Subgroups — C₃×#10604753 #14294308

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×D₅⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×(C₂×AGL(1,𝔽₅))⋊C₈	C₂	1	4	yes	maximal, complemented
5	#10604753	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×AGL(1,𝔽₅)	C₄	1	2	yes	—
7	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×#704	C₄	1	2	yes	complemented
9	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
10	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
11	C₂×C₃×C₄×AGL(1,𝔽₅)	C₄	1	2	yes	—
12	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
13	C₃×D₅⋊M₁₆	—	2	2	no	—
14	C₃×D₅⋊M₁₆	—	2	2	no	—
15	C₂×C₃×#700	C₄	1	2	yes	complemented
16	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃×C₅×M₁₆	C₄	1	1	yes	characteristic, complemented
18	C₂×C₃×#681	C₄	1	1	yes	characteristic, complemented
19	C₃×D₅×M₁₆	—	2	2	no	—
20	C₃×D₅×M₁₆	—	2	2	no	—
21	C₂×C₃×#676	C₄	1	2	yes	complemented
22	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
23	C₃×#1728	—	5	1	no	maximal, Hall
24	C₂²×C₄×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
25	C₂×D₅⋊M₁₆	C₂×C₃	1	1	yes	characteristic
26	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic
27	(C₂×AGL(1,𝔽₅))⋊C₈	C₂×C₃	1	4	yes	complemented
28	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
30	C₂²×C₃×AGL(1,𝔽₅)	—	2	8	no	—
31	C₂²×C₃×AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
38	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
39	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
40	C₂×C₃×C₄×D₅	Q₈	1	2	yes	—
41	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
42	C₃×#704	—	2	4	no	—
43	C₂×C₃×#170	C₂×C₄	1	4	yes	complemented
44	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
45	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
46	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
47	C₃×#700	—	2	4	no	—
48	C₃×D₅⋊C₈	—	2	2	no	—
49	C₃×D₅⋊C₈	—	2	2	no	—
50	C₃×C₅×M₁₆	—	2	2	no	—
51	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	complemented
52	C₃×#681	—	2	2	no	—
53	C₂×C₃×#168	C₂×C₄	1	2	yes	complemented
54	C₃×#676	—	2	4	no	—
55	C₃×C₈×D₅	—	2	2	no	—
56	C₃×C₈×D₅	—	2	2	no	—
57	C₂²×C₃×M₁₆	—	5	1	no	—
58	C₂²×C₃×M₁₆	—	5	1	no	—
59	C₂²×C₃×C₄²	—	5	1	no	—
60	C₃×#336	—	5	4	no	—
61	C₂³×AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
62	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
63	C₂×#704	C₃×C₄	1	2	yes	complemented
64	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
65	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
66	C₂×C₄×AGL(1,𝔽₅)	C₃×C₄	1	2	yes	—
67	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
68	D₅⋊M₁₆	—	2	2	no	—
69	D₅⋊M₁₆	—	2	2	no	—
70	C₂×#700	C₃×C₄	1	2	yes	complemented
71	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
72	C₂×C₅×M₁₆	C₃×C₄	1	1	yes	characteristic, complemented
73	C₂×#681	C₃×C₄	1	1	yes	characteristic, complemented
74	D₅×M₁₆	—	2	2	no	—
75	D₅×M₁₆	—	2	2	no	—
76	C₂×#676	C₃×C₄	1	2	yes	complemented
77	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
78	#1728	—	5	1	no	Sylow
79	C₂³×C₃×C₅	C₄²	1	1	yes	characteristic
80	C₂²×C₃×D₅	—	2	4	no	—
81	C₂²×C₃×D₅	C₄²	1	1	yes	characteristic
82	C₂²×C₃×D₅	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
84	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₃×AGL(1,𝔽₅)	—	2	16	no	—
86	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
87	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
88	C₂×C₃×AGL(1,𝔽₅)	M₁₆	1	8	yes	complemented
89	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×Dic₅	C₄²	1	1	yes	characteristic
94	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
95	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
96	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
97	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
98	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
99	C₃×C₄×D₅	C₂²⋊C₄	1	2	yes	—
100	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
101	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
102	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
103	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
104	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
105	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
106	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
107	C₃×#170	—	2	4	no	—
108	C₃×C₅×C₈	—	2	2	no	—
109	C₃×#168	—	2	2	no	—
110	C₂³×C₃×C₄	—	5	1	no	—
111	C₂³×C₃×C₄	—	5	2	no	—
112	C₂×C₃×M₁₆	—	5	2	no	—
113	C₂×C₃×M₁₆	—	5	2	no	—
114	C₂×C₃×M₁₆	—	5	1	no	—
115	C₂×C₃×M₁₆	—	5	2	no	—
116	C₂×C₃×M₁₆	—	10	2	no	—
117	C₂×C₃×M₁₆	—	10	2	no	—
118	C₂×C₃×M₁₆	—	10	2	no	—
119	C₂×C₃×M₁₆	—	10	2	no	—
120	C₂×C₃×M₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
121	C₂²×C₃×C₈	—	5	2	no	—
122	C₂²×C₃×C₈	—	5	2	no	—
123	C₂×C₃×C₄²	—	5	2	no	—
124	C₂×C₃×C₄²	—	5	2	no	—
125	C₂×C₃×C₄²	—	10	2	no	—
126	C₂×C₃×C₄²	—	10	2	no	—
127	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
128	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
129	C₂²×AGL(1,𝔽₅)	—	2	8	no	—
130	C₂²×AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
131	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
137	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
138	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
139	C₂×C₄×D₅	C₃×Q₈	1	2	yes	—
140	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
141	#704	—	2	4	no	—
142	C₂×#170	C₂×C₃×C₄	1	4	yes	complemented
143	C₄×AGL(1,𝔽₅)	—	2	4	no	—
144	C₄×AGL(1,𝔽₅)	—	2	2	no	—
145	C₄×AGL(1,𝔽₅)	—	2	2	no	—
146	#700	—	2	4	no	—
147	D₅⋊C₈	—	2	2	no	—
148	D₅⋊C₈	—	2	2	no	—
149	C₅×M₁₆	—	2	2	no	—
150	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	complemented
151	#681	—	2	2	no	—
152	C₂×#168	C₂×C₃×C₄	1	2	yes	complemented
153	#676	—	2	4	no	—
154	C₈×D₅	—	2	2	no	—
155	C₈×D₅	—	2	2	no	—
156	C₂²×M₁₆	—	5	1	no	—
157	C₂²×M₁₆	—	5	1	no	—
158	C₂²×C₄²	—	5	1	no	—
159	#336	—	5	4	no	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	#95	1	2	yes	—
162	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₃×D₅	—	2	2	no	—
164	C₂×C₃×D₅	—	2	4	no	—
165	C₂×C₃×D₅	—	2	4	no	—
166	C₂×C₃×D₅	#95	1	2	yes	—
167	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₃×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	—
170	C₃×AGL(1,𝔽₅)	—	2	8	no	—
171	C₃×C₄×C₅	#95	1	2	yes	—
172	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₃×Dic₅	#95	1	2	yes	—
175	C₃×Dic₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂⁴×C₃	—	5	1	no	—
178	C₂²×C₃×C₄	—	5	1	no	—
179	C₂²×C₃×C₄	—	5	1	no	—
180	C₂²×C₃×C₄	—	5	1	no	—
181	C₂²×C₃×C₄	—	5	2	no	—
182	C₂²×C₃×C₄	—	5	2	no	—
183	C₂²×C₃×C₄	—	5	2	no	—
184	C₂²×C₃×C₄	—	5	2	no	—
185	C₂²×C₃×C₄	—	5	1	no	—
186	C₂²×C₃×C₄	—	5	1	no	—
187	C₂²×C₃×C₄	—	5	4	no	—
188	C₂²×C₃×C₄	—	10	8	no	—
189	C₂²×C₃×C₄	—	10	4	no	—
190	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
191	C₃×M₁₆	—	2	2	no	—
192	C₃×M₁₆	—	10	4	no	—
193	C₃×M₁₆	—	10	4	no	—
194	C₃×M₁₆	—	10	4	no	—
195	C₃×M₁₆	—	10	2	no	—
196	C₂×C₃×C₈	—	5	4	no	—
197	C₂×C₃×C₈	—	5	2	no	—
198	C₂×C₃×C₈	—	10	2	no	—
199	C₂×C₃×C₈	—	10	2	no	—
200	C₂×C₃×C₈	—	10	2	no	—
201	C₂×C₃×C₈	—	10	2	no	—
202	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
203	C₃×C₄²	—	10	2	no	—
204	C₃×C₄²	—	10	2	no	—
205	C₃×C₄²	—	10	4	no	—
206	C₂³×C₅	C₃×C₄²	1	1	yes	characteristic
207	C₂²×D₅	—	2	4	no	—
208	C₂²×D₅	C₃×C₄²	1	1	yes	characteristic
209	C₂²×D₅	C₃×C₂²⋊C₄	1	2	yes	—
210	C₂²×D₅	C₃×C₄⋊C₄	1	2	yes	—
211	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
212	C₂×AGL(1,𝔽₅)	—	2	16	no	—
213	C₂×AGL(1,𝔽₅)	—	2	4	no	—
214	C₂×AGL(1,𝔽₅)	—	2	4	no	—
215	C₂×AGL(1,𝔽₅)	C₃×M₁₆	1	8	yes	complemented
216	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
217	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
218	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
219	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
220	C₂×Dic₅	C₃×C₄²	1	1	yes	characteristic
221	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
222	C₂×Dic₅	C₃×C₄⋊C₄	1	2	yes	—
223	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
224	C₄×D₅	C₃×C₂²⋊C₄	1	2	yes	—
225	C₄×D₅	C₃×C₂²⋊C₄	1	2	yes	—
226	C₄×D₅	C₃×C₂²⋊C₄	1	2	yes	—
227	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
228	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
229	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
230	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
231	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
232	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
233	C₄×D₅	C₂×C₃×Q₈	1	1	yes	characteristic
234	#170	—	2	4	no	—
235	C₅×C₈	—	2	2	no	—
236	#168	—	2	2	no	—
237	C₂³×C₄	—	5	1	no	—
238	C₂³×C₄	—	5	2	no	—
239	C₂×M₁₆	—	5	2	no	—
240	C₂×M₁₆	—	5	2	no	—
241	C₂×M₁₆	—	5	1	no	—
242	C₂×M₁₆	—	5	2	no	—
243	C₂×M₁₆	—	10	2	no	—
244	C₂×M₁₆	—	10	2	no	—
245	C₂×M₁₆	—	10	2	no	—
246	C₂×M₁₆	—	10	2	no	—
247	C₂×M₁₆	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
248	C₂²×C₈	—	5	2	no	—
249	C₂²×C₈	—	5	2	no	—
250	C₂×C₄²	—	5	2	no	—
251	C₂×C₄²	—	5	2	no	—
252	C₂×C₄²	—	10	2	no	—
253	C₂×C₄²	—	10	2	no	—
254	C₂×C₃×C₅	—	2	2	no	—
255	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
256	C₂×C₃×C₅	C₄×M₁₆	1	2	yes	—
257	C₃×D₅	—	2	2	no	—
258	C₃×D₅	#407	1	2	yes	—
259	C₃×D₅	#423	1	2	yes	—
260	C₂³×C₃	—	5	1	no	—
261	C₂³×C₃	—	5	1	no	—
262	C₂³×C₃	—	5	2	no	—
263	C₂³×C₃	—	5	2	no	—
264	C₂³×C₃	—	10	4	no	—
265	C₂³×C₃	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
266	C₂×C₃×C₄	—	5	1	no	—
267	C₂×C₃×C₄	—	5	1	no	—
268	C₂×C₃×C₄	—	5	2	no	—
269	C₂×C₃×C₄	—	5	2	no	—
270	C₂×C₃×C₄	—	5	2	no	—
271	C₂×C₃×C₄	—	5	1	no	—
272	C₂×C₃×C₄	—	5	1	no	—
273	C₂×C₃×C₄	—	5	2	no	—
274	C₂×C₃×C₄	—	5	1	no	—
275	C₂×C₃×C₄	—	5	1	no	—
276	C₂×C₃×C₄	—	5	2	no	—
277	C₂×C₃×C₄	—	5	2	no	—
278	C₂×C₃×C₄	—	5	2	no	—
279	C₂×C₃×C₄	—	5	2	no	—
280	C₂×C₃×C₄	—	5	8	no	—
281	C₂×C₃×C₄	—	10	4	no	—
282	C₂×C₃×C₄	—	10	4	no	—
283	C₂×C₃×C₄	—	10	16	no	—
284	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
285	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
286	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
287	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
288	C₃×C₈	—	2	2	no	—
289	C₃×C₈	—	10	4	no	—
290	C₃×C₈	—	10	2	no	—
291	C₂²×C₅	—	2	2	no	—
292	C₂²×C₅	C₃×#95	1	2	yes	—
293	C₂²×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
294	C₂×D₅	—	2	2	no	—
295	C₂×D₅	—	2	4	no	—
296	C₂×D₅	—	2	4	no	—
297	C₂×D₅	C₃×#95	1	2	yes	—
298	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×D₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
300	C₂×D₅	C₂×C₃×M₁₆	1	4	yes	—
301	AGL(1,𝔽₅)	—	2	8	no	—
302	C₄×C₅	C₃×#95	1	2	yes	—
303	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
304	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
305	Dic₅	C₃×#95	1	2	yes	—
306	Dic₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
307	Dic₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
308	C₂⁴	—	5	1	no	—
309	C₂²×C₄	—	5	1	no	—
310	C₂²×C₄	—	5	1	no	—
311	C₂²×C₄	—	5	1	no	—
312	C₂²×C₄	—	5	2	no	—
313	C₂²×C₄	—	5	2	no	—
314	C₂²×C₄	—	5	2	no	—
315	C₂²×C₄	—	5	2	no	—
316	C₂²×C₄	—	5	1	no	—
317	C₂²×C₄	—	5	1	no	—
318	C₂²×C₄	—	5	4	no	—
319	C₂²×C₄	—	10	8	no	—
320	C₂²×C₄	—	10	4	no	—
321	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
322	M₁₆	—	2	2	no	—
323	M₁₆	—	10	4	no	—
324	M₁₆	—	10	4	no	—
325	M₁₆	—	10	4	no	—
326	M₁₆	—	10	2	no	—
327	C₂×C₈	—	5	4	no	—
328	C₂×C₈	—	5	2	no	—
329	C₂×C₈	—	10	2	no	—
330	C₂×C₈	—	10	2	no	—
331	C₂×C₈	—	10	2	no	—
332	C₂×C₈	—	10	2	no	—
333	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
334	C₄²	—	10	2	no	—
335	C₄²	—	10	4	no	—
336	C₄²	—	10	2	no	—
337	C₃×C₅	#1728	1	1	yes	characteristic, complemented, Hall
338	C₂²×C₃	—	2	2	no	—
339	C₂²×C₃	—	5	4	no	—
340	C₂²×C₃	—	5	1	no	—
341	C₂²×C₃	—	5	1	no	—
342	C₂²×C₃	—	5	2	no	—
343	C₂²×C₃	—	10	4	no	—
344	C₂²×C₃	—	10	4	no	—
345	C₂²×C₃	—	10	2	no	—
346	C₂²×C₃	(C₂×AGL(1,𝔽₅))⋊C₄	1	2	yes	—
347	C₂²×C₃	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
348	C₃×C₄	—	5	2	no	—
349	C₃×C₄	—	5	1	no	—
350	C₃×C₄	—	5	1	no	—
351	C₃×C₄	—	10	8	no	—
352	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	2	yes	—
353	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
354	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
355	C₂×C₅	—	2	2	no	—
356	C₂×C₅	C₂×C₃×#95	1	1	yes	characteristic
357	C₂×C₅	C₃×C₄×M₁₆	1	2	yes	—
358	D₅	—	2	2	no	—
359	D₅	C₃×#407	1	2	yes	—
360	D₅	C₃×#423	1	2	yes	—
361	C₂³	—	5	1	no	—
362	C₂³	—	5	1	no	—
363	C₂³	—	5	2	no	—
364	C₂³	—	5	2	no	—
365	C₂³	—	10	4	no	—
366	C₂³	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₂×C₄	—	5	1	no	—
368	C₂×C₄	—	5	1	no	—
369	C₂×C₄	—	5	2	no	—
370	C₂×C₄	—	5	2	no	—
371	C₂×C₄	—	5	1	no	—
372	C₂×C₄	—	5	2	no	—
373	C₂×C₄	—	5	1	no	—
374	C₂×C₄	—	5	2	no	—
375	C₂×C₄	—	5	2	no	—
376	C₂×C₄	—	5	2	no	—
377	C₂×C₄	—	5	2	no	—
378	C₂×C₄	—	5	1	no	—
379	C₂×C₄	—	5	1	no	—
380	C₂×C₄	—	5	2	no	—
381	C₂×C₄	—	5	8	no	—
382	C₂×C₄	—	10	4	no	—
383	C₂×C₄	—	10	4	no	—
384	C₂×C₄	—	10	16	no	—
385	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
386	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
387	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	2	yes	—
388	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	10	4	no	—
391	C₈	—	10	2	no	—
392	C₂×C₃	—	2	2	no	—
393	C₂×C₃	—	5	2	no	—
394	C₂×C₃	—	5	2	no	—
395	C₂×C₃	—	10	2	no	—
396	C₂×C₃	M₁₆×AGL(1,𝔽₅)	1	2	yes	—
397	C₂×C₃	C₂×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
398	C₅	C₃×#1728	1	1	yes	characteristic, complemented, Sylow
399	C₂²	—	2	2	no	—
400	C₂²	—	5	4	no	—
401	C₂²	—	5	1	no	—
402	C₂²	—	5	1	no	—
403	C₂²	—	5	2	no	—
404	C₂²	—	10	4	no	—
405	C₂²	—	10	4	no	—
406	C₂²	—	10	2	no	—
407	C₂²	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	2	yes	—
408	C₂²	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
409	C₄	—	5	1	no	—
410	C₄	—	5	2	no	—
411	C₄	—	5	1	no	—
412	C₄	—	10	8	no	—
413	C₄	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	2	yes	—
414	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
415	C₄	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
416	C₃	#10604753	1	1	yes	characteristic, direct product factor, Sylow
417	C₂	—	2	2	no	—
418	C₂	—	5	2	no	—
419	C₂	—	5	2	no	—
420	C₂	—	10	2	no	—
421	C₂	C₃×M₁₆×AGL(1,𝔽₅)	1	2	yes	—
422	C₂	C₂×C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂×C₃×C₄²
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×M₁₆	C₄
socle	C₂²×C₃×C₅	C₂×C₄²
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₄×D₅	C₂³×C₃
hypercenter	C₂×C₃×M₁₆	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1728
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
4. C₃×(C₂×AGL(1,𝔽₅))⋊C₈	C₂	semidirect
5. #10604753	C₃	direct (N × H)
8. C₂×C₃×#704	C₄	semidirect
15. C₂×C₃×#700	C₄	semidirect
17. C₂×C₃×C₅×M₁₆	C₄	semidirect
18. C₂×C₃×#681	C₄	semidirect
21. C₂×C₃×#676	C₄	semidirect
27. (C₂×AGL(1,𝔽₅))⋊C₈	C₂×C₃	semidirect
43. C₂×C₃×#170	C₂×C₄	semidirect
51. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
53. C₂×C₃×#168	C₂×C₄	semidirect
63. C₂×#704	C₃×C₄	semidirect
70. C₂×#700	C₃×C₄	semidirect
72. C₂×C₅×M₁₆	C₃×C₄	semidirect
73. C₂×#681	C₃×C₄	semidirect
76. C₂×#676	C₃×C₄	semidirect
88. C₂×C₃×AGL(1,𝔽₅)	M₁₆	semidirect
120. C₂×C₃×M₁₆	AGL(1,𝔽₅)	semidirect
142. C₂×#170	C₂×C₃×C₄	semidirect
150. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
152. C₂×#168	C₂×C₃×C₄	semidirect
202. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
215. C₂×AGL(1,𝔽₅)	C₃×M₁₆	semidirect
247. C₂×M₁₆	C₃×AGL(1,𝔽₅)	semidirect
333. C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
337. C₃×C₅	#1728	semidirect
398. C₅	C₃×#1728	semidirect
416. C₃	#10604753	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×C₄×AGL(1,𝔽₅)	2
C₂×C₃×D₅⋊M₁₆	2
C₂×C₃×D₅×M₁₆	2
C₃×(C₂×AGL(1,𝔽₅))⋊C₈	2
#10604753	3
C₃×#1728	5

Subgroups — C3×#10604753 #14294308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10604753 #14294308