Subgroups — C₅×#83289 #14439294

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#951	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#949	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5086	C₂	1	2	yes	maximal, complemented
6	C₅×#5074	C₂	1	2	yes	maximal, complemented
7	C₅×#5059	C₂	1	4	yes	maximal, complemented
8	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3153	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
15	C₃×C₅×#124	C₂²	1	2	yes	complemented
16	C₃×C₅×#121	—	2	2	no	—
17	C₃×C₄×C₅×D₄	—	2	2	no	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₅×#951	—	2	8	no	—
20	C₅×#949	—	2	8	no	—
21	C₂×C₅×#216	C₂²	1	4	yes	complemented
22	C₂×C₅×#215	C₂²	1	4	yes	—
23	C₂×C₅×#214	C₂²	1	4	yes	complemented
24	C₂×C₅×#213	C₂²	1	4	yes	—
25	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
26	C₂×C₅×#208	C₂²	1	2	yes	—
27	C₅×#875	—	2	2	no	—
28	C₅×#875	C₂²	1	2	yes	—
29	C₅×#875	C₂²	1	2	yes	—
30	C₅×#803	C₂²	1	2	yes	complemented
31	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
32	#83289	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂×C₅×#137	—	3	2	no	—
34	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
35	C₅×#532	D₃	1	1	yes	characteristic, complemented
36	C₂×C₅×#124	—	3	1	no	—
37	C₅×#497	—	3	2	no	—
38	C₅×#496	—	3	2	no	—
39	C₅×#495	—	3	4	no	—
40	C₄×C₅×M₁₆	—	3	1	no	—
41	C₂³×C₅×D₃	—	2	1	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₃×C₅×#41	—	2	4	no	—
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	—	2	2	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₅×Dic₃	—	2	1	no	—
52	C₂×C₅×D₁₂	—	2	4	no	—
53	C₂×C₅×D₁₂	—	2	1	no	—
54	C₂×C₅×D₁₂	C₂³	1	2	yes	—
55	C₂×C₅×Dic₆	—	2	4	no	—
56	C₂×C₅×Dic₆	—	2	1	no	—
57	C₂×C₅×Dic₆	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
60	C₃×C₄²×C₅	D₄	1	2	yes	—
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₅×#216	—	2	8	no	—
64	C₅×#215	—	2	8	no	—
65	C₅×#214	—	2	8	no	—
66	C₅×#213	—	2	8	no	—
67	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
68	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
69	C₅×#208	D₄	1	8	yes	complemented
70	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
71	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#951	C₂×C₅	1	2	yes	complemented
73	C₂×#949	C₂×C₅	1	2	yes	complemented
74	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
75	#5086	C₂×C₅	1	2	yes	complemented
76	#5074	C₂×C₅	1	2	yes	complemented
77	#5059	C₂×C₅	1	4	yes	complemented
78	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×C₅×#41	C₂×D₃	1	2	yes	—
80	C₂²×C₅×Q₈	—	3	1	no	—
81	C₂²×C₅×D₄	—	3	1	no	—
82	C₅×#137	—	6	8	no	—
83	C₅×AGL(1,ℤ/8)	—	6	8	no	—
84	C₂×C₅×Q₁₆	—	3	4	no	—
85	C₂×C₅×SD₁₆	—	3	4	no	—
86	C₂×C₅×SD₁₆	—	3	4	no	—
87	C₂×C₅×D₈	—	3	4	no	—
88	C₂×C₅×M₁₆	—	3	2	no	—
89	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
90	C₅×#127	C₂×D₃	1	1	yes	characteristic, complemented
91	C₅×#124	—	3	2	no	—
92	C₅×#124	—	3	2	no	—
93	C₅×#124	—	6	2	no	—
94	C₅×#124	C₂×D₃	1	2	yes	complemented
95	C₅×#121	—	2	2	no	—
96	C₄×C₅×D₄	—	2	2	no	—
97	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
98	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
99	C₅×#97	—	3	2	no	—
100	C₄×C₅×C₈	—	3	2	no	—
101	#3153	—	3	1	no	Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₅×D₃	—	2	2	no	—
105	C₂²×C₅×D₃	—	4	4	no	—
106	C₂²×C₅×D₃	—	4	2	no	—
107	C₃×C₅×Q₈	—	2	2	no	—
108	C₃×C₅×Q₈	—	2	2	no	—
109	C₃×C₅×D₄	—	2	2	no	—
110	C₃×C₅×D₄	—	2	2	no	—
111	C₃×C₅×D₄	—	4	4	no	—
112	C₃×C₅×D₄	—	4	4	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	4	2	no	—
115	C₂×C₃×C₄×C₅	—	4	4	no	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₅×Dic₃	—	4	2	no	—
123	C₅×D₁₂	—	2	4	no	—
124	C₅×D₁₂	—	4	2	no	—
125	C₅×Dic₆	—	2	4	no	—
126	C₅×Dic₆	—	4	2	no	—
127	C₅×C₃⋊C₈	C₂×D₄	1	8	yes	—
128	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
129	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
130	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
131	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
132	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
133	C₃×#124	C₂²×C₅	1	2	yes	complemented
134	C₃×#121	—	2	2	no	—
135	C₃×C₄×D₄	—	2	2	no	—
136	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
137	#951	—	2	8	no	—
138	#949	—	2	8	no	—
139	C₂×#216	C₂²×C₅	1	4	yes	complemented
140	C₂×#215	C₂²×C₅	1	4	yes	—
141	C₂×#214	C₂²×C₅	1	4	yes	complemented
142	C₂×#213	C₂²×C₅	1	4	yes	—
143	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
144	C₂×#208	C₂²×C₅	1	2	yes	—
145	#875	—	2	2	no	—
146	#875	C₂²×C₅	1	2	yes	—
147	#875	C₂²×C₅	1	2	yes	—
148	#803	C₂²×C₅	1	2	yes	complemented
149	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
150	C₂⁴×C₅	—	6	1	no	—
151	C₅×#41	—	2	4	no	—
152	C₅×#41	—	2	4	no	—
153	C₂×C₅×Q₈	—	3	2	no	—
154	C₂×C₅×Q₈	—	6	1	no	—
155	C₂×C₅×Q₈	—	6	4	no	—
156	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
157	C₂×C₅×D₄	—	2	2	no	—
158	C₂×C₅×D₄	—	2	2	no	—
159	C₂×C₅×D₄	—	3	2	no	—
160	C₂×C₅×D₄	—	6	4	no	—
161	C₂×C₅×D₄	—	6	1	no	—
162	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
163	C₂²×C₄×C₅	—	2	2	no	—
164	C₂²×C₄×C₅	—	6	1	no	—
165	C₂²×C₄×C₅	#67	1	2	yes	—
166	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₅×Q₁₆	—	6	8	no	—
168	C₅×SD₁₆	—	6	8	no	—
169	C₅×SD₁₆	—	6	8	no	—
170	C₅×D₈	—	6	8	no	—
171	C₅×M₁₆	—	3	8	no	—
172	C₂×C₅×C₈	—	3	4	no	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₂²⋊C₄	—	2	4	no	—
175	C₅×C₂²⋊C₄	—	6	4	no	—
176	C₅×C₂²⋊C₄	—	6	4	no	—
177	C₄²×C₅	#67	1	2	yes	—
178	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₂×#137	—	3	2	no	—
181	C₂×AGL(1,ℤ/8)	—	3	2	no	—
182	#532	C₅×D₃	1	1	yes	characteristic, complemented
183	C₂×#124	—	3	1	no	—
184	#497	—	3	2	no	—
185	#496	—	3	2	no	—
186	#495	—	3	4	no	—
187	C₄×M₁₆	—	3	1	no	—
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	—	4	2	no	—
190	C₂²×C₃×C₅	—	4	4	no	—
191	C₂²×C₃×C₅	#127	1	2	yes	—
192	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₅×D₃	—	4	2	no	—
194	C₂×C₅×D₃	—	4	4	no	—
195	C₂×C₅×D₃	—	8	4	no	—
196	C₃×C₄×C₅	—	2	2	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	#127	1	2	yes	—
200	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
201	C₅×Dic₃	—	4	2	no	—
202	C₂³×D₃	—	2	1	no	—
203	C₃×#41	—	2	4	no	—
204	C₃×#41	—	2	4	no	—
205	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
206	C₂×C₃×D₄	—	2	2	no	—
207	C₂×C₃×D₄	—	2	2	no	—
208	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	—	2	2	no	—
210	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
211	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
212	C₂²×Dic₃	—	2	1	no	—
213	C₂×D₁₂	—	2	4	no	—
214	C₂×D₁₂	—	2	1	no	—
215	C₂×D₁₂	C₂³×C₅	1	2	yes	—
216	C₂×Dic₆	—	2	4	no	—
217	C₂×Dic₆	—	2	1	no	—
218	C₂×Dic₆	C₂³×C₅	1	2	yes	—
219	C₃×C₄⋊C₄	—	2	2	no	—
220	C₃×C₂²⋊C₄	—	2	4	no	—
221	C₃×C₄²	C₅×D₄	1	2	yes	—
222	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
223	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
224	#216	—	2	8	no	—
225	#215	—	2	8	no	—
226	#214	—	2	8	no	—
227	#213	—	2	8	no	—
228	(C₂×D₃)⋊C₄	—	2	4	no	—
229	(C₂×D₃)⋊C₄	—	2	4	no	—
230	#208	C₅×D₄	1	8	yes	complemented
231	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
232	C₂³×C₅	—	2	2	no	—
233	C₂³×C₅	—	6	2	no	—
234	C₂³×C₅	—	12	4	no	—
235	C₂³×C₅	—	12	2	no	—
236	C₂³×C₅	C₂×#67	1	1	yes	characteristic
237	C₅×Q₈	—	2	2	no	—
238	C₅×Q₈	—	2	2	no	—
239	C₅×Q₈	—	6	4	no	—
240	C₅×Q₈	—	12	2	no	—
241	C₅×D₄	—	2	2	no	—
242	C₅×D₄	—	2	2	no	—
243	C₅×D₄	—	4	4	no	—
244	C₅×D₄	—	4	4	no	—
245	C₅×D₄	—	6	4	no	—
246	C₅×D₄	—	12	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	4	4	no	—
250	C₂×C₄×C₅	—	6	2	no	—
251	C₂×C₄×C₅	—	12	2	no	—
252	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
253	C₂×C₄×C₅	C₂×#67	1	2	yes	—
254	C₂×C₄×C₅	C₂×#67	1	2	yes	—
255	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
257	C₅×C₈	—	3	8	no	—
258	C₂×#41	C₂×C₅×D₃	1	2	yes	—
259	C₂²×Q₈	—	3	1	no	—
260	C₂²×D₄	—	3	1	no	—
261	#137	—	6	8	no	—
262	AGL(1,ℤ/8)	—	6	8	no	—
263	C₂×Q₁₆	—	3	4	no	—
264	C₂×SD₁₆	—	3	4	no	—
265	C₂×SD₁₆	—	3	4	no	—
266	C₂×D₈	—	3	4	no	—
267	C₂×M₁₆	—	3	2	no	—
268	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
269	#127	C₂×C₅×D₃	1	1	yes	characteristic, complemented
270	#124	—	3	2	no	—
271	#124	—	3	2	no	—
272	#124	—	6	2	no	—
273	#124	C₂×C₅×D₃	1	2	yes	complemented
274	#121	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	6	2	no	—
277	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
278	#97	—	3	2	no	—
279	C₄×C₈	—	3	2	no	—
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	—	8	2	no	—
282	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
283	C₂×C₃×C₅	#575	1	2	yes	—
284	C₅×D₃	—	8	2	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
287	C₂²×D₃	—	2	2	no	—
288	C₂²×D₃	—	4	4	no	—
289	C₂²×D₃	—	4	2	no	—
290	C₃×Q₈	—	2	2	no	—
291	C₃×Q₈	—	2	2	no	—
292	C₃×D₄	—	2	2	no	—
293	C₃×D₄	—	2	2	no	—
294	C₃×D₄	—	4	4	no	—
295	C₃×D₄	—	4	4	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	4	2	no	—
298	C₂×C₃×C₄	—	4	4	no	—
299	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
300	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
301	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
302	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
304	C₂×Dic₃	—	2	2	no	—
305	C₂×Dic₃	—	4	2	no	—
306	D₁₂	—	2	4	no	—
307	D₁₂	—	4	2	no	—
308	Dic₆	—	2	4	no	—
309	Dic₆	—	4	2	no	—
310	C₃⋊C₈	C₂×C₅×D₄	1	8	yes	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	4	2	no	—
313	C₂²×C₅	—	4	4	no	—
314	C₂²×C₅	—	12	2	no	—
315	C₂²×C₅	—	12	4	no	—
316	C₂²×C₅	—	24	4	no	—
317	C₂²×C₅	#940	1	2	yes	—
318	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	—	12	2	no	—
323	C₄×C₅	#940	1	2	yes	—
324	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
325	C₂⁴	—	6	1	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	C₂×Q₈	—	3	2	no	—
329	C₂×Q₈	—	6	1	no	—
330	C₂×Q₈	—	6	4	no	—
331	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	3	2	no	—
335	C₂×D₄	—	6	4	no	—
336	C₂×D₄	—	6	1	no	—
337	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	6	1	no	—
340	C₂²×C₄	C₅×#67	1	2	yes	—
341	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
342	Q₁₆	—	6	8	no	—
343	SD₁₆	—	6	8	no	—
344	SD₁₆	—	6	8	no	—
345	D₈	—	6	8	no	—
346	M₁₆	—	3	8	no	—
347	C₂×C₈	—	3	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	6	4	no	—
351	C₂²⋊C₄	—	6	4	no	—
352	C₄²	C₅×#67	1	2	yes	—
353	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
354	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
355	C₃×C₅	#3153	1	1	yes	characteristic, complemented, Hall
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	—	4	4	no	—
359	C₂²×C₃	C₅×#127	1	2	yes	—
360	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
361	C₂×D₃	—	4	2	no	—
362	C₂×D₃	—	4	4	no	—
363	C₂×D₃	—	8	4	no	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	C₅×#127	1	2	yes	—
368	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
369	Dic₃	—	4	2	no	—
370	C₂×C₅	—	2	2	no	—
371	C₂×C₅	—	8	2	no	—
372	C₂×C₅	—	24	2	no	—
373	C₂×C₅	C₂×#940	1	1	yes	characteristic
374	C₂×C₅	#5822	1	2	yes	—
375	C₂³	—	2	2	no	—
376	C₂³	—	6	2	no	—
377	C₂³	—	12	4	no	—
378	C₂³	—	12	2	no	—
379	C₂³	C₂×C₅×#67	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	6	4	no	—
383	Q₈	—	12	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	6	4	no	—
389	D₄	—	12	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	6	2	no	—
394	C₂×C₄	—	12	2	no	—
395	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
396	C₂×C₄	C₂×C₅×#67	1	2	yes	—
397	C₂×C₄	C₂×C₅×#67	1	2	yes	—
398	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
399	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
400	C₈	—	3	8	no	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	8	2	no	—
403	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
404	C₂×C₃	C₅×#575	1	2	yes	—
405	D₃	—	8	2	no	—
406	C₅	#83289	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	2	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	12	2	no	—
411	C₂²	—	12	4	no	—
412	C₂²	—	24	4	no	—
413	C₂²	C₅×#940	1	2	yes	—
414	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	12	2	no	—
419	C₄	C₅×#940	1	2	yes	—
420	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
421	C₃	C₅×#3153	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	—	24	2	no	—
425	C₂	C₂×C₅×#940	1	1	yes	characteristic
426	C₂	C₅×#5822	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#532	D₃
hypocenter	C₃	C₅×#3153
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#532

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₂×C₅×#951	C₂	semidirect
3. C₂×C₅×#949	C₂	semidirect
4. C₂×C₅×#875	C₂	semidirect
5. C₅×#5086	C₂	semidirect
6. C₅×#5074	C₂	semidirect
7. C₅×#5059	C₂	semidirect
8. C₄×C₅×#208	C₂	semidirect
13. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
14. C₃×C₅×#127	C₂²	semidirect
15. C₃×C₅×#124	C₂²	semidirect
21. C₂×C₅×#216	C₂²	semidirect
23. C₂×C₅×#214	C₂²	semidirect
30. C₅×#803	C₂²	semidirect
31. C₄×C₅×C₃⋊C₈	C₂²	semidirect
32. #83289	C₅	direct (N × H)
35. C₅×#532	D₃	semidirect
69. C₅×#208	D₄	semidirect
71. C₃×#532	C₂×C₅	semidirect
72. C₂×#951	C₂×C₅	semidirect
73. C₂×#949	C₂×C₅	semidirect
74. C₂×#875	C₂×C₅	semidirect
75. #5086	C₂×C₅	semidirect
76. #5074	C₂×C₅	semidirect
77. #5059	C₂×C₅	semidirect
78. C₄×#208	C₂×C₅	semidirect
89. C₅×C₄⋊Q₈	C₂×D₃	semidirect
90. C₅×#127	C₂×D₃	semidirect
94. C₅×#124	C₂×D₃	semidirect
131. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
132. C₃×#127	C₂²×C₅	semidirect
133. C₃×#124	C₂²×C₅	semidirect
139. C₂×#216	C₂²×C₅	semidirect
141. C₂×#214	C₂²×C₅	semidirect
148. #803	C₂²×C₅	semidirect
149. C₄×C₃⋊C₈	C₂²×C₅	semidirect
182. #532	C₅×D₃	semidirect
230. #208	C₅×D₄	semidirect
268. C₄⋊Q₈	C₂×C₅×D₃	semidirect
269. #127	C₂×C₅×D₃	semidirect
273. #124	C₂×C₅×D₃	semidirect
355. C₃×C₅	#3153	semidirect
406. C₅	#83289	direct (N × H)
421. C₃	C₅×#3153	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#532	2
C₂×C₅×#951	2
C₂×C₅×#949	2
C₂×C₅×#875	2
C₅×#5086	2
C₅×#5074	2
C₅×#5059	2
C₄×C₅×#208	2
C₅×#3153	3
#83289	5

Subgroups — C5×#83289 #14439294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83289 #14439294