Subgroups — C₅×#5615 #11756000

Order 960.

480 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	C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#940	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#929	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#883	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#540	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂×C₅×#67	C₂²	1	1	yes	characteristic
23	C₂×C₅×#67	C₂²	1	1	yes	characteristic
24	C₂×C₅×#67	C₂²	1	1	yes	characteristic
25	C₂×C₅×#67	C₂²	1	1	yes	characteristic
26	C₂×C₅×#67	C₂²	1	1	yes	characteristic
27	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
29	C₂×C₅×D₁₂	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	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₅×#217	C₂²	1	1	yes	characteristic
36	C₅×#217	C₂²	1	1	yes	characteristic
37	C₅×#217	C₂²	1	1	yes	characteristic
38	C₅×#217	C₂²	1	1	yes	characteristic
39	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₅×(C₂×D₃)⋊C₄	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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
44	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₅×Dic₃⋊C₄	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	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
51	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
52	#5615	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×#127	—	3	1	no	—
54	C₅×#125	—	3	1	no	—
55	C₅×#123	—	3	1	no	—
56	C₅×#123	—	3	1	no	—
57	C₅×#123	—	3	1	no	—
58	C₅×#123	—	3	1	no	—
59	C₅×#121	—	3	1	no	—
60	C₅×#121	—	3	1	no	—
61	C₅×#121	—	3	1	no	—
62	C₅×#121	—	3	1	no	—
63	C₅×#121	—	3	1	no	—
64	C₅×#121	D₃	1	1	yes	characteristic, complemented
65	C₄×C₅×D₄	—	3	1	no	—
66	C₄×C₅×D₄	—	3	1	no	—
67	C₅×#117	—	3	1	no	—
68	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
72	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
73	C₃×C₅×D₄	—	4	1	no	—
74	C₃×C₅×D₄	—	4	1	no	—
75	C₃×C₅×D₄	—	4	1	no	—
76	C₂×C₃×C₄×C₅	—	4	1	no	—
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	—	4	1	no	—
84	C₅×#67	—	4	1	no	—
85	C₅×#67	—	4	1	no	—
86	C₅×#67	—	4	1	no	—
87	C₂×C₅×Dic₃	—	2	2	no	—
88	C₂×C₅×Dic₃	—	4	1	no	—
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	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₅×D₁₂	—	4	1	no	—
96	C₄×C₅×D₃	—	4	1	no	—
97	C₄×C₅×D₃	—	4	1	no	—
98	C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
99	#940	C₂×C₅	1	1	yes	characteristic, complemented
100	#939	C₂×C₅	1	1	yes	characteristic, complemented
101	#939	C₂×C₅	1	1	yes	characteristic, complemented
102	#939	C₂×C₅	1	1	yes	characteristic, complemented
103	#938	C₂×C₅	1	1	yes	characteristic, complemented
104	#935	C₂×C₅	1	1	yes	characteristic, complemented
105	#929	C₂×C₅	1	1	yes	characteristic, complemented
106	C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
107	#894	C₂×C₅	1	1	yes	characteristic, complemented
108	#889	C₂×C₅	1	1	yes	characteristic, complemented
109	#884	C₂×C₅	1	1	yes	characteristic, complemented
110	#883	C₂×C₅	1	1	yes	characteristic, complemented
111	#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
112	#877	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×C₅×D₄	—	3	1	no	—
114	C₂×C₅×D₄	—	3	1	no	—
115	C₂×C₅×D₄	—	3	1	no	—
116	C₂×C₅×D₄	—	3	1	no	—
117	C₂×C₅×D₄	—	3	1	no	—
118	C₂×C₅×D₄	—	3	1	no	—
119	C₂×C₅×D₄	—	3	1	no	—
120	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
121	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
122	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
123	C₂²×C₄×C₅	—	3	1	no	—
124	C₂²×C₄×C₅	—	3	1	no	—
125	C₂²×C₄×C₅	—	3	1	no	—
126	C₂²×C₄×C₅	—	3	1	no	—
127	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
128	C₅×C₄⋊C₄	—	3	1	no	—
129	C₅×C₄⋊C₄	—	3	1	no	—
130	C₅×C₄⋊C₄	—	3	1	no	—
131	C₅×C₄⋊C₄	—	3	1	no	—
132	C₅×C₄⋊C₄	—	3	1	no	—
133	C₅×C₄⋊C₄	—	3	1	no	—
134	C₅×C₄⋊C₄	—	3	1	no	—
135	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
136	C₅×C₂²⋊C₄	—	3	1	no	—
137	C₅×C₂²⋊C₄	—	3	1	no	—
138	C₅×C₂²⋊C₄	—	3	1	no	—
139	C₅×C₂²⋊C₄	—	3	1	no	—
140	C₅×C₂²⋊C₄	—	3	1	no	—
141	C₅×C₂²⋊C₄	—	3	1	no	—
142	C₅×C₂²⋊C₄	—	3	1	no	—
143	C₅×C₂²⋊C₄	—	3	1	no	—
144	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
145	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
146	C₄²×C₅	—	3	1	no	—
147	C₄²×C₅	—	3	1	no	—
148	#540	—	3	1	no	Sylow
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	—	2	1	no	—
152	C₂²×C₃×C₅	—	2	1	no	—
153	C₂²×C₃×C₅	—	2	1	no	—
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	C₂⁴	1	1	yes	characteristic
159	C₂×C₅×D₃	—	2	1	no	—
160	C₂×C₅×D₃	—	2	1	no	—
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	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	2	1	no	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	—	2	1	no	—
169	C₅×Dic₃	—	2	1	no	—
170	C₅×Dic₃	—	2	1	no	—
171	C₅×Dic₃	—	2	1	no	—
172	C₅×Dic₃	—	2	1	no	—
173	C₅×Dic₃	—	2	1	no	—
174	C₅×Dic₃	#41	1	2	yes	—
175	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
179	C₂×#67	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	C₂×#67	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	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
189	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
190	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
193	#217	C₂²×C₅	1	1	yes	characteristic
194	#217	C₂²×C₅	1	1	yes	characteristic
195	#217	C₂²×C₅	1	1	yes	characteristic
196	#217	C₂²×C₅	1	1	yes	characteristic
197	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
198	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
199	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
200	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
201	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
202	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
203	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
204	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
205	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
206	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
207	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
208	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
209	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
210	C₂³×C₅	—	3	1	no	—
211	C₂³×C₅	—	3	1	no	—
212	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
214	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
215	C₅×D₄	—	4	1	no	—
216	C₅×D₄	—	4	1	no	—
217	C₅×D₄	—	4	1	no	—
218	C₅×D₄	—	6	2	no	—
219	C₅×D₄	—	6	2	no	—
220	C₅×D₄	—	12	1	no	—
221	C₅×D₄	—	12	1	no	—
222	C₅×D₄	—	12	1	no	—
223	C₅×D₄	—	12	1	no	—
224	C₅×D₄	—	12	1	no	—
225	C₂×C₄×C₅	—	3	1	no	—
226	C₂×C₄×C₅	—	3	1	no	—
227	C₂×C₄×C₅	—	3	1	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	—	4	1	no	—
232	C₂×C₄×C₅	—	6	2	no	—
233	C₂×C₄×C₅	—	12	1	no	—
234	C₂×C₄×C₅	—	12	1	no	—
235	C₂×C₄×C₅	—	12	1	no	—
236	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
240	#127	—	3	1	no	—
241	#125	—	3	1	no	—
242	#123	—	3	1	no	—
243	#123	—	3	1	no	—
244	#123	—	3	1	no	—
245	#123	—	3	1	no	—
246	#121	—	3	1	no	—
247	#121	—	3	1	no	—
248	#121	—	3	1	no	—
249	#121	—	3	1	no	—
250	#121	—	3	1	no	—
251	#121	C₅×D₃	1	1	yes	characteristic, complemented
252	C₄×D₄	—	3	1	no	—
253	C₄×D₄	—	3	1	no	—
254	#117	—	3	1	no	—
255	C₂×C₃×C₅	—	4	1	no	—
256	C₂×C₃×C₅	—	4	1	no	—
257	C₂×C₃×C₅	—	4	1	no	—
258	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
259	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
261	C₅×D₃	—	4	1	no	—
262	C₅×D₃	—	4	1	no	—
263	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
264	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
265	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
266	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
267	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
268	C₃×D₄	—	4	1	no	—
269	C₃×D₄	—	4	1	no	—
270	C₃×D₄	—	4	1	no	—
271	C₂×C₃×C₄	—	4	1	no	—
272	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
276	#67	—	2	2	no	—
277	#67	—	2	2	no	—
278	#67	—	4	1	no	—
279	#67	—	4	1	no	—
280	#67	—	4	1	no	—
281	#67	—	4	1	no	—
282	C₂×Dic₃	—	2	2	no	—
283	C₂×Dic₃	—	4	1	no	—
284	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
285	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
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	D₁₂	—	4	1	no	—
291	C₄×D₃	—	4	1	no	—
292	C₄×D₃	—	4	1	no	—
293	C₂²×C₅	—	2	1	no	—
294	C₂²×C₅	—	2	1	no	—
295	C₂²×C₅	—	2	1	no	—
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	—	2	1	no	—
298	C₂²×C₅	—	2	1	no	—
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	6	1	no	—
303	C₂²×C₅	—	6	1	no	—
304	C₂²×C₅	—	6	1	no	—
305	C₂²×C₅	—	6	1	no	—
306	C₂²×C₅	—	6	1	no	—
307	C₂²×C₅	—	6	1	no	—
308	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	3	2	no	—
314	C₄×C₅	—	6	1	no	—
315	C₄×C₅	—	6	1	no	—
316	C₄×C₅	—	6	1	no	—
317	C₄×C₅	—	6	1	no	—
318	C₄×C₅	—	6	1	no	—
319	C₂×D₄	—	3	1	no	—
320	C₂×D₄	—	3	1	no	—
321	C₂×D₄	—	3	1	no	—
322	C₂×D₄	—	3	1	no	—
323	C₂×D₄	—	3	1	no	—
324	C₂×D₄	—	3	1	no	—
325	C₂×D₄	—	3	1	no	—
326	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
327	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
328	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
329	C₂²×C₄	—	3	1	no	—
330	C₂²×C₄	—	3	1	no	—
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic
334	C₄⋊C₄	—	3	1	no	—
335	C₄⋊C₄	—	3	1	no	—
336	C₄⋊C₄	—	3	1	no	—
337	C₄⋊C₄	—	3	1	no	—
338	C₄⋊C₄	—	3	1	no	—
339	C₄⋊C₄	—	3	1	no	—
340	C₄⋊C₄	—	3	1	no	—
341	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
342	C₂²⋊C₄	—	3	1	no	—
343	C₂²⋊C₄	—	3	1	no	—
344	C₂²⋊C₄	—	3	1	no	—
345	C₂²⋊C₄	—	3	1	no	—
346	C₂²⋊C₄	—	3	1	no	—
347	C₂²⋊C₄	—	3	1	no	—
348	C₂²⋊C₄	—	3	1	no	—
349	C₂²⋊C₄	—	3	1	no	—
350	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
351	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
352	C₄²	—	3	1	no	—
353	C₄²	—	3	1	no	—
354	C₃×C₅	#540	1	1	yes	characteristic, complemented, Hall
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	2	1	no	—
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
365	C₂×D₃	—	2	1	no	—
366	C₂×D₃	—	2	1	no	—
367	C₂×D₃	—	2	1	no	—
368	C₂×D₃	—	2	1	no	—
369	C₂×D₃	—	2	1	no	—
370	C₂×D₃	—	2	1	no	—
371	C₃×C₄	—	2	1	no	—
372	C₃×C₄	—	2	1	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	Dic₃	—	2	1	no	—
376	Dic₃	—	2	1	no	—
377	Dic₃	—	2	1	no	—
378	Dic₃	—	2	1	no	—
379	Dic₃	—	2	1	no	—
380	Dic₃	C₅×#41	1	2	yes	—
381	C₂×C₅	—	4	1	no	—
382	C₂×C₅	—	4	1	no	—
383	C₂×C₅	—	4	1	no	—
384	C₂×C₅	—	12	1	no	—
385	C₂×C₅	—	12	1	no	—
386	C₂×C₅	#1004	1	1	yes	characteristic
387	C₂×C₅	#1004	1	1	yes	characteristic
388	C₂×C₅	D₃×#41	1	1	yes	characteristic
389	C₂³	—	3	1	no	—
390	C₂³	—	3	1	no	—
391	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
392	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
393	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
394	D₄	—	4	1	no	—
395	D₄	—	4	1	no	—
396	D₄	—	4	1	no	—
397	D₄	—	6	2	no	—
398	D₄	—	6	2	no	—
399	D₄	—	12	1	no	—
400	D₄	—	12	1	no	—
401	D₄	—	12	1	no	—
402	D₄	—	12	1	no	—
403	D₄	—	12	1	no	—
404	C₂×C₄	—	3	1	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	—	4	1	no	—
411	C₂×C₄	—	6	2	no	—
412	C₂×C₄	—	12	1	no	—
413	C₂×C₄	—	12	1	no	—
414	C₂×C₄	—	12	1	no	—
415	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
419	C₂×C₃	—	4	1	no	—
420	C₂×C₃	—	4	1	no	—
421	C₂×C₃	—	4	1	no	—
422	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
423	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
425	D₃	—	4	1	no	—
426	D₃	—	4	1	no	—
427	C₅	#5615	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
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	—	2	1	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	—	6	1	no	—
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	—	3	2	no	—
449	C₄	—	6	1	no	—
450	C₄	—	6	1	no	—
451	C₄	—	6	1	no	—
452	C₄	—	6	1	no	—
453	C₄	—	6	1	no	—
454	C₃	C₅×#540	1	1	yes	characteristic, complemented, Sylow
455	C₂	—	4	1	no	—
456	C₂	—	4	1	no	—
457	C₂	—	4	1	no	—
458	C₂	—	12	1	no	—
459	C₂	—	12	1	no	—
460	C₂	C₅×#1004	1	1	yes	characteristic
461	C₂	C₅×#1004	1	1	yes	characteristic
462	C₂	C₅×D₃×#41	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×#121	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×#121	D₃
hypocenter	C₃	C₅×#540
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#121

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#121	C₂	semidirect
2. C₅×#940	C₂	semidirect
3. C₅×#939	C₂	semidirect
4. C₅×#939	C₂	semidirect
5. C₅×#939	C₂	semidirect
6. C₅×#938	C₂	semidirect
7. C₅×#935	C₂	semidirect
8. C₅×#929	C₂	semidirect
9. C₄×C₅×#67	C₂	semidirect
10. C₅×#894	C₂	semidirect
11. C₅×#889	C₂	semidirect
12. C₅×#884	C₂	semidirect
13. C₅×#883	C₂	semidirect
14. C₅×#67⋊C₄	C₂	semidirect
15. C₅×#877	C₂	semidirect
52. #5615	C₅	direct (N × H)
64. C₅×#121	D₃	semidirect
98. C₃×#121	C₂×C₅	semidirect
99. #940	C₂×C₅	semidirect
100. #939	C₂×C₅	semidirect
101. #939	C₂×C₅	semidirect
102. #939	C₂×C₅	semidirect
103. #938	C₂×C₅	semidirect
104. #935	C₂×C₅	semidirect
105. #929	C₂×C₅	semidirect
106. C₄×#67	C₂×C₅	semidirect
107. #894	C₂×C₅	semidirect
108. #889	C₂×C₅	semidirect
109. #884	C₂×C₅	semidirect
110. #883	C₂×C₅	semidirect
111. #67⋊C₄	C₂×C₅	semidirect
112. #877	C₂×C₅	semidirect
251. #121	C₅×D₃	semidirect
354. C₃×C₅	#540	semidirect
427. C₅	#5615	direct (N × H)
454. C₃	C₅×#540	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#121	2
C₅×#940	2
C₅×#939	2
C₅×#938	2
C₅×#935	2
C₅×#929	2
C₄×C₅×#67	2
C₅×#894	2
C₅×#889	2
C₅×#884	2
C₅×#883	2
C₅×#67⋊C₄	2
C₅×#877	2
C₅×#540	3
#5615	5

Subgroups — C5×#5615 #11756000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5615 #11756000