Subgroups — C₅×#74004 #14322593

Order 1920.

1344 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5212	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4990	C₂	1	4	yes	maximal, complemented
5	C₅×#4955	C₂	1	2	yes	maximal
6	C₅×Dic₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₅×#4670	C₂	1	4	yes	maximal, complemented
8	C₅×#2312	—	3	1	no	maximal, Hall
9	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
14	C₂×C₅×#217	C₂²	1	2	yes	—
15	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	8	yes	complemented
16	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
21	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	complemented
22	C₃×C₅×#95	C₂²	1	2	yes	complemented
23	C₅×C₃⋊#95	C₂²	1	4	yes	complemented
24	C₅×C₃⋊#95	C₂²	1	2	yes	complemented
25	#74004	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
27	C₅×#388	—	3	4	no	—
28	C₅×#388	—	3	4	no	—
29	C₅×#380	—	3	1	no	—
30	C₅×#380	D₃	1	1	yes	characteristic, complemented
31	C₅×#379	—	3	2	no	—
32	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂³×C₅×D₃	—	2	2	no	—
35	C₂³×C₅×D₃	—	2	2	no	—
36	C₂³×C₅×D₃	—	4	2	no	—
37	C₂³×C₅×D₃	—	4	2	no	—
38	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
39	C₂³×C₅×D₃	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	—	4	2	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	—	4	2	no	—
46	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
47	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
48	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
49	C₃×C₅×C₄⋊C₄	—	4	2	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
51	C₅×#217	—	2	4	no	—
52	C₅×(C₂×D₃)⋊C₄	—	4	4	no	—
53	C₅×(C₂×D₃)⋊C₄	—	4	4	no	—
54	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
55	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
56	C₅×C₄⋊Dic₃	—	4	2	no	—
57	C₄×C₅×Dic₃	—	4	4	no	—
58	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic
59	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
60	#5212	C₂×C₅	1	1	yes	characteristic, complemented
61	#4990	C₂×C₅	1	4	yes	complemented
62	#4955	C₂×C₅	1	2	yes	—
63	Dic₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
64	#4670	C₂×C₅	1	4	yes	complemented
65	C₂⁵×C₅	—	3	1	no	—
66	C₂³×C₄×C₅	—	3	1	no	—
67	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	—	3	2	no	—
69	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
70	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
71	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
73	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
74	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
75	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
76	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
77	C₂×C₄²×C₅	—	3	4	no	—
78	C₅×#95	—	3	4	no	—
79	C₅×#95	—	3	2	no	—
80	C₅×#95	C₂×D₃	1	2	yes	complemented
81	#2312	—	3	1	no	Sylow
82	C₂³×C₃×C₅	—	2	2	no	—
83	C₂³×C₃×C₅	—	2	2	no	—
84	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
85	C₂³×C₃×C₅	#41	1	2	yes	—
86	C₂³×C₃×C₅	#41	1	2	yes	—
87	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
88	C₂²×C₅×D₃	—	2	8	no	—
89	C₂²×C₅×D₃	—	2	2	no	—
90	C₂²×C₅×D₃	—	2	2	no	—
91	C₂²×C₅×D₃	—	2	4	no	—
92	C₂²×C₅×D₃	—	2	4	no	—
93	C₂²×C₅×D₃	—	4	4	no	—
94	C₂²×C₅×D₃	—	4	4	no	—
95	C₂²×C₅×D₃	—	4	8	no	—
96	C₂²×C₅×D₃	—	4	8	no	—
97	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	4	4	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂×C₅×Dic₃	—	2	4	no	—
107	C₂×C₅×Dic₃	—	2	4	no	—
108	C₂×C₅×Dic₃	—	2	4	no	—
109	C₂×C₅×Dic₃	—	2	4	no	—
110	C₂×C₅×Dic₃	—	4	4	no	—
111	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
112	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
113	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
114	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
115	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
116	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
117	C₂×#217	C₂²×C₅	1	2	yes	—
118	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	8	yes	complemented
119	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
120	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
121	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
122	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
123	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
124	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	complemented
125	C₃×#95	C₂²×C₅	1	2	yes	complemented
126	C₃⋊#95	C₂²×C₅	1	4	yes	complemented
127	C₃⋊#95	C₂²×C₅	1	2	yes	complemented
128	C₂⁴×C₅	—	3	2	no	—
129	C₂⁴×C₅	—	3	4	no	—
130	C₂⁴×C₅	—	6	2	no	—
131	C₂⁴×C₅	—	6	2	no	—
132	C₂⁴×C₅	—	12	2	no	—
133	C₂⁴×C₅	—	12	2	no	—
134	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
135	C₂²×C₄×C₅	—	3	2	no	—
136	C₂²×C₄×C₅	—	3	4	no	—
137	C₂²×C₄×C₅	—	3	4	no	—
138	C₂²×C₄×C₅	—	4	2	no	—
139	C₂²×C₄×C₅	—	12	2	no	—
140	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
141	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
142	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
143	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₅×C₄⋊C₄	—	4	2	no	—
145	C₅×C₄⋊C₄	—	12	2	no	—
146	C₅×C₂²⋊C₄	—	2	4	no	—
147	C₅×C₂²⋊C₄	—	3	8	no	—
148	C₅×C₂²⋊C₄	—	3	8	no	—
149	C₅×C₂²⋊C₄	—	6	4	no	—
150	C₅×C₂²⋊C₄	—	12	4	no	—
151	C₅×C₂²⋊C₄	—	12	4	no	—
152	C₄²×C₅	—	12	4	no	—
153	C₂²×C₂²⋊C₄	—	3	1	no	—
154	#388	—	3	4	no	—
155	#388	—	3	4	no	—
156	#380	—	3	1	no	—
157	#380	C₅×D₃	1	1	yes	characteristic, complemented
158	#379	—	3	2	no	—
159	C₄×C₂²⋊C₄	—	3	2	no	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	—	2	2	no	—
162	C₂²×C₃×C₅	—	2	4	no	—
163	C₂²×C₃×C₅	—	2	4	no	—
164	C₂²×C₃×C₅	#117	1	4	yes	—
165	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
168	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
169	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
170	C₂×C₅×D₃	—	2	4	no	—
171	C₂×C₅×D₃	—	2	4	no	—
172	C₂×C₅×D₃	—	2	4	no	—
173	C₂×C₅×D₃	—	4	16	no	—
174	C₂×C₅×D₃	—	4	4	no	—
175	C₂×C₅×D₃	—	4	4	no	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	—	2	2	no	—
178	C₃×C₄×C₅	—	4	4	no	—
179	C₅×Dic₃	—	2	4	no	—
180	C₅×Dic₃	—	4	4	no	—
181	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
182	C₂³×D₃	—	2	2	no	—
183	C₂³×D₃	—	2	2	no	—
184	C₂³×D₃	—	4	2	no	—
185	C₂³×D₃	—	4	2	no	—
186	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
187	C₂³×D₃	C₂³×C₅	1	2	yes	—
188	C₂²×C₃×C₄	—	4	2	no	—
189	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
190	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
191	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
193	C₂²×Dic₃	—	4	2	no	—
194	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
195	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
196	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
197	C₃×C₄⋊C₄	—	4	2	no	—
198	C₃×C₂²⋊C₄	—	2	4	no	—
199	#217	—	2	4	no	—
200	(C₂×D₃)⋊C₄	—	4	4	no	—
201	(C₂×D₃)⋊C₄	—	4	4	no	—
202	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
203	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
204	C₄⋊Dic₃	—	4	2	no	—
205	C₄×Dic₃	—	4	4	no	—
206	C₂³×C₅	—	2	2	no	—
207	C₂³×C₅	—	2	2	no	—
208	C₂³×C₅	—	3	4	no	—
209	C₂³×C₅	—	6	8	no	—
210	C₂³×C₅	—	6	2	no	—
211	C₂³×C₅	—	6	4	no	—
212	C₂³×C₅	—	6	2	no	—
213	C₂³×C₅	—	6	4	no	—
214	C₂³×C₅	—	12	4	no	—
215	C₂³×C₅	—	12	4	no	—
216	C₂³×C₅	—	12	8	no	—
217	C₂³×C₅	—	12	8	no	—
218	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
219	C₂³×C₅	#237	1	2	yes	—
220	C₂³×C₅	#239	1	2	yes	—
221	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	4	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	2	4	no	—
227	C₂×C₄×C₅	—	3	4	no	—
228	C₂×C₄×C₅	—	4	4	no	—
229	C₂×C₄×C₅	—	6	4	no	—
230	C₂×C₄×C₅	—	6	4	no	—
231	C₂×C₄×C₅	—	6	4	no	—
232	C₂×C₄×C₅	—	6	4	no	—
233	C₂×C₄×C₅	—	12	4	no	—
234	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
235	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
236	C₂⁵	—	3	1	no	—
237	C₂³×C₄	—	3	1	no	—
238	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
239	C₂×C₄⋊C₄	—	3	2	no	—
240	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
241	C₂×C₂²⋊C₄	—	3	8	no	—
242	C₂×C₂²⋊C₄	—	3	2	no	—
243	C₂×C₂²⋊C₄	—	3	2	no	—
244	C₂×C₂²⋊C₄	—	3	2	no	—
245	C₂×C₂²⋊C₄	—	3	4	no	—
246	C₂×C₂²⋊C₄	—	3	4	no	—
247	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
248	C₂×C₄²	—	3	4	no	—
249	#95	—	3	4	no	—
250	#95	—	3	2	no	—
251	#95	C₂×C₅×D₃	1	2	yes	complemented
252	C₂×C₃×C₅	—	2	4	no	—
253	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
254	C₂×C₃×C₅	#518	1	1	yes	characteristic
255	C₂×C₃×C₅	#518	1	1	yes	characteristic
256	C₂×C₃×C₅	#538	1	2	yes	—
257	C₂×C₃×C₅	#538	1	2	yes	—
258	C₅×D₃	—	4	4	no	—
259	C₂³×C₃	—	2	2	no	—
260	C₂³×C₃	—	2	2	no	—
261	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
262	C₂³×C₃	C₅×#41	1	2	yes	—
263	C₂³×C₃	C₅×#41	1	2	yes	—
264	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
265	C₂²×D₃	—	2	8	no	—
266	C₂²×D₃	—	2	2	no	—
267	C₂²×D₃	—	2	2	no	—
268	C₂²×D₃	—	2	4	no	—
269	C₂²×D₃	—	2	4	no	—
270	C₂²×D₃	—	4	4	no	—
271	C₂²×D₃	—	4	4	no	—
272	C₂²×D₃	—	4	8	no	—
273	C₂²×D₃	—	4	8	no	—
274	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	4	4	no	—
281	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
282	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
283	C₂×Dic₃	—	2	4	no	—
284	C₂×Dic₃	—	2	4	no	—
285	C₂×Dic₃	—	2	4	no	—
286	C₂×Dic₃	—	2	4	no	—
287	C₂×Dic₃	—	4	4	no	—
288	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
289	C₂²×C₅	—	2	4	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	—	2	2	no	—
292	C₂²×C₅	—	2	4	no	—
293	C₂²×C₅	—	6	4	no	—
294	C₂²×C₅	—	6	4	no	—
295	C₂²×C₅	—	6	4	no	—
296	C₂²×C₅	—	12	16	no	—
297	C₂²×C₅	—	12	4	no	—
298	C₂²×C₅	—	12	4	no	—
299	C₂²×C₅	#892	1	4	yes	—
300	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
301	C₂²×C₅	C₂×#237	1	1	yes	characteristic
302	C₂²×C₅	#1004	1	2	yes	—
303	C₂²×C₅	C₂×#239	1	1	yes	characteristic
304	C₂²×C₅	#1009	1	2	yes	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	4	4	no	—
308	C₄×C₅	—	6	4	no	—
309	C₄×C₅	—	12	4	no	—
310	C₂⁴	—	3	2	no	—
311	C₂⁴	—	3	4	no	—
312	C₂⁴	—	6	2	no	—
313	C₂⁴	—	6	2	no	—
314	C₂⁴	—	12	2	no	—
315	C₂⁴	—	12	2	no	—
316	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
317	C₂²×C₄	—	3	2	no	—
318	C₂²×C₄	—	3	4	no	—
319	C₂²×C₄	—	3	4	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	12	2	no	—
322	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
323	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
324	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	12	2	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	3	8	no	—
330	C₂²⋊C₄	—	3	8	no	—
331	C₂²⋊C₄	—	6	4	no	—
332	C₂²⋊C₄	—	12	4	no	—
333	C₂²⋊C₄	—	12	4	no	—
334	C₄²	—	12	4	no	—
335	C₃×C₅	#2312	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	4	no	—
339	C₂²×C₃	—	2	4	no	—
340	C₂²×C₃	C₅×#117	1	4	yes	—
341	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
342	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
343	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
344	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
345	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
346	C₂×D₃	—	2	4	no	—
347	C₂×D₃	—	2	4	no	—
348	C₂×D₃	—	2	4	no	—
349	C₂×D₃	—	4	16	no	—
350	C₂×D₃	—	4	4	no	—
351	C₂×D₃	—	4	4	no	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	2	2	no	—
354	C₃×C₄	—	4	4	no	—
355	Dic₃	—	2	4	no	—
356	Dic₃	—	4	4	no	—
357	C₂×C₅	—	2	4	no	—
358	C₂×C₅	—	12	4	no	—
359	C₂×C₅	#5486	1	1	yes	characteristic
360	C₂×C₅	C₂×#892	1	1	yes	characteristic
361	C₂×C₅	#5521	1	1	yes	characteristic
362	C₂×C₅	#5617	1	2	yes	—
363	C₂×C₅	#5644	1	2	yes	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	3	4	no	—
367	C₂³	—	6	8	no	—
368	C₂³	—	6	2	no	—
369	C₂³	—	6	4	no	—
370	C₂³	—	6	2	no	—
371	C₂³	—	6	4	no	—
372	C₂³	—	12	4	no	—
373	C₂³	—	12	4	no	—
374	C₂³	—	12	8	no	—
375	C₂³	—	12	8	no	—
376	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
377	C₂³	C₅×#237	1	2	yes	—
378	C₂³	C₅×#239	1	2	yes	—
379	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	3	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	6	4	no	—
388	C₂×C₄	—	6	4	no	—
389	C₂×C₄	—	6	4	no	—
390	C₂×C₄	—	6	4	no	—
391	C₂×C₄	—	12	4	no	—
392	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
393	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
394	C₂×C₃	—	2	4	no	—
395	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
396	C₂×C₃	C₅×#518	1	1	yes	characteristic
397	C₂×C₃	C₅×#518	1	1	yes	characteristic
398	C₂×C₃	C₅×#538	1	2	yes	—
399	C₂×C₃	C₅×#538	1	2	yes	—
400	D₃	—	4	4	no	—
401	C₅	#74004	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	6	4	no	—
407	C₂²	—	6	4	no	—
408	C₂²	—	6	4	no	—
409	C₂²	—	12	16	no	—
410	C₂²	—	12	4	no	—
411	C₂²	—	12	4	no	—
412	C₂²	C₅×#892	1	4	yes	—
413	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
414	C₂²	C₂×C₅×#237	1	1	yes	characteristic
415	C₂²	C₅×#1004	1	2	yes	—
416	C₂²	C₂×C₅×#239	1	1	yes	characteristic
417	C₂²	C₅×#1009	1	2	yes	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	4	4	no	—
421	C₄	—	6	4	no	—
422	C₄	—	12	4	no	—
423	C₃	C₅×#2312	1	1	yes	characteristic, complemented, Sylow
424	C₂	—	2	4	no	—
425	C₂	—	12	4	no	—
426	C₂	C₅×#5486	1	1	yes	characteristic
427	C₂	C₂×C₅×#892	1	1	yes	characteristic
428	C₂	C₅×#5521	1	1	yes	characteristic
429	C₂	C₅×#5617	1	2	yes	—
430	C₂	C₅×#5644	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#380	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₅×D₃	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#380	D₃
hypocenter	C₃	C₅×#2312
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#380

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#380	C₂	semidirect
3. C₅×#5212	C₂	semidirect
4. C₅×#4990	C₂	semidirect
6. C₅×Dic₃×C₂²⋊C₄	C₂	semidirect
7. C₅×#4670	C₂	semidirect
12. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
15. C₂×C₅×(C₂×D₃)⋊C₄	C₄	semidirect
20. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
21. C₂×C₄×C₅×Dic₃	C₂²	semidirect
22. C₃×C₅×#95	C₂²	semidirect
23. C₅×C₃⋊#95	C₂²	semidirect
24. C₅×C₃⋊#95	C₂²	semidirect
25. #74004	C₅	direct (N × H)
30. C₅×#380	D₃	semidirect
59. C₃×#380	C₂×C₅	semidirect
60. #5212	C₂×C₅	semidirect
61. #4990	C₂×C₅	semidirect
63. Dic₃×C₂²⋊C₄	C₂×C₅	semidirect
64. #4670	C₂×C₅	semidirect
69. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
80. C₅×#95	C₂×D₃	semidirect
115. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
118. C₂×(C₂×D₃)⋊C₄	C₄×C₅	semidirect
123. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
124. C₂×C₄×Dic₃	C₂²×C₅	semidirect
125. C₃×#95	C₂²×C₅	semidirect
126. C₃⋊#95	C₂²×C₅	semidirect
127. C₃⋊#95	C₂²×C₅	semidirect
157. #380	C₅×D₃	semidirect
240. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
251. #95	C₂×C₅×D₃	semidirect
335. C₃×C₅	#2312	semidirect
401. C₅	#74004	direct (N × H)
423. C₃	C₅×#2312	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₃×C₅×#380	2
C₅×#5212	2
C₅×#4990	2
C₅×#4955	2
C₅×Dic₃×C₂²⋊C₄	2
C₅×#4670	2
C₅×#2312	3
#74004	5

Subgroups — C5×#74004 #14322593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#74004 #14322593