Subgroups — C₅×#73395 #14330136

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4940	C₂	1	2	yes	maximal, complemented
4	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₅×#4932	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4669	C₂	1	2	yes	maximal, complemented
7	C₅×#4666	C₂	1	2	yes	maximal, complemented
8	C₅×#4665	C₂	1	2	yes	maximal
9	C₅×#4646	C₂	1	2	yes	maximal, complemented
10	C₅×#2372	—	3	1	no	maximal, Hall
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
13	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
21	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
22	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
23	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
24	C₅×#875	C₄	1	8	yes	complemented
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	1	yes	characteristic
28	C₅×C₃⋊#95	C₂²	1	2	yes	—
29	C₅×C₃⋊#95	C₂²	1	2	yes	—
30	C₅×C₃⋊#95	C₂²	1	2	yes	—
31	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
32	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
33	#73395	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#124	—	3	1	no	—
35	C₅×#391	—	3	2	no	—
36	C₅×#388	—	3	2	no	—
37	C₅×#388	—	3	2	no	—
38	C₅×#386	—	3	2	no	—
39	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
40	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
41	C₅×#376	—	3	1	no	—
42	C₅×#376	D₃	1	1	yes	characteristic, complemented
43	C₂³×C₅×D₃	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
50	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
51	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
52	C₂×C₅×D₁₂	—	4	1	no	—
53	C₂×C₅×D₁₂	—	4	1	no	—
54	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
55	C₂×C₄×C₅×D₃	—	2	4	no	—
56	C₂×C₄×C₅×D₃	—	2	4	no	—
57	C₂×C₄×C₅×D₃	—	4	2	no	—
58	C₂×C₅×Dic₆	—	4	1	no	—
59	C₂×C₅×Dic₆	—	4	1	no	—
60	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
63	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
65	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
66	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
67	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
68	C₅×Dic₃⋊C₄	—	4	2	no	—
69	C₄×C₅×Dic₃	—	2	4	no	—
70	C₄×C₅×Dic₃	—	4	2	no	—
71	C₂×#875	C₂×C₅	1	1	yes	characteristic
72	C₃×#376	C₂×C₅	1	1	yes	characteristic, complemented
73	#4940	C₂×C₅	1	2	yes	complemented
74	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	complemented
75	#4932	C₂×C₅	1	1	yes	characteristic, complemented
76	#4669	C₂×C₅	1	2	yes	complemented
77	#4666	C₂×C₅	1	2	yes	complemented
78	#4665	C₂×C₅	1	2	yes	—
79	#4646	C₂×C₅	1	2	yes	complemented
80	C₂²×C₅×Q₈	—	3	1	no	—
81	C₂²×C₅×D₄	—	3	1	no	—
82	C₂³×C₄×C₅	—	3	2	no	—
83	C₅×#124	—	3	8	no	—
84	C₂×C₅×C₄⋊C₄	—	3	2	no	—
85	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
86	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
87	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
88	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
89	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
90	C₂×C₄²×C₅	—	3	2	no	—
91	C₂×C₄²×C₅	—	3	2	no	—
92	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
93	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
94	C₅×#95	—	3	1	no	—
95	C₅×#95	—	3	2	no	—
96	C₅×#95	—	3	1	no	—
97	C₅×#95	—	3	2	no	—
98	C₅×#95	—	3	2	no	—
99	C₅×#95	C₂×D₃	1	1	yes	characteristic
100	C₅×#95	C₂×D₃	1	2	yes	—
101	C₅×#95	C₂×D₃	1	1	yes	characteristic
102	#2372	—	3	1	no	Sylow
103	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
104	C₂²×C₅×D₃	—	2	2	no	—
105	C₂²×C₅×D₃	—	2	2	no	—
106	C₂²×C₅×D₃	—	2	2	no	—
107	C₂²×C₅×D₃	—	2	2	no	—
108	C₂²×C₅×D₃	—	2	2	no	—
109	C₂²×C₅×D₃	—	2	2	no	—
110	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	1	no	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	#41	1	4	yes	—
124	C₂×C₅×Dic₃	—	2	2	no	—
125	C₂×C₅×Dic₃	—	2	2	no	—
126	C₂×C₅×Dic₃	—	2	2	no	—
127	C₂×C₅×Dic₃	—	2	2	no	—
128	C₂×C₅×Dic₃	—	2	2	no	—
129	C₂×C₅×Dic₃	—	2	2	no	—
130	C₂×C₅×Dic₃	—	2	2	no	—
131	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
132	C₂×C₅×Dic₃	#41	1	4	yes	—
133	C₅×D₁₂	—	4	4	no	—
134	C₄×C₅×D₃	—	4	8	no	—
135	C₅×Dic₆	—	4	4	no	—
136	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
137	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
138	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
141	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
142	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
143	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
144	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
145	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
146	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
147	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
148	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
149	#875	C₄×C₅	1	8	yes	complemented
150	C₃×#95	C₂²×C₅	1	2	yes	—
151	C₃×#95	C₂²×C₅	1	1	yes	characteristic
152	C₃×#95	C₂²×C₅	1	1	yes	characteristic
153	C₃⋊#95	C₂²×C₅	1	2	yes	—
154	C₃⋊#95	C₂²×C₅	1	2	yes	—
155	C₃⋊#95	C₂²×C₅	1	2	yes	—
156	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
157	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
158	C₂⁴×C₅	—	3	2	no	—
159	C₂×C₅×Q₈	—	3	4	no	—
160	C₂×C₅×Q₈	—	12	1	no	—
161	C₂×C₅×Q₈	—	12	1	no	—
162	C₂×C₅×D₄	—	3	4	no	—
163	C₂×C₅×D₄	—	12	1	no	—
164	C₂×C₅×D₄	—	12	1	no	—
165	C₂²×C₄×C₅	—	3	2	no	—
166	C₂²×C₄×C₅	—	3	2	no	—
167	C₂²×C₄×C₅	—	3	2	no	—
168	C₂²×C₄×C₅	—	6	4	no	—
169	C₂²×C₄×C₅	—	6	4	no	—
170	C₂²×C₄×C₅	—	12	2	no	—
171	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
172	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
176	C₅×C₄⋊C₄	—	12	2	no	—
177	C₅×C₂²⋊C₄	—	3	8	no	—
178	C₅×C₂²⋊C₄	—	3	8	no	—
179	C₅×C₂²⋊C₄	—	6	4	no	—
180	C₅×C₂²⋊C₄	—	6	4	no	—
181	C₅×C₂²⋊C₄	—	12	2	no	—
182	C₄²×C₅	—	2	4	no	—
183	C₄²×C₅	—	6	4	no	—
184	C₄²×C₅	—	12	2	no	—
185	C₄²×C₅	C₄×D₃	1	4	yes	complemented
186	C₂×#124	—	3	1	no	—
187	#391	—	3	2	no	—
188	#388	—	3	2	no	—
189	#388	—	3	2	no	—
190	#386	—	3	2	no	—
191	C₄×C₂²⋊C₄	—	3	2	no	—
192	C₄×C₂²⋊C₄	—	3	2	no	—
193	#376	—	3	1	no	—
194	#376	C₅×D₃	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
196	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
197	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
198	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₅×D₃	—	2	4	no	—
201	C₂×C₅×D₃	—	2	4	no	—
202	C₂×C₅×D₃	—	2	4	no	—
203	C₂×C₅×D₃	—	4	2	no	—
204	C₂×C₅×D₃	—	4	2	no	—
205	C₂×C₅×D₃	—	4	2	no	—
206	C₂×C₅×D₃	—	4	2	no	—
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	—	2	2	no	—
209	C₃×C₄×C₅	—	2	2	no	—
210	C₃×C₄×C₅	—	2	4	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₅×Dic₃	—	2	4	no	—
213	C₅×Dic₃	—	2	4	no	—
214	C₅×Dic₃	—	4	2	no	—
215	C₂³×D₃	C₂³×C₅	1	2	yes	—
216	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
217	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
221	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
222	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
223	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
224	C₂×D₁₂	—	4	1	no	—
225	C₂×D₁₂	—	4	1	no	—
226	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
227	C₂×C₄×D₃	—	2	4	no	—
228	C₂×C₄×D₃	—	2	4	no	—
229	C₂×C₄×D₃	—	4	2	no	—
230	C₂×Dic₆	—	4	1	no	—
231	C₂×Dic₆	—	4	1	no	—
232	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
233	C₃×C₄²	—	2	4	no	—
234	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
235	(C₂×D₃)⋊C₄	—	2	4	no	—
236	(C₂×D₃)⋊C₄	—	2	4	no	—
237	(C₂×D₃)⋊C₄	—	4	2	no	—
238	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
239	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
240	Dic₃⋊C₄	—	4	2	no	—
241	C₄×Dic₃	—	2	4	no	—
242	C₄×Dic₃	—	4	2	no	—
243	C₂³×C₅	—	3	4	no	—
244	C₂³×C₅	—	6	2	no	—
245	C₂³×C₅	—	6	2	no	—
246	C₂³×C₅	—	6	2	no	—
247	C₂³×C₅	—	6	2	no	—
248	C₂³×C₅	—	6	2	no	—
249	C₂³×C₅	—	6	2	no	—
250	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
251	C₅×Q₈	—	12	4	no	—
252	C₅×D₄	—	12	4	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	3	4	no	—
263	C₂×C₄×C₅	—	3	4	no	—
264	C₂×C₄×C₅	—	6	2	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	6	2	no	—
267	C₂×C₄×C₅	—	6	2	no	—
268	C₂×C₄×C₅	—	6	2	no	—
269	C₂×C₄×C₅	—	6	2	no	—
270	C₂×C₄×C₅	—	6	2	no	—
271	C₂×C₄×C₅	—	12	8	no	—
272	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
273	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
274	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
275	C₂×C₄×C₅	#235	1	4	yes	—
276	C₂²×Q₈	—	3	1	no	—
277	C₂²×D₄	—	3	1	no	—
278	C₂³×C₄	—	3	2	no	—
279	#124	—	3	8	no	—
280	C₂×C₄⋊C₄	—	3	2	no	—
281	C₂×C₂²⋊C₄	—	3	2	no	—
282	C₂×C₂²⋊C₄	—	3	2	no	—
283	C₂×C₂²⋊C₄	—	3	2	no	—
284	C₂×C₂²⋊C₄	—	3	2	no	—
285	C₂×C₂²⋊C₄	—	3	2	no	—
286	C₂×C₄²	—	3	2	no	—
287	C₂×C₄²	—	3	2	no	—
288	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
289	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
290	#95	—	3	1	no	—
291	#95	—	3	2	no	—
292	#95	—	3	1	no	—
293	#95	—	3	2	no	—
294	#95	—	3	2	no	—
295	#95	C₂×C₅×D₃	1	1	yes	characteristic
296	#95	C₂×C₅×D₃	1	2	yes	—
297	#95	C₂×C₅×D₃	1	1	yes	characteristic
298	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
299	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
300	C₂×C₃×C₅	#518	1	1	yes	characteristic
301	C₂×C₃×C₅	#551	1	2	yes	—
302	C₂×C₃×C₅	#555	1	2	yes	—
303	C₅×D₃	—	4	4	no	—
304	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
305	C₂²×D₃	—	2	2	no	—
306	C₂²×D₃	—	2	2	no	—
307	C₂²×D₃	—	2	2	no	—
308	C₂²×D₃	—	2	2	no	—
309	C₂²×D₃	—	2	2	no	—
310	C₂²×D₃	—	2	2	no	—
311	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
322	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
323	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
324	C₂×C₃×C₄	C₅×#41	1	4	yes	—
325	C₂×Dic₃	—	2	2	no	—
326	C₂×Dic₃	—	2	2	no	—
327	C₂×Dic₃	—	2	2	no	—
328	C₂×Dic₃	—	2	2	no	—
329	C₂×Dic₃	—	2	2	no	—
330	C₂×Dic₃	—	2	2	no	—
331	C₂×Dic₃	—	2	2	no	—
332	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
333	C₂×Dic₃	C₅×#41	1	4	yes	—
334	D₁₂	—	4	4	no	—
335	C₄×D₃	—	4	8	no	—
336	Dic₆	—	4	4	no	—
337	C₂²×C₅	—	6	4	no	—
338	C₂²×C₅	—	6	4	no	—
339	C₂²×C₅	—	6	4	no	—
340	C₂²×C₅	—	12	2	no	—
341	C₂²×C₅	—	12	2	no	—
342	C₂²×C₅	—	12	2	no	—
343	C₂²×C₅	—	12	2	no	—
344	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
345	C₂²×C₅	C₂×#235	1	2	yes	—
346	C₂²×C₅	D₃×#41	1	2	yes	—
347	C₂²×C₅	#1009	1	1	yes	characteristic
348	C₂²×C₅	#1009	1	1	yes	characteristic
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	2	2	no	—
352	C₄×C₅	—	2	4	no	—
353	C₄×C₅	—	4	2	no	—
354	C₄×C₅	—	6	4	no	—
355	C₄×C₅	—	6	4	no	—
356	C₄×C₅	—	12	2	no	—
357	C₂⁴	—	3	2	no	—
358	C₂×Q₈	—	3	4	no	—
359	C₂×Q₈	—	12	1	no	—
360	C₂×Q₈	—	12	1	no	—
361	C₂×D₄	—	3	4	no	—
362	C₂×D₄	—	12	1	no	—
363	C₂×D₄	—	12	1	no	—
364	C₂²×C₄	—	3	2	no	—
365	C₂²×C₄	—	3	2	no	—
366	C₂²×C₄	—	3	2	no	—
367	C₂²×C₄	—	6	4	no	—
368	C₂²×C₄	—	6	4	no	—
369	C₂²×C₄	—	12	2	no	—
370	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
371	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
374	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
375	C₄⋊C₄	—	12	2	no	—
376	C₂²⋊C₄	—	3	8	no	—
377	C₂²⋊C₄	—	3	8	no	—
378	C₂²⋊C₄	—	6	4	no	—
379	C₂²⋊C₄	—	6	4	no	—
380	C₂²⋊C₄	—	12	2	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	6	4	no	—
383	C₄²	—	12	2	no	—
384	C₄²	C₄×C₅×D₃	1	4	yes	complemented
385	C₃×C₅	#2372	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
387	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
388	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
389	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
391	C₂×D₃	—	2	4	no	—
392	C₂×D₃	—	2	4	no	—
393	C₂×D₃	—	2	4	no	—
394	C₂×D₃	—	4	2	no	—
395	C₂×D₃	—	4	2	no	—
396	C₂×D₃	—	4	2	no	—
397	C₂×D₃	—	4	2	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	2	4	no	—
402	C₃×C₄	—	4	2	no	—
403	Dic₃	—	2	4	no	—
404	Dic₃	—	2	4	no	—
405	Dic₃	—	4	2	no	—
406	C₂×C₅	—	12	4	no	—
407	C₂×C₅	C₄×#235	1	1	yes	characteristic
408	C₂×C₅	#5521	1	1	yes	characteristic
409	C₂×C₅	#5522	1	1	yes	characteristic
410	C₂×C₅	#5527	1	2	yes	—
411	C₂×C₅	#5532	1	2	yes	—
412	C₂³	—	3	4	no	—
413	C₂³	—	6	2	no	—
414	C₂³	—	6	2	no	—
415	C₂³	—	6	2	no	—
416	C₂³	—	6	2	no	—
417	C₂³	—	6	2	no	—
418	C₂³	—	6	2	no	—
419	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
420	Q₈	—	12	4	no	—
421	D₄	—	12	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	3	4	no	—
432	C₂×C₄	—	3	4	no	—
433	C₂×C₄	—	6	2	no	—
434	C₂×C₄	—	6	2	no	—
435	C₂×C₄	—	6	2	no	—
436	C₂×C₄	—	6	2	no	—
437	C₂×C₄	—	6	2	no	—
438	C₂×C₄	—	6	2	no	—
439	C₂×C₄	—	6	2	no	—
440	C₂×C₄	—	12	8	no	—
441	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
442	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
443	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
444	C₂×C₄	C₅×#235	1	4	yes	—
445	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
446	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
447	C₂×C₃	C₅×#518	1	1	yes	characteristic
448	C₂×C₃	C₅×#551	1	2	yes	—
449	C₂×C₃	C₅×#555	1	2	yes	—
450	D₃	—	4	4	no	—
451	C₅	#73395	1	1	yes	characteristic, direct product factor, Sylow
452	C₂²	—	6	4	no	—
453	C₂²	—	6	4	no	—
454	C₂²	—	6	4	no	—
455	C₂²	—	12	2	no	—
456	C₂²	—	12	2	no	—
457	C₂²	—	12	2	no	—
458	C₂²	—	12	2	no	—
459	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
460	C₂²	C₂×C₅×#235	1	2	yes	—
461	C₂²	C₅×D₃×#41	1	2	yes	—
462	C₂²	C₅×#1009	1	1	yes	characteristic
463	C₂²	C₅×#1009	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	6	4	no	—
470	C₄	—	6	4	no	—
471	C₄	—	12	2	no	—
472	C₃	C₅×#2372	1	1	yes	characteristic, complemented, Sylow
473	C₂	—	12	4	no	—
474	C₂	C₄×C₅×#235	1	1	yes	characteristic
475	C₂	C₅×#5521	1	1	yes	characteristic
476	C₂	C₅×#5522	1	1	yes	characteristic
477	C₂	C₅×#5527	1	2	yes	—
478	C₂	C₅×#5532	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×#376	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#376	D₃
hypocenter	C₃	C₅×#2372
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#376	C₂	semidirect
3. C₅×#4940	C₂	semidirect
4. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₅×#4932	C₂	semidirect
6. C₅×#4669	C₂	semidirect
7. C₅×#4666	C₂	semidirect
9. C₅×#4646	C₂	semidirect
24. C₅×#875	C₄	semidirect
33. #73395	C₅	direct (N × H)
42. C₅×#376	D₃	semidirect
60. C₂×C₅×Dic₆	C₂×C₄	semidirect
62. C₃×C₄²×C₅	C₂×C₄	semidirect
66. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
67. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
72. C₃×#376	C₂×C₅	semidirect
73. #4940	C₂×C₅	semidirect
74. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
75. #4932	C₂×C₅	semidirect
76. #4669	C₂×C₅	semidirect
77. #4666	C₂×C₅	semidirect
79. #4646	C₂×C₅	semidirect
149. #875	C₄×C₅	semidirect
185. C₄²×C₅	C₄×D₃	semidirect
194. #376	C₅×D₃	semidirect
232. C₂×Dic₆	C₂×C₄×C₅	semidirect
234. C₃×C₄²	C₂×C₄×C₅	semidirect
238. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
239. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
384. C₄²	C₄×C₅×D₃	semidirect
385. C₃×C₅	#2372	semidirect
451. C₅	#73395	direct (N × H)
472. C₃	C₅×#2372	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#875	2
C₃×C₅×#376	2
C₅×#4940	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#4932	2
C₅×#4669	2
C₅×#4666	2
C₅×#4665	2
C₅×#4646	2
C₅×#2372	3
#73395	5

Subgroups — C5×#73395 #14330136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73395 #14330136