Subgroups — C₂²×C₃×#3955 #14412042

Order 1920.

1984 conjugacy classes of subgroups.

The subgroup lattice has 364 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	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3955	C₂	1	12	yes	maximal, direct product factor
5	C₂²×#3955	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂⁴×C₃×D₅	C₄	1	2	yes	—
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×D₂₀	—	2	1	no	—
9	C₂²×C₃×D₂₀	—	2	3	no	—
10	C₂²×C₃×D₂₀	—	2	1	no	—
11	C₂²×C₃×D₂₀	—	2	3	no	—
12	C₂²×C₃×D₂₀	C₄	1	6	yes	—
13	C₂²×C₃×D₂₀	C₂²	1	6	yes	—
14	C₂×C₃×C₅×M₁₆	—	2	3	no	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	6	yes	complemented
16	C₂²×C₃×C₅×C₈	—	2	1	no	—
17	C₂×C₃×#681	—	2	3	no	—
18	C₂×C₃×#681	C₂²	1	6	yes	complemented
19	C₂²×C₃×#168	—	2	1	no	—
20	C₃×#3955	C₂²	1	16	yes	direct product factor
21	C₂²×C₃×#100	—	5	1	no	maximal, Hall
22	C₂³×D₂₀	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×#681	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×#3955	C₂×C₃	1	12	yes	direct product factor
26	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₃×D₅	—	2	6	no	—
28	C₂³×C₃×D₅	—	2	2	no	—
29	C₂³×C₃×D₅	—	4	8	no	—
30	C₂³×C₃×D₅	C₂×C₄	1	12	yes	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	3	yes	—
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	D₄	1	3	yes	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	3	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
37	C₂×C₃×D₂₀	—	2	12	no	—
38	C₂×C₃×D₂₀	—	2	6	no	—
39	C₂×C₃×D₂₀	—	2	6	no	—
40	C₂×C₃×D₂₀	—	2	6	no	—
41	C₂×C₃×D₂₀	—	2	6	no	—
42	C₂×C₃×D₂₀	—	2	6	no	—
43	C₂×C₃×D₂₀	—	2	6	no	—
44	C₂×C₃×D₂₀	C₂×C₄	1	12	yes	—
45	C₂×C₃×D₂₀	C₂³	1	4	yes	—
46	C₃×C₅×M₁₆	—	2	6	no	—
47	C₃×C₅×M₁₆	C₂³	1	4	yes	complemented
48	C₂×C₃×C₅×C₈	—	2	6	no	—
49	C₃×#681	—	2	6	no	—
50	C₃×#681	C₂³	1	4	yes	complemented
51	C₂×C₃×#168	—	2	6	no	—
52	C₂³×C₃×D₄	—	5	1	no	—
53	C₂²×C₃×M₁₆	—	5	1	no	—
54	C₂²×C₃×M₁₆	D₅	1	1	yes	characteristic, complemented
55	C₂×C₃×#100	—	5	12	no	—
56	C₂⁴×D₅	C₃×C₄	1	2	yes	—
57	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
58	C₂²×D₂₀	—	2	1	no	—
59	C₂²×D₂₀	—	2	3	no	—
60	C₂²×D₂₀	—	2	1	no	—
61	C₂²×D₂₀	—	2	3	no	—
62	C₂²×D₂₀	C₃×C₄	1	6	yes	—
63	C₂²×D₂₀	C₂²×C₃	1	6	yes	—
64	C₂×C₅×M₁₆	—	2	3	no	—
65	C₂×C₅×M₁₆	C₂²×C₃	1	6	yes	complemented
66	C₂²×C₅×C₈	—	2	1	no	—
67	C₂×#681	—	2	3	no	—
68	C₂×#681	C₂²×C₃	1	6	yes	complemented
69	C₂²×#168	—	2	1	no	—
70	#3955	C₂²×C₃	1	16	yes	direct product factor
71	C₂²×#100	—	5	1	no	Sylow
72	C₂³×C₃×C₅	—	2	4	no	—
73	C₂³×C₃×C₅	C₂²⋊C₄	1	3	yes	—
74	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
75	C₂³×C₃×C₅	C₂²×C₄	1	3	yes	—
76	C₂²×C₃×D₅	—	2	12	no	—
77	C₂²×C₃×D₅	—	2	12	no	—
78	C₂²×C₃×D₅	—	4	24	no	—
79	C₂²×C₃×D₅	—	4	8	no	—
80	C₂²×C₃×D₅	—	4	24	no	—
81	C₂²×C₃×D₅	C₂²×C₄	1	8	yes	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	6	yes	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	3	yes	—
84	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	3	yes	—
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
86	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
90	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
91	C₃×D₂₀	—	2	12	no	—
92	C₃×D₂₀	—	2	12	no	—
93	C₃×D₂₀	—	2	4	no	—
94	C₃×D₂₀	—	2	4	no	—
95	C₃×C₅×C₈	—	2	4	no	—
96	C₃×#168	—	2	4	no	—
97	C₂⁵×C₃	—	5	2	no	—
98	C₂²×C₃×D₄	—	5	6	no	—
99	C₂²×C₃×D₄	—	5	6	no	—
100	C₂²×C₃×D₄	—	10	3	no	—
101	C₂²×C₃×D₄	—	10	1	no	—
102	C₂²×C₃×D₄	—	10	3	no	—
103	C₂²×C₃×D₄	—	10	1	no	—
104	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
105	C₂×C₃×M₁₆	—	2	3	no	—
106	C₂×C₃×M₁₆	—	5	6	no	—
107	C₂×C₃×M₁₆	—	10	3	no	—
108	C₂×C₃×M₁₆	C₂×D₅	1	6	yes	complemented
109	C₂²×C₃×C₈	—	2	1	no	—
110	C₂²×C₃×C₈	—	10	1	no	—
111	C₃×#100	—	5	16	no	—
112	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
113	C₂³×D₅	—	2	6	no	—
114	C₂³×D₅	—	2	2	no	—
115	C₂³×D₅	—	4	8	no	—
116	C₂³×D₅	C₂×C₃×C₄	1	12	yes	—
117	C₂²×C₄×C₅	C₂×C₃×C₄	1	3	yes	—
118	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₃×D₄	1	3	yes	—
120	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₃×D₄	1	3	yes	—
122	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
123	C₂×D₂₀	—	2	12	no	—
124	C₂×D₂₀	—	2	6	no	—
125	C₂×D₂₀	—	2	6	no	—
126	C₂×D₂₀	—	2	6	no	—
127	C₂×D₂₀	—	2	6	no	—
128	C₂×D₂₀	—	2	6	no	—
129	C₂×D₂₀	—	2	6	no	—
130	C₂×D₂₀	C₂×C₃×C₄	1	12	yes	—
131	C₂×D₂₀	C₂³×C₃	1	4	yes	—
132	C₅×M₁₆	—	2	6	no	—
133	C₅×M₁₆	C₂³×C₃	1	4	yes	complemented
134	C₂×C₅×C₈	—	2	6	no	—
135	#681	—	2	6	no	—
136	#681	C₂³×C₃	1	4	yes	complemented
137	C₂×#168	—	2	6	no	—
138	C₂³×D₄	—	5	1	no	—
139	C₂²×M₁₆	—	5	1	no	—
140	C₂²×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
141	C₂×#100	—	5	12	no	—
142	C₂²×C₃×C₅	—	2	6	no	—
143	C₂²×C₃×C₅	—	2	6	no	—
144	C₂²×C₃×C₅	#100	1	4	yes	complemented
145	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	3	yes	—
146	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	3	yes	—
147	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₃×D₅	—	2	8	no	—
149	C₂×C₃×D₅	—	4	24	no	—
150	C₂×C₃×D₅	—	4	24	no	—
151	C₂×C₃×D₅	—	4	8	no	—
152	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	3	yes	—
153	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	3	yes	—
154	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
156	C₂⁴×C₃	—	5	12	no	—
157	C₂⁴×C₃	—	10	6	no	—
158	C₂⁴×C₃	—	10	2	no	—
159	C₂⁴×C₃	—	20	8	no	—
160	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
161	C₂×C₃×D₄	—	5	12	no	—
162	C₂×C₃×D₄	—	5	4	no	—
163	C₂×C₃×D₄	—	10	12	no	—
164	C₂×C₃×D₄	—	10	6	no	—
165	C₂×C₃×D₄	—	10	6	no	—
166	C₂×C₃×D₄	—	10	6	no	—
167	C₂×C₃×D₄	—	10	6	no	—
168	C₂×C₃×D₄	—	10	6	no	—
169	C₂×C₃×D₄	—	10	6	no	—
170	C₂²×C₃×C₄	C₄×D₅	1	3	yes	—
171	C₂²×C₃×C₄	D₂₀	1	3	yes	—
172	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂²⋊D₅	1	3	yes	—
174	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
176	C₃×M₁₆	—	2	6	no	—
177	C₃×M₁₆	—	5	4	no	—
178	C₃×M₁₆	—	10	6	no	—
179	C₃×M₁₆	C₂²×D₅	1	4	yes	complemented
180	C₂×C₃×C₈	—	2	6	no	—
181	C₂×C₃×C₈	—	10	6	no	—
182	C₂³×C₅	—	2	4	no	—
183	C₂³×C₅	C₃×C₂²⋊C₄	1	3	yes	—
184	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
185	C₂³×C₅	C₂²×C₃×C₄	1	3	yes	—
186	C₂²×D₅	—	2	12	no	—
187	C₂²×D₅	—	2	12	no	—
188	C₂²×D₅	—	4	24	no	—
189	C₂²×D₅	—	4	8	no	—
190	C₂²×D₅	—	4	24	no	—
191	C₂²×D₅	C₂²×C₃×C₄	1	8	yes	—
192	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	6	yes	—
193	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	3	yes	—
194	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	3	yes	—
195	C₂×C₄×C₅	C₂²×C₃×C₄	1	3	yes	—
196	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
197	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
198	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
199	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
200	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
201	D₂₀	—	2	12	no	—
202	D₂₀	—	2	12	no	—
203	D₂₀	—	2	4	no	—
204	D₂₀	—	2	4	no	—
205	C₅×C₈	—	2	4	no	—
206	#168	—	2	4	no	—
207	C₂⁵	—	5	2	no	—
208	C₂²×D₄	—	5	6	no	—
209	C₂²×D₄	—	5	6	no	—
210	C₂²×D₄	—	10	1	no	—
211	C₂²×D₄	—	10	3	no	—
212	C₂²×D₄	—	10	1	no	—
213	C₂²×D₄	—	10	3	no	—
214	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
215	C₂×M₁₆	—	2	3	no	—
216	C₂×M₁₆	—	5	6	no	—
217	C₂×M₁₆	—	10	3	no	—
218	C₂×M₁₆	C₂×C₃×D₅	1	6	yes	complemented
219	C₂²×C₈	—	2	1	no	—
220	C₂²×C₈	—	10	1	no	—
221	#100	—	5	16	no	—
222	C₂×C₃×C₅	—	2	3	no	—
223	C₂×C₃×C₅	—	2	1	no	—
224	C₂×C₃×C₅	C₂×#100	1	6	yes	complemented
225	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
226	C₃×D₅	—	4	8	no	—
227	C₂³×C₃	—	2	4	no	—
228	C₂³×C₃	—	5	8	no	—
229	C₂³×C₃	—	10	12	no	—
230	C₂³×C₃	—	10	12	no	—
231	C₂³×C₃	—	20	24	no	—
232	C₂³×C₃	—	20	24	no	—
233	C₂³×C₃	—	20	8	no	—
234	C₂³×C₃	#685	1	3	yes	—
235	C₂³×C₃	#685	1	1	yes	characteristic
236	C₂³×C₃	C₂×C₄×D₅	1	3	yes	—
237	C₃×D₄	—	10	4	no	—
238	C₃×D₄	—	10	4	no	—
239	C₃×D₄	—	10	12	no	—
240	C₃×D₄	—	10	12	no	—
241	C₂×C₃×C₄	#685	1	6	yes	—
242	C₂×C₃×C₄	#685	1	3	yes	—
243	C₂×C₃×C₄	#685	1	3	yes	—
244	C₂×C₃×C₄	C₂×C₄×D₅	1	3	yes	—
245	C₂×C₃×C₄	C₂×D₂₀	1	3	yes	—
246	C₂×C₃×C₄	C₂×D₂₀	1	3	yes	—
247	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	3	yes	—
248	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	3	yes	—
249	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
250	C₃×C₈	—	2	4	no	—
251	C₃×C₈	—	10	4	no	—
252	C₂²×C₅	—	2	6	no	—
253	C₂²×C₅	—	2	6	no	—
254	C₂²×C₅	C₃×#100	1	4	yes	complemented
255	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	3	yes	—
256	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	3	yes	—
257	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
258	C₂×D₅	—	2	8	no	—
259	C₂×D₅	—	4	24	no	—
260	C₂×D₅	—	4	24	no	—
261	C₂×D₅	—	4	8	no	—
262	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	3	yes	—
263	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	3	yes	—
264	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
265	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
266	C₂⁴	—	5	12	no	—
267	C₂⁴	—	10	6	no	—
268	C₂⁴	—	10	2	no	—
269	C₂⁴	—	20	8	no	—
270	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
271	C₂×D₄	—	5	12	no	—
272	C₂×D₄	—	5	4	no	—
273	C₂×D₄	—	10	12	no	—
274	C₂×D₄	—	10	6	no	—
275	C₂×D₄	—	10	6	no	—
276	C₂×D₄	—	10	6	no	—
277	C₂×D₄	—	10	6	no	—
278	C₂×D₄	—	10	6	no	—
279	C₂×D₄	—	10	6	no	—
280	C₂²×C₄	C₃×C₄×D₅	1	3	yes	—
281	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
282	C₂²×C₄	C₃×D₂₀	1	3	yes	—
283	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
284	C₂²×C₄	C₃×C₂²⋊D₅	1	3	yes	—
285	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
286	M₁₆	—	2	6	no	—
287	M₁₆	—	5	4	no	—
288	M₁₆	—	10	6	no	—
289	M₁₆	C₂²×C₃×D₅	1	4	yes	complemented
290	C₂×C₈	—	2	6	no	—
291	C₂×C₈	—	10	6	no	—
292	C₃×C₅	C₂²×#100	1	1	yes	characteristic, complemented, Hall
293	C₂²×C₃	—	2	6	no	—
294	C₂²×C₃	—	2	6	no	—
295	C₂²×C₃	—	10	8	no	—
296	C₂²×C₃	—	20	8	no	—
297	C₂²×C₃	—	20	24	no	—
298	C₂²×C₃	—	20	24	no	—
299	C₂²×C₃	#3955	1	4	yes	direct product factor
300	C₂²×C₃	C₂×#685	1	3	yes	—
301	C₂²×C₃	C₂×#685	1	3	yes	—
302	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
303	C₃×C₄	C₂×#685	1	3	yes	—
304	C₃×C₄	C₂×#685	1	3	yes	—
305	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
306	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
307	C₂×C₅	—	2	3	no	—
308	C₂×C₅	—	2	1	no	—
309	C₂×C₅	C₂×C₃×#100	1	6	yes	complemented
310	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
311	D₅	—	4	8	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	5	8	no	—
314	C₂³	—	10	12	no	—
315	C₂³	—	10	12	no	—
316	C₂³	—	20	24	no	—
317	C₂³	—	20	24	no	—
318	C₂³	—	20	8	no	—
319	C₂³	C₃×#685	1	3	yes	—
320	C₂³	C₃×#685	1	1	yes	characteristic
321	C₂³	C₂×C₃×C₄×D₅	1	3	yes	—
322	D₄	—	10	4	no	—
323	D₄	—	10	4	no	—
324	D₄	—	10	12	no	—
325	D₄	—	10	12	no	—
326	C₂×C₄	C₃×#685	1	6	yes	—
327	C₂×C₄	C₃×#685	1	3	yes	—
328	C₂×C₄	C₃×#685	1	3	yes	—
329	C₂×C₄	C₂×C₃×C₄×D₅	1	3	yes	—
330	C₂×C₄	C₂×C₃×D₂₀	1	3	yes	—
331	C₂×C₄	C₂×C₃×D₂₀	1	3	yes	—
332	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	3	yes	—
333	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	3	yes	—
334	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
335	C₈	—	2	4	no	—
336	C₈	—	10	4	no	—
337	C₂×C₃	—	2	1	no	—
338	C₂×C₃	—	2	3	no	—
339	C₂×C₃	—	20	8	no	—
340	C₂×C₃	C₂×#3955	1	6	yes	direct product factor
341	C₂×C₃	C₂²×#685	1	1	yes	characteristic
342	C₅	C₂²×C₃×#100	1	1	yes	characteristic, complemented, Sylow
343	C₂²	—	2	6	no	—
344	C₂²	—	2	6	no	—
345	C₂²	—	10	8	no	—
346	C₂²	—	20	8	no	—
347	C₂²	—	20	24	no	—
348	C₂²	—	20	24	no	—
349	C₂²	C₃×#3955	1	4	yes	direct product factor
350	C₂²	C₂×C₃×#685	1	3	yes	—
351	C₂²	C₂×C₃×#685	1	3	yes	—
352	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
353	C₄	C₂×C₃×#685	1	3	yes	—
354	C₄	C₂×C₃×#685	1	3	yes	—
355	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
356	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
357	C₃	C₂²×#3955	1	1	yes	characteristic, direct product factor, Sylow
358	C₂	—	2	1	no	—
359	C₂	—	2	3	no	—
360	C₂	—	20	8	no	—
361	C₂	C₂×C₃×#3955	1	6	yes	direct product factor
362	C₂	C₂²×C₃×#685	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	#685
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂³×C₃×C₅	C₂²⋊C₄
prime radical	C₂³×C₃×D₂₀	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×M₁₆	D₅
hypocenter	C₅	C₂²×C₃×#100
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₂²×C₃×#681	C₂	semidirect
4. C₂×C₃×#3955	C₂	direct (N × H)
5. C₂²×#3955	C₃	direct (N × H)
15. C₂×C₃×C₅×M₁₆	C₂²	semidirect
18. C₂×C₃×#681	C₂²	semidirect
20. C₃×#3955	C₂²	direct (N × H)
23. C₂²×C₅×M₁₆	C₂×C₃	semidirect
24. C₂²×#681	C₂×C₃	semidirect
25. C₂×#3955	C₂×C₃	direct (N × H)
47. C₃×C₅×M₁₆	C₂³	semidirect
50. C₃×#681	C₂³	semidirect
54. C₂²×C₃×M₁₆	D₅	semidirect
65. C₂×C₅×M₁₆	C₂²×C₃	semidirect
68. C₂×#681	C₂²×C₃	semidirect
70. #3955	C₂²×C₃	direct (N × H)
108. C₂×C₃×M₁₆	C₂×D₅	semidirect
133. C₅×M₁₆	C₂³×C₃	semidirect
136. #681	C₂³×C₃	semidirect
140. C₂²×M₁₆	C₃×D₅	semidirect
144. C₂²×C₃×C₅	#100	semidirect
179. C₃×M₁₆	C₂²×D₅	semidirect
218. C₂×M₁₆	C₂×C₃×D₅	semidirect
224. C₂×C₃×C₅	C₂×#100	semidirect
254. C₂²×C₅	C₃×#100	semidirect
289. M₁₆	C₂²×C₃×D₅	semidirect
292. C₃×C₅	C₂²×#100	semidirect
299. C₂²×C₃	#3955	direct (N × H)
309. C₂×C₅	C₂×C₃×#100	semidirect
340. C₂×C₃	C₂×#3955	direct (N × H)
342. C₅	C₂²×C₃×#100	semidirect
349. C₂²	C₃×#3955	direct (N × H)
357. C₃	C₂²×#3955	direct (N × H)
361. C₂	C₂×C₃×#3955	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
C₂²×C₃×C₅×M₁₆	2
C₂²×C₃×#681	2
C₂×C₃×#3955	2
C₂²×#3955	3
C₂²×C₃×#100	5

Subgroups — C22×C3×#3955 #14412042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#3955 #14412042