Subgroups — C₅×#83474 #14430762

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5521	C₂	1	1	yes	maximal, characteristic
3	C₅×#5087	C₂	1	2	yes	maximal, complemented
4	C₅×#5084	C₂	1	2	yes	maximal, complemented
5	C₅×#5066	C₂	1	2	yes	maximal, complemented
6	C₅×#5066	C₂	1	2	yes	maximal, complemented
7	C₅×#5001	C₂	1	1	yes	maximal, characteristic
8	C₅×#4999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#809	C₂	1	1	yes	maximal, characteristic
11	C₅×#4964	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3081	—	3	1	no	maximal, Hall
13	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
16	C₃×C₅×#125	—	2	1	no	—
17	C₃×C₅×#125	C₂²	1	2	yes	complemented
18	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₅×#926	C₂²	1	1	yes	characteristic
23	C₂×C₅×#208	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₅×#893	—	2	1	no	—
26	C₅×#893	—	2	1	no	—
27	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
28	C₄×C₅×D₁₂	C₂²	1	2	yes	—
29	C₄×C₅×D₁₂	C₂²	1	2	yes	—
30	C₅×#809	C₂²	1	2	yes	—
31	C₅×#809	C₂²	1	2	yes	—
32	C₅×#809	C₂²	1	2	yes	—
33	C₅×#809	C₂²	1	2	yes	—
34	C₅×#808	C₂²	1	2	yes	complemented
35	C₅×#808	C₂²	1	1	yes	characteristic, complemented
36	C₅×#808	C₂²	1	1	yes	characteristic, complemented
37	C₅×#807	C₂²	1	2	yes	complemented
38	C₅×#807	C₂²	1	1	yes	characteristic, complemented
39	C₅×#807	C₂²	1	1	yes	characteristic, complemented
40	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
41	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
42	#83474	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#544	D₃	1	1	yes	characteristic, complemented
44	C₅×#518	—	3	1	no	—
45	C₅×#478	—	3	2	no	—
46	C₅×#478	—	3	2	no	—
47	C₅×#476	—	3	2	no	—
48	C₅×#474	—	3	2	no	—
49	C₅×#428	—	3	1	no	—
50	C₅×#427	—	3	1	no	—
51	C₅×#424	—	3	1	no	—
52	C₅×#418	—	3	1	no	—
53	C₂×C₅×#102	—	3	1	no	—
54	C₂³×C₅×D₃	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	—	2	1	no	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₅×D₁₂	—	2	1	no	—
59	C₂×C₅×D₁₂	—	2	2	no	—
60	C₂×C₅×D₁₂	Q₈	1	4	yes	complemented
61	C₂×C₅×D₁₂	C₂³	1	2	yes	—
62	C₂×C₄×C₅×D₃	—	2	2	no	—
63	C₂×C₄×C₅×D₃	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	—	2	1	no	—
65	C₃×C₅×C₄⋊C₄	—	2	2	no	—
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
75	C₃×C₄²×C₅	—	2	1	no	—
76	C₃×C₄²×C₅	C₂³	1	2	yes	—
77	C₅×#217	—	2	1	no	—
78	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
79	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
80	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
81	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
82	C₄×C₅×Dic₃	—	2	1	no	—
83	C₅×#208	—	2	2	no	—
84	C₂×C₅×C₃⋊C₈	—	2	2	no	—
85	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
88	C₃×#544	C₂×C₅	1	1	yes	characteristic, complemented
89	#5521	C₂×C₅	1	1	yes	characteristic
90	#5087	C₂×C₅	1	2	yes	complemented
91	#5084	C₂×C₅	1	2	yes	complemented
92	#5066	C₂×C₅	1	2	yes	complemented
93	#5066	C₂×C₅	1	2	yes	complemented
94	#5001	C₂×C₅	1	1	yes	characteristic
95	#4999	C₂×C₅	1	1	yes	characteristic, complemented
96	#4998	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂×#809	C₂×C₅	1	1	yes	characteristic
98	#4964	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂²×C₅×D₄	—	3	1	no	—
100	C₂×C₅×M₁₆	—	3	1	no	—
101	C₂²×C₅×C₈	—	3	1	no	—
102	C₅×C₄⋊Q₈	—	2	1	no	—
103	C₅×C₄⋊Q₈	C₂×D₃	1	2	yes	complemented
104	C₅×#125	—	2	1	no	—
105	C₅×#125	C₂×D₃	1	2	yes	complemented
106	C₅×C₂²⋊Q₈	—	2	2	no	—
107	C₄×C₅×D₄	—	3	2	no	—
108	C₄×C₅×D₄	—	3	2	no	—
109	C₄×C₅×D₄	—	6	1	no	—
110	C₄×C₅×D₄	—	6	1	no	—
111	C₅×#117	—	3	1	no	—
112	C₅×#117	C₂×D₃	1	1	yes	characteristic
113	C₅×#117	C₂×D₃	1	1	yes	characteristic
114	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
115	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
116	C₅×#107	—	3	1	no	—
117	C₅×#107	—	3	1	no	—
118	C₅×#107	—	3	2	no	—
119	C₅×#106	—	3	1	no	—
120	C₅×#106	—	3	1	no	—
121	C₅×#106	—	3	2	no	—
122	C₅×C₄⋊C₈	—	3	2	no	—
123	C₅×C₄⋊C₈	—	3	2	no	—
124	C₅×#102	—	3	2	no	—
125	C₅×#102	—	3	2	no	—
126	C₅×#102	—	3	2	no	—
127	C₅×#102	—	3	2	no	—
128	#3081	—	3	1	no	Sylow
129	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₅×D₃	—	2	2	no	—
131	C₂²×C₅×D₃	—	2	4	no	—
132	C₂²×C₅×D₃	—	8	1	no	—
133	C₂²×C₅×D₃	—	8	1	no	—
134	C₃×C₅×Q₈	—	8	2	no	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	8	1	no	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
143	C₂×C₃×C₄×C₅	#41	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₂×C₅×Dic₃	—	2	1	no	—
146	C₂×C₅×Dic₃	—	2	1	no	—
147	C₅×D₁₂	—	2	4	no	—
148	C₅×D₁₂	—	2	2	no	—
149	C₅×D₁₂	C₂×Q₈	1	4	yes	—
150	C₄×C₅×D₃	—	8	2	no	—
151	C₄×C₅×D₃	—	8	2	no	—
152	C₅×C₃⋊C₈	—	2	1	no	—
153	C₅×C₃⋊C₈	—	2	1	no	—
154	C₅×C₃⋊C₈	—	2	2	no	—
155	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
156	C₃×C₄⋊Q₈	—	2	1	no	—
157	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
158	C₃×#125	—	2	1	no	—
159	C₃×#125	C₂²×C₅	1	2	yes	complemented
160	C₃×C₂²⋊Q₈	—	2	2	no	—
161	C₃×#117	C₂²×C₅	1	1	yes	characteristic
162	C₃×#117	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
164	#926	C₂²×C₅	1	1	yes	characteristic
165	C₂×#208	C₂²×C₅	1	1	yes	characteristic
166	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
167	#893	—	2	1	no	—
168	#893	—	2	1	no	—
169	D₃×C₂²⋊C₄	—	2	2	no	—
170	C₄×D₁₂	C₂²×C₅	1	2	yes	—
171	C₄×D₁₂	C₂²×C₅	1	2	yes	—
172	#809	C₂²×C₅	1	2	yes	—
173	#809	C₂²×C₅	1	2	yes	—
174	#809	C₂²×C₅	1	2	yes	—
175	#809	C₂²×C₅	1	2	yes	—
176	#808	C₂²×C₅	1	2	yes	complemented
177	#808	C₂²×C₅	1	1	yes	characteristic, complemented
178	#808	C₂²×C₅	1	1	yes	characteristic, complemented
179	#807	C₂²×C₅	1	2	yes	complemented
180	#807	C₂²×C₅	1	1	yes	characteristic, complemented
181	#807	C₂²×C₅	1	1	yes	characteristic, complemented
182	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	complemented
183	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	complemented
184	C₂⁴×C₅	—	6	1	no	—
185	C₂×C₅×Q₈	—	2	2	no	—
186	C₂×C₅×D₄	—	3	4	no	—
187	C₂×C₅×D₄	—	3	2	no	—
188	C₂×C₅×D₄	—	6	2	no	—
189	C₂×C₅×D₄	—	6	1	no	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	6	2	no	—
192	C₂²×C₄×C₅	—	6	2	no	—
193	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
194	C₅×M₁₆	—	6	2	no	—
195	C₂×C₅×C₈	—	3	1	no	—
196	C₂×C₅×C₈	—	3	1	no	—
197	C₂×C₅×C₈	—	3	2	no	—
198	C₂×C₅×C₈	—	6	2	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	2	no	—
201	C₅×C₄⋊C₄	—	2	2	no	—
202	C₅×C₄⋊C₄	—	2	2	no	—
203	C₅×C₄⋊C₄	—	3	1	no	—
204	C₅×C₄⋊C₄	—	3	1	no	—
205	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
206	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
207	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
208	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
209	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
210	C₅×C₂²⋊C₄	—	2	1	no	—
211	C₅×C₂²⋊C₄	—	6	1	no	—
212	C₅×C₂²⋊C₄	—	6	2	no	—
213	C₅×C₂²⋊C₄	—	6	2	no	—
214	C₅×C₂²⋊C₄	#67	1	2	yes	—
215	C₄²×C₅	—	2	1	no	—
216	C₄²×C₅	—	6	1	no	—
217	C₄²×C₅	C₂²×D₃	1	2	yes	—
218	#544	C₅×D₃	1	1	yes	characteristic, complemented
219	#518	—	3	1	no	—
220	#478	—	3	2	no	—
221	#478	—	3	2	no	—
222	#476	—	3	2	no	—
223	#474	—	3	2	no	—
224	#428	—	3	1	no	—
225	#427	—	3	1	no	—
226	#424	—	3	1	no	—
227	#418	—	3	1	no	—
228	C₂×#102	—	3	1	no	—
229	C₂²×C₃×C₅	—	2	1	no	—
230	C₂²×C₃×C₅	—	2	1	no	—
231	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
232	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₅×D₃	—	2	4	no	—
234	C₂×C₅×D₃	—	4	2	no	—
235	C₂×C₅×D₃	—	4	2	no	—
236	C₂×C₅×D₃	—	8	4	no	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	4	2	no	—
240	C₃×C₄×C₅	—	4	1	no	—
241	C₃×C₄×C₅	—	4	1	no	—
242	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
243	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
244	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
245	C₅×Dic₃	—	4	1	no	—
246	C₅×Dic₃	—	4	1	no	—
247	C₂³×D₃	—	2	1	no	—
248	C₂×C₃×Q₈	—	2	2	no	—
249	C₂²×C₃×C₄	—	2	1	no	—
250	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂×D₁₂	—	2	1	no	—
252	C₂×D₁₂	—	2	2	no	—
253	C₂×D₁₂	C₅×Q₈	1	4	yes	complemented
254	C₂×D₁₂	C₂³×C₅	1	2	yes	—
255	C₂×C₄×D₃	—	2	2	no	—
256	C₂×C₄×D₃	—	2	2	no	—
257	C₃×C₄⋊C₄	—	2	1	no	—
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	—	2	2	no	—
260	C₃×C₄⋊C₄	—	2	2	no	—
261	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
262	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
263	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
264	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
265	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
266	C₃×C₂²⋊C₄	—	2	1	no	—
267	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
268	C₃×C₄²	—	2	1	no	—
269	C₃×C₄²	C₂³×C₅	1	2	yes	—
270	#217	—	2	1	no	—
271	(C₂×D₃)⋊C₄	—	2	2	no	—
272	(C₂×D₃)⋊C₄	—	2	2	no	—
273	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
274	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
275	C₄×Dic₃	—	2	1	no	—
276	#208	—	2	2	no	—
277	C₂×C₃⋊C₈	—	2	2	no	—
278	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
279	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
280	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
281	C₂³×C₅	—	6	2	no	—
282	C₂³×C₅	—	6	4	no	—
283	C₂³×C₅	—	24	1	no	—
284	C₂³×C₅	—	24	1	no	—
285	C₂³×C₅	C₂×#67	1	1	yes	characteristic
286	C₅×Q₈	—	8	2	no	—
287	C₅×D₄	—	3	4	no	—
288	C₅×D₄	—	6	4	no	—
289	C₅×D₄	—	6	2	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	6	1	no	—
294	C₂×C₄×C₅	—	6	1	no	—
295	C₂×C₄×C₅	—	8	1	no	—
296	C₂×C₄×C₅	—	24	2	no	—
297	C₂×C₄×C₅	—	24	2	no	—
298	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
299	C₂×C₄×C₅	#239	1	2	yes	—
300	C₂×C₄×C₅	C₂×#67	1	2	yes	—
301	C₂×C₄×C₅	C₂×#67	1	2	yes	—
302	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
304	C₅×C₈	—	6	1	no	—
305	C₅×C₈	—	6	1	no	—
306	C₅×C₈	—	6	2	no	—
307	C₂²×D₄	—	3	1	no	—
308	C₂×M₁₆	—	3	1	no	—
309	C₂²×C₈	—	3	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
312	#125	—	2	1	no	—
313	#125	C₂×C₅×D₃	1	2	yes	complemented
314	C₂²⋊Q₈	—	2	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	6	1	no	—
318	C₄×D₄	—	6	1	no	—
319	#117	—	3	1	no	—
320	#117	C₂×C₅×D₃	1	1	yes	characteristic
321	#117	C₂×C₅×D₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	6	2	no	—
324	#107	—	3	1	no	—
325	#107	—	3	1	no	—
326	#107	—	3	2	no	—
327	#106	—	3	1	no	—
328	#106	—	3	1	no	—
329	#106	—	3	2	no	—
330	C₄⋊C₈	—	3	2	no	—
331	C₄⋊C₈	—	3	2	no	—
332	#102	—	3	2	no	—
333	#102	—	3	2	no	—
334	#102	—	3	2	no	—
335	#102	—	3	2	no	—
336	C₂×C₃×C₅	—	2	2	no	—
337	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
338	C₂×C₃×C₅	#576	1	1	yes	characteristic
339	C₂×C₃×C₅	#577	1	1	yes	characteristic
340	C₅×D₃	—	4	4	no	—
341	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂²×D₃	—	2	2	no	—
343	C₂²×D₃	—	2	4	no	—
344	C₂²×D₃	—	8	1	no	—
345	C₂²×D₃	—	8	1	no	—
346	C₃×Q₈	—	8	2	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	8	1	no	—
351	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
352	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
353	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
355	C₂×C₃×C₄	C₅×#41	1	2	yes	—
356	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
357	C₂×Dic₃	—	2	1	no	—
358	C₂×Dic₃	—	2	1	no	—
359	D₁₂	—	2	4	no	—
360	D₁₂	—	2	2	no	—
361	D₁₂	C₂×C₅×Q₈	1	4	yes	—
362	C₄×D₃	—	8	2	no	—
363	C₄×D₃	—	8	2	no	—
364	C₃⋊C₈	—	2	1	no	—
365	C₃⋊C₈	—	2	1	no	—
366	C₃⋊C₈	—	2	2	no	—
367	C₂²×C₅	—	2	1	no	—
368	C₂²×C₅	—	2	1	no	—
369	C₂²×C₅	—	6	4	no	—
370	C₂²×C₅	—	12	2	no	—
371	C₂²×C₅	—	12	2	no	—
372	C₂²×C₅	—	24	4	no	—
373	C₂²×C₅	#946	1	2	yes	—
374	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
375	C₄×C₅	—	2	2	no	—
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	4	2	no	—
378	C₄×C₅	—	4	1	no	—
379	C₄×C₅	—	4	1	no	—
380	C₄×C₅	—	12	1	no	—
381	C₄×C₅	—	12	1	no	—
382	C₄×C₅	#946	1	2	yes	—
383	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
384	C₄×C₅	C₂×#239	1	1	yes	characteristic
385	C₂⁴	—	6	1	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×D₄	—	3	4	no	—
388	C₂×D₄	—	3	2	no	—
389	C₂×D₄	—	6	2	no	—
390	C₂×D₄	—	6	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	6	2	no	—
393	C₂²×C₄	—	6	2	no	—
394	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
395	M₁₆	—	6	2	no	—
396	C₂×C₈	—	3	1	no	—
397	C₂×C₈	—	3	2	no	—
398	C₂×C₈	—	3	1	no	—
399	C₂×C₈	—	6	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	3	1	no	—
405	C₄⋊C₄	—	3	1	no	—
406	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
407	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
408	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
409	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
410	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	6	1	no	—
413	C₂²⋊C₄	—	6	2	no	—
414	C₂²⋊C₄	—	6	2	no	—
415	C₂²⋊C₄	C₅×#67	1	2	yes	—
416	C₄²	—	2	1	no	—
417	C₄²	—	6	1	no	—
418	C₄²	C₂²×C₅×D₃	1	2	yes	—
419	C₃×C₅	#3081	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	—	2	1	no	—
421	C₂²×C₃	—	2	1	no	—
422	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
423	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
424	C₂×D₃	—	2	4	no	—
425	C₂×D₃	—	4	2	no	—
426	C₂×D₃	—	4	2	no	—
427	C₂×D₃	—	8	4	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	4	2	no	—
431	C₃×C₄	—	4	1	no	—
432	C₃×C₄	—	4	1	no	—
433	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
434	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
435	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
436	Dic₃	—	4	1	no	—
437	Dic₃	—	4	1	no	—
438	C₂×C₅	—	2	2	no	—
439	C₂×C₅	—	12	4	no	—
440	C₂×C₅	C₂×#946	1	1	yes	characteristic
441	C₂×C₅	#5835	1	1	yes	characteristic
442	C₂×C₅	#5837	1	1	yes	characteristic
443	C₂³	—	6	2	no	—
444	C₂³	—	6	4	no	—
445	C₂³	—	24	1	no	—
446	C₂³	—	24	1	no	—
447	C₂³	C₂×C₅×#67	1	1	yes	characteristic
448	Q₈	—	8	2	no	—
449	D₄	—	3	4	no	—
450	D₄	—	6	4	no	—
451	D₄	—	6	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	6	1	no	—
456	C₂×C₄	—	6	1	no	—
457	C₂×C₄	—	8	1	no	—
458	C₂×C₄	—	24	2	no	—
459	C₂×C₄	—	24	2	no	—
460	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
461	C₂×C₄	C₅×#239	1	2	yes	—
462	C₂×C₄	C₂×C₅×#67	1	2	yes	—
463	C₂×C₄	C₂×C₅×#67	1	2	yes	—
464	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
465	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
466	C₈	—	6	1	no	—
467	C₈	—	6	1	no	—
468	C₈	—	6	2	no	—
469	C₂×C₃	—	2	2	no	—
470	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
471	C₂×C₃	C₅×#576	1	1	yes	characteristic
472	C₂×C₃	C₅×#577	1	1	yes	characteristic
473	D₃	—	4	4	no	—
474	C₅	#83474	1	1	yes	characteristic, direct product factor, Sylow
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	6	4	no	—
478	C₂²	—	12	2	no	—
479	C₂²	—	12	2	no	—
480	C₂²	—	24	4	no	—
481	C₂²	C₅×#946	1	2	yes	—
482	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	12	1	no	—
489	C₄	—	12	1	no	—
490	C₄	C₅×#946	1	2	yes	—
491	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
492	C₄	C₂×C₅×#239	1	1	yes	characteristic
493	C₃	C₅×#3081	1	1	yes	characteristic, complemented, Sylow
494	C₂	—	2	2	no	—
495	C₂	—	12	4	no	—
496	C₂	C₂×C₅×#946	1	1	yes	characteristic
497	C₂	C₅×#5835	1	1	yes	characteristic
498	C₂	C₅×#5837	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#544	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₅×#544	D₃
hypocenter	C₃	C₅×#3081
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#544

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#544	C₂	semidirect
3. C₅×#5087	C₂	semidirect
4. C₅×#5084	C₂	semidirect
5. C₅×#5066	C₂	semidirect
6. C₅×#5066	C₂	semidirect
8. C₅×#4999	C₂	semidirect
9. C₅×#4998	C₂	semidirect
11. C₅×#4964	C₂	semidirect
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
17. C₃×C₅×#125	C₂²	semidirect
34. C₅×#808	C₂²	semidirect
35. C₅×#808	C₂²	semidirect
36. C₅×#808	C₂²	semidirect
37. C₅×#807	C₂²	semidirect
38. C₅×#807	C₂²	semidirect
39. C₅×#807	C₂²	semidirect
40. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
41. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
42. #83474	C₅	direct (N × H)
43. C₅×#544	D₃	semidirect
60. C₂×C₅×D₁₂	Q₈	semidirect
88. C₃×#544	C₂×C₅	semidirect
90. #5087	C₂×C₅	semidirect
91. #5084	C₂×C₅	semidirect
92. #5066	C₂×C₅	semidirect
93. #5066	C₂×C₅	semidirect
95. #4999	C₂×C₅	semidirect
96. #4998	C₂×C₅	semidirect
98. #4964	C₂×C₅	semidirect
103. C₅×C₄⋊Q₈	C₂×D₃	semidirect
105. C₅×#125	C₂×D₃	semidirect
157. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
159. C₃×#125	C₂²×C₅	semidirect
176. #808	C₂²×C₅	semidirect
177. #808	C₂²×C₅	semidirect
178. #808	C₂²×C₅	semidirect
179. #807	C₂²×C₅	semidirect
180. #807	C₂²×C₅	semidirect
181. #807	C₂²×C₅	semidirect
182. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
183. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
218. #544	C₅×D₃	semidirect
253. C₂×D₁₂	C₅×Q₈	semidirect
311. C₄⋊Q₈	C₂×C₅×D₃	semidirect
313. #125	C₂×C₅×D₃	semidirect
419. C₃×C₅	#3081	semidirect
474. C₅	#83474	direct (N × H)
493. C₃	C₅×#3081	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#544	2
C₅×#5521	2
C₅×#5087	2
C₅×#5084	2
C₅×#5066	2
C₅×#5001	2
C₅×#4999	2
C₅×#4998	2
C₂×C₅×#809	2
C₅×#4964	2
C₅×#3081	3
#83474	5

Subgroups — C5×#83474 #14430762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83474 #14430762