Subgroups — C₃×#10617409 #14413410

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4130	C₂	1	2	yes	maximal
2	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×#65727	C₂	1	8	yes	maximal, complemented
4	C₃×#65721	C₂	1	4	yes	maximal, complemented
5	#10617409	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
8	C₃×#4130	—	2	2	no	—
9	C₃×#4130	—	2	2	no	—
10	C₃×#4130	C₂²	1	4	yes	—
11	C₃×#4130	C₂²	1	4	yes	—
12	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
13	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
14	C₂×C₃×C₅×M₁₆	C₄	1	1	yes	characteristic, complemented
15	C₂×C₃×#681	C₄	1	1	yes	characteristic, complemented
16	C₃×D₅×M₁₆	C₄	1	4	yes	complemented
17	C₃×D₅×M₁₆	C₂²	1	4	yes	—
18	C₂×C₃×#676	C₄	1	2	yes	complemented
19	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
20	C₃×#3994	C₂²	1	8	yes	complemented
21	C₃×#3993	C₂²	1	8	yes	complemented
22	C₃×#2911	—	5	1	no	maximal, Hall
23	C₂×#4130	C₂×C₃	1	2	yes	—
24	C₂×D₅×M₁₆	C₂×C₃	1	1	yes	characteristic
25	#65727	C₂×C₃	1	8	yes	complemented
26	#65721	C₂×C₃	1	4	yes	complemented
27	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
28	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×Dic₅	Q₈	1	1	yes	characteristic
31	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
32	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
33	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
34	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
35	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
36	C₂×C₃×C₄×D₅	Q₈	1	2	yes	—
37	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
38	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
39	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
40	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
41	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
42	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	8	yes	—
43	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
44	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
45	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
46	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	complemented
47	C₃×#681	C₂×C₄	1	4	yes	complemented
48	C₂×C₃×#168	C₂×C₄	1	2	yes	complemented
49	C₃×#676	C₂×C₄	1	8	yes	complemented
50	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
51	C₃×C₈×D₅	C₂³	1	4	yes	—
52	C₂²×C₃×M₁₆	—	5	1	no	—
53	C₂×C₃×#117	—	5	2	no	—
54	C₃×#428	—	5	8	no	—
55	C₃×#427	—	5	4	no	—
56	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
58	#4130	—	2	2	no	—
59	#4130	—	2	2	no	—
60	#4130	C₂²×C₃	1	4	yes	—
61	#4130	C₂²×C₃	1	4	yes	—
62	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
63	C₂×C₄×AGL(1,𝔽₅)	—	2	2	no	—
64	C₂×C₅×M₁₆	C₃×C₄	1	1	yes	characteristic, complemented
65	C₂×#681	C₃×C₄	1	1	yes	characteristic, complemented
66	D₅×M₁₆	C₃×C₄	1	4	yes	complemented
67	D₅×M₁₆	C₂²×C₃	1	4	yes	—
68	C₂×#676	C₃×C₄	1	2	yes	complemented
69	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
70	#3994	C₂²×C₃	1	8	yes	complemented
71	#3993	C₂²×C₃	1	8	yes	complemented
72	#2911	—	5	1	no	Sylow
73	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₃×D₅	—	4	2	no	—
75	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₃×D₅	C₄⋊C₄	1	2	yes	—
77	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
79	C₂×C₃×AGL(1,𝔽₅)	—	2	8	no	—
80	C₂×C₃×AGL(1,𝔽₅)	—	4	8	no	—
81	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
83	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
85	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₃×Dic₅	C₄⋊C₄	1	2	yes	—
87	C₂×C₃×Dic₅	C₂×Q₈	1	2	yes	—
88	C₂×C₃×Dic₅	C₂×Q₈	1	1	yes	characteristic
89	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
90	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
91	C₃×C₄×D₅	C₄⋊C₄	1	2	yes	—
92	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
93	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
94	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
95	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
96	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
97	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
98	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
99	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
100	C₃×#168	C₂²×C₄	1	4	yes	—
101	C₂³×C₃×C₄	—	5	1	no	—
102	C₂×C₃×M₁₆	—	5	1	no	—
103	C₂×C₃×M₁₆	—	5	4	no	—
104	C₂×C₃×M₁₆	—	5	4	no	—
105	C₂×C₃×M₁₆	—	5	2	no	—
106	C₂×C₃×M₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
107	C₂²×C₃×C₈	—	5	2	no	—
108	C₃×#117	—	5	4	no	—
109	C₃×#117	—	5	4	no	—
110	C₃×#117	—	10	2	no	—
111	C₃×#117	—	10	2	no	—
112	C₂×C₃×C₄⋊C₄	—	5	4	no	—
113	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
114	C₂×C₃×C₄²	—	10	2	no	—
115	C₃×#107	—	5	8	no	—
116	C₃×#106	—	5	8	no	—
117	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
118	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
119	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂²×Dic₅	C₃×Q₈	1	1	yes	characteristic
121	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
123	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
124	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
125	C₂×C₄×D₅	C₃×Q₈	1	2	yes	—
126	C₂×C₄×D₅	C₃×Q₈	1	1	yes	characteristic
127	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
128	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
130	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
131	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
132	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	8	yes	—
133	C₄×AGL(1,𝔽₅)	—	2	4	no	—
134	C₄×AGL(1,𝔽₅)	—	2	4	no	—
135	C₅×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
136	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	complemented
137	#681	C₂×C₃×C₄	1	4	yes	complemented
138	C₂×#168	C₂×C₃×C₄	1	2	yes	complemented
139	#676	C₂×C₃×C₄	1	8	yes	complemented
140	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
141	C₈×D₅	C₂³×C₃	1	4	yes	—
142	C₂²×M₁₆	—	5	1	no	—
143	C₂×#117	—	5	2	no	—
144	#428	—	5	8	no	—
145	#427	—	5	4	no	—
146	C₂²×C₃×C₅	—	4	1	no	—
147	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₃×D₅	—	2	4	no	—
150	C₂×C₃×D₅	—	2	2	no	—
151	C₂×C₃×D₅	—	4	1	no	—
152	C₂×C₃×D₅	—	4	2	no	—
153	C₂×C₃×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
156	C₃×AGL(1,𝔽₅)	—	4	8	no	—
157	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
158	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
160	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
162	C₃×Dic₅	C₂²×Q₈	1	1	yes	characteristic
163	C₂⁴×C₃	—	5	1	no	—
164	C₂²×C₃×C₄	—	5	1	no	—
165	C₂²×C₃×C₄	—	5	2	no	—
166	C₂²×C₃×C₄	—	5	1	no	—
167	C₂²×C₃×C₄	—	5	1	no	—
168	C₂²×C₃×C₄	—	5	2	no	—
169	C₂²×C₃×C₄	—	5	2	no	—
170	C₂²×C₃×C₄	—	5	1	no	—
171	C₂²×C₃×C₄	—	5	2	no	—
172	C₂²×C₃×C₄	—	5	1	no	—
173	C₂²×C₃×C₄	—	10	4	no	—
174	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
175	C₃×M₁₆	—	5	4	no	—
176	C₃×M₁₆	—	5	8	no	—
177	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
178	C₂×C₃×C₈	—	5	2	no	—
179	C₂×C₃×C₈	—	5	4	no	—
180	C₂×C₃×C₈	—	5	4	no	—
181	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
182	C₃×C₄⋊C₄	—	5	8	no	—
183	C₃×C₄⋊C₄	—	10	4	no	—
184	C₃×C₂²⋊C₄	—	10	4	no	—
185	C₃×C₂²⋊C₄	—	10	4	no	—
186	C₃×C₄²	—	10	4	no	—
187	C₃×C₄²	—	10	4	no	—
188	C₂³×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
189	C₂²×D₅	—	4	2	no	—
190	C₂²×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
191	C₂²×D₅	C₃×C₄⋊C₄	1	2	yes	—
192	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
193	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
194	C₂×AGL(1,𝔽₅)	—	2	8	no	—
195	C₂×AGL(1,𝔽₅)	—	4	8	no	—
196	C₂×C₄×C₅	C₃×C₄⋊C₄	1	2	yes	—
197	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
200	C₂×Dic₅	C₃×C₄⋊C₄	1	1	yes	characteristic
201	C₂×Dic₅	C₃×C₄⋊C₄	1	2	yes	—
202	C₂×Dic₅	C₂×C₃×Q₈	1	2	yes	—
203	C₂×Dic₅	C₂×C₃×Q₈	1	1	yes	characteristic
204	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
205	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
206	C₄×D₅	C₃×C₄⋊C₄	1	2	yes	—
207	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
208	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
209	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
210	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
211	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
212	C₄×D₅	C₂×C₃×Q₈	1	1	yes	characteristic
213	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
214	C₅×C₈	C₂²×C₃×C₄	1	4	yes	—
215	#168	C₂²×C₃×C₄	1	4	yes	—
216	C₂³×C₄	—	5	1	no	—
217	C₂×M₁₆	—	5	1	no	—
218	C₂×M₁₆	—	5	4	no	—
219	C₂×M₁₆	—	5	4	no	—
220	C₂×M₁₆	—	5	2	no	—
221	C₂×M₁₆	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
222	C₂²×C₈	—	5	2	no	—
223	#117	—	5	4	no	—
224	#117	—	5	4	no	—
225	#117	—	10	2	no	—
226	#117	—	10	2	no	—
227	C₂×C₄⋊C₄	—	5	4	no	—
228	C₂×C₂²⋊C₄	—	10	2	no	—
229	C₂×C₄²	—	10	2	no	—
230	#107	—	5	8	no	—
231	#106	—	5	8	no	—
232	C₂×C₃×C₅	—	2	2	no	—
233	C₂×C₃×C₅	—	2	1	no	—
234	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
235	C₃×D₅	—	2	2	no	—
236	C₃×D₅	—	2	1	no	—
237	C₃×D₅	#575	1	2	yes	—
238	C₂³×C₃	—	5	1	no	—
239	C₂³×C₃	—	5	2	no	—
240	C₂³×C₃	—	5	2	no	—
241	C₂³×C₃	—	5	1	no	—
242	C₂³×C₃	—	20	2	no	—
243	C₂³×C₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
244	C₂×C₃×C₄	—	5	2	no	—
245	C₂×C₃×C₄	—	5	1	no	—
246	C₂×C₃×C₄	—	5	2	no	—
247	C₂×C₃×C₄	—	5	1	no	—
248	C₂×C₃×C₄	—	5	2	no	—
249	C₂×C₃×C₄	—	5	2	no	—
250	C₂×C₃×C₄	—	5	2	no	—
251	C₂×C₃×C₄	—	5	2	no	—
252	C₂×C₃×C₄	—	5	2	no	—
253	C₂×C₃×C₄	—	5	1	no	—
254	C₂×C₃×C₄	—	5	1	no	—
255	C₂×C₃×C₄	—	5	1	no	—
256	C₂×C₃×C₄	—	5	2	no	—
257	C₂×C₃×C₄	—	5	1	no	—
258	C₂×C₃×C₄	—	10	8	no	—
259	C₂×C₃×C₄	—	20	8	no	—
260	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
261	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
262	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
263	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
264	C₃×C₈	—	5	4	no	—
265	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	4	yes	—
266	C₂²×C₅	—	4	1	no	—
267	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
268	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
269	C₂×D₅	—	2	4	no	—
270	C₂×D₅	—	2	2	no	—
271	C₂×D₅	—	4	1	no	—
272	C₂×D₅	—	4	2	no	—
273	C₂×D₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
274	C₂×D₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
275	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
276	AGL(1,𝔽₅)	—	4	8	no	—
277	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
278	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
279	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
280	Dic₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
281	Dic₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
282	Dic₅	C₂²×C₃×Q₈	1	1	yes	characteristic
283	C₂⁴	—	5	1	no	—
284	C₂²×C₄	—	5	1	no	—
285	C₂²×C₄	—	5	2	no	—
286	C₂²×C₄	—	5	1	no	—
287	C₂²×C₄	—	5	2	no	—
288	C₂²×C₄	—	5	1	no	—
289	C₂²×C₄	—	5	2	no	—
290	C₂²×C₄	—	5	1	no	—
291	C₂²×C₄	—	5	2	no	—
292	C₂²×C₄	—	5	1	no	—
293	C₂²×C₄	—	10	4	no	—
294	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
295	M₁₆	—	5	4	no	—
296	M₁₆	—	5	8	no	—
297	M₁₆	C₂×C₃×AGL(1,𝔽₅)	1	4	yes	complemented
298	C₂×C₈	—	5	2	no	—
299	C₂×C₈	—	5	4	no	—
300	C₂×C₈	—	5	4	no	—
301	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
302	C₄⋊C₄	—	5	8	no	—
303	C₄⋊C₄	—	10	4	no	—
304	C₂²⋊C₄	—	10	4	no	—
305	C₂²⋊C₄	—	10	4	no	—
306	C₄²	—	10	4	no	—
307	C₄²	—	10	4	no	—
308	C₃×C₅	#2911	1	1	yes	characteristic, complemented, Hall
309	C₂²×C₃	—	4	1	no	—
310	C₂²×C₃	—	5	1	no	—
311	C₂²×C₃	—	5	1	no	—
312	C₂²×C₃	—	5	2	no	—
313	C₂²×C₃	—	10	4	no	—
314	C₂²×C₃	—	10	2	no	—
315	C₂²×C₃	—	20	2	no	—
316	C₂²×C₃	—	20	1	no	—
317	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
318	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
319	C₃×C₄	—	5	1	no	—
320	C₃×C₄	—	5	2	no	—
321	C₃×C₄	—	5	1	no	—
322	C₃×C₄	—	20	8	no	—
323	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
324	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
325	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
326	C₂×C₅	—	2	2	no	—
327	C₂×C₅	—	2	1	no	—
328	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
329	D₅	—	2	2	no	—
330	D₅	—	2	1	no	—
331	D₅	C₃×#575	1	2	yes	—
332	C₂³	—	5	1	no	—
333	C₂³	—	5	2	no	—
334	C₂³	—	5	2	no	—
335	C₂³	—	5	1	no	—
336	C₂³	—	20	2	no	—
337	C₂³	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
338	C₂×C₄	—	5	2	no	—
339	C₂×C₄	—	5	1	no	—
340	C₂×C₄	—	5	2	no	—
341	C₂×C₄	—	5	1	no	—
342	C₂×C₄	—	5	1	no	—
343	C₂×C₄	—	5	2	no	—
344	C₂×C₄	—	5	2	no	—
345	C₂×C₄	—	5	2	no	—
346	C₂×C₄	—	5	2	no	—
347	C₂×C₄	—	5	2	no	—
348	C₂×C₄	—	5	1	no	—
349	C₂×C₄	—	5	1	no	—
350	C₂×C₄	—	5	1	no	—
351	C₂×C₄	—	5	2	no	—
352	C₂×C₄	—	10	8	no	—
353	C₂×C₄	—	20	8	no	—
354	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
355	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
356	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
358	C₈	—	5	4	no	—
359	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
360	C₂×C₃	—	2	2	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	5	2	no	—
363	C₂×C₃	—	10	2	no	—
364	C₂×C₃	—	10	1	no	—
365	C₂×C₃	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
366	C₅	C₃×#2911	1	1	yes	characteristic, complemented, Sylow
367	C₂²	—	4	1	no	—
368	C₂²	—	5	1	no	—
369	C₂²	—	5	1	no	—
370	C₂²	—	5	2	no	—
371	C₂²	—	10	4	no	—
372	C₂²	—	10	2	no	—
373	C₂²	—	20	2	no	—
374	C₂²	—	20	1	no	—
375	C₂²	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
376	C₂²	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
377	C₄	—	5	1	no	—
378	C₄	—	5	2	no	—
379	C₄	—	5	1	no	—
380	C₄	—	20	8	no	—
381	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
382	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
384	C₃	#10617409	1	1	yes	characteristic, direct product factor, Sylow
385	C₂	—	2	2	no	—
386	C₂	—	2	1	no	—
387	C₂	—	5	2	no	—
388	C₂	—	10	2	no	—
389	C₂	—	10	1	no	—
390	C₂	C₂²×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₄	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×M₁₆	C₄
socle	C₂×C₃×C₅	C₂²×C₄⋊C₄
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₂×C₃×M₁₆	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2911
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₃×#65727	C₂	semidirect
4. C₃×#65721	C₂	semidirect
5. #10617409	C₃	direct (N × H)
14. C₂×C₃×C₅×M₁₆	C₄	semidirect
15. C₂×C₃×#681	C₄	semidirect
16. C₃×D₅×M₁₆	C₄	semidirect
18. C₂×C₃×#676	C₄	semidirect
20. C₃×#3994	C₂²	semidirect
21. C₃×#3993	C₂²	semidirect
25. #65727	C₂×C₃	semidirect
26. #65721	C₂×C₃	semidirect
45. C₃×C₅×M₁₆	C₂×C₄	semidirect
46. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
47. C₃×#681	C₂×C₄	semidirect
48. C₂×C₃×#168	C₂×C₄	semidirect
49. C₃×#676	C₂×C₄	semidirect
50. C₃×C₈×D₅	C₂×C₄	semidirect
64. C₂×C₅×M₁₆	C₃×C₄	semidirect
65. C₂×#681	C₃×C₄	semidirect
66. D₅×M₁₆	C₃×C₄	semidirect
68. C₂×#676	C₃×C₄	semidirect
70. #3994	C₂²×C₃	semidirect
71. #3993	C₂²×C₃	semidirect
106. C₂×C₃×M₁₆	AGL(1,𝔽₅)	semidirect
135. C₅×M₁₆	C₂×C₃×C₄	semidirect
136. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
137. #681	C₂×C₃×C₄	semidirect
138. C₂×#168	C₂×C₃×C₄	semidirect
139. #676	C₂×C₃×C₄	semidirect
140. C₈×D₅	C₂×C₃×C₄	semidirect
177. C₃×M₁₆	C₂×AGL(1,𝔽₅)	semidirect
181. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
221. C₂×M₁₆	C₃×AGL(1,𝔽₅)	semidirect
297. M₁₆	C₂×C₃×AGL(1,𝔽₅)	semidirect
301. C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
308. C₃×C₅	#2911	semidirect
366. C₅	C₃×#2911	semidirect
384. C₃	#10617409	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×#4130	2
C₂×C₃×D₅×M₁₆	2
C₃×#65727	2
C₃×#65721	2
#10617409	3
C₃×#2911	5

Subgroups — C3×#10617409 #14413410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617409 #14413410