Subgroups — C₅×#5709 #11756094

Order 960.

476 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#898	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#886	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#553	—	3	1	no	maximal, Hall
17	C₂×C₅×#67	C₂²	1	1	yes	characteristic
18	C₂×C₅×#67	C₂²	1	1	yes	characteristic
19	C₂×C₅×#67	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₅×D₁₂	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×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₂²⋊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	C₃×C₄²×C₅	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
44	C₅×C₄⋊Dic₃	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	#5709	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×#126	—	3	1	no	—
54	C₅×#126	D₃	1	1	yes	characteristic, complemented
55	C₅×#125	—	3	1	no	—
56	C₅×#123	—	3	1	no	—
57	C₅×#123	—	3	1	no	—
58	C₅×#121	—	3	1	no	—
59	C₅×#121	—	3	1	no	—
60	C₅×#121	—	3	1	no	—
61	C₅×#121	—	3	1	no	—
62	C₄×C₅×D₄	—	3	1	no	—
63	C₄×C₅×D₄	—	3	1	no	—
64	C₄×C₅×D₄	—	3	1	no	—
65	C₄×C₅×D₄	—	3	1	no	—
66	C₅×#117	—	3	1	no	—
67	C₂×C₅×C₄⋊C₄	—	3	1	no	—
68	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₅×#67	—	2	2	no	—
79	C₅×#67	—	2	2	no	—
80	C₅×#67	—	4	1	no	—
81	C₂×C₅×Dic₃	—	4	1	no	—
82	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
86	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₅×D₁₂	—	2	2	no	—
88	C₅×D₁₂	—	2	2	no	—
89	C₅×D₁₂	—	4	1	no	—
90	C₄×C₅×D₃	—	2	2	no	—
91	C₄×C₅×D₃	—	2	2	no	—
92	C₄×C₅×D₃	—	4	1	no	—
93	C₄×C₅×D₃	—	4	1	no	—
94	C₄×C₅×D₃	—	4	1	no	—
95	C₃×#126	C₂×C₅	1	1	yes	characteristic, complemented
96	#898	C₂×C₅	1	1	yes	characteristic, complemented
97	#895	C₂×C₅	1	1	yes	characteristic, complemented
98	#894	C₂×C₅	1	1	yes	characteristic, complemented
99	#893	C₂×C₅	1	1	yes	characteristic, complemented
100	D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
101	#889	C₂×C₅	1	1	yes	characteristic, complemented
102	#886	C₂×C₅	1	1	yes	characteristic, complemented
103	#884	C₂×C₅	1	1	yes	characteristic, complemented
104	#884	C₂×C₅	1	1	yes	characteristic, complemented
105	#884	C₂×C₅	1	1	yes	characteristic, complemented
106	#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
107	#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
108	C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
109	#872	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂×C₅×D₄	—	3	1	no	—
111	C₂×C₅×D₄	—	3	1	no	—
112	C₂×C₅×D₄	—	3	1	no	—
113	C₂×C₅×D₄	—	3	1	no	—
114	C₂×C₅×D₄	—	3	1	no	—
115	C₂×C₅×D₄	—	3	1	no	—
116	C₂²×C₄×C₅	—	3	1	no	—
117	C₂²×C₄×C₅	—	3	1	no	—
118	C₂²×C₄×C₅	—	3	1	no	—
119	C₂²×C₄×C₅	—	3	1	no	—
120	C₂²×C₄×C₅	—	3	1	no	—
121	C₂²×C₄×C₅	—	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	—	3	1	no	—
128	C₅×C₄⋊C₄	—	3	1	no	—
129	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
130	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
131	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	1	yes	characteristic
140	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
141	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
142	C₄²×C₅	—	3	1	no	—
143	C₄²×C₅	—	3	1	no	—
144	C₄²×C₅	C₂×D₃	1	1	yes	characteristic
145	#553	—	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	C₂⁴	1	1	yes	characteristic
150	C₂×C₅×D₃	—	2	1	no	—
151	C₂×C₅×D₃	—	2	1	no	—
152	C₂×C₅×D₃	—	2	1	no	—
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	#41	1	2	yes	—
159	C₃×C₄×C₅	—	2	1	no	—
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	#41	1	2	yes	—
170	C₂×#67	C₂²×C₅	1	1	yes	characteristic
171	C₂×#67	C₂²×C₅	1	1	yes	characteristic
172	C₂×#67	C₂²×C₅	1	1	yes	characteristic
173	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
174	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
175	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
176	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄×D₃	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×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
182	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
186	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
187	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
188	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
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	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
197	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
198	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
199	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
200	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
201	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
202	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
203	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
204	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
205	C₂³×C₅	—	3	1	no	—
206	C₂³×C₅	—	3	1	no	—
207	C₂³×C₅	—	3	1	no	—
208	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
209	C₅×D₄	—	6	2	no	—
210	C₅×D₄	—	6	2	no	—
211	C₅×D₄	—	6	2	no	—
212	C₅×D₄	—	6	2	no	—
213	C₅×D₄	—	12	1	no	—
214	C₅×D₄	—	12	1	no	—
215	C₂×C₄×C₅	—	3	1	no	—
216	C₂×C₄×C₅	—	3	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	—	6	2	no	—
221	C₂×C₄×C₅	—	6	2	no	—
222	C₂×C₄×C₅	—	12	1	no	—
223	C₂×C₄×C₅	—	12	1	no	—
224	C₂×C₄×C₅	—	12	1	no	—
225	C₂×C₄×C₅	—	12	1	no	—
226	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
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	#126	—	3	1	no	—
233	#126	C₅×D₃	1	1	yes	characteristic, complemented
234	#125	—	3	1	no	—
235	#123	—	3	1	no	—
236	#123	—	3	1	no	—
237	#121	—	3	1	no	—
238	#121	—	3	1	no	—
239	#121	—	3	1	no	—
240	#121	—	3	1	no	—
241	C₄×D₄	—	3	1	no	—
242	C₄×D₄	—	3	1	no	—
243	C₄×D₄	—	3	1	no	—
244	C₄×D₄	—	3	1	no	—
245	#117	—	3	1	no	—
246	C₂×C₄⋊C₄	—	3	1	no	—
247	C₂×C₃×C₅	—	4	1	no	—
248	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
249	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
250	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
251	C₅×D₃	—	2	2	no	—
252	C₅×D₃	—	4	1	no	—
253	C₅×D₃	—	4	1	no	—
254	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
255	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
256	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
257	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
264	#67	—	2	2	no	—
265	#67	—	2	2	no	—
266	#67	—	4	1	no	—
267	C₂×Dic₃	—	4	1	no	—
268	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
269	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
270	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
271	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
272	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
273	D₁₂	—	2	2	no	—
274	D₁₂	—	2	2	no	—
275	D₁₂	—	4	1	no	—
276	C₄×D₃	—	2	2	no	—
277	C₄×D₃	—	2	2	no	—
278	C₄×D₃	—	4	1	no	—
279	C₄×D₃	—	4	1	no	—
280	C₄×D₃	—	4	1	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	2	1	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	3	2	no	—
285	C₂²×C₅	—	6	1	no	—
286	C₂²×C₅	—	6	1	no	—
287	C₂²×C₅	—	6	1	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	C₂³×D₃	1	1	yes	characteristic
294	C₄×C₅	—	2	1	no	—
295	C₄×C₅	—	2	1	no	—
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	—	3	2	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	C₂×D₄	—	3	1	no	—
306	C₂×D₄	—	3	1	no	—
307	C₂×D₄	—	3	1	no	—
308	C₂×D₄	—	3	1	no	—
309	C₂×D₄	—	3	1	no	—
310	C₂×D₄	—	3	1	no	—
311	C₂²×C₄	—	3	1	no	—
312	C₂²×C₄	—	3	1	no	—
313	C₂²×C₄	—	3	1	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	—	3	1	no	—
316	C₂²×C₄	—	3	1	no	—
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
325	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
326	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
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	C₂×C₅×D₃	1	1	yes	characteristic
335	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
336	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
337	C₄²	—	3	1	no	—
338	C₄²	—	3	1	no	—
339	C₄²	C₂×C₅×D₃	1	1	yes	characteristic
340	C₃×C₅	#553	1	1	yes	characteristic, complemented, Hall
341	C₂²×C₃	—	2	1	no	—
342	C₂²×C₃	—	2	1	no	—
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
345	C₂×D₃	—	2	1	no	—
346	C₂×D₃	—	2	1	no	—
347	C₂×D₃	—	2	1	no	—
348	C₂×D₃	—	2	1	no	—
349	C₂×D₃	—	2	1	no	—
350	C₂×D₃	—	2	1	no	—
351	C₂×D₃	—	2	1	no	—
352	C₂×D₃	—	2	1	no	—
353	C₂×D₃	C₅×#41	1	2	yes	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	2	1	no	—
360	Dic₃	—	2	1	no	—
361	Dic₃	—	2	1	no	—
362	Dic₃	—	2	1	no	—
363	Dic₃	—	2	1	no	—
364	Dic₃	C₅×#41	1	2	yes	—
365	C₂×C₅	—	4	1	no	—
366	C₂×C₅	—	6	2	no	—
367	C₂×C₅	—	12	1	no	—
368	C₂×C₅	—	12	1	no	—
369	C₂×C₅	D₃×#41	1	1	yes	characteristic
370	C₂×C₅	D₃×#41	1	1	yes	characteristic
371	C₂×C₅	#1009	1	1	yes	characteristic
372	C₂³	—	3	1	no	—
373	C₂³	—	3	1	no	—
374	C₂³	—	3	1	no	—
375	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
376	D₄	—	6	2	no	—
377	D₄	—	6	2	no	—
378	D₄	—	6	2	no	—
379	D₄	—	6	2	no	—
380	D₄	—	12	1	no	—
381	D₄	—	12	1	no	—
382	C₂×C₄	—	3	1	no	—
383	C₂×C₄	—	3	1	no	—
384	C₂×C₄	—	3	1	no	—
385	C₂×C₄	—	3	1	no	—
386	C₂×C₄	—	3	1	no	—
387	C₂×C₄	—	6	2	no	—
388	C₂×C₄	—	6	2	no	—
389	C₂×C₄	—	12	1	no	—
390	C₂×C₄	—	12	1	no	—
391	C₂×C₄	—	12	1	no	—
392	C₂×C₄	—	12	1	no	—
393	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
399	C₂×C₃	—	4	1	no	—
400	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
401	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
402	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
403	D₃	—	2	2	no	—
404	D₃	—	4	1	no	—
405	D₃	—	4	1	no	—
406	C₅	#5709	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	3	2	no	—
411	C₂²	—	6	1	no	—
412	C₂²	—	6	1	no	—
413	C₂²	—	6	1	no	—
414	C₂²	—	6	1	no	—
415	C₂²	—	6	1	no	—
416	C₂²	—	6	1	no	—
417	C₂²	—	6	1	no	—
418	C₂²	—	6	1	no	—
419	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	3	2	no	—
427	C₄	—	6	1	no	—
428	C₄	—	6	1	no	—
429	C₄	—	6	1	no	—
430	C₄	—	6	1	no	—
431	C₃	C₅×#553	1	1	yes	characteristic, complemented, Sylow
432	C₂	—	4	1	no	—
433	C₂	—	6	2	no	—
434	C₂	—	12	1	no	—
435	C₂	—	12	1	no	—
436	C₂	C₅×D₃×#41	1	1	yes	characteristic
437	C₂	C₅×D₃×#41	1	1	yes	characteristic
438	C₂	C₅×#1009	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×#126	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×#126	D₃
hypocenter	C₃	C₅×#553
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#126

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#126	C₂	semidirect
2. C₅×#898	C₂	semidirect
3. C₅×#895	C₂	semidirect
4. C₅×#894	C₂	semidirect
5. C₅×#893	C₂	semidirect
6. C₅×D₃×C₄⋊C₄	C₂	semidirect
7. C₅×#889	C₂	semidirect
8. C₅×#886	C₂	semidirect
9. C₅×#884	C₂	semidirect
10. C₅×#884	C₂	semidirect
11. C₅×#884	C₂	semidirect
12. C₅×#67⋊C₄	C₂	semidirect
13. C₅×#67⋊C₄	C₂	semidirect
14. C₄×C₅×D₁₂	C₂	semidirect
15. C₅×#872	C₂	semidirect
52. #5709	C₅	direct (N × H)
54. C₅×#126	D₃	semidirect
95. C₃×#126	C₂×C₅	semidirect
96. #898	C₂×C₅	semidirect
97. #895	C₂×C₅	semidirect
98. #894	C₂×C₅	semidirect
99. #893	C₂×C₅	semidirect
100. D₃×C₄⋊C₄	C₂×C₅	semidirect
101. #889	C₂×C₅	semidirect
102. #886	C₂×C₅	semidirect
103. #884	C₂×C₅	semidirect
104. #884	C₂×C₅	semidirect
105. #884	C₂×C₅	semidirect
106. #67⋊C₄	C₂×C₅	semidirect
107. #67⋊C₄	C₂×C₅	semidirect
108. C₄×D₁₂	C₂×C₅	semidirect
109. #872	C₂×C₅	semidirect
233. #126	C₅×D₃	semidirect
340. C₃×C₅	#553	semidirect
406. C₅	#5709	direct (N × H)
431. C₃	C₅×#553	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#126	2
C₅×#898	2
C₅×#895	2
C₅×#894	2
C₅×#893	2
C₅×D₃×C₄⋊C₄	2
C₅×#889	2
C₅×#886	2
C₅×#884	2
C₅×#67⋊C₄	2
C₄×C₅×D₁₂	2
C₅×#872	2
C₅×#553	3
#5709	5

Subgroups — C5×#5709 #11756094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5709 #11756094