Subgroups — C₂×C₃×#65844 #14480573

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#709	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4076	C₂	1	4	yes	maximal, complemented
4	C₃×#65844	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4043	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×#4041	C₂	1	4	yes	maximal, complemented
7	C₂×#65844	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₂²⋊D₅	C₂²	1	4	yes	—
11	C₂×C₃×#709	—	2	16	no	—
12	C₂×C₃×#709	C₂²	1	16	yes	complemented
13	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
14	C₂²×C₃×D₂₀	C₂²	1	4	yes	—
15	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	—
16	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	complemented
19	C₃×#4076	C₂²	1	32	yes	complemented
20	C₂×C₃×#685	C₂²	1	8	yes	—
21	C₂×C₃×C₄⋊Dic₅	C₂²	1	4	yes	—
22	C₃×#4043	C₂²	1	32	yes	complemented
23	C₃×#4041	C₂²	1	32	yes	complemented
24	C₂×C₃×#537	—	5	1	no	maximal, Hall
25	C₂²×#709	C₂×C₃	1	2	yes	complemented
26	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#4076	C₂×C₃	1	4	yes	complemented
28	#65844	C₂×C₃	1	16	yes	direct product factor
29	C₂×#4043	C₂×C₃	1	4	yes	complemented
30	C₂×#4041	C₂×C₃	1	4	yes	complemented
31	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
32	C₂³×C₃×D₅	C₂³	1	4	yes	—
33	C₂²×C₃×C₄×C₅	—	4	4	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
35	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
39	C₂×C₃×C₂²⋊D₅	—	2	16	no	—
40	C₂×C₃×C₂²⋊D₅	C₂³	1	16	yes	—
41	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
42	C₃×#709	—	2	64	no	—
43	C₂×C₃×D₂₀	—	2	8	no	—
44	C₂×C₃×D₂₀	—	4	8	no	—
45	C₂×C₃×D₂₀	C₂³	1	8	yes	—
46	C₂×C₃×D₂₀	C₂³	1	16	yes	—
47	C₂×C₃×C₄×D₅	—	2	16	no	—
48	C₂×C₃×C₄×D₅	C₂³	1	16	yes	—
49	C₂×C₃×Dic₁₀	—	2	8	no	—
50	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
51	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
52	C₃×#685	C₂³	1	32	yes	—
53	C₃×C₄⋊Dic₅	C₂³	1	16	yes	—
54	C₂²×C₃×#41	—	5	2	no	—
55	C₃×#537	—	5	16	no	—
56	C₂×C₃×C₂²⋊Q₈	—	5	4	no	—
57	C₂×C₃×#121	—	5	4	no	—
58	C₂×C₃×#121	—	5	4	no	—
59	C₂²×C₃×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
60	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
63	C₂×#709	—	2	16	no	—
64	C₂×#709	C₂²×C₃	1	16	yes	complemented
65	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
66	C₂²×D₂₀	C₂²×C₃	1	4	yes	—
67	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	—
68	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
71	#4076	C₂²×C₃	1	32	yes	complemented
72	C₂×#685	C₂²×C₃	1	8	yes	—
73	C₂×C₄⋊Dic₅	C₂²×C₃	1	4	yes	—
74	#4043	C₂²×C₃	1	32	yes	complemented
75	#4041	C₂²×C₃	1	32	yes	complemented
76	C₂×#537	—	5	1	no	Sylow
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
80	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
81	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
82	C₂²×C₃×D₅	—	2	8	no	—
83	C₂²×C₃×D₅	—	2	8	no	—
84	C₂²×C₃×D₅	—	2	8	no	—
85	C₂²×C₃×D₅	C₂⁴	1	8	yes	—
86	C₂×C₃×C₄×C₅	—	2	8	no	—
87	C₂×C₃×C₄×C₅	—	4	8	no	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	complemented
90	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
91	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
92	C₃×C₂²⋊D₅	—	2	32	no	—
93	C₂×C₃×Dic₅	—	2	8	no	—
94	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
95	C₃×D₂₀	—	2	16	no	—
96	C₃×D₂₀	—	4	16	no	—
97	C₃×C₄×D₅	—	2	32	no	—
98	C₃×Dic₁₀	—	2	16	no	—
99	C₂×C₃×#41	—	5	16	no	—
100	C₂×C₃×#41	—	10	16	no	—
101	C₂²×C₃×Q₈	—	5	2	no	—
102	C₂²×C₃×D₄	—	5	4	no	—
103	C₂²×C₃×D₄	—	5	2	no	—
104	C₂²×C₃×D₄	—	5	4	no	—
105	C₂³×C₃×C₄	—	5	4	no	—
106	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
107	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
108	C₃×C₂²⋊Q₈	—	5	32	no	—
109	C₃×#121	—	5	32	no	—
110	C₃×#121	—	5	32	no	—
111	C₂×C₃×C₄⋊C₄	—	5	4	no	—
112	C₂×C₃×C₄⋊C₄	C₂×D₅	1	4	yes	—
113	C₂×C₃×C₄⋊C₄	C₂×D₅	1	8	yes	complemented
114	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
115	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
116	C₂³×D₅	C₂³×C₃	1	4	yes	—
117	C₂²×C₄×C₅	—	4	4	no	—
118	C₂²×C₄×C₅	C₃×D₄	1	8	yes	complemented
119	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
120	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
121	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
122	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
123	C₂×C₂²⋊D₅	—	2	16	no	—
124	C₂×C₂²⋊D₅	C₂³×C₃	1	16	yes	—
125	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
126	#709	—	2	64	no	—
127	C₂×D₂₀	—	2	8	no	—
128	C₂×D₂₀	—	4	8	no	—
129	C₂×D₂₀	C₂³×C₃	1	8	yes	—
130	C₂×D₂₀	C₂³×C₃	1	16	yes	—
131	C₂×C₄×D₅	—	2	16	no	—
132	C₂×C₄×D₅	C₂³×C₃	1	16	yes	—
133	C₂×Dic₁₀	—	2	8	no	—
134	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
135	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
136	#685	C₂³×C₃	1	32	yes	—
137	C₄⋊Dic₅	C₂³×C₃	1	16	yes	—
138	C₂²×#41	—	5	2	no	—
139	#537	—	5	16	no	—
140	C₂×C₂²⋊Q₈	—	5	4	no	—
141	C₂×#121	—	5	4	no	—
142	C₂×#121	—	5	4	no	—
143	C₂²×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
144	C₂²×C₃×C₅	—	2	8	no	—
145	C₂²×C₃×C₅	—	2	2	no	—
146	C₂²×C₃×C₅	—	2	2	no	—
147	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
148	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
149	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
150	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
151	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
152	C₂×C₃×D₅	—	2	8	no	—
153	C₂×C₃×D₅	—	2	8	no	—
154	C₂×C₃×D₅	—	2	8	no	—
155	C₂×C₃×D₅	—	4	16	no	—
156	C₃×C₄×C₅	—	2	8	no	—
157	C₃×C₄×C₅	C₂²×D₄	1	8	yes	—
158	C₃×Dic₅	—	2	8	no	—
159	C₂⁴×C₃	—	5	4	no	—
160	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
161	C₃×#41	—	10	64	no	—
162	C₂×C₃×Q₈	—	5	8	no	—
163	C₂×C₃×Q₈	—	10	8	no	—
164	C₂×C₃×D₄	—	5	16	no	—
165	C₂×C₃×D₄	—	5	8	no	—
166	C₂×C₃×D₄	—	5	16	no	—
167	C₂×C₃×D₄	—	10	16	no	—
168	C₂×C₃×D₄	—	10	8	no	—
169	C₂×C₃×D₄	—	20	8	no	—
170	C₂²×C₃×C₄	—	4	4	no	—
171	C₂²×C₃×C₄	—	5	4	no	—
172	C₂²×C₃×C₄	—	5	16	no	—
173	C₂²×C₃×C₄	—	10	16	no	—
174	C₂²×C₃×C₄	D₂₀	1	8	yes	complemented
175	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
176	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	—
177	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
178	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
179	C₃×C₄⋊C₄	—	5	16	no	—
180	C₃×C₄⋊C₄	C₂²×D₅	1	16	yes	—
181	C₃×C₂²⋊C₄	—	5	32	no	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	—	2	2	no	—
184	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
185	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
186	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
187	C₂²×D₅	—	2	8	no	—
188	C₂²×D₅	—	2	8	no	—
189	C₂²×D₅	—	2	8	no	—
190	C₂²×D₅	C₂⁴×C₃	1	8	yes	—
191	C₂×C₄×C₅	—	2	8	no	—
192	C₂×C₄×C₅	—	4	8	no	—
193	C₂×C₄×C₅	C₂×C₃×D₄	1	8	yes	—
194	C₂×C₄×C₅	C₂×C₃×D₄	1	16	yes	complemented
195	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
196	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
197	C₂²⋊D₅	—	2	32	no	—
198	C₂×Dic₅	—	2	8	no	—
199	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
200	D₂₀	—	2	16	no	—
201	D₂₀	—	4	16	no	—
202	C₄×D₅	—	2	32	no	—
203	Dic₁₀	—	2	16	no	—
204	C₂×#41	—	5	16	no	—
205	C₂×#41	—	10	16	no	—
206	C₂²×Q₈	—	5	2	no	—
207	C₂²×D₄	—	5	4	no	—
208	C₂²×D₄	—	5	2	no	—
209	C₂²×D₄	—	5	4	no	—
210	C₂³×C₄	—	5	4	no	—
211	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
212	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
213	C₂²⋊Q₈	—	5	32	no	—
214	#121	—	5	32	no	—
215	#121	—	5	32	no	—
216	C₂×C₄⋊C₄	—	5	4	no	—
217	C₂×C₄⋊C₄	C₂×C₃×D₅	1	4	yes	—
218	C₂×C₄⋊C₄	C₂×C₃×D₅	1	8	yes	complemented
219	C₂×C₂²⋊C₄	—	5	8	no	—
220	C₂×C₃×C₅	—	2	4	no	—
221	C₂×C₃×C₅	#537	1	4	yes	complemented
222	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
223	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
225	C₃×D₅	—	4	8	no	—
226	C₂³×C₃	—	2	2	no	—
227	C₂³×C₃	—	2	2	no	—
228	C₂³×C₃	—	5	8	no	—
229	C₂³×C₃	—	10	8	no	—
230	C₂³×C₃	—	10	8	no	—
231	C₂³×C₃	—	10	8	no	—
232	C₂³×C₃	C₂×D₂₀	1	4	yes	—
233	C₂³×C₃	C₂³×D₅	1	2	yes	—
234	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
235	C₃×Q₈	—	10	16	no	—
236	C₃×D₄	—	10	32	no	—
237	C₃×D₄	—	10	16	no	—
238	C₃×D₄	—	20	16	no	—
239	C₂×C₃×C₄	—	2	8	no	—
240	C₂×C₃×C₄	—	4	8	no	—
241	C₂×C₃×C₄	—	5	8	no	—
242	C₂×C₃×C₄	—	10	8	no	—
243	C₂×C₃×C₄	—	10	32	no	—
244	C₂×C₃×C₄	C₂×D₂₀	1	8	yes	—
245	C₂×C₃×C₄	C₂×D₂₀	1	16	yes	complemented
246	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
247	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
248	C₂²×C₅	—	2	2	no	—
249	C₂²×C₅	—	2	2	no	—
250	C₂²×C₅	—	2	8	no	—
251	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
252	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
253	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
254	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
255	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
256	C₂×D₅	—	2	8	no	—
257	C₂×D₅	—	2	8	no	—
258	C₂×D₅	—	2	8	no	—
259	C₂×D₅	—	4	16	no	—
260	C₄×C₅	—	2	8	no	—
261	C₄×C₅	C₂²×C₃×D₄	1	8	yes	—
262	Dic₅	—	2	8	no	—
263	C₂⁴	—	5	4	no	—
264	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
265	#41	—	10	64	no	—
266	C₂×Q₈	—	5	8	no	—
267	C₂×Q₈	—	10	8	no	—
268	C₂×D₄	—	5	16	no	—
269	C₂×D₄	—	5	8	no	—
270	C₂×D₄	—	5	16	no	—
271	C₂×D₄	—	10	16	no	—
272	C₂×D₄	—	10	8	no	—
273	C₂×D₄	—	20	8	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	—	5	4	no	—
276	C₂²×C₄	—	5	16	no	—
277	C₂²×C₄	—	10	16	no	—
278	C₂²×C₄	C₃×D₂₀	1	8	yes	complemented
279	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
280	C₂²×C₄	C₂²×C₃×D₅	1	8	yes	—
281	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
282	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
283	C₄⋊C₄	—	5	16	no	—
284	C₄⋊C₄	C₂²×C₃×D₅	1	16	yes	—
285	C₂²⋊C₄	—	5	32	no	—
286	C₃×C₅	C₂×#537	1	1	yes	characteristic, complemented, Hall
287	C₂²×C₃	—	2	8	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	10	8	no	—
291	C₂²×C₃	—	10	8	no	—
292	C₂²×C₃	—	10	8	no	—
293	C₂²×C₃	—	20	16	no	—
294	C₂²×C₃	C₂²×D₂₀	1	4	yes	—
295	C₂²×C₃	C₂²×D₂₀	1	2	yes	—
296	C₂²×C₃	#4144	1	2	yes	—
297	C₂²×C₃	#4147	1	2	yes	—
298	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
299	C₃×C₄	—	2	8	no	—
300	C₃×C₄	—	10	8	no	—
301	C₃×C₄	C₂²×D₂₀	1	8	yes	—
302	C₂×C₅	—	2	4	no	—
303	C₂×C₅	C₃×#537	1	4	yes	complemented
304	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
305	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
307	D₅	—	4	8	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	5	8	no	—
311	C₂³	—	10	8	no	—
312	C₂³	—	10	8	no	—
313	C₂³	—	10	8	no	—
314	C₂³	C₂×C₃×D₂₀	1	4	yes	—
315	C₂³	C₂³×C₃×D₅	1	2	yes	—
316	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
317	Q₈	—	10	16	no	—
318	D₄	—	10	32	no	—
319	D₄	—	10	16	no	—
320	D₄	—	20	16	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	4	8	no	—
323	C₂×C₄	—	5	8	no	—
324	C₂×C₄	—	10	8	no	—
325	C₂×C₄	—	10	32	no	—
326	C₂×C₄	C₂×C₃×D₂₀	1	8	yes	—
327	C₂×C₄	C₂×C₃×D₂₀	1	16	yes	complemented
328	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
329	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
330	C₂×C₃	—	2	4	no	—
331	C₂×C₃	—	20	8	no	—
332	C₂×C₃	#65844	1	4	yes	direct product factor
333	C₂×C₃	C₂³×D₂₀	1	1	yes	characteristic
334	C₂×C₃	C₂×#4144	1	1	yes	characteristic
335	C₂×C₃	C₂×#4147	1	1	yes	characteristic
336	C₅	C₂×C₃×#537	1	1	yes	characteristic, complemented, Sylow
337	C₂²	—	2	8	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	10	8	no	—
341	C₂²	—	10	8	no	—
342	C₂²	—	10	8	no	—
343	C₂²	—	20	16	no	—
344	C₂²	C₂²×C₃×D₂₀	1	4	yes	—
345	C₂²	C₂²×C₃×D₂₀	1	2	yes	—
346	C₂²	C₃×#4144	1	2	yes	—
347	C₂²	C₃×#4147	1	2	yes	—
348	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
349	C₄	—	2	8	no	—
350	C₄	—	10	8	no	—
351	C₄	C₂²×C₃×D₂₀	1	8	yes	—
352	C₃	C₂×#65844	1	1	yes	characteristic, direct product factor, Sylow
353	C₂	—	2	4	no	—
354	C₂	—	20	8	no	—
355	C₂	C₃×#65844	1	4	yes	direct product factor
356	C₂	C₂³×C₃×D₂₀	1	1	yes	characteristic
357	C₂	C₂×C₃×#4144	1	1	yes	characteristic
358	C₂	C₂×C₃×#4147	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₃×C₄⋊C₄	D₅
hypocenter	C₅	C₂×C₃×#537
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#709	C₂	semidirect
2. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₂×C₃×#4076	C₂	semidirect
4. C₃×#65844	C₂	direct (N × H)
5. C₂×C₃×#4043	C₂	semidirect
6. C₂×C₃×#4041	C₂	semidirect
7. C₂×#65844	C₃	direct (N × H)
12. C₂×C₃×#709	C₂²	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
19. C₃×#4076	C₂²	semidirect
22. C₃×#4043	C₂²	semidirect
23. C₃×#4041	C₂²	semidirect
25. C₂²×#709	C₂×C₃	semidirect
26. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
27. C₂×#4076	C₂×C₃	semidirect
28. #65844	C₂×C₃	direct (N × H)
29. C₂×#4043	C₂×C₃	semidirect
30. C₂×#4041	C₂×C₃	semidirect
34. C₂²×C₃×C₄×C₅	D₄	semidirect
59. C₂²×C₃×C₄⋊C₄	D₅	semidirect
64. C₂×#709	C₂²×C₃	semidirect
70. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
71. #4076	C₂²×C₃	semidirect
74. #4043	C₂²×C₃	semidirect
75. #4041	C₂²×C₃	semidirect
89. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
113. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
118. C₂²×C₄×C₅	C₃×D₄	semidirect
143. C₂²×C₄⋊C₄	C₃×D₅	semidirect
174. C₂²×C₃×C₄	D₂₀	semidirect
194. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
218. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
221. C₂×C₃×C₅	#537	semidirect
245. C₂×C₃×C₄	C₂×D₂₀	semidirect
278. C₂²×C₄	C₃×D₂₀	semidirect
286. C₃×C₅	C₂×#537	semidirect
303. C₂×C₅	C₃×#537	semidirect
327. C₂×C₄	C₂×C₃×D₂₀	semidirect
332. C₂×C₃	#65844	direct (N × H)
336. C₅	C₂×C₃×#537	semidirect
352. C₃	C₂×#65844	direct (N × H)
355. C₂	C₃×#65844	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×#709	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₂×C₃×#4076	2
C₃×#65844	2
C₂×C₃×#4043	2
C₂×C₃×#4041	2
C₂×#65844	3
C₂×C₃×#537	5

Subgroups — C2×C3×#65844 #14480573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65844 #14480573