Subgroups — C₅×#82922 #14427792

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5791	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5233	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5051	C₂	1	2	yes	maximal, complemented
7	C₅×#5048	C₂	1	2	yes	maximal, complemented
8	C₅×#5041	C₂	1	2	yes	maximal, complemented
9	C₅×#5038	C₂	1	2	yes	maximal, complemented
10	C₅×#5002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4998	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3050	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×#235	C₂²	1	1	yes	characteristic
16	C₃×C₅×#123	—	2	1	no	—
17	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₃×C₅×#121	C₂²	1	2	yes	—
19	C₃×C₅×#120	—	2	1	no	—
20	C₃×C₄×C₅×D₄	—	2	2	no	—
21	C₃×C₅×#117	C₂²	1	1	yes	characteristic
22	C₅×#953	—	2	1	no	—
23	C₅×#950	—	2	4	no	—
24	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
28	C₅×#930	C₂²	1	2	yes	—
29	C₅×#929	—	2	1	no	—
30	C₄×C₅×#67	—	2	2	no	—
31	C₅×#926	C₂²	1	1	yes	characteristic
32	C₅×#924	C₂²	1	2	yes	—
33	C₂²×C₅×C₃⋊C₈	—	2	4	no	—
34	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
35	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
36	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
37	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×#835	C₂²	1	2	yes	complemented
39	C₅×#832	C₂²	1	2	yes	complemented
40	C₅×#810	C₂²	1	2	yes	complemented
41	C₅×#809	C₂²	1	2	yes	complemented
42	C₅×#808	C₂²	1	2	yes	complemented
43	C₅×#807	C₂²	1	2	yes	complemented
44	#82922	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#135	—	3	1	no	—
46	C₂³×C₅×C₈	—	3	1	no	—
47	C₅×#525	—	3	1	no	—
48	C₅×#525	D₃	1	1	yes	characteristic, complemented
49	C₅×#467	—	3	2	no	—
50	C₅×#466	—	3	2	no	—
51	C₅×#465	—	3	2	no	—
52	C₅×#465	—	3	2	no	—
53	C₅×#427	—	3	1	no	—
54	C₅×#416	—	3	1	no	—
55	C₅×#416	—	3	1	no	—
56	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	2	no	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
67	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₅×#67	—	2	2	no	—
71	C₂×C₅×#67	—	2	1	no	—
72	C₅×#235	—	2	2	no	—
73	C₅×#235	—	2	2	no	—
74	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
75	C₂×C₄×C₅×D₃	—	2	1	no	—
76	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
79	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
80	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
82	C₃×C₄²×C₅	—	2	1	no	—
83	C₅×#217	—	2	2	no	—
84	C₅×#217	—	2	1	no	—
85	C₅×#216	—	2	2	no	—
86	C₅×#215	—	2	2	no	—
87	C₅×#214	—	2	2	no	—
88	C₅×#213	—	2	2	no	—
89	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
90	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
91	C₅×Dic₃⋊C₄	—	2	2	no	—
92	C₄×C₅×Dic₃	—	2	1	no	—
93	C₂×C₅×C₃⋊C₈	—	2	2	no	—
94	C₂×C₅×C₃⋊C₈	—	2	4	no	—
95	C₂×C₅×C₃⋊C₈	—	2	4	no	—
96	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
97	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
98	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
100	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#950	C₂×C₅	1	1	yes	characteristic, complemented
102	#5791	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂³×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
104	#5233	C₂×C₅	1	1	yes	characteristic, complemented
105	#5051	C₂×C₅	1	2	yes	complemented
106	#5048	C₂×C₅	1	2	yes	complemented
107	#5041	C₂×C₅	1	2	yes	complemented
108	#5038	C₂×C₅	1	2	yes	complemented
109	#5002	C₂×C₅	1	1	yes	characteristic, complemented
110	#4998	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂×C₅×#41	—	3	1	no	—
112	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
113	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
114	C₅×#135	—	6	4	no	—
115	C₂×C₅×Q₁₆	—	3	1	no	—
116	C₂×C₅×SD₁₆	—	3	1	no	—
117	C₂×C₅×SD₁₆	—	3	1	no	—
118	C₂×C₅×D₈	—	3	1	no	—
119	C₂²×C₅×C₈	—	3	1	no	—
120	C₂²×C₅×C₈	—	3	1	no	—
121	C₂²×C₅×C₈	—	3	2	no	—
122	C₂²×C₅×C₈	—	3	2	no	—
123	C₂²×C₅×C₈	—	6	4	no	—
124	C₅×#123	—	2	1	no	—
125	C₅×#123	—	6	1	no	—
126	C₅×C₂²⋊Q₈	—	3	2	no	—
127	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
128	C₅×#121	—	3	2	no	—
129	C₅×#121	C₂×D₃	1	2	yes	—
130	C₅×#120	—	2	1	no	—
131	C₅×#120	—	6	1	no	—
132	C₄×C₅×D₄	—	2	2	no	—
133	C₄×C₅×D₄	—	6	2	no	—
134	C₅×#117	—	3	1	no	—
135	C₅×#117	C₂×D₃	1	1	yes	characteristic
136	C₅×#107	—	3	2	no	—
137	C₅×#106	—	3	2	no	—
138	C₅×#103	—	3	2	no	—
139	C₅×#103	—	3	2	no	—
140	C₅×#102	—	3	2	no	—
141	C₅×#102	—	3	2	no	—
142	#3050	—	3	1	no	Sylow
143	C₂³×C₃×C₅	—	2	2	no	—
144	C₂³×C₃×C₅	—	2	4	no	—
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
148	C₂²×C₅×D₃	—	2	1	no	—
149	C₃×C₅×Q₈	—	2	1	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×D₄	—	2	1	no	—
152	C₃×C₅×D₄	—	2	1	no	—
153	C₃×C₅×D₄	—	4	2	no	—
154	C₃×C₅×D₄	—	4	4	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	4	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	2	no	—
160	C₂×C₃×C₄×C₅	—	2	1	no	—
161	C₂×C₃×C₄×C₅	—	4	2	no	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
165	C₂×C₃×C₄×C₅	#41	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
167	C₅×#67	—	4	2	no	—
168	C₅×#67	—	4	4	no	—
169	C₂×C₅×Dic₃	—	2	2	no	—
170	C₂×C₅×Dic₃	—	2	1	no	—
171	C₅×D₁₂	—	2	1	no	—
172	C₅×D₁₂	—	2	1	no	—
173	C₄×C₅×D₃	—	4	2	no	—
174	C₅×Dic₆	—	2	1	no	—
175	C₅×Dic₆	—	2	1	no	—
176	C₅×C₃⋊C₈	—	2	2	no	—
177	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
178	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
179	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
180	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
181	C₂×#235	C₂²×C₅	1	1	yes	characteristic
182	C₃×#123	—	2	1	no	—
183	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
184	C₃×#121	C₂²×C₅	1	2	yes	—
185	C₃×#120	—	2	1	no	—
186	C₃×C₄×D₄	—	2	2	no	—
187	C₃×#117	C₂²×C₅	1	1	yes	characteristic
188	#953	—	2	1	no	—
189	#950	—	2	4	no	—
190	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
191	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
192	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
194	#930	C₂²×C₅	1	2	yes	—
195	#929	—	2	1	no	—
196	C₄×#67	—	2	2	no	—
197	#926	C₂²×C₅	1	1	yes	characteristic
198	#924	C₂²×C₅	1	2	yes	—
199	C₂²×C₃⋊C₈	—	2	4	no	—
200	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
201	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
202	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
203	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
204	#835	C₂²×C₅	1	2	yes	complemented
205	#832	C₂²×C₅	1	2	yes	complemented
206	#810	C₂²×C₅	1	2	yes	complemented
207	#809	C₂²×C₅	1	2	yes	complemented
208	#808	C₂²×C₅	1	2	yes	complemented
209	#807	C₂²×C₅	1	2	yes	complemented
210	C₂⁴×C₅	#67	1	1	yes	characteristic
211	C₅×#41	—	2	2	no	—
212	C₅×#41	—	2	2	no	—
213	C₅×#41	—	6	2	no	—
214	C₅×#41	—	6	2	no	—
215	C₂×C₅×Q₈	—	3	1	no	—
216	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
217	C₂×C₅×D₄	—	2	2	no	—
218	C₂×C₅×D₄	—	2	1	no	—
219	C₂×C₅×D₄	—	3	1	no	—
220	C₂×C₅×D₄	—	6	2	no	—
221	C₂×C₅×D₄	—	6	1	no	—
222	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
223	C₂²×C₄×C₅	—	2	2	no	—
224	C₂²×C₄×C₅	—	2	2	no	—
225	C₂²×C₄×C₅	—	2	1	no	—
226	C₂²×C₄×C₅	—	6	1	no	—
227	C₂²×C₄×C₅	#67	1	1	yes	characteristic
228	C₂²×C₄×C₅	#67	1	2	yes	—
229	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
230	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
231	C₅×Q₁₆	—	6	2	no	—
232	C₅×SD₁₆	—	6	2	no	—
233	C₅×SD₁₆	—	6	2	no	—
234	C₅×D₈	—	6	2	no	—
235	C₂×C₅×C₈	—	3	4	no	—
236	C₂×C₅×C₈	—	3	1	no	—
237	C₂×C₅×C₈	—	3	1	no	—
238	C₂×C₅×C₈	—	3	2	no	—
239	C₂×C₅×C₈	—	6	4	no	—
240	C₂×C₅×C₈	—	6	4	no	—
241	C₂×C₅×C₈	—	6	2	no	—
242	C₅×C₄⋊C₄	—	2	2	no	—
243	C₅×C₄⋊C₄	—	3	2	no	—
244	C₅×C₄⋊C₄	—	6	2	no	—
245	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
246	C₅×C₂²⋊C₄	—	2	1	no	—
247	C₅×C₂²⋊C₄	—	2	2	no	—
248	C₅×C₂²⋊C₄	—	2	2	no	—
249	C₅×C₂²⋊C₄	—	6	1	no	—
250	C₅×C₂²⋊C₄	—	6	2	no	—
251	C₅×C₂²⋊C₄	—	6	2	no	—
252	C₄²×C₅	—	2	1	no	—
253	C₄²×C₅	—	6	1	no	—
254	C₂×#135	—	3	1	no	—
255	C₂³×C₈	—	3	1	no	—
256	#525	—	3	1	no	—
257	#525	C₅×D₃	1	1	yes	characteristic, complemented
258	#467	—	3	2	no	—
259	#466	—	3	2	no	—
260	#465	—	3	2	no	—
261	#465	—	3	2	no	—
262	#427	—	3	1	no	—
263	#416	—	3	1	no	—
264	#416	—	3	1	no	—
265	C₂²×C₃×C₅	—	2	8	no	—
266	C₂²×C₃×C₅	—	2	2	no	—
267	C₂²×C₃×C₅	—	2	2	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	4	1	no	—
270	C₂²×C₃×C₅	—	4	2	no	—
271	C₂²×C₃×C₅	#121	1	2	yes	—
272	C₂²×C₃×C₅	#135	1	4	yes	complemented
273	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₅×D₃	—	4	1	no	—
275	C₂×C₅×D₃	—	4	2	no	—
276	C₃×C₄×C₅	—	2	2	no	—
277	C₃×C₄×C₅	—	4	1	no	—
278	C₃×C₄×C₅	—	4	2	no	—
279	C₃×C₄×C₅	#121	1	2	yes	—
280	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
281	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
282	C₅×Dic₃	—	4	1	no	—
283	C₅×Dic₃	—	4	2	no	—
284	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
285	C₃×#41	—	2	2	no	—
286	C₃×#41	—	2	2	no	—
287	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
288	C₂×C₃×D₄	—	2	2	no	—
289	C₂×C₃×D₄	—	2	1	no	—
290	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
291	C₂²×C₃×C₄	—	2	2	no	—
292	C₂²×C₃×C₄	—	2	2	no	—
293	C₂²×C₃×C₄	—	2	1	no	—
294	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
295	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
296	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
297	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
298	C₂×#67	—	2	2	no	—
299	C₂×#67	—	2	1	no	—
300	#235	—	2	2	no	—
301	#235	—	2	2	no	—
302	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₄×D₃	—	2	1	no	—
304	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
305	C₃×C₄⋊C₄	—	2	2	no	—
306	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
307	C₃×C₂²⋊C₄	—	2	1	no	—
308	C₃×C₂²⋊C₄	—	2	2	no	—
309	C₃×C₂²⋊C₄	—	2	2	no	—
310	C₃×C₄²	—	2	1	no	—
311	#217	—	2	2	no	—
312	#217	—	2	1	no	—
313	#216	—	2	2	no	—
314	#215	—	2	2	no	—
315	#214	—	2	2	no	—
316	#213	—	2	2	no	—
317	(C₂×D₃)⋊C₄	—	2	2	no	—
318	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
319	Dic₃⋊C₄	—	2	2	no	—
320	C₄×Dic₃	—	2	1	no	—
321	C₂×C₃⋊C₈	—	2	2	no	—
322	C₂×C₃⋊C₈	—	2	4	no	—
323	C₂×C₃⋊C₈	—	2	4	no	—
324	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
325	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
326	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
327	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
328	C₂³×C₅	—	2	2	no	—
329	C₂³×C₅	—	2	4	no	—
330	C₂³×C₅	—	2	1	no	—
331	C₂³×C₅	—	6	1	no	—
332	C₂³×C₅	C₂×#67	1	1	yes	characteristic
333	C₂³×C₅	C₂×#67	1	2	yes	—
334	C₅×Q₈	—	2	1	no	—
335	C₅×Q₈	—	2	1	no	—
336	C₅×Q₈	—	6	1	no	—
337	C₅×Q₈	—	6	1	no	—
338	C₅×D₄	—	2	1	no	—
339	C₅×D₄	—	2	1	no	—
340	C₅×D₄	—	4	2	no	—
341	C₅×D₄	—	4	4	no	—
342	C₅×D₄	—	6	1	no	—
343	C₅×D₄	—	6	1	no	—
344	C₅×D₄	—	12	2	no	—
345	C₅×D₄	—	12	4	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	2	4	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	2	2	no	—
350	C₂×C₄×C₅	—	2	2	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	4	2	no	—
353	C₂×C₄×C₅	—	6	2	no	—
354	C₂×C₄×C₅	—	6	1	no	—
355	C₂×C₄×C₅	—	12	2	no	—
356	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
357	C₂×C₄×C₅	#237	1	2	yes	—
358	C₂×C₄×C₅	C₂×#67	1	2	yes	—
359	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
360	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
361	C₅×C₈	—	3	2	no	—
362	C₅×C₈	—	3	2	no	—
363	C₅×C₈	—	6	2	no	—
364	C₂×#41	—	3	1	no	—
365	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
366	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
367	#135	—	6	4	no	—
368	C₂×Q₁₆	—	3	1	no	—
369	C₂×SD₁₆	—	3	1	no	—
370	C₂×SD₁₆	—	3	1	no	—
371	C₂×D₈	—	3	1	no	—
372	C₂²×C₈	—	3	1	no	—
373	C₂²×C₈	—	3	1	no	—
374	C₂²×C₈	—	3	2	no	—
375	C₂²×C₈	—	3	2	no	—
376	C₂²×C₈	—	6	4	no	—
377	#123	—	2	1	no	—
378	#123	—	6	1	no	—
379	C₂²⋊Q₈	—	3	2	no	—
380	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	—
381	#121	—	3	2	no	—
382	#121	C₂×C₅×D₃	1	2	yes	—
383	#120	—	2	1	no	—
384	#120	—	6	1	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	6	2	no	—
387	#117	—	3	1	no	—
388	#117	C₂×C₅×D₃	1	1	yes	characteristic
389	#107	—	3	2	no	—
390	#106	—	3	2	no	—
391	#103	—	3	2	no	—
392	#103	—	3	2	no	—
393	#102	—	3	2	no	—
394	#102	—	3	2	no	—
395	C₂×C₃×C₅	—	2	2	no	—
396	C₂×C₃×C₅	—	2	4	no	—
397	C₂×C₃×C₅	—	8	1	no	—
398	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
399	C₂×C₃×C₅	C₂×#135	1	2	yes	—
400	C₅×D₃	—	8	1	no	—
401	C₂³×C₃	—	2	2	no	—
402	C₂³×C₃	—	2	4	no	—
403	C₂³×C₃	—	2	1	no	—
404	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
406	C₂²×D₃	—	2	1	no	—
407	C₃×Q₈	—	2	1	no	—
408	C₃×Q₈	—	2	1	no	—
409	C₃×D₄	—	2	1	no	—
410	C₃×D₄	—	2	1	no	—
411	C₃×D₄	—	4	2	no	—
412	C₃×D₄	—	4	4	no	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	4	no	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	2	no	—
418	C₂×C₃×C₄	—	2	1	no	—
419	C₂×C₃×C₄	—	4	2	no	—
420	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
421	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
422	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
423	C₂×C₃×C₄	C₅×#41	1	2	yes	—
424	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
425	#67	—	4	2	no	—
426	#67	—	4	4	no	—
427	C₂×Dic₃	—	2	2	no	—
428	C₂×Dic₃	—	2	1	no	—
429	D₁₂	—	2	1	no	—
430	D₁₂	—	2	1	no	—
431	C₄×D₃	—	4	2	no	—
432	Dic₆	—	2	1	no	—
433	Dic₆	—	2	1	no	—
434	C₃⋊C₈	—	2	2	no	—
435	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
436	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
437	C₂²×C₅	—	2	8	no	—
438	C₂²×C₅	—	2	2	no	—
439	C₂²×C₅	—	2	2	no	—
440	C₂²×C₅	—	2	2	no	—
441	C₂²×C₅	—	4	1	no	—
442	C₂²×C₅	—	4	2	no	—
443	C₂²×C₅	—	12	1	no	—
444	C₂²×C₅	—	12	2	no	—
445	C₂²×C₅	#939	1	2	yes	—
446	C₂²×C₅	#950	1	4	yes	complemented
447	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
448	C₄×C₅	—	2	2	no	—
449	C₄×C₅	—	4	1	no	—
450	C₄×C₅	—	4	2	no	—
451	C₄×C₅	—	12	1	no	—
452	C₄×C₅	—	12	2	no	—
453	C₄×C₅	#939	1	2	yes	—
454	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
455	C₄×C₅	C₂×#237	1	1	yes	characteristic
456	C₂⁴	C₅×#67	1	1	yes	characteristic
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	6	2	no	—
460	#41	—	6	2	no	—
461	C₂×Q₈	—	3	1	no	—
462	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	3	1	no	—
466	C₂×D₄	—	6	2	no	—
467	C₂×D₄	—	6	1	no	—
468	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	6	1	no	—
473	C₂²×C₄	C₅×#67	1	2	yes	—
474	C₂²×C₄	C₅×#67	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
476	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
477	Q₁₆	—	6	2	no	—
478	SD₁₆	—	6	2	no	—
479	SD₁₆	—	6	2	no	—
480	D₈	—	6	2	no	—
481	C₂×C₈	—	3	4	no	—
482	C₂×C₈	—	3	1	no	—
483	C₂×C₈	—	3	1	no	—
484	C₂×C₈	—	3	2	no	—
485	C₂×C₈	—	6	4	no	—
486	C₂×C₈	—	6	4	no	—
487	C₂×C₈	—	6	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	3	2	no	—
490	C₄⋊C₄	—	6	2	no	—
491	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	6	1	no	—
496	C₂²⋊C₄	—	6	2	no	—
497	C₂²⋊C₄	—	6	2	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	6	1	no	—
500	C₃×C₅	#3050	1	1	yes	characteristic, complemented, Hall
501	C₂²×C₃	—	2	8	no	—
502	C₂²×C₃	—	2	2	no	—
503	C₂²×C₃	—	2	2	no	—
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	4	1	no	—
506	C₂²×C₃	—	4	2	no	—
507	C₂²×C₃	C₅×#121	1	2	yes	—
508	C₂²×C₃	C₅×#135	1	4	yes	complemented
509	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
510	C₂×D₃	—	4	1	no	—
511	C₂×D₃	—	4	2	no	—
512	C₃×C₄	—	2	2	no	—
513	C₃×C₄	—	4	1	no	—
514	C₃×C₄	—	4	2	no	—
515	C₃×C₄	C₅×#121	1	2	yes	—
516	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
517	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
518	Dic₃	—	4	1	no	—
519	Dic₃	—	4	2	no	—
520	C₂×C₅	—	2	2	no	—
521	C₂×C₅	—	2	4	no	—
522	C₂×C₅	—	8	1	no	—
523	C₂×C₅	—	24	1	no	—
524	C₂×C₅	C₂×#939	1	1	yes	characteristic
525	C₂×C₅	C₂×#950	1	2	yes	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	6	1	no	—
530	C₂³	C₂×C₅×#67	1	1	yes	characteristic
531	C₂³	C₂×C₅×#67	1	2	yes	—
532	Q₈	—	2	1	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	6	1	no	—
535	Q₈	—	6	1	no	—
536	D₄	—	2	1	no	—
537	D₄	—	2	1	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	4	no	—
540	D₄	—	6	1	no	—
541	D₄	—	6	1	no	—
542	D₄	—	12	2	no	—
543	D₄	—	12	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	6	2	no	—
552	C₂×C₄	—	6	1	no	—
553	C₂×C₄	—	12	2	no	—
554	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
555	C₂×C₄	C₅×#237	1	2	yes	—
556	C₂×C₄	C₂×C₅×#67	1	2	yes	—
557	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
558	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
559	C₈	—	3	2	no	—
560	C₈	—	3	2	no	—
561	C₈	—	6	2	no	—
562	C₂×C₃	—	2	2	no	—
563	C₂×C₃	—	2	4	no	—
564	C₂×C₃	—	8	1	no	—
565	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
566	C₂×C₃	C₂×C₅×#135	1	2	yes	—
567	D₃	—	8	1	no	—
568	C₅	#82922	1	1	yes	characteristic, direct product factor, Sylow
569	C₂²	—	2	8	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	12	1	no	—
576	C₂²	—	12	2	no	—
577	C₂²	C₅×#939	1	2	yes	—
578	C₂²	C₅×#950	1	4	yes	complemented
579	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	2	no	—
583	C₄	—	12	1	no	—
584	C₄	—	12	2	no	—
585	C₄	C₅×#939	1	2	yes	—
586	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
587	C₄	C₂×C₅×#237	1	1	yes	characteristic
588	C₃	C₅×#3050	1	1	yes	characteristic, complemented, Sylow
589	C₂	—	2	2	no	—
590	C₂	—	2	4	no	—
591	C₂	—	8	1	no	—
592	C₂	—	24	1	no	—
593	C₂	C₂×C₅×#939	1	1	yes	characteristic
594	C₂	C₂×C₅×#950	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#525	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#525	D₃
hypocenter	C₃	C₅×#3050
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₅×#525

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#525	C₂	semidirect
2. C₂×C₅×#950	C₂	semidirect
3. C₅×#5791	C₂	semidirect
4. C₂³×C₅×C₃⋊C₈	C₂	semidirect
5. C₅×#5233	C₂	semidirect
6. C₅×#5051	C₂	semidirect
7. C₅×#5048	C₂	semidirect
8. C₅×#5041	C₂	semidirect
9. C₅×#5038	C₂	semidirect
10. C₅×#5002	C₂	semidirect
11. C₅×#4998	C₂	semidirect
24. C₂×C₅×#216	C₂²	semidirect
25. C₂×C₅×#215	C₂²	semidirect
26. C₂×C₅×#214	C₂²	semidirect
27. C₂×C₅×#213	C₂²	semidirect
38. C₅×#835	C₂²	semidirect
39. C₅×#832	C₂²	semidirect
40. C₅×#810	C₂²	semidirect
41. C₅×#809	C₂²	semidirect
42. C₅×#808	C₂²	semidirect
43. C₅×#807	C₂²	semidirect
44. #82922	C₅	direct (N × H)
48. C₅×#525	D₃	semidirect
96. C₂×C₅×C₃⋊C₈	D₄	semidirect
100. C₃×#525	C₂×C₅	semidirect
101. C₂×#950	C₂×C₅	semidirect
102. #5791	C₂×C₅	semidirect
103. C₂³×C₃⋊C₈	C₂×C₅	semidirect
104. #5233	C₂×C₅	semidirect
105. #5051	C₂×C₅	semidirect
106. #5048	C₂×C₅	semidirect
107. #5041	C₂×C₅	semidirect
108. #5038	C₂×C₅	semidirect
109. #5002	C₂×C₅	semidirect
110. #4998	C₂×C₅	semidirect
190. C₂×#216	C₂²×C₅	semidirect
191. C₂×#215	C₂²×C₅	semidirect
192. C₂×#214	C₂²×C₅	semidirect
193. C₂×#213	C₂²×C₅	semidirect
204. #835	C₂²×C₅	semidirect
205. #832	C₂²×C₅	semidirect
206. #810	C₂²×C₅	semidirect
207. #809	C₂²×C₅	semidirect
208. #808	C₂²×C₅	semidirect
209. #807	C₂²×C₅	semidirect
257. #525	C₅×D₃	semidirect
272. C₂²×C₃×C₅	#135	semidirect
324. C₂×C₃⋊C₈	C₅×D₄	semidirect
446. C₂²×C₅	#950	semidirect
500. C₃×C₅	#3050	semidirect
508. C₂²×C₃	C₅×#135	semidirect
568. C₅	#82922	direct (N × H)
578. C₂²	C₅×#950	semidirect
588. C₃	C₅×#3050	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#525	2
C₂×C₅×#950	2
C₅×#5791	2
C₂³×C₅×C₃⋊C₈	2
C₅×#5233	2
C₅×#5051	2
C₅×#5048	2
C₅×#5041	2
C₅×#5038	2
C₅×#5002	2
C₅×#4998	2
C₅×#3050	3
#82922	5

Subgroups — C5×#82922 #14427792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82922 #14427792