Subgroups — C₃×D₅⋊#433 #14413839

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₃×D₅⋊(C₂²⋊C₈)	C₂	1	2	yes	maximal
3	C₃×#65706	C₂	1	4	yes	maximal, complemented
4	C₃×#65697	C₂	1	4	yes	maximal, complemented
5	C₃×D₅⋊(C₄⋊C₈)	C₂	1	2	yes	maximal, complemented
6	C₃×#65676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×D₅⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅⋊#433	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
11	C₂×C₃×D₅⋊C₈	C₂²	1	2	yes	—
12	C₃×C₅×#117	C₄	1	1	yes	characteristic
13	C₃×#4072	C₄	1	1	yes	characteristic
14	C₃×#4038	C₂²	1	2	yes	—
15	C₃×D₅×C₄⋊C₄	C₄	1	2	yes	—
16	C₃×D₅×C₂²⋊C₄	C₄	1	2	yes	—
17	C₃×#4023	C₂²	1	2	yes	—
18	C₃×#4018	C₄	1	1	yes	characteristic
19	C₃×#4018	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×C₂²⋊#170	C₂²	1	4	yes	—
23	C₃×#4004	C₂²	1	4	yes	complemented
24	C₃×#4003	C₂²	1	4	yes	—
25	C₃×#4002	C₂²	1	4	yes	complemented
26	C₃×C₄⋊#170	C₂²	1	4	yes	complemented
27	C₃×C₄×#170	C₂²	1	4	yes	complemented
28	C₂×C₃×#433	—	5	1	no	maximal, Hall
29	D₅×#117	C₂×C₃	1	1	yes	characteristic
30	D₅⋊(C₂²⋊C₈)	C₂×C₃	1	2	yes	—
31	#65706	C₂×C₃	1	4	yes	complemented
32	#65697	C₂×C₃	1	4	yes	complemented
33	D₅⋊(C₄⋊C₈)	C₂×C₃	1	2	yes	complemented
34	#65676	C₂×C₃	1	1	yes	characteristic, complemented
35	C₄×D₅⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
39	C₂×C₃×C₄×D₅	—	2	4	no	—
40	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×#170	C₂³	1	4	yes	—
47	C₂×C₃×#170	C₂³	1	4	yes	—
48	C₃×D₅⋊C₈	—	2	4	no	—
49	C₃×D₅⋊C₈	—	2	4	no	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
52	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
54	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
55	C₃×#685	C₂×C₄	1	2	yes	—
56	C₃×#685	C₂×C₄	1	2	yes	—
57	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
58	C₃×#683	C₂×C₄	1	2	yes	—
59	C₃×#683	C₂×C₄	1	2	yes	—
60	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
61	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄×Dic₅	C₂³	1	2	yes	—
63	C₃×C₄×Dic₅	C₂³	1	2	yes	—
64	C₂×C₃×#117	—	5	1	no	—
65	C₃×#433	—	5	4	no	—
66	C₃×#433	—	5	4	no	—
67	C₂×C₃×C₄⋊C₈	—	5	2	no	—
68	C₂×C₃×C₂²⋊C₈	—	5	2	no	—
69	C₂×C₃×#97	—	5	1	no	—
70	C₂×C₃×C₄×C₈	—	5	1	no	—
71	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
73	C₂×D₅⋊C₈	C₂²×C₃	1	2	yes	—
74	C₅×#117	C₃×C₄	1	1	yes	characteristic
75	#4072	C₃×C₄	1	1	yes	characteristic
76	#4038	C₂²×C₃	1	2	yes	—
77	D₅×C₄⋊C₄	C₃×C₄	1	2	yes	—
78	D₅×C₂²⋊C₄	C₃×C₄	1	2	yes	—
79	#4023	C₂²×C₃	1	2	yes	—
80	#4018	C₃×C₄	1	1	yes	characteristic
81	#4018	C₃×C₄	1	1	yes	characteristic
82	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
83	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
84	C₂²⋊#170	C₂²×C₃	1	4	yes	—
85	#4004	C₂²×C₃	1	4	yes	complemented
86	#4003	C₂²×C₃	1	4	yes	—
87	#4002	C₂²×C₃	1	4	yes	complemented
88	C₄⋊#170	C₂²×C₃	1	4	yes	complemented
89	C₄×#170	C₂²×C₃	1	4	yes	complemented
90	C₂×#433	—	5	1	no	Sylow
91	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₃×D₅	—	2	2	no	—
93	C₂²×C₃×D₅	—	2	4	no	—
94	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×Dic₅	—	2	2	no	—
102	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
106	C₃×C₄×D₅	—	2	2	no	—
107	C₃×C₄×D₅	—	2	4	no	—
108	C₃×C₄×D₅	—	2	4	no	—
109	C₃×C₄×D₅	—	2	2	no	—
110	C₃×C₄×D₅	—	2	2	no	—
111	C₃×C₄×D₅	#41	1	4	yes	—
112	C₃×#170	—	2	4	no	—
113	C₃×#170	—	2	4	no	—
114	C₂³×C₃×C₄	—	5	1	no	—
115	C₂²×C₃×C₈	—	5	2	no	—
116	C₂²×C₃×C₈	—	5	2	no	—
117	C₃×#117	—	5	1	no	—
118	C₃×#117	—	5	2	no	—
119	C₃×#117	—	5	2	no	—
120	C₃×#117	—	5	1	no	—
121	C₃×#117	—	5	1	no	—
122	C₃×#117	AGL(1,𝔽₅)	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	—	5	2	no	—
124	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
125	C₂×C₃×C₄²	—	5	1	no	—
126	C₂×C₃×C₄²	—	5	1	no	—
127	C₃×C₄⋊C₈	—	5	4	no	—
128	C₃×C₄⋊C₈	—	5	4	no	—
129	C₃×C₂²⋊C₈	—	5	4	no	—
130	C₃×C₂²⋊C₈	—	5	4	no	—
131	C₃×#97	—	5	4	no	—
132	C₃×C₄×C₈	—	5	4	no	—
133	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
135	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
136	C₂×C₄×D₅	—	2	4	no	—
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	2	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	C₂×#170	C₂³×C₃	1	4	yes	—
144	C₂×#170	C₂³×C₃	1	4	yes	—
145	D₅⋊C₈	—	2	4	no	—
146	D₅⋊C₈	—	2	4	no	—
147	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
148	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
149	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
150	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
151	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
152	#685	C₂×C₃×C₄	1	2	yes	—
153	#685	C₂×C₃×C₄	1	2	yes	—
154	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
155	#683	C₂×C₃×C₄	1	2	yes	—
156	#683	C₂×C₃×C₄	1	2	yes	—
157	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
158	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
159	C₄×Dic₅	C₂³×C₃	1	2	yes	—
160	C₄×Dic₅	C₂³×C₃	1	2	yes	—
161	C₂×#117	—	5	1	no	—
162	#433	—	5	4	no	—
163	#433	—	5	4	no	—
164	C₂×C₄⋊C₈	—	5	2	no	—
165	C₂×C₂²⋊C₈	—	5	2	no	—
166	C₂×#97	—	5	1	no	—
167	C₂×C₄×C₈	—	5	1	no	—
168	C₂²×C₃×C₅	—	2	1	no	—
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₃×D₅	—	2	1	no	—
172	C₂×C₃×D₅	—	2	2	no	—
173	C₂×C₃×D₅	—	4	4	no	—
174	C₂×C₃×D₅	#117	1	2	yes	—
175	C₂×C₃×D₅	#131	1	4	yes	—
176	C₃×C₄×C₅	—	2	1	no	—
177	C₃×C₄×C₅	—	2	2	no	—
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	#117	1	2	yes	—
180	C₃×Dic₅	—	2	1	no	—
181	C₃×Dic₅	—	2	2	no	—
182	C₃×Dic₅	—	2	2	no	—
183	C₃×Dic₅	C₂×#41	1	2	yes	—
184	C₂⁴×C₃	—	5	1	no	—
185	C₂²×C₃×C₄	—	5	1	no	—
186	C₂²×C₃×C₄	—	5	1	no	—
187	C₂²×C₃×C₄	—	5	1	no	—
188	C₂²×C₃×C₄	—	5	2	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	—	10	4	no	—
193	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
194	C₂×C₃×C₈	—	5	4	no	—
195	C₂×C₃×C₈	—	5	4	no	—
196	C₂×C₃×C₈	—	10	4	no	—
197	C₂×C₃×C₈	—	10	4	no	—
198	C₃×C₄⋊C₄	—	5	2	no	—
199	C₃×C₄⋊C₄	—	5	2	no	—
200	C₃×C₄⋊C₄	—	5	2	no	—
201	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
202	C₃×C₂²⋊C₄	—	5	2	no	—
203	C₃×C₂²⋊C₄	—	5	2	no	—
204	C₃×C₂²⋊C₄	—	5	2	no	—
205	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
206	C₃×C₄²	—	5	2	no	—
207	C₃×C₄²	—	5	2	no	—
208	C₃×C₄²	—	5	1	no	—
209	C₃×C₄²	—	5	1	no	—
210	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
211	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
212	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
213	C₂²×D₅	—	2	2	no	—
214	C₂²×D₅	—	2	4	no	—
215	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
216	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
219	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
220	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
222	C₂×Dic₅	—	2	2	no	—
223	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
224	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
225	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
226	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
227	C₄×D₅	—	2	2	no	—
228	C₄×D₅	—	2	4	no	—
229	C₄×D₅	—	2	4	no	—
230	C₄×D₅	—	2	2	no	—
231	C₄×D₅	—	2	2	no	—
232	C₄×D₅	C₃×#41	1	4	yes	—
233	#170	—	2	4	no	—
234	#170	—	2	4	no	—
235	C₂³×C₄	—	5	1	no	—
236	C₂²×C₈	—	5	2	no	—
237	C₂²×C₈	—	5	2	no	—
238	#117	—	5	1	no	—
239	#117	—	5	2	no	—
240	#117	—	5	2	no	—
241	#117	—	5	1	no	—
242	#117	—	5	1	no	—
243	#117	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
244	C₂×C₄⋊C₄	—	5	2	no	—
245	C₂×C₂²⋊C₄	—	5	2	no	—
246	C₂×C₄²	—	5	1	no	—
247	C₂×C₄²	—	5	1	no	—
248	C₄⋊C₈	—	5	4	no	—
249	C₄⋊C₈	—	5	4	no	—
250	C₂²⋊C₈	—	5	4	no	—
251	C₂²⋊C₈	—	5	4	no	—
252	#97	—	5	4	no	—
253	C₄×C₈	—	5	4	no	—
254	C₂×C₃×C₅	—	4	1	no	—
255	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
256	C₂×C₃×C₅	C₂×#131	1	2	yes	—
257	C₃×D₅	—	4	1	no	—
258	C₃×D₅	#433	1	4	yes	complemented
259	C₂³×C₃	—	5	1	no	—
260	C₂³×C₃	—	5	1	no	—
261	C₂³×C₃	—	10	2	no	—
262	C₂³×C₃	—	10	4	no	—
263	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	5	1	no	—
266	C₂×C₃×C₄	—	5	4	no	—
267	C₂×C₃×C₄	—	5	2	no	—
268	C₂×C₃×C₄	—	5	2	no	—
269	C₂×C₃×C₄	—	5	1	no	—
270	C₂×C₃×C₄	—	10	2	no	—
271	C₂×C₃×C₄	—	10	4	no	—
272	C₂×C₃×C₄	—	10	4	no	—
273	C₂×C₃×C₄	—	10	2	no	—
274	C₂×C₃×C₄	—	10	2	no	—
275	C₂×C₃×C₄	—	10	2	no	—
276	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
277	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
278	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
280	C₃×C₈	—	10	4	no	—
281	C₃×C₈	—	10	4	no	—
282	C₂²×C₅	—	2	2	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
285	C₂×D₅	—	2	2	no	—
286	C₂×D₅	—	2	1	no	—
287	C₂×D₅	—	4	4	no	—
288	C₂×D₅	C₃×#117	1	2	yes	—
289	C₂×D₅	C₃×#131	1	4	yes	—
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	C₃×#117	1	2	yes	—
294	Dic₅	—	2	2	no	—
295	Dic₅	—	2	2	no	—
296	Dic₅	—	2	1	no	—
297	Dic₅	C₂×C₃×#41	1	2	yes	—
298	C₂⁴	—	5	1	no	—
299	C₂²×C₄	—	5	1	no	—
300	C₂²×C₄	—	5	1	no	—
301	C₂²×C₄	—	5	1	no	—
302	C₂²×C₄	—	5	2	no	—
303	C₂²×C₄	—	5	2	no	—
304	C₂²×C₄	—	5	1	no	—
305	C₂²×C₄	—	5	1	no	—
306	C₂²×C₄	—	10	4	no	—
307	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
308	C₂×C₈	—	5	4	no	—
309	C₂×C₈	—	5	4	no	—
310	C₂×C₈	—	10	4	no	—
311	C₂×C₈	—	10	4	no	—
312	C₄⋊C₄	—	5	2	no	—
313	C₄⋊C₄	—	5	2	no	—
314	C₄⋊C₄	—	5	2	no	—
315	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
316	C₂²⋊C₄	—	5	2	no	—
317	C₂²⋊C₄	—	5	2	no	—
318	C₂²⋊C₄	—	5	2	no	—
319	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
320	C₄²	—	5	2	no	—
321	C₄²	—	5	2	no	—
322	C₄²	—	5	1	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	1	yes	characteristic
326	C₃×C₅	C₂×#433	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	5	2	no	—
330	C₂²×C₃	—	5	4	no	—
331	C₂²×C₃	—	10	1	no	—
332	C₂²×C₃	—	10	2	no	—
333	C₂²×C₃	—	20	4	no	—
334	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	2	no	—
337	C₃×C₄	—	2	2	no	—
338	C₃×C₄	—	5	2	no	—
339	C₃×C₄	—	10	1	no	—
340	C₃×C₄	—	10	2	no	—
341	C₃×C₄	—	10	2	no	—
342	C₃×C₄	#4130	1	2	yes	—
343	C₂×C₅	—	4	1	no	—
344	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
345	C₂×C₅	C₂×C₃×#131	1	2	yes	—
346	D₅	—	4	1	no	—
347	D₅	C₃×#433	1	4	yes	complemented
348	C₂³	—	5	1	no	—
349	C₂³	—	5	1	no	—
350	C₂³	—	10	2	no	—
351	C₂³	—	10	4	no	—
352	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	5	1	no	—
355	C₂×C₄	—	5	4	no	—
356	C₂×C₄	—	5	2	no	—
357	C₂×C₄	—	5	2	no	—
358	C₂×C₄	—	5	1	no	—
359	C₂×C₄	—	10	2	no	—
360	C₂×C₄	—	10	2	no	—
361	C₂×C₄	—	10	4	no	—
362	C₂×C₄	—	10	4	no	—
363	C₂×C₄	—	10	2	no	—
364	C₂×C₄	—	10	2	no	—
365	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
366	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
367	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
369	C₈	—	10	4	no	—
370	C₈	—	10	4	no	—
371	C₂×C₃	—	4	1	no	—
372	C₂×C₃	—	5	4	no	—
373	C₂×C₃	—	20	1	no	—
374	C₂×C₃	C₂×#4130	1	1	yes	characteristic
375	C₂×C₃	D₅⋊#131	1	2	yes	—
376	C₅	C₂×C₃×#433	1	1	yes	characteristic, complemented, Sylow
377	C₂²	—	2	1	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	5	2	no	—
380	C₂²	—	5	4	no	—
381	C₂²	—	10	1	no	—
382	C₂²	—	10	2	no	—
383	C₂²	—	20	4	no	—
384	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	5	2	no	—
389	C₄	—	10	1	no	—
390	C₄	—	10	2	no	—
391	C₄	—	10	2	no	—
392	C₄	C₃×#4130	1	2	yes	—
393	C₃	D₅⋊#433	1	1	yes	characteristic, direct product factor, Sylow
394	C₂	—	4	1	no	—
395	C₂	—	5	4	no	—
396	C₂	—	20	1	no	—
397	C₂	C₂×C₃×#4130	1	1	yes	characteristic
398	C₂	C₃×D₅⋊#131	1	2	yes	—

	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	C₃×C₅×#117	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#117	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×#433
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
3. C₃×#65706	C₂	semidirect
4. C₃×#65697	C₂	semidirect
5. C₃×D₅⋊(C₄⋊C₈)	C₂	semidirect
6. C₃×#65676	C₂	semidirect
7. C₃×C₄×D₅⋊C₈	C₂	semidirect
8. D₅⋊#433	C₃	direct (N × H)
23. C₃×#4004	C₂²	semidirect
25. C₃×#4002	C₂²	semidirect
26. C₃×C₄⋊#170	C₂²	semidirect
27. C₃×C₄×#170	C₂²	semidirect
31. #65706	C₂×C₃	semidirect
32. #65697	C₂×C₃	semidirect
33. D₅⋊(C₄⋊C₈)	C₂×C₃	semidirect
34. #65676	C₂×C₃	semidirect
35. C₄×D₅⋊C₈	C₂×C₃	semidirect
85. #4004	C₂²×C₃	semidirect
87. #4002	C₂²×C₃	semidirect
88. C₄⋊#170	C₂²×C₃	semidirect
89. C₄×#170	C₂²×C₃	semidirect
258. C₃×D₅	#433	semidirect
326. C₃×C₅	C₂×#433	semidirect
347. D₅	C₃×#433	semidirect
376. C₅	C₂×C₃×#433	semidirect
393. C₃	D₅⋊#433	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₅×#117	2
C₃×D₅⋊(C₂²⋊C₈)	2
C₃×#65706	2
C₃×#65697	2
C₃×D₅⋊(C₄⋊C₈)	2
C₃×#65676	2
C₃×C₄×D₅⋊C₈	2
D₅⋊#433	3
C₂×C₃×#433	5

Subgroups — C3×D5⋊#433 #14413839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅⋊#433 #14413839