Subgroups — C₃×D₅⋊#423 #14413012

Order 1920.

1152 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	C₂×C₃×D₅⋊M₁₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×#65758	C₂	1	4	yes	maximal, complemented
4	C₃×#65682	C₂	1	2	yes	maximal, complemented
5	C₃×#65681	C₂	1	2	yes	maximal, complemented
6	C₃×D₅⋊(C₄⋊C₈)	C₂	1	4	yes	maximal, complemented
7	D₅⋊#423	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	—	2	8	no	—
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	2	yes	—
21	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
22	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
23	C₃×#4004	C₂²	1	8	yes	complemented
24	C₃×C₄⋊#170	C₂²	1	8	yes	complemented
25	C₂×C₃×#423	—	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	#65758	C₂×C₃	1	4	yes	complemented
29	#65682	C₂×C₃	1	2	yes	complemented
30	#65681	C₂×C₃	1	2	yes	complemented
31	D₅⋊(C₄⋊C₈)	C₂×C₃	1	4	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	2	yes	—
44	C₂×C₃×C₄×D₅	D₄	1	4	yes	—
45	C₂×C₃×C₄×D₅	Q₈	1	4	yes	—
46	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
48	C₃×#704	—	2	8	no	—
49	C₂×C₃×#170	C₂³	1	8	yes	—
50	C₃×#700	—	2	8	no	—
51	C₃×D₅⋊C₈	—	2	8	no	—
52	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
54	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
56	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
57	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
59	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
60	C₃×C₄×Dic₅	C₂³	1	2	yes	—
61	C₃×C₄×Dic₅	C₂³	1	2	yes	—
62	C₂²×C₃×M₁₆	—	5	2	no	—
63	C₂²×C₃×C₄²	—	5	1	no	—
64	C₃×#423	—	5	2	no	—
65	C₃×#423	—	5	2	no	—
66	C₃×#423	—	5	4	no	—
67	C₂×C₃×C₄⋊C₈	—	5	4	no	—
68	C₂²×C₄×D₅	C₃×C₄	1	2	yes	—
69	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
70	C₂×#704	C₂²×C₃	1	4	yes	—
71	D₅⋊M₁₆	—	2	8	no	—
72	C₂×#700	C₂²×C₃	1	4	yes	—
73	C₂×D₅⋊C₈	C₂²×C₃	1	4	yes	—
74	C₂×C₄²×C₅	C₃×C₄	1	1	yes	characteristic
75	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
76	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
77	C₄²×D₅	C₃×C₄	1	1	yes	characteristic
78	C₄²×D₅	C₃×C₄	1	2	yes	—
79	C₄²×D₅	C₃×C₄	1	1	yes	characteristic
80	C₄²×D₅	C₂²×C₃	1	2	yes	—
81	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
82	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
83	#4004	C₂²×C₃	1	8	yes	complemented
84	C₄⋊#170	C₂²×C₃	1	8	yes	complemented
85	C₂×#423	—	5	1	no	Sylow
86	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₃×D₅	—	2	4	no	—
88	C₂²×C₃×D₅	C₄⋊C₄	1	4	yes	—
89	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂×C₃×Dic₅	—	2	4	no	—
98	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
101	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×Dic₅	C₂×Q₈	1	2	yes	—
103	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
104	C₃×C₄×D₅	—	2	4	no	—
105	C₃×C₄×D₅	—	2	4	no	—
106	C₃×C₄×D₅	—	2	4	no	—
107	C₃×C₄×D₅	C₄⋊C₄	1	4	yes	—
108	C₃×C₄×D₅	C₄⋊C₄	1	4	yes	—
109	C₃×C₄×D₅	M₁₆	1	8	yes	complemented
110	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
111	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
112	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
113	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
114	C₃×#170	—	2	8	no	—
115	C₂³×C₃×C₄	—	5	1	no	—
116	C₂³×C₃×C₄	—	5	2	no	—
117	C₂×C₃×M₁₆	—	5	4	no	—
118	C₂×C₃×M₁₆	—	5	4	no	—
119	C₂×C₃×M₁₆	—	10	8	no	—
120	C₂²×C₃×C₈	—	5	4	no	—
121	C₂×C₃×C₄²	—	5	2	no	—
122	C₂×C₃×C₄²	—	5	1	no	—
123	C₂×C₃×C₄²	—	5	2	no	—
124	C₂×C₃×C₄²	—	5	1	no	—
125	C₂×C₃×C₄²	—	5	1	no	—
126	C₂×C₃×C₄²	—	5	1	no	—
127	C₂×C₃×C₄²	—	5	1	no	—
128	C₂×C₃×C₄²	—	5	2	no	—
129	C₂×C₃×C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic
130	C₃×C₄⋊C₈	—	5	8	no	—
131	C₃×C₄⋊C₈	—	5	8	no	—
132	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
134	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
136	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
137	C₂×C₄×D₅	—	2	8	no	—
138	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
139	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
140	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
141	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
142	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
143	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
144	C₂×C₄×D₅	C₃×D₄	1	4	yes	—
145	C₂×C₄×D₅	C₃×Q₈	1	4	yes	—
146	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
148	#704	—	2	8	no	—
149	C₂×#170	C₂³×C₃	1	8	yes	—
150	#700	—	2	8	no	—
151	D₅⋊C₈	—	2	8	no	—
152	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
154	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
155	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
156	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
157	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
158	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
159	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
160	C₄×Dic₅	C₂³×C₃	1	2	yes	—
161	C₄×Dic₅	C₂³×C₃	1	2	yes	—
162	C₂²×M₁₆	—	5	2	no	—
163	C₂²×C₄²	—	5	1	no	—
164	#423	—	5	2	no	—
165	#423	—	5	2	no	—
166	#423	—	5	4	no	—
167	C₂×C₄⋊C₈	—	5	4	no	—
168	C₂²×C₃×C₅	—	2	2	no	—
169	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
170	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₃×D₅	—	2	2	no	—
172	C₂×C₃×D₅	—	2	8	no	—
173	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₃×D₅	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
178	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
179	C₃×C₄×C₅	C₂×M₁₆	1	4	yes	complemented
180	C₃×Dic₅	—	2	2	no	—
181	C₃×Dic₅	C₂×C₄⋊C₄	1	2	yes	—
182	C₃×Dic₅	C₂×M₁₆	1	4	yes	complemented
183	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
184	C₃×Dic₅	C₂²×Q₈	1	1	yes	characteristic
185	C₂⁴×C₃	—	5	1	no	—
186	C₂²×C₃×C₄	—	5	1	no	—
187	C₂²×C₃×C₄	—	5	4	no	—
188	C₂²×C₃×C₄	—	5	4	no	—
189	C₂²×C₃×C₄	—	5	2	no	—
190	C₂²×C₃×C₄	—	5	1	no	—
191	C₂²×C₃×C₄	—	5	1	no	—
192	C₂²×C₃×C₄	—	5	1	no	—
193	C₂²×C₃×C₄	—	5	1	no	—
194	C₂²×C₃×C₄	—	5	2	no	—
195	C₂²×C₃×C₄	—	5	2	no	—
196	C₂²×C₃×C₄	—	5	2	no	—
197	C₂²×C₃×C₄	—	5	2	no	—
198	C₂²×C₃×C₄	—	10	8	no	—
199	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
200	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
201	C₃×M₁₆	—	10	8	no	—
202	C₃×M₁₆	—	10	8	no	—
203	C₂×C₃×C₈	—	5	8	no	—
204	C₂×C₃×C₈	—	10	8	no	—
205	C₃×C₄²	—	5	2	no	—
206	C₃×C₄²	—	5	1	no	—
207	C₃×C₄²	—	5	2	no	—
208	C₃×C₄²	—	5	1	no	—
209	C₃×C₄²	—	5	2	no	—
210	C₃×C₄²	—	5	2	no	—
211	C₃×C₄²	—	5	2	no	—
212	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
213	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
214	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	—
215	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
216	C₂²×D₅	—	2	4	no	—
217	C₂²×D₅	C₃×C₄⋊C₄	1	4	yes	—
218	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
219	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	—	2	4	no	—
221	C₂×C₄×C₅	C₃×C₄⋊C₄	1	4	yes	—
222	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
223	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
226	C₂×Dic₅	—	2	4	no	—
227	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
228	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
229	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
230	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
231	C₂×Dic₅	C₂×C₃×Q₈	1	2	yes	—
232	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
233	C₄×D₅	—	2	4	no	—
234	C₄×D₅	—	2	4	no	—
235	C₄×D₅	—	2	4	no	—
236	C₄×D₅	C₃×C₄⋊C₄	1	4	yes	—
237	C₄×D₅	C₃×C₄⋊C₄	1	4	yes	—
238	C₄×D₅	C₃×M₁₆	1	8	yes	complemented
239	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
240	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
241	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
242	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
243	#170	—	2	8	no	—
244	C₂³×C₄	—	5	1	no	—
245	C₂³×C₄	—	5	2	no	—
246	C₂×M₁₆	—	5	4	no	—
247	C₂×M₁₆	—	5	4	no	—
248	C₂×M₁₆	—	10	8	no	—
249	C₂²×C₈	—	5	4	no	—
250	C₂×C₄²	—	5	2	no	—
251	C₂×C₄²	—	5	1	no	—
252	C₂×C₄²	—	5	2	no	—
253	C₂×C₄²	—	5	1	no	—
254	C₂×C₄²	—	5	1	no	—
255	C₂×C₄²	—	5	1	no	—
256	C₂×C₄²	—	5	2	no	—
257	C₂×C₄²	—	5	1	no	—
258	C₂×C₄²	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
259	C₄⋊C₈	—	5	8	no	—
260	C₄⋊C₈	—	5	8	no	—
261	C₂×C₃×C₅	—	2	2	no	—
262	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
263	C₂×C₃×C₅	C₂²×M₁₆	1	2	yes	—
264	C₃×D₅	—	2	2	no	—
265	C₃×D₅	#423	1	4	yes	complemented
266	C₂³×C₃	—	5	1	no	—
267	C₂³×C₃	—	5	4	no	—
268	C₂³×C₃	—	5	1	no	—
269	C₂³×C₃	—	10	4	no	—
270	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	5	2	no	—
273	C₂×C₃×C₄	—	5	2	no	—
274	C₂×C₃×C₄	—	5	2	no	—
275	C₂×C₃×C₄	—	5	1	no	—
276	C₂×C₃×C₄	—	5	1	no	—
277	C₂×C₃×C₄	—	5	8	no	—
278	C₂×C₃×C₄	—	5	4	no	—
279	C₂×C₃×C₄	—	5	4	no	—
280	C₂×C₃×C₄	—	5	2	no	—
281	C₂×C₃×C₄	—	5	2	no	—
282	C₂×C₃×C₄	—	5	2	no	—
283	C₂×C₃×C₄	—	5	2	no	—
284	C₂×C₃×C₄	—	5	2	no	—
285	C₂×C₃×C₄	—	10	4	no	—
286	C₂×C₃×C₄	—	10	4	no	—
287	C₂×C₃×C₄	—	10	4	no	—
288	C₂×C₃×C₄	—	10	4	no	—
289	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	4	yes	—
290	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
291	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
292	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
294	C₃×C₈	—	10	8	no	—
295	C₂²×C₅	—	2	2	no	—
296	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
297	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
298	C₂×D₅	—	2	2	no	—
299	C₂×D₅	—	2	8	no	—
300	C₂×D₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
301	C₂×D₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
302	C₂×D₅	C₂×C₃×M₁₆	1	4	yes	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
305	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
306	C₄×C₅	C₂×C₃×M₁₆	1	4	yes	complemented
307	Dic₅	—	2	2	no	—
308	Dic₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
309	Dic₅	C₂×C₃×M₁₆	1	4	yes	complemented
310	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
311	Dic₅	C₂²×C₃×Q₈	1	1	yes	characteristic
312	C₂⁴	—	5	1	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	5	4	no	—
315	C₂²×C₄	—	5	4	no	—
316	C₂²×C₄	—	5	1	no	—
317	C₂²×C₄	—	5	1	no	—
318	C₂²×C₄	—	5	2	no	—
319	C₂²×C₄	—	5	1	no	—
320	C₂²×C₄	—	5	1	no	—
321	C₂²×C₄	—	5	2	no	—
322	C₂²×C₄	—	5	2	no	—
323	C₂²×C₄	—	5	2	no	—
324	C₂²×C₄	—	5	2	no	—
325	C₂²×C₄	—	10	8	no	—
326	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
327	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
328	M₁₆	—	10	8	no	—
329	M₁₆	—	10	8	no	—
330	C₂×C₈	—	5	8	no	—
331	C₂×C₈	—	10	8	no	—
332	C₄²	—	5	2	no	—
333	C₄²	—	5	2	no	—
334	C₄²	—	5	2	no	—
335	C₄²	—	5	1	no	—
336	C₄²	—	5	2	no	—
337	C₄²	—	5	2	no	—
338	C₄²	—	5	1	no	—
339	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
340	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
341	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
342	C₃×C₅	C₂×#423	1	1	yes	characteristic, complemented, Hall
343	C₂²×C₃	—	2	2	no	—
344	C₂²×C₃	—	5	4	no	—
345	C₂²×C₃	—	5	2	no	—
346	C₂²×C₃	—	5	2	no	—
347	C₂²×C₃	—	10	8	no	—
348	C₂²×C₃	—	10	2	no	—
349	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
350	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
351	C₃×C₄	—	2	2	no	—
352	C₃×C₄	—	5	4	no	—
353	C₃×C₄	—	5	2	no	—
354	C₃×C₄	—	5	1	no	—
355	C₃×C₄	—	5	1	no	—
356	C₃×C₄	—	10	2	no	—
357	C₃×C₄	D₅⋊M₁₆	1	4	yes	complemented
358	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
359	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
360	C₂×C₅	—	2	2	no	—
361	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
362	C₂×C₅	C₂²×C₃×M₁₆	1	2	yes	—
363	D₅	—	2	2	no	—
364	D₅	C₃×#423	1	4	yes	complemented
365	C₂³	—	5	1	no	—
366	C₂³	—	5	4	no	—
367	C₂³	—	5	1	no	—
368	C₂³	—	10	4	no	—
369	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	5	2	no	—
372	C₂×C₄	—	5	2	no	—
373	C₂×C₄	—	5	1	no	—
374	C₂×C₄	—	5	2	no	—
375	C₂×C₄	—	5	1	no	—
376	C₂×C₄	—	5	8	no	—
377	C₂×C₄	—	5	2	no	—
378	C₂×C₄	—	5	2	no	—
379	C₂×C₄	—	5	4	no	—
380	C₂×C₄	—	5	4	no	—
381	C₂×C₄	—	5	2	no	—
382	C₂×C₄	—	5	2	no	—
383	C₂×C₄	—	5	2	no	—
384	C₂×C₄	—	10	4	no	—
385	C₂×C₄	—	10	4	no	—
386	C₂×C₄	—	10	4	no	—
387	C₂×C₄	—	10	4	no	—
388	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	4	yes	—
389	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
390	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
391	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
393	C₈	—	10	8	no	—
394	C₂×C₃	—	2	2	no	—
395	C₂×C₃	—	5	4	no	—
396	C₂×C₃	—	10	2	no	—
397	C₂×C₃	C₂×D₅⋊M₁₆	1	2	yes	—
398	C₂×C₃	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
399	C₅	C₂×C₃×#423	1	1	yes	characteristic, complemented, Sylow
400	C₂²	—	2	2	no	—
401	C₂²	—	5	4	no	—
402	C₂²	—	5	2	no	—
403	C₂²	—	5	2	no	—
404	C₂²	—	10	8	no	—
405	C₂²	—	10	2	no	—
406	C₂²	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
407	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	5	4	no	—
410	C₄	—	5	1	no	—
411	C₄	—	5	2	no	—
412	C₄	—	5	1	no	—
413	C₄	—	10	2	no	—
414	C₄	C₃×D₅⋊M₁₆	1	4	yes	complemented
415	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
416	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
417	C₃	D₅⋊#423	1	1	yes	characteristic, direct product factor, Sylow
418	C₂	—	2	2	no	—
419	C₂	—	5	4	no	—
420	C₂	—	10	2	no	—
421	C₂	C₂×C₃×D₅⋊M₁₆	1	2	yes	—
422	C₂	C₂²×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
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×#423
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄²

Complements

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

N	H ≅ G/N	type
3. C₃×#65758	C₂	semidirect
4. C₃×#65682	C₂	semidirect
5. C₃×#65681	C₂	semidirect
6. C₃×D₅⋊(C₄⋊C₈)	C₂	semidirect
7. D₅⋊#423	C₃	direct (N × H)
23. C₃×#4004	C₂²	semidirect
24. C₃×C₄⋊#170	C₂²	semidirect
28. #65758	C₂×C₃	semidirect
29. #65682	C₂×C₃	semidirect
30. #65681	C₂×C₃	semidirect
31. D₅⋊(C₄⋊C₈)	C₂×C₃	semidirect
83. #4004	C₂²×C₃	semidirect
84. C₄⋊#170	C₂²×C₃	semidirect
109. C₃×C₄×D₅	M₁₆	semidirect
179. C₃×C₄×C₅	C₂×M₁₆	semidirect
182. C₃×Dic₅	C₂×M₁₆	semidirect
238. C₄×D₅	C₃×M₁₆	semidirect
265. C₃×D₅	#423	semidirect
306. C₄×C₅	C₂×C₃×M₁₆	semidirect
309. Dic₅	C₂×C₃×M₁₆	semidirect
342. C₃×C₅	C₂×#423	semidirect
357. C₃×C₄	D₅⋊M₁₆	semidirect
364. D₅	C₃×#423	semidirect
399. C₅	C₂×C₃×#423	semidirect
414. C₄	C₃×D₅⋊M₁₆	semidirect
417. C₃	D₅⋊#423	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×#65758	2
C₃×#65682	2
C₃×#65681	2
C₃×D₅⋊(C₄⋊C₈)	2
D₅⋊#423	3
C₂×C₃×#423	5

Subgroups — C3×D5⋊#423 #14413012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅⋊#423 #14413012