	2	64	no	—
199	C₂×Dic₅	—	2	8	no	—
200	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
201	D₂₀	C₂×C₃×D₄	1	32	yes	complemented
202	C₄×D₅	—	2	32	no	—
203	C₂⁵	—	5	4	no	—
204	C₂²×D₄	—	5	8	no	—
205	C₂²×D₄	—	5	32	no	—
206	C₂²×D₄	—	5	2	no	—
207	C₂²×D₄	—	10	32	no	—
208	C₂²×D₄	C₂×C₃×D₅	1	4	yes	complemented
209	C₂²×D₄	C₂×C₃×D₅	1	2	yes	complemented
210	C₂³×C₄	—	5	4	no	—
211	#127	C₂×C₃×D₅	1	8	yes	complemented
212	#121	—	5	32	no	—
213	#120	—	5	32	no	—
214	C₄×D₄	—	5	16	no	—
215	C₂×C₄⋊C₄	—	5	2	no	—
216	C₂×C₂²⋊C₄	—	5	4	no	—
217	C₂×C₂²⋊C₄	—	5	4	no	—
218	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
219	C₂×C₃×C₅	—	4	8	no	—
220	C₂×C₃×C₅	D₄²	1	4	yes	complemented
221	C₂×C₃×C₅	C₂³×D₄	1	2	yes	—
222	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
223	C₃×D₅	—	2	16	no	—
224	C₂³×C₃	—	2	16	no	—
225	C₂³×C₃	—	2	8	no	—
226	C₂³×C₃	—	5	16	no	—
227	C₂³×C₃	—	5	8	no	—
228	C₂³×C₃	—	10	64	no	—
229	C₂³×C₃	—	10	8	no	—
230	C₂³×C₃	—	10	8	no	—
231	C₂³×C₃	—	20	16	no	—
232	C₂³×C₃	—	20	64	no	—
233	C₂³×C₃	C₂³×D₅	1	8	yes	—
234	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
235	C₃×D₄	—	2	32	no	—
236	C₃×D₄	—	4	8	no	—
237	C₃×D₄	—	5	32	no	—
238	C₃×D₄	—	10	64	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	5	8	no	—
241	C₂×C₃×C₄	—	10	8	no	—
242	C₂×C₃×C₄	—	10	32	no	—
243	C₂×C₃×C₄	D₄×D₅	1	8	yes	complemented
244	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
245	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
246	C₂²×C₅	—	2	16	no	—
247	C₂²×C₅	—	2	8	no	—
248	C₂²×C₅	—	4	16	no	—
249	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
250	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
251	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
252	C₂×D₅	—	2	8	no	—
253	C₂×D₅	—	2	8	no	—
254	C₂×D₅	—	2	32	no	—
255	C₂×D₅	—	4	64	no	—
256	C₂×D₅	C₂²×C₃×D₄	1	16	yes	complemented
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	C₂²×C₃×D₄	1	8	yes	complemented
259	Dic₅	—	2	8	no	—
260	C₂⁴	—	5	4	no	—
261	C₂⁴	—	5	16	no	—
262	C₂⁴	—	10	32	no	—
263	C₂⁴	—	20	8	no	—
264	C₂⁴	C₂²×C₃×D₅	1	4	yes	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	4	4	no	—
267	C₂×D₄	—	5	32	no	—
268	C₂×D₄	—	5	16	no	—
269	C₂×D₄	—	5	8	no	—
270	C₂×D₄	—	10	128	no	—
271	C₂×D₄	—	10	32	no	—
272	C₂×D₄	C₂²×C₃×D₅	1	16	yes	complemented
273	C₂×D₄	C₂²×C₃×D₅	1	8	yes	complemented
274	C₂²×C₄	—	5	4	no	—
275	C₂²×C₄	—	5	16	no	—
276	C₂²×C₄	—	10	16	no	—
277	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
279	C₄⋊C₄	—	5	8	no	—
280	C₂²⋊C₄	—	5	16	no	—
281	C₂²⋊C₄	—	5	16	no	—
282	C₄²	C₂²×C₃×D₅	1	4	yes	complemented
283	C₃×C₅	C₂×D₄²	1	1	yes	characteristic, complemented, Hall
284	C₂²×C₃	—	2	16	no	—
285	C₂²×C₃	—	2	8	no	—
286	C₂²×C₃	—	4	16	no	—
287	C₂²×C₃	—	5	16	no	—
288	C₂²×C₃	—	10	32	no	—
289	C₂²×C₃	—	10	8	no	—
290	C₂²×C₃	—	10	8	no	—
291	C₂²×C₃	—	20	64	no	—
292	C₂²×C₃	C₂×D₄×D₅	1	4	yes	—
293	C₂²×C₃	#4144	1	2	yes	—
294	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	—	10	8	no	—
297	C₃×C₄	C₂×D₄×D₅	1	8	yes	complemented
298	C₂×C₅	—	4	8	no	—
299	C₂×C₅	C₃×D₄²	1	4	yes	complemented
300	C₂×C₅	C₂³×C₃×D₄	1	2	yes	—
301	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
302	D₅	—	2	16	no	—
303	C₂³	—	2	16	no	—
304	C₂³	—	2	8	no	—
305	C₂³	—	5	16	no	—
306	C₂³	—	5	8	no	—
307	C₂³	—	10	64	no	—
308	C₂³	—	10	8	no	—
309	C₂³	—	10	8	no	—
310	C₂³	—	20	16	no	—
311	C₂³	—	20	64	no	—
312	C₂³	C₂³×C₃×D₅	1	8	yes	—
313	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
314	D₄	—	2	32	no	—
315	D₄	—	4	8	no	—
316	D₄	—	5	32	no	—
317	D₄	—	10	64	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	5	8	no	—
320	C₂×C₄	—	10	8	no	—
321	C₂×C₄	—	10	32	no	—
322	C₂×C₄	C₃×D₄×D₅	1	8	yes	complemented
323	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
324	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
325	C₂×C₃	—	4	8	no	—
326	C₂×C₃	—	10	16	no	—
327	C₂×C₃	#66051	1	4	yes	direct product factor
328	C₂×C₃	C₂²×D₄×D₅	1	2	yes	—
329	C₂×C₃	C₂×#4144	1	1	yes	characteristic
330	C₅	C₂×C₃×D₄²	1	1	yes	characteristic, complemented, Sylow
331	C₂²	—	2	16	no	—
332	C₂²	—	2	8	no	—
333	C₂²	—	4	16	no	—
334	C₂²	—	5	16	no	—
335	C₂²	—	10	8	no	—
336	C₂²	—	10	8	no	—
337	C₂²	—	10	32	no	—
338	C₂²	—	20	64	no	—
339	C₂²	C₂×C₃×D₄×D₅	1	4	yes	—
340	C₂²	C₃×#4144	1	2	yes	—
341	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	10	8	no	—
344	C₄	C₂×C₃×D₄×D₅	1	8	yes	complemented
345	C₃	C₂×#66051	1	1	yes	characteristic, direct product factor, Sylow
346	C₂	—	4	8	no	—
347	C₂	—	10	16	no	—
348	C₂	C₃×#66051	1	4	yes	direct product factor
349	C₂	C₂²×C₃×D₄×D₅	1	2	yes	—
350	C₂	C₂×C₃×#4144	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#127	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×#127	D₅
hypocenter	C₅	C₂×C₃×D₄²
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#127

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄×D₅	C₂	semidirect
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₂×C₃×#4084	C₂	semidirect
4. C₂×C₃×#4083	C₂	semidirect
5. C₃×#66051	C₂	direct (N × H)
6. C₂×C₃×C₄×D₂₀	C₂	semidirect
7. C₂×#66051	C₃	direct (N × H)
8. C₂⁴×C₃×D₅	C₂²	semidirect
9. C₂²×C₃×C₅×D₄	C₂²	semidirect
10. C₂²×C₃×C₅×D₄	C₂²	semidirect
11. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
13. C₂×C₃×D₄×D₅	C₂²	semidirect
15. C₂²×C₃×C₄×D₅	C₂²	semidirect
16. C₃×C₅×#127	C₂²	semidirect
17. C₂×C₃×C₄²×C₅	C₂²	semidirect
18. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
19. C₃×#4084	C₂²	semidirect
20. C₃×#4083	C₂²	semidirect
21. C₂×C₃×#685	C₂²	semidirect
22. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
23. C₃×C₄×D₂₀	C₂²	semidirect
25. C₂²×D₄×D₅	C₂×C₃	semidirect
26. C₂×C₅×#127	C₂×C₃	semidirect
27. C₂×#4084	C₂×C₃	semidirect
28. C₂×#4083	C₂×C₃	semidirect
29. #66051	C₂×C₃	direct (N × H)
30. C₂×C₄×D₂₀	C₂×C₃	semidirect
35. C₂³×C₃×D₅	C₂³	semidirect
38. C₂×C₃×C₅×D₄	C₂³	semidirect
39. C₂×C₃×C₅×D₄	C₂³	semidirect
43. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
46. C₂×C₃×D₂₀	D₄	semidirect
49. C₂×C₃×C₄×D₅	C₂³	semidirect
50. C₃×C₄²×C₅	C₂³	semidirect
51. C₃×C₂²⋊Dic₅	C₂³	semidirect
52. C₃×#685	C₂³	semidirect
53. C₃×C₄⋊Dic₅	C₂³	semidirect
56. C₂×C₃×#127	D₅	semidirect
60. C₂⁴×D₅	C₂²×C₃	semidirect
61. C₂²×C₅×D₄	C₂²×C₃	semidirect
62. C₂²×C₅×D₄	C₂²×C₃	semidirect
63. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
65. C₂×D₄×D₅	C₂²×C₃	semidirect
67. C₂²×C₄×D₅	C₂²×C₃	semidirect
68. C₅×#127	C₂²×C₃	semidirect
69. C₂×C₄²×C₅	C₂²×C₃	semidirect
70. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
71. #4084	C₂²×C₃	semidirect
72. #4083	C₂²×C₃	semidirect
73. C₂×#685	C₂²×C₃	semidirect
74. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
75. C₄×D₂₀	C₂²×C₃	semidirect
86. C₂²×C₃×D₅	C₂×D₄	semidirect
91. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
97. C₃×D₂₀	C₂×D₄	semidirect
104. C₂²×C₃×D₄	C₂×D₅	semidirect
105. C₂²×C₃×D₄	C₂×D₅	semidirect
107. C₃×#127	C₂×D₅	semidirect
114. C₂×C₃×C₄²	C₂×D₅	semidirect
119. C₂³×D₅	C₂³×C₃	semidirect
122. C₂×C₅×D₄	C₂³×C₃	semidirect
123. C₂×C₅×D₄	C₂³×C₃	semidirect
127. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
130. C₂×D₂₀	C₃×D₄	semidirect
133. C₂×C₄×D₅	C₂³×C₃	semidirect
134. C₄²×C₅	C₂³×C₃	semidirect
135. C₂²⋊Dic₅	C₂³×C₃	semidirect
136. #685	C₂³×C₃	semidirect
137. C₄⋊Dic₅	C₂³×C₃	semidirect
140. C₂×#127	C₃×D₅	semidirect
154. C₂×C₃×D₅	C₂²×D₄	semidirect
156. C₃×C₄×C₅	C₂²×D₄	semidirect
170. C₂×C₃×D₄	C₂²×D₅	semidirect
171. C₂×C₃×D₄	C₂²×D₅	semidirect
180. C₃×C₄²	C₂²×D₅	semidirect
190. C₂²×D₅	C₂×C₃×D₄	semidirect
195. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
201. D₂₀	C₂×C₃×D₄	semidirect
208. C₂²×D₄	C₂×C₃×D₅	semidirect
209. C₂²×D₄	C₂×C₃×D₅	semidirect
211. #127	C₂×C₃×D₅	semidirect
218. C₂×C₄²	C₂×C₃×D₅	semidirect
220. C₂×C₃×C₅	D₄²	semidirect
243. C₂×C₃×C₄	D₄×D₅	semidirect
256. C₂×D₅	C₂²×C₃×D₄	semidirect
258. C₄×C₅	C₂²×C₃×D₄	semidirect
272. C₂×D₄	C₂²×C₃×D₅	semidirect
273. C₂×D₄	C₂²×C₃×D₅	semidirect
282. C₄²	C₂²×C₃×D₅	semidirect
283. C₃×C₅	C₂×D₄²	semidirect
297. C₃×C₄	C₂×D₄×D₅	semidirect
299. C₂×C₅	C₃×D₄²	semidirect
322. C₂×C₄	C₃×D₄×D₅	semidirect
327. C₂×C₃	#66051	direct (N × H)
330. C₅	C₂×C₃×D₄²	semidirect
344. C₄	C₂×C₃×D₄×D₅	semidirect
345. C₃	C₂×#66051	direct (N × H)
348. C₂	C₃×#66051	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×C₃×D₄×D₅	2
C₂×C₃×C₅×#127	2
C₂×C₃×#4084	2
C₂×C₃×#4083	2
C₃×#66051	2
C₂×C₃×C₄×D₂₀	2
C₂×#66051	3
C₂×C₃×D₄²	5

Subgroups — C2×C3×#66051 #14482413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66051 #14482413