Subgroups — C₃×C₄×D₅⋊M₁₆ #14411244

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×#704	C₂	1	4	yes	maximal, complemented
4	C₃×C₄×#700	C₂	1	4	yes	maximal, complemented
5	C₃×#65676	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×D₅⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₄×D₅⋊M₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₄×D₅	C₄	1	2	yes	—
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×#704	C₂²	1	4	yes	—
11	C₃×D₅⋊M₁₆	C₄	1	16	yes	direct product factor
12	C₂×C₃×#700	C₂²	1	4	yes	—
13	C₂×C₃×D₅⋊C₈	C₂²	1	4	yes	—
14	C₂×C₃×C₄²×C₅	C₄	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
17	C₃×C₄²×D₅	C₄	1	1	yes	characteristic
18	C₃×C₄²×D₅	C₄	1	2	yes	—
19	C₃×C₄²×D₅	C₄	1	1	yes	characteristic
20	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
21	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
22	C₃×C₄²×D₅	C₂²	1	2	yes	—
23	C₃×#4002	C₂²	1	8	yes	complemented
24	C₃×C₄×#170	C₂²	1	8	yes	complemented
25	C₂×C₃×C₄×M₁₆	—	5	1	no	maximal, Hall
26	C₂×D₅⋊M₁₆	C₂×C₃	1	2	yes	—
27	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
28	C₄×#704	C₂×C₃	1	4	yes	complemented
29	C₄×#700	C₂×C₃	1	4	yes	complemented
30	#65676	C₂×C₃	1	2	yes	complemented
31	C₄×D₅⋊C₈	C₂×C₃	1	2	yes	complemented
32	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
36	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	—	2	8	no	—
38	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
39	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
44	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
47	C₃×#704	C₂×C₄	1	16	yes	complemented
48	C₂×C₃×#170	C₂³	1	8	yes	—
49	C₃×#700	C₂×C₄	1	16	yes	complemented
50	C₃×D₅⋊C₈	C₂×C₄	1	16	yes	complemented
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
53	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
54	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
55	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
56	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
58	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄×Dic₅	C₂³	1	2	yes	—
60	C₃×C₄×Dic₅	C₂³	1	2	yes	—
61	C₂²×C₃×M₁₆	—	5	2	no	—
62	C₂²×C₃×C₄²	—	5	1	no	—
63	C₃×C₄×M₁₆	—	5	4	no	—
64	C₃×C₄×M₁₆	—	5	4	no	—
65	C₂×C₃×#97	—	5	2	no	—
66	C₂×C₃×C₄×C₈	—	5	2	no	—
67	C₂²×C₄×D₅	C₃×C₄	1	2	yes	—
68	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
69	C₂×#704	C₂²×C₃	1	4	yes	—
70	D₅⋊M₁₆	C₃×C₄	1	16	yes	direct product factor
71	C₂×#700	C₂²×C₃	1	4	yes	—
72	C₂×D₅⋊C₈	C₂²×C₃	1	4	yes	—
73	C₂×C₄²×C₅	C₃×C₄	1	1	yes	characteristic
74	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
75	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
76	C₄²×D₅	C₃×C₄	1	1	yes	characteristic
77	C₄²×D₅	C₃×C₄	1	1	yes	characteristic
78	C₄²×D₅	C₃×C₄	1	2	yes	—
79	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
80	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
81	C₄²×D₅	C₂²×C₃	1	2	yes	—
82	#4002	C₂²×C₃	1	8	yes	complemented
83	C₄×#170	C₂²×C₃	1	8	yes	complemented
84	C₂×C₄×M₁₆	—	5	1	no	Sylow
85	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₃×D₅	—	2	4	no	—
87	C₂²×C₃×D₅	C₄²	1	4	yes	—
88	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂×C₃×Dic₅	—	2	4	no	—
97	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
100	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
102	C₃×C₄×D₅	—	2	4	no	—
103	C₃×C₄×D₅	—	2	4	no	—
104	C₃×C₄×D₅	—	2	4	no	—
105	C₃×C₄×D₅	C₄²	1	4	yes	—
106	C₃×C₄×D₅	C₄²	1	4	yes	—
107	C₃×C₄×D₅	M₁₆	1	8	yes	complemented
108	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
109	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
110	C₃×#170	C₂²×C₄	1	16	yes	complemented
111	C₂³×C₃×C₄	—	5	1	no	—
112	C₂³×C₃×C₄	—	5	2	no	—
113	C₂×C₃×M₁₆	—	5	4	no	—
114	C₂×C₃×M₁₆	—	5	16	no	—
115	C₂×C₃×M₁₆	—	5	4	no	—
116	C₂²×C₃×C₈	—	5	4	no	—
117	C₂×C₃×C₄²	—	5	2	no	—
118	C₂×C₃×C₄²	—	5	1	no	—
119	C₂×C₃×C₄²	—	5	1	no	—
120	C₂×C₃×C₄²	—	5	2	no	—
121	C₂×C₃×C₄²	—	5	2	no	—
122	C₂×C₃×C₄²	—	5	1	no	—
123	C₂×C₃×C₄²	—	5	1	no	—
124	C₂×C₃×C₄²	—	5	1	no	—
125	C₂×C₃×C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic
126	C₃×#97	—	5	8	no	—
127	C₃×C₄×C₈	—	5	8	no	—
128	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
131	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
132	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
133	C₂×C₄×D₅	—	2	8	no	—
134	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
135	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
136	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
137	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	—
140	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
141	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
143	#704	C₂×C₃×C₄	1	16	yes	complemented
144	C₂×#170	C₂³×C₃	1	8	yes	—
145	#700	C₂×C₃×C₄	1	16	yes	complemented
146	D₅⋊C₈	C₂×C₃×C₄	1	16	yes	complemented
147	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
148	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
149	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
150	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
151	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
152	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
154	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
155	C₄×Dic₅	C₂³×C₃	1	2	yes	—
156	C₄×Dic₅	C₂³×C₃	1	2	yes	—
157	C₂²×M₁₆	—	5	2	no	—
158	C₂²×C₄²	—	5	1	no	—
159	C₄×M₁₆	—	5	4	no	—
160	C₄×M₁₆	—	5	4	no	—
161	C₂×#97	—	5	2	no	—
162	C₂×C₄×C₈	—	5	2	no	—
163	C₂²×C₃×C₅	—	2	2	no	—
164	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
165	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₃×D₅	—	2	2	no	—
167	C₂×C₃×D₅	—	2	8	no	—
168	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
169	C₂×C₃×D₅	C₂×C₄²	1	2	yes	—
170	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	—
171	C₃×C₄×C₅	—	2	2	no	—
172	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
173	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
174	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
175	C₃×Dic₅	—	2	2	no	—
176	C₃×Dic₅	C₂×C₄²	1	2	yes	—
177	C₃×Dic₅	C₂×M₁₆	1	4	yes	complemented
178	C₃×Dic₅	C₂³×C₄	1	2	yes	—
179	C₂⁴×C₃	—	5	1	no	—
180	C₂²×C₃×C₄	—	5	1	no	—
181	C₂²×C₃×C₄	—	5	8	no	—
182	C₂²×C₃×C₄	—	5	2	no	—
183	C₂²×C₃×C₄	—	5	1	no	—
184	C₂²×C₃×C₄	—	5	1	no	—
185	C₂²×C₃×C₄	—	5	1	no	—
186	C₂²×C₃×C₄	—	5	1	no	—
187	C₂²×C₃×C₄	—	5	2	no	—
188	C₂²×C₃×C₄	—	5	2	no	—
189	C₂²×C₃×C₄	—	5	2	no	—
190	C₂²×C₃×C₄	—	5	2	no	—
191	C₂²×C₃×C₄	—	10	8	no	—
192	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
193	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
194	C₃×M₁₆	—	5	16	no	—
195	C₃×M₁₆	—	5	16	no	—
196	C₂×C₃×C₈	—	5	8	no	—
197	C₂×C₃×C₈	—	5	16	no	—
198	C₃×C₄²	—	5	2	no	—
199	C₃×C₄²	—	5	1	no	—
200	C₃×C₄²	—	5	2	no	—
201	C₃×C₄²	—	5	2	no	—
202	C₃×C₄²	—	5	1	no	—
203	C₃×C₄²	—	5	2	no	—
204	C₃×C₄²	—	5	2	no	—
205	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
206	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	—
207	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
208	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
209	C₂²×D₅	—	2	4	no	—
210	C₂²×D₅	C₃×C₄²	1	4	yes	—
211	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
212	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	C₃×C₄²	1	4	yes	—
215	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
219	C₂×Dic₅	—	2	4	no	—
220	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
221	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
222	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
223	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
224	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
225	C₄×D₅	—	2	4	no	—
226	C₄×D₅	—	2	4	no	—
227	C₄×D₅	—	2	4	no	—
228	C₄×D₅	C₃×C₄²	1	4	yes	—
229	C₄×D₅	C₃×C₄²	1	4	yes	—
230	C₄×D₅	C₃×M₁₆	1	8	yes	complemented
231	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
232	C₄×D₅	C₂²×C₃×C₄	1	4	yes	—
233	#170	C₂²×C₃×C₄	1	16	yes	complemented
234	C₂³×C₄	—	5	1	no	—
235	C₂³×C₄	—	5	2	no	—
236	C₂×M₁₆	—	5	4	no	—
237	C₂×M₁₆	—	5	16	no	—
238	C₂×M₁₆	—	5	4	no	—
239	C₂²×C₈	—	5	4	no	—
240	C₂×C₄²	—	5	2	no	—
241	C₂×C₄²	—	5	1	no	—
242	C₂×C₄²	—	5	1	no	—
243	C₂×C₄²	—	5	1	no	—
244	C₂×C₄²	—	5	2	no	—
245	C₂×C₄²	—	5	2	no	—
246	C₂×C₄²	—	5	1	no	—
247	C₂×C₄²	—	5	1	no	—
248	C₂×C₄²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
249	#97	—	5	8	no	—
250	C₄×C₈	—	5	8	no	—
251	C₂×C₃×C₅	—	2	2	no	—
252	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
253	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
254	C₃×D₅	—	2	2	no	—
255	C₃×D₅	C₄×M₁₆	1	4	yes	complemented
256	C₂³×C₃	—	5	1	no	—
257	C₂³×C₃	—	5	4	no	—
258	C₂³×C₃	—	5	1	no	—
259	C₂³×C₃	—	10	4	no	—
260	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	5	4	no	—
263	C₂×C₃×C₄	—	5	2	no	—
264	C₂×C₃×C₄	—	5	1	no	—
265	C₂×C₃×C₄	—	5	1	no	—
266	C₂×C₃×C₄	—	5	8	no	—
267	C₂×C₃×C₄	—	5	4	no	—
268	C₂×C₃×C₄	—	5	4	no	—
269	C₂×C₃×C₄	—	5	4	no	—
270	C₂×C₃×C₄	—	5	4	no	—
271	C₂×C₃×C₄	—	5	2	no	—
272	C₂×C₃×C₄	—	10	4	no	—
273	C₂×C₃×C₄	—	10	4	no	—
274	C₂×C₃×C₄	—	10	4	no	—
275	C₂×C₃×C₄	—	10	4	no	—
276	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	4	yes	—
277	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
278	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
279	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
281	C₃×C₈	—	5	16	no	—
282	C₂²×C₅	—	2	2	no	—
283	C₂²×C₅	C₂×C₃×C₄²	1	2	yes	—
284	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
285	C₂×D₅	—	2	2	no	—
286	C₂×D₅	—	2	8	no	—
287	C₂×D₅	C₂×C₃×C₄²	1	2	yes	—
288	C₂×D₅	C₂×C₃×C₄²	1	2	yes	—
289	C₂×D₅	C₂×C₃×M₁₆	1	4	yes	—
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
292	C₄×C₅	C₂×C₃×C₄²	1	2	yes	—
293	C₄×C₅	C₂×C₃×M₁₆	1	4	yes	complemented
294	Dic₅	—	2	2	no	—
295	Dic₅	C₂×C₃×C₄²	1	2	yes	—
296	Dic₅	C₂×C₃×M₁₆	1	4	yes	complemented
297	Dic₅	C₂³×C₃×C₄	1	2	yes	—
298	C₂⁴	—	5	1	no	—
299	C₂²×C₄	—	5	1	no	—
300	C₂²×C₄	—	5	8	no	—
301	C₂²×C₄	—	5	1	no	—
302	C₂²×C₄	—	5	1	no	—
303	C₂²×C₄	—	5	2	no	—
304	C₂²×C₄	—	5	1	no	—
305	C₂²×C₄	—	5	1	no	—
306	C₂²×C₄	—	5	2	no	—
307	C₂²×C₄	—	5	2	no	—
308	C₂²×C₄	—	5	2	no	—
309	C₂²×C₄	—	5	2	no	—
310	C₂²×C₄	—	10	8	no	—
311	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
312	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
313	M₁₆	—	5	16	no	—
314	M₁₆	—	5	16	no	—
315	C₂×C₈	—	5	8	no	—
316	C₂×C₈	—	5	16	no	—
317	C₄²	—	5	2	no	—
318	C₄²	—	5	2	no	—
319	C₄²	—	5	2	no	—
320	C₄²	—	5	1	no	—
321	C₄²	—	5	2	no	—
322	C₄²	—	5	2	no	—
323	C₄²	—	5	1	no	—
324	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
325	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
326	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
327	C₃×C₅	C₂×C₄×M₁₆	1	1	yes	characteristic, complemented, Hall
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	5	4	no	—
330	C₂²×C₃	—	5	2	no	—
331	C₂²×C₃	—	5	2	no	—
332	C₂²×C₃	—	10	8	no	—
333	C₂²×C₃	—	10	2	no	—
334	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
335	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	5	4	no	—
338	C₃×C₄	—	5	2	no	—
339	C₃×C₄	—	5	2	no	—
340	C₃×C₄	—	10	2	no	—
341	C₃×C₄	D₅⋊M₁₆	1	4	yes	direct product factor
342	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
343	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	—
344	C₂×C₅	—	2	2	no	—
345	C₂×C₅	C₂²×C₃×C₄²	1	1	yes	characteristic
346	C₂×C₅	C₂²×C₃×M₁₆	1	2	yes	—
347	D₅	—	2	2	no	—
348	D₅	C₃×C₄×M₁₆	1	4	yes	complemented
349	C₂³	—	5	1	no	—
350	C₂³	—	5	4	no	—
351	C₂³	—	5	1	no	—
352	C₂³	—	10	4	no	—
353	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	5	4	no	—
356	C₂×C₄	—	5	1	no	—
357	C₂×C₄	—	5	2	no	—
358	C₂×C₄	—	5	1	no	—
359	C₂×C₄	—	5	8	no	—
360	C₂×C₄	—	5	4	no	—
361	C₂×C₄	—	5	4	no	—
362	C₂×C₄	—	5	4	no	—
363	C₂×C₄	—	5	4	no	—
364	C₂×C₄	—	5	2	no	—
365	C₂×C₄	—	10	4	no	—
366	C₂×C₄	—	10	4	no	—
367	C₂×C₄	—	10	4	no	—
368	C₂×C₄	—	10	4	no	—
369	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	4	yes	—
370	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
371	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
372	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₈	—	5	16	no	—
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	5	4	no	—
377	C₂×C₃	—	10	2	no	—
378	C₂×C₃	C₂×D₅⋊M₁₆	1	2	yes	—
379	C₂×C₃	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
380	C₅	C₂×C₃×C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
381	C₂²	—	2	2	no	—
382	C₂²	—	5	4	no	—
383	C₂²	—	5	2	no	—
384	C₂²	—	5	2	no	—
385	C₂²	—	10	8	no	—
386	C₂²	—	10	2	no	—
387	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
388	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	5	4	no	—
391	C₄	—	5	2	no	—
392	C₄	—	5	2	no	—
393	C₄	—	10	2	no	—
394	C₄	C₃×D₅⋊M₁₆	1	4	yes	direct product factor
395	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
396	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	2	yes	—
397	C₃	C₄×D₅⋊M₁₆	1	1	yes	characteristic, direct product factor, Sylow
398	C₂	—	2	2	no	—
399	C₂	—	5	4	no	—
400	C₂	—	10	2	no	—
401	C₂	C₂×C₃×D₅⋊M₁₆	1	2	yes	—
402	C₂	C₂²×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄²	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄²
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₄²×C₅	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄²	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×C₄×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄² ◁ C₂×C₃×C₄²

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×#704	C₂	semidirect
4. C₃×C₄×#700	C₂	semidirect
5. C₃×#65676	C₂	semidirect
6. C₃×C₄×D₅⋊C₈	C₂	semidirect
7. C₄×D₅⋊M₁₆	C₃	direct (N × H)
11. C₃×D₅⋊M₁₆	C₄	direct (N × H)
23. C₃×#4002	C₂²	semidirect
24. C₃×C₄×#170	C₂²	semidirect
28. C₄×#704	C₂×C₃	semidirect
29. C₄×#700	C₂×C₃	semidirect
30. #65676	C₂×C₃	semidirect
31. C₄×D₅⋊C₈	C₂×C₃	semidirect
47. C₃×#704	C₂×C₄	semidirect
49. C₃×#700	C₂×C₄	semidirect
50. C₃×D₅⋊C₈	C₂×C₄	semidirect
70. D₅⋊M₁₆	C₃×C₄	direct (N × H)
82. #4002	C₂²×C₃	semidirect
83. C₄×#170	C₂²×C₃	semidirect
107. C₃×C₄×D₅	M₁₆	semidirect
110. C₃×#170	C₂²×C₄	semidirect
143. #704	C₂×C₃×C₄	semidirect
145. #700	C₂×C₃×C₄	semidirect
146. D₅⋊C₈	C₂×C₃×C₄	semidirect
174. C₃×C₄×C₅	C₂×M₁₆	semidirect
177. C₃×Dic₅	C₂×M₁₆	semidirect
230. C₄×D₅	C₃×M₁₆	semidirect
233. #170	C₂²×C₃×C₄	semidirect
255. C₃×D₅	C₄×M₁₆	semidirect
293. C₄×C₅	C₂×C₃×M₁₆	semidirect
296. Dic₅	C₂×C₃×M₁₆	semidirect
327. C₃×C₅	C₂×C₄×M₁₆	semidirect
341. C₃×C₄	D₅⋊M₁₆	direct (N × H)
348. D₅	C₃×C₄×M₁₆	semidirect
380. C₅	C₂×C₃×C₄×M₁₆	semidirect
394. C₄	C₃×D₅⋊M₁₆	direct (N × H)
397. C₃	C₄×D₅⋊M₁₆	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×D₅⋊M₁₆	2
C₂×C₃×C₄²×D₅	2
C₃×C₄×#704	2
C₃×C₄×#700	2
C₃×#65676	2
C₃×C₄×D₅⋊C₈	2
C₄×D₅⋊M₁₆	3
C₂×C₃×C₄×M₁₆	5

Subgroups — C3×C4×D5⋊M16 #14411244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₅⋊M₁₆ #14411244