Subgroups — C₅×#83296 #14426208

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 604 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×#950	C₂	1	2	yes	maximal, complemented
3	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5233	C₂	1	2	yes	maximal, complemented
5	C₅×#5090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5075	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5072	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5057	C₂	1	2	yes	maximal, complemented
10	C₅×#5054	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3035	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂×C₅×#235	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#127	C₂²	1	1	yes	characteristic
17	C₃×C₅×#124	C₂²	1	2	yes	—
18	C₃×C₅×#121	—	2	1	no	—
19	C₃×C₅×#121	—	2	1	no	—
20	C₃×C₄×C₅×D₄	—	2	1	no	—
21	C₃×C₄×C₅×D₄	—	2	1	no	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₅×#950	—	2	8	no	—
24	C₂×C₅×#216	C₂²	1	2	yes	—
25	C₂×C₅×#215	C₂²	1	2	yes	—
26	C₂×C₅×#214	C₂²	1	2	yes	—
27	C₂×C₅×#213	C₂²	1	2	yes	—
28	C₄×C₅×#67	—	2	1	no	—
29	C₄×C₅×#67	—	2	1	no	—
30	C₅×#926	C₂²	1	1	yes	characteristic
31	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
32	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
33	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
34	C₅×#872	—	2	1	no	—
35	C₄²×C₅×D₃	—	2	1	no	—
36	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
37	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
38	C₅×#835	C₂²	1	2	yes	—
39	C₅×#835	C₂²	1	2	yes	—
40	C₅×#832	C₂²	1	2	yes	—
41	C₅×#832	C₂²	1	2	yes	—
42	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
43	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
44	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
45	#83296	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂×C₅×#135	—	3	2	no	—
47	C₅×#532	D₃	1	1	yes	characteristic, complemented
48	C₄×C₅×#41	—	3	1	no	—
49	C₅×#464	—	3	2	no	—
50	C₅×#463	—	3	2	no	—
51	C₅×#462	—	3	1	no	—
52	C₅×#461	—	3	1	no	—
53	C₅×#460	—	3	1	no	—
54	C₅×#459	—	3	1	no	—
55	C₂×C₅×C₄⋊C₈	—	3	1	no	—
56	C₅×#416	—	3	2	no	—
57	C₃×C₅×#41	—	2	4	no	—
58	C₃×C₅×#41	—	2	4	no	—
59	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₅×#67	—	2	1	no	—
69	C₅×#235	—	2	2	no	—
70	C₅×#235	D₄	1	4	yes	complemented
71	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
72	C₂×C₄×C₅×D₃	—	2	1	no	—
73	C₂×C₄×C₅×D₃	—	2	1	no	—
74	C₂×C₄×C₅×D₃	—	2	1	no	—
75	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
80	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
81	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
82	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₅×#217	—	2	1	no	—
85	C₅×#216	—	2	4	no	—
86	C₅×#215	—	2	4	no	—
87	C₅×#214	—	2	4	no	—
88	C₅×#213	—	2	4	no	—
89	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
90	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
91	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
92	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
93	C₅×Dic₃⋊C₄	—	2	1	no	—
94	C₅×Dic₃⋊C₄	—	2	1	no	—
95	C₄×C₅×Dic₃	—	2	1	no	—
96	C₄×C₅×Dic₃	—	2	1	no	—
97	C₄×C₅×Dic₃	—	2	1	no	—
98	C₂×C₅×C₃⋊C₈	—	2	4	no	—
99	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
100	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
101	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×#950	C₂×C₅	1	2	yes	complemented
103	C₄×#235	C₂×C₅	1	1	yes	characteristic, complemented
104	#5233	C₂×C₅	1	2	yes	complemented
105	#5090	C₂×C₅	1	1	yes	characteristic, complemented
106	#5083	C₂×C₅	1	1	yes	characteristic, complemented
107	#5075	C₂×C₅	1	1	yes	characteristic, complemented
108	#5072	C₂×C₅	1	1	yes	characteristic, complemented
109	#5057	C₂×C₅	1	2	yes	complemented
110	#5054	C₂×C₅	1	2	yes	complemented
111	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₅×#41	—	3	1	no	—
113	C₂×C₅×#41	C₂×D₃	1	2	yes	—
114	C₅×#135	—	6	8	no	—
115	C₂×C₅×Q₁₆	—	3	2	no	—
116	C₂×C₅×SD₁₆	—	3	2	no	—
117	C₂×C₅×SD₁₆	—	3	2	no	—
118	C₂×C₅×D₈	—	3	2	no	—
119	C₂²×C₅×C₈	—	3	2	no	—
120	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
121	C₅×#127	C₂×D₃	1	1	yes	characteristic
122	C₅×#124	C₂×D₃	1	2	yes	—
123	C₅×#121	—	2	1	no	—
124	C₅×#121	—	2	1	no	—
125	C₄×C₅×Q₈	—	3	1	no	—
126	C₄×C₅×Q₈	—	3	1	no	—
127	C₄×C₅×D₄	—	2	1	no	—
128	C₄×C₅×D₄	—	2	1	no	—
129	C₄×C₅×D₄	—	3	1	no	—
130	C₄×C₅×D₄	—	3	1	no	—
131	C₄×C₅×D₄	—	6	1	no	—
132	C₄×C₅×D₄	—	6	1	no	—
133	C₅×#117	—	3	1	no	—
134	C₅×#117	—	6	1	no	—
135	C₂×C₄²×C₅	—	6	1	no	—
136	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
137	C₅×C₄⋊C₈	—	3	1	no	—
138	C₅×C₄⋊C₈	—	3	1	no	—
139	C₅×C₄⋊C₈	—	3	2	no	—
140	C₅×#103	—	3	2	no	—
141	C₅×#103	—	3	2	no	—
142	C₅×#102	—	3	2	no	—
143	C₅×#102	—	3	2	no	—
144	#3035	—	3	1	no	Sylow
145	C₂³×C₃×C₅	—	2	2	no	—
146	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₅×D₃	—	2	1	no	—
148	C₃×C₅×Q₈	—	2	2	no	—
149	C₃×C₅×Q₈	—	2	2	no	—
150	C₃×C₅×D₄	—	2	2	no	—
151	C₃×C₅×D₄	—	2	2	no	—
152	C₃×C₅×D₄	—	4	2	no	—
153	C₃×C₅×D₄	—	4	4	no	—
154	C₃×C₅×D₄	—	4	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	4	1	no	—
158	C₂×C₃×C₄×C₅	—	4	4	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
164	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	#41	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
167	C₅×#67	—	2	4	no	—
168	C₂×C₅×Dic₃	—	2	1	no	—
169	C₂×C₅×Dic₃	—	2	1	no	—
170	C₂×C₅×Dic₃	—	2	1	no	—
171	C₅×D₁₂	—	2	1	no	—
172	C₅×D₁₂	C₂×D₄	1	2	yes	—
173	C₄×C₅×D₃	—	2	4	no	—
174	C₄×C₅×D₃	—	4	2	no	—
175	C₄×C₅×D₃	—	4	2	no	—
176	C₅×Dic₆	—	2	1	no	—
177	C₅×Dic₆	C₂×D₄	1	2	yes	—
178	C₅×C₃⋊C₈	—	2	2	no	—
179	C₅×C₃⋊C₈	—	2	2	no	—
180	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
181	C₂×#235	C₂²×C₅	1	1	yes	characteristic
182	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
183	C₃×#127	C₂²×C₅	1	1	yes	characteristic
184	C₃×#124	C₂²×C₅	1	2	yes	—
185	C₃×#121	—	2	1	no	—
186	C₃×#121	—	2	1	no	—
187	C₃×C₄×D₄	—	2	1	no	—
188	C₃×C₄×D₄	—	2	1	no	—
189	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
190	#950	—	2	8	no	—
191	C₂×#216	C₂²×C₅	1	2	yes	—
192	C₂×#215	C₂²×C₅	1	2	yes	—
193	C₂×#214	C₂²×C₅	1	2	yes	—
194	C₂×#213	C₂²×C₅	1	2	yes	—
195	C₄×#67	—	2	1	no	—
196	C₄×#67	—	2	1	no	—
197	#926	C₂²×C₅	1	1	yes	characteristic
198	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
199	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
200	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
201	#872	—	2	1	no	—
202	C₄²×D₃	—	2	1	no	—
203	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
204	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
205	#835	C₂²×C₅	1	2	yes	—
206	#835	C₂²×C₅	1	2	yes	—
207	#832	C₂²×C₅	1	2	yes	—
208	#832	C₂²×C₅	1	2	yes	—
209	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
210	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
211	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
212	C₅×#41	—	2	4	no	—
213	C₅×#41	—	2	4	no	—
214	C₅×#41	—	3	4	no	—
215	C₅×#41	—	6	2	no	—
216	C₂×C₅×Q₈	—	3	1	no	—
217	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
218	C₂×C₅×D₄	—	2	2	no	—
219	C₂×C₅×D₄	—	2	1	no	—
220	C₂×C₅×D₄	—	2	1	no	—
221	C₂×C₅×D₄	—	3	1	no	—
222	C₂×C₅×D₄	—	6	1	no	—
223	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
224	C₂²×C₄×C₅	—	2	2	no	—
225	C₂²×C₄×C₅	—	6	1	no	—
226	C₂²×C₄×C₅	—	6	1	no	—
227	C₂²×C₄×C₅	—	6	1	no	—
228	C₂²×C₄×C₅	#67	1	1	yes	characteristic
229	C₂²×C₄×C₅	#67	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
231	C₅×Q₁₆	—	6	4	no	—
232	C₅×SD₁₆	—	6	4	no	—
233	C₅×SD₁₆	—	6	4	no	—
234	C₅×D₈	—	6	4	no	—
235	C₂×C₅×C₈	—	3	2	no	—
236	C₂×C₅×C₈	—	3	2	no	—
237	C₂×C₅×C₈	—	6	4	no	—
238	C₅×C₄⋊C₄	—	2	1	no	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	3	1	no	—
241	C₅×C₄⋊C₄	—	3	1	no	—
242	C₅×C₄⋊C₄	—	6	1	no	—
243	C₅×C₄⋊C₄	—	6	1	no	—
244	C₅×C₂²⋊C₄	—	2	2	no	—
245	C₅×C₂²⋊C₄	—	2	2	no	—
246	C₅×C₂²⋊C₄	—	6	1	no	—
247	C₅×C₂²⋊C₄	—	6	1	no	—
248	C₅×C₂²⋊C₄	—	6	1	no	—
249	C₄²×C₅	—	6	1	no	—
250	C₄²×C₅	—	6	1	no	—
251	C₄²×C₅	—	6	1	no	—
252	C₄²×C₅	#67	1	1	yes	characteristic
253	C₄²×C₅	#67	1	1	yes	characteristic
254	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
255	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
256	C₂×#135	—	3	2	no	—
257	#532	C₅×D₃	1	1	yes	characteristic, complemented
258	C₄×#41	—	3	1	no	—
259	#464	—	3	2	no	—
260	#463	—	3	2	no	—
261	#462	—	3	1	no	—
262	#461	—	3	1	no	—
263	#460	—	3	1	no	—
264	#459	—	3	1	no	—
265	C₂×C₄⋊C₈	—	3	1	no	—
266	#416	—	3	2	no	—
267	C₂²×C₃×C₅	—	2	1	no	—
268	C₂²×C₃×C₅	—	2	1	no	—
269	C₂²×C₃×C₅	—	4	2	no	—
270	C₂²×C₃×C₅	—	4	2	no	—
271	C₂²×C₃×C₅	—	4	2	no	—
272	C₂²×C₃×C₅	#121	1	2	yes	—
273	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₅×D₃	—	2	2	no	—
275	C₂×C₅×D₃	—	4	1	no	—
276	C₂×C₅×D₃	—	4	1	no	—
277	C₃×C₄×C₅	—	2	1	no	—
278	C₃×C₄×C₅	—	2	1	no	—
279	C₃×C₄×C₅	—	2	1	no	—
280	C₃×C₄×C₅	—	4	2	no	—
281	C₃×C₄×C₅	#121	1	2	yes	—
282	C₃×C₄×C₅	#135	1	2	yes	complemented
283	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
284	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
285	C₅×Dic₃	—	2	2	no	—
286	C₅×Dic₃	—	4	1	no	—
287	C₅×Dic₃	—	4	1	no	—
288	C₃×#41	—	2	4	no	—
289	C₃×#41	—	2	4	no	—
290	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
291	C₂×C₃×D₄	—	2	2	no	—
292	C₂×C₃×D₄	—	2	1	no	—
293	C₂×C₃×D₄	—	2	1	no	—
294	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
295	C₂²×C₃×C₄	—	2	2	no	—
296	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
297	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
298	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
299	C₂×#67	—	2	1	no	—
300	#235	—	2	2	no	—
301	#235	C₅×D₄	1	4	yes	complemented
302	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
303	C₂×C₄×D₃	—	2	1	no	—
304	C₂×C₄×D₃	—	2	1	no	—
305	C₂×C₄×D₃	—	2	1	no	—
306	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
307	C₃×C₄⋊C₄	—	2	1	no	—
308	C₃×C₄⋊C₄	—	2	1	no	—
309	C₃×C₂²⋊C₄	—	2	2	no	—
310	C₃×C₂²⋊C₄	—	2	2	no	—
311	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
312	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
313	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
314	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
315	#217	—	2	1	no	—
316	#216	—	2	4	no	—
317	#215	—	2	4	no	—
318	#214	—	2	4	no	—
319	#213	—	2	4	no	—
320	(C₂×D₃)⋊C₄	—	2	1	no	—
321	(C₂×D₃)⋊C₄	—	2	1	no	—
322	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
323	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
324	Dic₃⋊C₄	—	2	1	no	—
325	Dic₃⋊C₄	—	2	1	no	—
326	C₄×Dic₃	—	2	1	no	—
327	C₄×Dic₃	—	2	1	no	—
328	C₄×Dic₃	—	2	1	no	—
329	C₂×C₃⋊C₈	—	2	4	no	—
330	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
331	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
332	C₂³×C₅	—	2	2	no	—
333	C₂³×C₅	—	6	1	no	—
334	C₂³×C₅	C₂×#67	1	1	yes	characteristic
335	C₅×Q₈	—	2	2	no	—
336	C₅×Q₈	—	2	2	no	—
337	C₅×Q₈	—	3	2	no	—
338	C₅×Q₈	—	6	1	no	—
339	C₅×D₄	—	2	2	no	—
340	C₅×D₄	—	2	2	no	—
341	C₅×D₄	—	3	2	no	—
342	C₅×D₄	—	4	2	no	—
343	C₅×D₄	—	4	4	no	—
344	C₅×D₄	—	4	2	no	—
345	C₅×D₄	—	6	4	no	—
346	C₅×D₄	—	6	1	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	4	1	no	—
350	C₂×C₄×C₅	—	4	4	no	—
351	C₂×C₄×C₅	—	6	1	no	—
352	C₂×C₄×C₅	—	6	4	no	—
353	C₂×C₄×C₅	—	6	1	no	—
354	C₂×C₄×C₅	—	6	1	no	—
355	C₂×C₄×C₅	—	12	2	no	—
356	C₂×C₄×C₅	—	12	2	no	—
357	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
358	C₂×C₄×C₅	#237	1	2	yes	—
359	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
360	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
361	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
362	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
363	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
364	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
365	C₅×C₈	—	6	2	no	—
366	C₅×C₈	—	6	2	no	—
367	C₂×#41	—	3	1	no	—
368	C₂×#41	C₂×C₅×D₃	1	2	yes	—
369	#135	—	6	8	no	—
370	C₂×Q₁₆	—	3	2	no	—
371	C₂×SD₁₆	—	3	2	no	—
372	C₂×SD₁₆	—	3	2	no	—
373	C₂×D₈	—	3	2	no	—
374	C₂²×C₈	—	3	2	no	—
375	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
376	#127	C₂×C₅×D₃	1	1	yes	characteristic
377	#124	C₂×C₅×D₃	1	2	yes	—
378	#121	—	2	1	no	—
379	#121	—	2	1	no	—
380	C₄×Q₈	—	3	1	no	—
381	C₄×Q₈	—	3	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	3	1	no	—
385	C₄×D₄	—	3	1	no	—
386	C₄×D₄	—	6	1	no	—
387	C₄×D₄	—	6	1	no	—
388	#117	—	3	1	no	—
389	#117	—	6	1	no	—
390	C₂×C₄²	—	6	1	no	—
391	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
392	C₄⋊C₈	—	3	1	no	—
393	C₄⋊C₈	—	3	1	no	—
394	C₄⋊C₈	—	3	2	no	—
395	#103	—	3	2	no	—
396	#103	—	3	2	no	—
397	#102	—	3	2	no	—
398	#102	—	3	2	no	—
399	C₂×C₃×C₅	—	2	2	no	—
400	C₂×C₃×C₅	—	8	2	no	—
401	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
402	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
403	C₂×C₃×C₅	#575	1	1	yes	characteristic
404	C₅×D₃	—	4	2	no	—
405	C₂³×C₃	—	2	2	no	—
406	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
407	C₂²×D₃	—	2	1	no	—
408	C₃×Q₈	—	2	2	no	—
409	C₃×Q₈	—	2	2	no	—
410	C₃×D₄	—	2	2	no	—
411	C₃×D₄	—	2	2	no	—
412	C₃×D₄	—	4	2	no	—
413	C₃×D₄	—	4	4	no	—
414	C₃×D₄	—	4	2	no	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	4	1	no	—
418	C₂×C₃×C₄	—	4	4	no	—
419	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
420	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×C₃×C₄	C₅×#41	1	2	yes	—
426	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
427	#67	—	2	4	no	—
428	C₂×Dic₃	—	2	1	no	—
429	C₂×Dic₃	—	2	1	no	—
430	C₂×Dic₃	—	2	1	no	—
431	D₁₂	—	2	1	no	—
432	D₁₂	C₂×C₅×D₄	1	2	yes	—
433	C₄×D₃	—	2	4	no	—
434	C₄×D₃	—	4	2	no	—
435	C₄×D₃	—	4	2	no	—
436	Dic₆	—	2	1	no	—
437	Dic₆	C₂×C₅×D₄	1	2	yes	—
438	C₃⋊C₈	—	2	2	no	—
439	C₃⋊C₈	—	2	2	no	—
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	—	4	2	no	—
443	C₂²×C₅	—	4	2	no	—
444	C₂²×C₅	—	4	2	no	—
445	C₂²×C₅	—	6	2	no	—
446	C₂²×C₅	—	12	1	no	—
447	C₂²×C₅	—	12	1	no	—
448	C₂²×C₅	#938	1	2	yes	—
449	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
450	C₄×C₅	—	2	1	no	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	—	4	2	no	—
454	C₄×C₅	—	6	2	no	—
455	C₄×C₅	—	12	1	no	—
456	C₄×C₅	—	12	1	no	—
457	C₄×C₅	#938	1	2	yes	—
458	C₄×C₅	#950	1	2	yes	complemented
459	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
460	C₄×C₅	C₂×#237	1	1	yes	characteristic
461	#41	—	2	4	no	—
462	#41	—	2	4	no	—
463	#41	—	3	4	no	—
464	#41	—	6	2	no	—
465	C₂×Q₈	—	3	1	no	—
466	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	3	1	no	—
471	C₂×D₄	—	6	1	no	—
472	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	6	1	no	—
475	C₂²×C₄	—	6	1	no	—
476	C₂²×C₄	—	6	1	no	—
477	C₂²×C₄	C₅×#67	1	1	yes	characteristic
478	C₂²×C₄	C₅×#67	1	1	yes	characteristic
479	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
480	Q₁₆	—	6	4	no	—
481	SD₁₆	—	6	4	no	—
482	SD₁₆	—	6	4	no	—
483	D₈	—	6	4	no	—
484	C₂×C₈	—	3	2	no	—
485	C₂×C₈	—	3	2	no	—
486	C₂×C₈	—	6	4	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	3	1	no	—
490	C₄⋊C₄	—	3	1	no	—
491	C₄⋊C₄	—	6	1	no	—
492	C₄⋊C₄	—	6	1	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	6	1	no	—
496	C₂²⋊C₄	—	6	1	no	—
497	C₂²⋊C₄	—	6	1	no	—
498	C₄²	—	6	1	no	—
499	C₄²	—	6	1	no	—
500	C₄²	—	6	1	no	—
501	C₄²	C₅×#67	1	1	yes	characteristic
502	C₄²	C₅×#67	1	1	yes	characteristic
503	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
504	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
505	C₃×C₅	#3035	1	1	yes	characteristic, complemented, Hall
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	4	2	no	—
509	C₂²×C₃	—	4	2	no	—
510	C₂²×C₃	—	4	2	no	—
511	C₂²×C₃	C₅×#121	1	2	yes	—
512	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
513	C₂×D₃	—	2	2	no	—
514	C₂×D₃	—	4	1	no	—
515	C₂×D₃	—	4	1	no	—
516	C₃×C₄	—	2	1	no	—
517	C₃×C₄	—	2	1	no	—
518	C₃×C₄	—	2	1	no	—
519	C₃×C₄	—	4	2	no	—
520	C₃×C₄	C₅×#121	1	2	yes	—
521	C₃×C₄	C₅×#135	1	2	yes	complemented
522	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
523	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
524	Dic₃	—	2	2	no	—
525	Dic₃	—	4	1	no	—
526	Dic₃	—	4	1	no	—
527	C₂×C₅	—	2	2	no	—
528	C₂×C₅	—	8	2	no	—
529	C₂×C₅	—	12	2	no	—
530	C₂×C₅	C₂×#938	1	1	yes	characteristic
531	C₂×C₅	C₂×#950	1	1	yes	characteristic
532	C₂×C₅	#5822	1	1	yes	characteristic
533	C₂³	—	2	2	no	—
534	C₂³	—	6	1	no	—
535	C₂³	C₂×C₅×#67	1	1	yes	characteristic
536	Q₈	—	2	2	no	—
537	Q₈	—	2	2	no	—
538	Q₈	—	3	2	no	—
539	Q₈	—	6	1	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	2	no	—
542	D₄	—	3	2	no	—
543	D₄	—	4	2	no	—
544	D₄	—	4	4	no	—
545	D₄	—	4	2	no	—
546	D₄	—	6	4	no	—
547	D₄	—	6	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	4	no	—
552	C₂×C₄	—	6	1	no	—
553	C₂×C₄	—	6	4	no	—
554	C₂×C₄	—	6	1	no	—
555	C₂×C₄	—	6	1	no	—
556	C₂×C₄	—	12	2	no	—
557	C₂×C₄	—	12	2	no	—
558	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
559	C₂×C₄	C₅×#237	1	2	yes	—
560	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
561	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
562	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
563	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
564	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
565	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
566	C₈	—	6	2	no	—
567	C₈	—	6	2	no	—
568	C₂×C₃	—	2	2	no	—
569	C₂×C₃	—	8	2	no	—
570	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
571	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
572	C₂×C₃	C₅×#575	1	1	yes	characteristic
573	D₃	—	4	2	no	—
574	C₅	#83296	1	1	yes	characteristic, direct product factor, Sylow
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	6	2	no	—
581	C₂²	—	12	1	no	—
582	C₂²	—	12	1	no	—
583	C₂²	C₅×#938	1	2	yes	—
584	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	4	2	no	—
589	C₄	—	6	2	no	—
590	C₄	—	12	1	no	—
591	C₄	—	12	1	no	—
592	C₄	C₅×#938	1	2	yes	—
593	C₄	C₅×#950	1	2	yes	complemented
594	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
595	C₄	C₂×C₅×#237	1	1	yes	characteristic
596	C₃	C₅×#3035	1	1	yes	characteristic, complemented, Sylow
597	C₂	—	2	2	no	—
598	C₂	—	8	2	no	—
599	C₂	—	12	2	no	—
600	C₂	C₂×C₅×#938	1	1	yes	characteristic
601	C₂	C₂×C₅×#950	1	1	yes	characteristic
602	C₂	C₅×#5822	1	1	yes	characteristic

	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×#532	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#532	D₃
hypocenter	C₃	C₅×#3035
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×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×#950	C₂	semidirect
3. C₄×C₅×#235	C₂	semidirect
4. C₅×#5233	C₂	semidirect
5. C₅×#5090	C₂	semidirect
6. C₅×#5083	C₂	semidirect
7. C₅×#5075	C₂	semidirect
8. C₅×#5072	C₂	semidirect
9. C₅×#5057	C₂	semidirect
10. C₅×#5054	C₂	semidirect
11. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
45. #83296	C₅	direct (N × H)
47. C₅×#532	D₃	semidirect
70. C₅×#235	D₄	semidirect
101. C₃×#532	C₂×C₅	semidirect
102. C₂×#950	C₂×C₅	semidirect
103. C₄×#235	C₂×C₅	semidirect
104. #5233	C₂×C₅	semidirect
105. #5090	C₂×C₅	semidirect
106. #5083	C₂×C₅	semidirect
107. #5075	C₂×C₅	semidirect
108. #5072	C₂×C₅	semidirect
109. #5057	C₂×C₅	semidirect
110. #5054	C₂×C₅	semidirect
111. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
257. #532	C₅×D₃	semidirect
282. C₃×C₄×C₅	#135	semidirect
301. #235	C₅×D₄	semidirect
458. C₄×C₅	#950	semidirect
505. C₃×C₅	#3035	semidirect
521. C₃×C₄	C₅×#135	semidirect
574. C₅	#83296	direct (N × H)
593. C₄	C₅×#950	semidirect
596. C₃	C₅×#3035	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×#950	2
C₄×C₅×#235	2
C₅×#5233	2
C₅×#5090	2
C₅×#5083	2
C₅×#5075	2
C₅×#5072	2
C₅×#5057	2
C₅×#5054	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#3035	3
#83296	5

Subgroups — C5×#83296 #14426208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83296 #14426208