Subgroups — C₅×#5556 #11755941

Order 960.

496 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#937	C₂	1	1	yes	maximal, characteristic
3	C₅×#935	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#898	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#885	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#883	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#876	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#551	—	3	1	no	maximal, Hall
17	C₂³×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
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	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
31	C₅×#217	C₂²	1	1	yes	characteristic
32	C₅×#217	C₂²	1	1	yes	characteristic
33	C₅×#217	C₂²	1	1	yes	characteristic, complemented
34	C₅×#217	C₂²	1	1	yes	characteristic, complemented
35	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×(C₂×D₃)⋊C₄	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, complemented
44	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
52	#5556	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×#126	—	3	1	no	—
54	C₅×#126	—	3	1	no	—
55	C₅×#124	—	3	1	no	—
56	C₅×#123	—	3	1	no	—
57	C₅×#123	—	3	1	no	—
58	C₅×#123	—	3	1	no	—
59	C₅×C₂²⋊Q₈	—	3	1	no	—
60	C₅×C₂²⋊Q₈	—	3	1	no	—
61	C₅×#120	—	3	1	no	—
62	C₄×C₅×D₄	—	3	1	no	—
63	C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
64	C₅×#117	—	3	1	no	—
65	C₅×#117	—	3	1	no	—
66	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
67	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
68	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₅×D₃	—	2	2	no	—
71	C₂²×C₅×D₃	—	2	2	no	—
72	C₂²×C₅×D₃	—	4	1	no	—
73	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
74	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
75	C₃×C₅×D₄	—	2	2	no	—
76	C₂×C₃×C₄×C₅	—	4	1	no	—
77	C₂×C₃×C₄×C₅	—	4	1	no	—
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	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₅×#67	—	2	2	no	—
84	C₅×#67	—	4	1	no	—
85	C₂×C₅×Dic₃	—	2	2	no	—
86	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
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	C₄×C₅×D₃	—	2	2	no	—
93	C₄×C₅×D₃	—	4	1	no	—
94	C₅×Dic₆	—	4	1	no	—
95	C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
96	#937	C₂×C₅	1	1	yes	characteristic
97	#935	C₂×C₅	1	1	yes	characteristic, complemented
98	#929	C₂×C₅	1	1	yes	characteristic, complemented
99	C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
100	C₂×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
101	#924	C₂×C₅	1	1	yes	characteristic, complemented
102	#898	C₂×C₅	1	1	yes	characteristic, complemented
103	#896	C₂×C₅	1	1	yes	characteristic, complemented
104	#885	C₂×C₅	1	1	yes	characteristic, complemented
105	#883	C₂×C₅	1	1	yes	characteristic, complemented
106	D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
107	#877	C₂×C₅	1	1	yes	characteristic, complemented
108	#876	C₂×C₅	1	1	yes	characteristic, complemented
109	#872	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂⁴×C₅	—	3	1	no	—
111	C₂×C₅×Q₈	—	3	1	no	—
112	C₂×C₅×D₄	—	3	1	no	—
113	C₂×C₅×D₄	—	3	1	no	—
114	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
115	C₂²×C₄×C₅	—	3	1	no	—
116	C₂²×C₄×C₅	—	3	1	no	—
117	C₂²×C₄×C₅	—	3	1	no	—
118	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
120	C₅×C₄⋊C₄	—	3	1	no	—
121	C₅×C₄⋊C₄	—	3	1	no	—
122	C₅×C₄⋊C₄	—	3	1	no	—
123	C₅×C₄⋊C₄	—	3	1	no	—
124	C₅×C₄⋊C₄	—	3	1	no	—
125	C₅×C₄⋊C₄	—	3	1	no	—
126	C₅×C₄⋊C₄	—	3	1	no	—
127	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
128	C₅×C₂²⋊C₄	—	3	1	no	—
129	C₅×C₂²⋊C₄	—	3	1	no	—
130	C₅×C₂²⋊C₄	—	3	1	no	—
131	C₅×C₂²⋊C₄	—	3	1	no	—
132	C₅×C₂²⋊C₄	—	3	1	no	—
133	C₅×C₂²⋊C₄	—	3	1	no	—
134	C₅×C₂²⋊C₄	—	3	1	no	—
135	C₅×C₂²⋊C₄	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
141	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
142	C₄²×C₅	—	3	1	no	—
143	C₄²×C₅	—	3	1	no	—
144	C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
145	#551	—	3	1	no	Sylow
146	C₂²×C₃×C₅	—	2	1	no	—
147	C₂²×C₃×C₅	—	2	1	no	—
148	C₂²×C₃×C₅	—	2	1	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	#41	1	2	yes	—
152	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
153	C₂×C₅×D₃	—	2	1	no	—
154	C₂×C₅×D₃	—	2	1	no	—
155	C₂×C₅×D₃	—	2	1	no	—
156	C₂×C₅×D₃	—	2	1	no	—
157	C₂×C₅×D₃	—	2	1	no	—
158	C₂×C₅×D₃	—	4	4	no	—
159	C₂×C₅×D₃	#41	1	2	yes	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	—	2	1	no	—
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	2	1	no	—
165	C₅×Dic₃	—	2	1	no	—
166	C₅×Dic₃	—	2	1	no	—
167	C₅×Dic₃	—	2	1	no	—
168	C₅×Dic₃	—	2	1	no	—
169	C₅×Dic₃	—	2	1	no	—
170	C₅×Dic₃	—	2	1	no	—
171	C₂³×D₃	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
175	C₂×#67	C₂²×C₅	1	1	yes	characteristic
176	C₂×#67	C₂²×C₅	1	1	yes	characteristic
177	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
180	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
182	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
184	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
185	#217	C₂²×C₅	1	1	yes	characteristic
186	#217	C₂²×C₅	1	1	yes	characteristic
187	#217	C₂²×C₅	1	1	yes	characteristic, complemented
188	#217	C₂²×C₅	1	1	yes	characteristic, complemented
189	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
190	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
193	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
194	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
195	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
196	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
198	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
199	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
200	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
201	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
202	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
203	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
204	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
205	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
206	C₂³×C₅	—	3	1	no	—
207	C₂³×C₅	—	3	1	no	—
208	C₂³×C₅	—	6	2	no	—
209	C₂³×C₅	—	6	2	no	—
210	C₂³×C₅	—	12	1	no	—
211	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
212	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₅×Q₈	—	12	1	no	—
214	C₅×D₄	—	2	2	no	—
215	C₅×D₄	—	6	2	no	—
216	C₅×D₄	—	12	1	no	—
217	C₂×C₄×C₅	—	3	1	no	—
218	C₂×C₄×C₅	—	3	1	no	—
219	C₂×C₄×C₅	—	3	1	no	—
220	C₂×C₄×C₅	—	3	1	no	—
221	C₂×C₄×C₅	—	3	1	no	—
222	C₂×C₄×C₅	—	3	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	6	2	no	—
226	C₂×C₄×C₅	—	6	2	no	—
227	C₂×C₄×C₅	—	12	1	no	—
228	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
233	#126	—	3	1	no	—
234	#126	—	3	1	no	—
235	#124	—	3	1	no	—
236	#123	—	3	1	no	—
237	#123	—	3	1	no	—
238	#123	—	3	1	no	—
239	C₂²⋊Q₈	—	3	1	no	—
240	C₂²⋊Q₈	—	3	1	no	—
241	#120	—	3	1	no	—
242	C₄×D₄	—	3	1	no	—
243	C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
244	#117	—	3	1	no	—
245	#117	—	3	1	no	—
246	C₂×C₂²⋊C₄	—	3	1	no	—
247	C₂×C₂²⋊C₄	—	3	1	no	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	—	4	1	no	—
250	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
251	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
252	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
253	C₅×D₃	—	2	2	no	—
254	C₅×D₃	—	4	1	no	—
255	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
256	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
257	C₂²×D₃	—	2	2	no	—
258	C₂²×D₃	—	2	2	no	—
259	C₂²×D₃	—	4	1	no	—
260	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
261	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
262	C₃×D₄	—	2	2	no	—
263	C₂×C₃×C₄	—	4	1	no	—
264	C₂×C₃×C₄	—	4	1	no	—
265	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
270	#67	—	2	2	no	—
271	#67	—	4	1	no	—
272	C₂×Dic₃	—	2	2	no	—
273	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
274	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
275	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
276	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
277	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
278	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
279	C₄×D₃	—	2	2	no	—
280	C₄×D₃	—	4	1	no	—
281	Dic₆	—	4	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	—	3	2	no	—
288	C₂²×C₅	—	6	1	no	—
289	C₂²×C₅	—	6	1	no	—
290	C₂²×C₅	—	6	1	no	—
291	C₂²×C₅	—	6	1	no	—
292	C₂²×C₅	—	6	1	no	—
293	C₂²×C₅	—	12	4	no	—
294	C₂²×C₅	#235	1	2	yes	—
295	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
296	C₄×C₅	—	2	1	no	—
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	2	1	no	—
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	6	1	no	—
302	C₄×C₅	—	6	1	no	—
303	C₄×C₅	—	6	1	no	—
304	C₄×C₅	—	6	1	no	—
305	C₄×C₅	—	6	1	no	—
306	C₄×C₅	—	6	1	no	—
307	C₂⁴	—	3	1	no	—
308	C₂×Q₈	—	3	1	no	—
309	C₂×D₄	—	3	1	no	—
310	C₂×D₄	—	3	1	no	—
311	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
312	C₂²×C₄	—	3	1	no	—
313	C₂²×C₄	—	3	1	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
317	C₄⋊C₄	—	3	1	no	—
318	C₄⋊C₄	—	3	1	no	—
319	C₄⋊C₄	—	3	1	no	—
320	C₄⋊C₄	—	3	1	no	—
321	C₄⋊C₄	—	3	1	no	—
322	C₄⋊C₄	—	3	1	no	—
323	C₄⋊C₄	—	3	1	no	—
324	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
325	C₂²⋊C₄	—	3	1	no	—
326	C₂²⋊C₄	—	3	1	no	—
327	C₂²⋊C₄	—	3	1	no	—
328	C₂²⋊C₄	—	3	1	no	—
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	—	3	1	no	—
334	C₂²⋊C₄	—	3	1	no	—
335	C₂²⋊C₄	—	3	1	no	—
336	C₂²⋊C₄	—	3	1	no	—
337	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
338	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
339	C₄²	—	3	1	no	—
340	C₄²	—	3	1	no	—
341	C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
342	C₃×C₅	#551	1	1	yes	characteristic, complemented, Hall
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	C₅×#41	1	2	yes	—
349	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
350	C₂×D₃	—	2	1	no	—
351	C₂×D₃	—	2	1	no	—
352	C₂×D₃	—	2	1	no	—
353	C₂×D₃	—	2	1	no	—
354	C₂×D₃	—	2	1	no	—
355	C₂×D₃	—	4	4	no	—
356	C₂×D₃	C₅×#41	1	2	yes	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	2	1	no	—
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	2	1	no	—
362	Dic₃	—	2	1	no	—
363	Dic₃	—	2	1	no	—
364	Dic₃	—	2	1	no	—
365	Dic₃	—	2	1	no	—
366	Dic₃	—	2	1	no	—
367	Dic₃	—	2	1	no	—
368	C₂×C₅	—	2	2	no	—
369	C₂×C₅	—	4	1	no	—
370	C₂×C₅	—	6	2	no	—
371	C₂×C₅	—	12	1	no	—
372	C₂×C₅	C₂×#235	1	1	yes	characteristic
373	C₂×C₅	#1004	1	1	yes	characteristic
374	C₂×C₅	D₃×#41	1	1	yes	characteristic
375	C₂³	—	3	1	no	—
376	C₂³	—	3	1	no	—
377	C₂³	—	6	2	no	—
378	C₂³	—	6	2	no	—
379	C₂³	—	12	1	no	—
380	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
381	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
382	Q₈	—	12	1	no	—
383	D₄	—	2	2	no	—
384	D₄	—	6	2	no	—
385	D₄	—	12	1	no	—
386	C₂×C₄	—	3	1	no	—
387	C₂×C₄	—	3	1	no	—
388	C₂×C₄	—	3	1	no	—
389	C₂×C₄	—	3	1	no	—
390	C₂×C₄	—	3	1	no	—
391	C₂×C₄	—	3	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	6	2	no	—
395	C₂×C₄	—	6	2	no	—
396	C₂×C₄	—	12	1	no	—
397	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
402	C₂×C₃	—	2	2	no	—
403	C₂×C₃	—	4	1	no	—
404	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
405	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
406	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
407	D₃	—	2	2	no	—
408	D₃	—	4	1	no	—
409	C₅	#5556	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	3	2	no	—
416	C₂²	—	6	1	no	—
417	C₂²	—	6	1	no	—
418	C₂²	—	6	1	no	—
419	C₂²	—	6	1	no	—
420	C₂²	—	6	1	no	—
421	C₂²	—	12	4	no	—
422	C₂²	C₅×#235	1	2	yes	—
423	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	6	1	no	—
430	C₄	—	6	1	no	—
431	C₄	—	6	1	no	—
432	C₄	—	6	1	no	—
433	C₄	—	6	1	no	—
434	C₄	—	6	1	no	—
435	C₃	C₅×#551	1	1	yes	characteristic, complemented, Sylow
436	C₂	—	2	2	no	—
437	C₂	—	4	1	no	—
438	C₂	—	6	2	no	—
439	C₂	—	12	1	no	—
440	C₂	C₂×C₅×#235	1	1	yes	characteristic
441	C₂	C₅×#1004	1	1	yes	characteristic
442	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×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₅×#937	C₂
hypercenter	C₄×C₅×D₄	D₃
hypocenter	C₃	C₅×#551
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×C₅×D₄	C₂	semidirect
3. C₅×#935	C₂	semidirect
4. C₅×#929	C₂	semidirect
5. C₄×C₅×#67	C₂	semidirect
6. C₂×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₅×#924	C₂	semidirect
8. C₅×#898	C₂	semidirect
9. C₅×#896	C₂	semidirect
10. C₅×#885	C₂	semidirect
11. C₅×#883	C₂	semidirect
12. C₅×D₃×C₂²⋊C₄	C₂	semidirect
13. C₅×#877	C₂	semidirect
14. C₅×#876	C₂	semidirect
15. C₅×#872	C₂	semidirect
20. C₂²×C₃×C₄×C₅	C₂²	semidirect
26. C₂×C₅×Dic₆	C₂²	semidirect
27. C₃×C₅×C₄⋊C₄	C₂²	semidirect
29. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
30. C₃×C₄²×C₅	C₂²	semidirect
33. C₅×#217	C₂²	semidirect
34. C₅×#217	C₂²	semidirect
43. C₅×C₄⋊Dic₃	C₂²	semidirect
44. C₅×Dic₃⋊C₄	C₂²	semidirect
45. C₅×Dic₃⋊C₄	C₂²	semidirect
46. C₅×Dic₃⋊C₄	C₂²	semidirect
47. C₅×Dic₃⋊C₄	C₂²	semidirect
48. C₅×Dic₃⋊C₄	C₂²	semidirect
49. C₅×Dic₃⋊C₄	C₂²	semidirect
50. C₄×C₅×Dic₃	C₂²	semidirect
51. C₄×C₅×Dic₃	C₂²	semidirect
52. #5556	C₅	direct (N × H)
63. C₄×C₅×D₄	D₃	semidirect
95. C₃×C₄×D₄	C₂×C₅	semidirect
97. #935	C₂×C₅	semidirect
98. #929	C₂×C₅	semidirect
99. C₄×#67	C₂×C₅	semidirect
100. C₂×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
101. #924	C₂×C₅	semidirect
102. #898	C₂×C₅	semidirect
103. #896	C₂×C₅	semidirect
104. #885	C₂×C₅	semidirect
105. #883	C₂×C₅	semidirect
106. D₃×C₂²⋊C₄	C₂×C₅	semidirect
107. #877	C₂×C₅	semidirect
108. #876	C₂×C₅	semidirect
109. #872	C₂×C₅	semidirect
119. C₂²×C₄×C₅	C₂×D₃	semidirect
127. C₅×C₄⋊C₄	C₂×D₃	semidirect
141. C₅×C₂²⋊C₄	C₂×D₃	semidirect
144. C₄²×C₅	C₂×D₃	semidirect
174. C₂²×C₃×C₄	C₂²×C₅	semidirect
180. C₂×Dic₆	C₂²×C₅	semidirect
181. C₃×C₄⋊C₄	C₂²×C₅	semidirect
183. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
184. C₃×C₄²	C₂²×C₅	semidirect
187. #217	C₂²×C₅	semidirect
188. #217	C₂²×C₅	semidirect
197. C₄⋊Dic₃	C₂²×C₅	semidirect
198. Dic₃⋊C₄	C₂²×C₅	semidirect
199. Dic₃⋊C₄	C₂²×C₅	semidirect
200. Dic₃⋊C₄	C₂²×C₅	semidirect
201. Dic₃⋊C₄	C₂²×C₅	semidirect
202. Dic₃⋊C₄	C₂²×C₅	semidirect
203. Dic₃⋊C₄	C₂²×C₅	semidirect
204. C₄×Dic₃	C₂²×C₅	semidirect
205. C₄×Dic₃	C₂²×C₅	semidirect
243. C₄×D₄	C₅×D₃	semidirect
316. C₂²×C₄	C₂×C₅×D₃	semidirect
324. C₄⋊C₄	C₂×C₅×D₃	semidirect
338. C₂²⋊C₄	C₂×C₅×D₃	semidirect
341. C₄²	C₂×C₅×D₃	semidirect
342. C₃×C₅	#551	semidirect
409. C₅	#5556	direct (N × H)
435. C₃	C₅×#551	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×D₄	2
C₅×#937	2
C₅×#935	2
C₅×#929	2
C₄×C₅×#67	2
C₂×C₅×(C₂×D₃)⋊C₄	2
C₅×#924	2
C₅×#898	2
C₅×#896	2
C₅×#885	2
C₅×#883	2
C₅×D₃×C₂²⋊C₄	2
C₅×#877	2
C₅×#876	2
C₅×#872	2
C₅×#551	3
#5556	5

Subgroups — C5×#5556 #11755941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5556 #11755941