Subgroups — C₅×#5655 #11756040

Order 960.

584 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#547	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×#67	C₂²	1	1	yes	characteristic
20	C₂×C₅×#67	C₂²	1	1	yes	characteristic
21	C₂×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂×C₅×#67	C₂²	1	1	yes	characteristic
23	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
24	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
25	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
26	C₅×#237	—	2	4	no	—
27	C₅×#235	—	2	4	no	—
28	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
33	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic
34	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic
35	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₅×#217	C₂²	1	1	yes	characteristic
41	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
42	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
43	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
44	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
45	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
46	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
47	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
51	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
52	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
54	#5655	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×#41	—	3	1	no	—
56	C₂×C₅×#41	—	3	1	no	—
57	C₅×C₄⋊Q₈	—	3	1	no	—
58	C₅×#123	—	3	1	no	—
59	C₅×#123	—	3	1	no	—
60	C₅×#123	—	3	1	no	—
61	C₅×#123	D₃	1	1	yes	characteristic, complemented
62	C₅×C₂²⋊Q₈	—	3	1	no	—
63	C₅×C₂²⋊Q₈	—	3	1	no	—
64	C₅×#121	—	3	1	no	—
65	C₅×#121	—	3	1	no	—
66	C₄×C₅×D₄	—	3	1	no	—
67	C₄×C₅×D₄	—	3	1	no	—
68	C₂×C₅×C₄⋊C₄	—	3	1	no	—
69	C₂×C₅×C₄⋊C₄	—	3	1	no	—
70	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
73	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
74	C₃×C₅×D₄	—	2	2	no	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₅×#67	—	2	2	no	—
82	C₅×#67	—	2	2	no	—
83	C₅×#67	—	2	2	no	—
84	C₅×#67	D₄	1	4	yes	complemented
85	C₂×C₅×Dic₃	—	2	2	no	—
86	C₂×C₅×Dic₃	—	2	2	no	—
87	C₂×C₅×Dic₃	—	2	2	no	—
88	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
89	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
90	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
91	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
93	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
94	C₅×D₁₂	—	2	2	no	—
95	C₄×C₅×D₃	—	2	2	no	—
96	C₄×C₅×D₃	—	2	2	no	—
97	C₄×C₅×D₃	—	2	2	no	—
98	C₄×C₅×D₃	—	2	2	no	—
99	C₅×Dic₆	—	2	2	no	—
100	C₅×Dic₆	—	2	2	no	—
101	C₂×#237	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×#235	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
104	#939	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
106	#896	C₂×C₅	1	1	yes	characteristic, complemented
107	#894	C₂×C₅	1	1	yes	characteristic, complemented
108	D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
109	#888	C₂×C₅	1	1	yes	characteristic, complemented
110	#886	C₂×C₅	1	1	yes	characteristic, complemented
111	#884	C₂×C₅	1	1	yes	characteristic, complemented
112	#883	C₂×C₅	1	1	yes	characteristic, complemented
113	#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
114	#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
115	#878	C₂×C₅	1	1	yes	characteristic, complemented
116	C₅×#41	—	6	4	no	—
117	C₅×#41	—	6	4	no	—
118	C₂×C₅×Q₈	—	3	1	no	—
119	C₂×C₅×Q₈	—	3	1	no	—
120	C₂×C₅×D₄	—	3	1	no	—
121	C₂×C₅×D₄	—	3	1	no	—
122	C₂×C₅×D₄	—	3	1	no	—
123	C₂×C₅×D₄	—	3	1	no	—
124	C₂×C₅×D₄	—	3	1	no	—
125	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
126	C₂²×C₄×C₅	—	3	1	no	—
127	C₂²×C₄×C₅	—	3	1	no	—
128	C₂²×C₄×C₅	—	3	1	no	—
129	C₂²×C₄×C₅	—	3	1	no	—
130	C₂²×C₄×C₅	—	3	1	no	—
131	C₂²×C₄×C₅	—	3	1	no	—
132	C₂²×C₄×C₅	—	3	1	no	—
133	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
134	C₅×C₄⋊C₄	—	3	1	no	—
135	C₅×C₄⋊C₄	—	3	1	no	—
136	C₅×C₄⋊C₄	—	3	1	no	—
137	C₅×C₄⋊C₄	—	3	1	no	—
138	C₅×C₄⋊C₄	—	3	1	no	—
139	C₅×C₄⋊C₄	—	3	1	no	—
140	C₅×C₄⋊C₄	—	3	1	no	—
141	C₅×C₄⋊C₄	—	3	1	no	—
142	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
143	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
144	C₅×C₂²⋊C₄	—	3	1	no	—
145	C₅×C₂²⋊C₄	—	3	1	no	—
146	C₅×C₂²⋊C₄	—	3	1	no	—
147	C₅×C₂²⋊C₄	—	3	1	no	—
148	C₅×C₂²⋊C₄	—	3	1	no	—
149	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
150	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
151	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
152	C₄²×C₅	—	3	1	no	—
153	#547	—	3	1	no	Sylow
154	C₂²×C₃×C₅	—	2	1	no	—
155	C₂²×C₃×C₅	—	2	1	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	—	2	1	no	—
158	C₂²×C₃×C₅	—	2	1	no	—
159	C₂²×C₃×C₅	C₂×D₄	1	2	yes	—
160	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
161	C₂×C₅×D₃	—	2	1	no	—
162	C₂×C₅×D₃	—	2	1	no	—
163	C₂×C₅×D₃	—	2	1	no	—
164	C₂×C₅×D₃	—	2	1	no	—
165	C₂×C₅×D₃	—	2	1	no	—
166	C₂×C₅×D₃	C₂×D₄	1	2	yes	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	—	2	1	no	—
169	C₃×C₄×C₅	—	2	1	no	—
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	—	2	1	no	—
172	C₅×Dic₃	—	2	1	no	—
173	C₅×Dic₃	—	2	1	no	—
174	C₅×Dic₃	—	2	1	no	—
175	C₅×Dic₃	—	2	1	no	—
176	C₅×Dic₃	C₂×D₄	1	2	yes	—
177	C₅×Dic₃	#41	1	2	yes	complemented
178	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
180	C₂×#67	C₂²×C₅	1	1	yes	characteristic
181	C₂×#67	C₂²×C₅	1	1	yes	characteristic
182	C₂×#67	C₂²×C₅	1	1	yes	characteristic
183	C₂×#67	C₂²×C₅	1	1	yes	characteristic
184	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
185	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
186	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
187	#237	—	2	4	no	—
188	#235	—	2	4	no	—
189	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
190	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
193	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
194	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic
195	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
198	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
199	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
200	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
201	#217	C₂²×C₅	1	1	yes	characteristic
202	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
203	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
204	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
205	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
206	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
207	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
208	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
209	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
210	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
211	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
212	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
213	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
214	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
215	C₂³×C₅	—	3	1	no	—
216	C₂³×C₅	—	3	1	no	—
217	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
218	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₅×Q₈	—	6	2	no	—
220	C₅×Q₈	—	6	2	no	—
221	C₅×D₄	—	2	2	no	—
222	C₅×D₄	—	3	4	no	—
223	C₅×D₄	—	6	2	no	—
224	C₅×D₄	—	6	2	no	—
225	C₅×D₄	—	6	2	no	—
226	C₅×D₄	—	6	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	3	1	no	—
229	C₂×C₄×C₅	—	3	1	no	—
230	C₂×C₄×C₅	—	3	1	no	—
231	C₂×C₄×C₅	—	3	1	no	—
232	C₂×C₄×C₅	—	3	1	no	—
233	C₂×C₄×C₅	—	3	1	no	—
234	C₂×C₄×C₅	—	6	2	no	—
235	C₂×C₄×C₅	—	6	2	no	—
236	C₂×C₄×C₅	—	6	2	no	—
237	C₂×C₄×C₅	—	6	2	no	—
238	C₂×C₄×C₅	—	6	2	no	—
239	C₂×C₄×C₅	—	6	2	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
246	C₂×#41	—	3	1	no	—
247	C₂×#41	—	3	1	no	—
248	C₄⋊Q₈	—	3	1	no	—
249	#123	—	3	1	no	—
250	#123	—	3	1	no	—
251	#123	—	3	1	no	—
252	#123	C₅×D₃	1	1	yes	characteristic, complemented
253	C₂²⋊Q₈	—	3	1	no	—
254	C₂²⋊Q₈	—	3	1	no	—
255	#121	—	3	1	no	—
256	#121	—	3	1	no	—
257	C₄×D₄	—	3	1	no	—
258	C₄×D₄	—	3	1	no	—
259	C₂×C₄⋊C₄	—	3	1	no	—
260	C₂×C₄⋊C₄	—	3	1	no	—
261	C₂×C₃×C₅	—	2	2	no	—
262	C₂×C₃×C₅	—	4	1	no	—
263	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
265	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
266	C₅×D₃	—	2	2	no	—
267	C₅×D₃	—	4	1	no	—
268	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
269	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
270	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
271	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
272	C₃×D₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
279	#67	—	2	2	no	—
280	#67	—	2	2	no	—
281	#67	—	2	2	no	—
282	#67	C₅×D₄	1	4	yes	complemented
283	C₂×Dic₃	—	2	2	no	—
284	C₂×Dic₃	—	2	2	no	—
285	C₂×Dic₃	—	2	2	no	—
286	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
287	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
288	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
289	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
290	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
291	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
292	D₁₂	—	2	2	no	—
293	C₄×D₃	—	2	2	no	—
294	C₄×D₃	—	2	2	no	—
295	C₄×D₃	—	2	2	no	—
296	C₄×D₃	—	2	2	no	—
297	Dic₆	—	2	2	no	—
298	Dic₆	—	2	2	no	—
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	2	1	no	—
304	C₂²×C₅	—	3	2	no	—
305	C₂²×C₅	—	6	1	no	—
306	C₂²×C₅	—	6	1	no	—
307	C₂²×C₅	—	6	1	no	—
308	C₂²×C₅	—	6	1	no	—
309	C₂²×C₅	—	6	1	no	—
310	C₂²×C₅	D₃×D₄	1	2	yes	—
311	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	2	1	no	—
314	C₄×C₅	—	2	1	no	—
315	C₄×C₅	—	2	1	no	—
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	3	2	no	—
318	C₄×C₅	—	3	2	no	—
319	C₄×C₅	—	6	1	no	—
320	C₄×C₅	—	6	1	no	—
321	C₄×C₅	—	6	1	no	—
322	C₄×C₅	—	6	1	no	—
323	#41	—	6	4	no	—
324	#41	—	6	4	no	—
325	C₂×Q₈	—	3	1	no	—
326	C₂×Q₈	—	3	1	no	—
327	C₂×D₄	—	3	1	no	—
328	C₂×D₄	—	3	1	no	—
329	C₂×D₄	—	3	1	no	—
330	C₂×D₄	—	3	1	no	—
331	C₂×D₄	—	3	1	no	—
332	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	3	1	no	—
335	C₂²×C₄	—	3	1	no	—
336	C₂²×C₄	—	3	1	no	—
337	C₂²×C₄	—	3	1	no	—
338	C₂²×C₄	—	3	1	no	—
339	C₂²×C₄	—	3	1	no	—
340	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic
341	C₄⋊C₄	—	3	1	no	—
342	C₄⋊C₄	—	3	1	no	—
343	C₄⋊C₄	—	3	1	no	—
344	C₄⋊C₄	—	3	1	no	—
345	C₄⋊C₄	—	3	1	no	—
346	C₄⋊C₄	—	3	1	no	—
347	C₄⋊C₄	—	3	1	no	—
348	C₄⋊C₄	—	3	1	no	—
349	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
350	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
351	C₂²⋊C₄	—	3	1	no	—
352	C₂²⋊C₄	—	3	1	no	—
353	C₂²⋊C₄	—	3	1	no	—
354	C₂²⋊C₄	—	3	1	no	—
355	C₂²⋊C₄	—	3	1	no	—
356	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
357	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
358	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
359	C₄²	—	3	1	no	—
360	C₃×C₅	#547	1	1	yes	characteristic, complemented, Hall
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	—	2	1	no	—
366	C₂²×C₃	C₂×C₅×D₄	1	2	yes	—
367	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
368	C₂×D₃	—	2	1	no	—
369	C₂×D₃	—	2	1	no	—
370	C₂×D₃	—	2	1	no	—
371	C₂×D₃	—	2	1	no	—
372	C₂×D₃	—	2	1	no	—
373	C₂×D₃	C₂×C₅×D₄	1	2	yes	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	1	no	—
377	C₃×C₄	—	2	1	no	—
378	C₃×C₄	—	2	1	no	—
379	Dic₃	—	2	1	no	—
380	Dic₃	—	2	1	no	—
381	Dic₃	—	2	1	no	—
382	Dic₃	—	2	1	no	—
383	Dic₃	C₂×C₅×D₄	1	2	yes	—
384	Dic₃	C₅×#41	1	2	yes	complemented
385	C₂×C₅	—	2	2	no	—
386	C₂×C₅	—	4	1	no	—
387	C₂×C₅	—	6	2	no	—
388	C₂×C₅	—	12	1	no	—
389	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
390	C₂×C₅	D₃×#41	1	1	yes	characteristic
391	C₂×C₅	#1010	1	1	yes	characteristic
392	C₂³	—	3	1	no	—
393	C₂³	—	3	1	no	—
394	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
395	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
396	Q₈	—	6	2	no	—
397	Q₈	—	6	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	3	4	no	—
400	D₄	—	6	2	no	—
401	D₄	—	6	2	no	—
402	D₄	—	6	2	no	—
403	D₄	—	6	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	3	1	no	—
406	C₂×C₄	—	3	1	no	—
407	C₂×C₄	—	3	1	no	—
408	C₂×C₄	—	3	1	no	—
409	C₂×C₄	—	3	1	no	—
410	C₂×C₄	—	3	1	no	—
411	C₂×C₄	—	6	2	no	—
412	C₂×C₄	—	6	2	no	—
413	C₂×C₄	—	6	2	no	—
414	C₂×C₄	—	6	2	no	—
415	C₂×C₄	—	6	2	no	—
416	C₂×C₄	—	6	2	no	—
417	C₂×C₄	—	6	2	no	—
418	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
423	C₂×C₃	—	2	2	no	—
424	C₂×C₃	—	4	1	no	—
425	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
426	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
427	C₂×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
428	D₃	—	2	2	no	—
429	D₃	—	4	1	no	—
430	C₅	#5655	1	1	yes	characteristic, direct product factor, Sylow
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	3	2	no	—
437	C₂²	—	6	1	no	—
438	C₂²	—	6	1	no	—
439	C₂²	—	6	1	no	—
440	C₂²	—	6	1	no	—
441	C₂²	—	6	1	no	—
442	C₂²	C₅×D₃×D₄	1	2	yes	—
443	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	3	2	no	—
450	C₄	—	3	2	no	—
451	C₄	—	6	1	no	—
452	C₄	—	6	1	no	—
453	C₄	—	6	1	no	—
454	C₄	—	6	1	no	—
455	C₃	C₅×#547	1	1	yes	characteristic, complemented, Sylow
456	C₂	—	2	2	no	—
457	C₂	—	4	1	no	—
458	C₂	—	6	2	no	—
459	C₂	—	12	1	no	—
460	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic
461	C₂	C₅×D₃×#41	1	1	yes	characteristic
462	C₂	C₅×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₃×C₅×#123	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×#123	D₃
hypocenter	C₃	C₅×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#237	C₂	semidirect
2. C₂×C₅×#235	C₂	semidirect
3. C₃×C₅×#123	C₂	semidirect
4. C₅×#939	C₂	semidirect
5. C₂×C₅×Dic₃⋊C₄	C₂	semidirect
6. C₅×#896	C₂	semidirect
7. C₅×#894	C₂	semidirect
8. C₅×D₃×C₄⋊C₄	C₂	semidirect
9. C₅×#888	C₂	semidirect
10. C₅×#886	C₂	semidirect
11. C₅×#884	C₂	semidirect
12. C₅×#883	C₂	semidirect
13. C₅×#67⋊C₄	C₂	semidirect
14. C₅×#67⋊C₄	C₂	semidirect
15. C₅×#878	C₂	semidirect
54. #5655	C₅	direct (N × H)
61. C₅×#123	D₃	semidirect
84. C₅×#67	D₄	semidirect
101. C₂×#237	C₂×C₅	semidirect
102. C₂×#235	C₂×C₅	semidirect
103. C₃×#123	C₂×C₅	semidirect
104. #939	C₂×C₅	semidirect
105. C₂×Dic₃⋊C₄	C₂×C₅	semidirect
106. #896	C₂×C₅	semidirect
107. #894	C₂×C₅	semidirect
108. D₃×C₄⋊C₄	C₂×C₅	semidirect
109. #888	C₂×C₅	semidirect
110. #886	C₂×C₅	semidirect
111. #884	C₂×C₅	semidirect
112. #883	C₂×C₅	semidirect
113. #67⋊C₄	C₂×C₅	semidirect
114. #67⋊C₄	C₂×C₅	semidirect
115. #878	C₂×C₅	semidirect
177. C₅×Dic₃	#41	semidirect
252. #123	C₅×D₃	semidirect
282. #67	C₅×D₄	semidirect
360. C₃×C₅	#547	semidirect
384. Dic₃	C₅×#41	semidirect
430. C₅	#5655	direct (N × H)
455. C₃	C₅×#547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#237	2
C₂×C₅×#235	2
C₃×C₅×#123	2
C₅×#939	2
C₂×C₅×Dic₃⋊C₄	2
C₅×#896	2
C₅×#894	2
C₅×D₃×C₄⋊C₄	2
C₅×#888	2
C₅×#886	2
C₅×#884	2
C₅×#883	2
C₅×#67⋊C₄	2
C₅×#878	2
C₅×#547	3
#5655	5

Subgroups — C5×#5655 #11756040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5655 #11756040