Subgroups — C₅×#83381 #14439381

Order 1920.

1128 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×#535	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#951	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#950	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#932	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5526	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5076	C₂	1	2	yes	maximal, complemented
8	C₅×#5074	C₂	1	2	yes	maximal, complemented
9	C₅×#5060	C₂	1	2	yes	maximal, complemented
10	C₅×#5059	C₂	1	2	yes	maximal, complemented
11	C₅×#4997	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3154	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×#235	C₂²	1	1	yes	characteristic
16	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
17	C₃×C₅×#127	C₂²	1	2	yes	—
18	C₃×C₅×#124	C₂²	1	2	yes	—
19	C₃×C₅×#121	—	2	2	no	—
20	C₃×C₅×#120	—	2	2	no	—
21	C₃×C₅×#117	C₂²	1	1	yes	characteristic
22	C₅×#951	—	2	4	no	—
23	C₅×#950	—	2	4	no	—
24	C₂×C₅×#216	C₂²	1	2	yes	complemented
25	C₂×C₅×#216	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#214	—	2	4	no	—
28	C₂×C₅×#214	C₂²	1	2	yes	—
29	C₂×C₅×#214	C₂²	1	2	yes	—
30	C₂×C₅×#214	C₂²	1	2	yes	—
31	C₂×C₅×#214	C₂²	1	2	yes	complemented
32	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
33	C₅×#932	—	2	4	no	—
34	C₂×C₅×#213	C₂²	1	2	yes	—
35	C₂×C₅×#213	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×#208	C₂²	1	1	yes	characteristic
37	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×#897	—	2	2	no	—
39	C₅×#886	—	2	2	no	—
40	C₅×#875	C₂²	1	2	yes	complemented
41	C₅×#869	C₂²	1	2	yes	complemented
42	C₅×#803	C₂²	1	2	yes	complemented
43	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
44	#83381	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#137	—	3	1	no	—
46	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
47	C₂×C₅×#135	—	3	1	no	—
48	C₂²×C₅×SD₁₆	—	3	1	no	—
49	C₅×#536	—	3	1	no	—
50	C₅×#535	D₃	1	1	yes	characteristic, complemented
51	C₅×#497	—	3	2	no	—
52	C₅×#496	—	3	2	no	—
53	C₅×#495	—	3	2	no	—
54	C₅×#492	—	3	2	no	—
55	C₅×#405	—	3	1	no	—
56	C₂⁴×C₃×C₅	—	2	1	no	—
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	1	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	—	2	4	no	—
65	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
66	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	—	2	1	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₅×#67	—	2	1	no	—
70	C₂²×C₅×Dic₃	—	2	1	no	—
71	C₅×#235	—	2	2	no	—
72	C₅×#235	—	2	2	no	—
73	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
74	C₂×C₄×C₅×D₃	—	2	1	no	—
75	C₂×C₅×Dic₆	—	2	2	no	—
76	C₂×C₅×Dic₆	—	2	2	no	—
77	C₂×C₅×Dic₆	—	2	1	no	—
78	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
79	C₂×C₅×Dic₆	C₂³	1	2	yes	—
80	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
81	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
82	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
83	C₃×C₄²×C₅	C₂³	1	2	yes	—
84	C₅×#216	—	2	2	no	—
85	C₅×#216	—	2	4	no	—
86	C₅×#215	—	2	2	no	—
87	C₅×#214	—	2	4	no	—
88	C₅×#214	—	2	4	no	—
89	C₅×#214	—	2	4	no	—
90	C₅×#214	—	2	2	no	—
91	C₅×#214	—	2	4	no	—
92	C₅×#213	—	2	4	no	—
93	C₅×#213	—	2	2	no	—
94	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
95	C₅×C₄⋊Dic₃	—	2	4	no	—
96	C₅×#208	D₄	1	4	yes	complemented
97	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	complemented
98	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
100	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
101	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×#951	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×#950	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂²×#214	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×#932	C₂×C₅	1	1	yes	characteristic, complemented
106	#5526	C₂×C₅	1	1	yes	characteristic, complemented
107	#5076	C₂×C₅	1	2	yes	complemented
108	#5074	C₂×C₅	1	2	yes	complemented
109	#5060	C₂×C₅	1	2	yes	complemented
110	#5059	C₂×C₅	1	2	yes	complemented
111	#4997	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₅×#41	—	3	1	no	—
113	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
114	C₂²×C₅×Q₈	—	3	1	no	—
115	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
116	C₅×#137	—	6	4	no	—
117	C₅×AGL(1,ℤ/8)	—	6	4	no	—
118	C₅×#135	—	6	4	no	—
119	C₂×C₅×Q₁₆	—	3	2	no	—
120	C₂×C₅×Q₁₆	—	3	1	no	—
121	C₂×C₅×SD₁₆	—	3	1	no	—
122	C₂×C₅×SD₁₆	—	3	2	no	—
123	C₂×C₅×SD₁₆	—	3	2	no	—
124	C₂×C₅×SD₁₆	—	3	2	no	—
125	C₂×C₅×SD₁₆	—	3	1	no	—
126	C₂×C₅×SD₁₆	—	3	2	no	—
127	C₂×C₅×SD₁₆	—	6	4	no	—
128	C₂×C₅×D₈	—	3	2	no	—
129	C₂×C₅×D₈	—	3	1	no	—
130	C₂×C₅×M₁₆	—	3	1	no	—
131	C₂²×C₅×C₈	—	3	1	no	—
132	C₅×C₄⋊Q₈	—	3	2	no	—
133	C₅×#127	C₂×D₃	1	2	yes	—
134	C₅×#124	—	3	2	no	—
135	C₅×#124	C₂×D₃	1	2	yes	—
136	C₅×#123	—	6	2	no	—
137	C₅×C₂²⋊Q₈	—	6	2	no	—
138	C₅×#121	—	2	2	no	—
139	C₅×#120	—	2	2	no	—
140	C₅×#117	C₂×D₃	1	1	yes	characteristic
141	C₅×#97	—	3	2	no	—
142	C₄×C₅×C₈	—	3	2	no	—
143	#3154	—	3	1	no	Sylow
144	C₂³×C₃×C₅	—	2	2	no	—
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	4	2	no	—
147	C₂³×C₃×C₅	—	8	2	no	—
148	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₅×D₃	—	2	1	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×Q₈	—	2	1	no	—
152	C₃×C₅×D₄	—	2	2	no	—
153	C₃×C₅×D₄	—	2	1	no	—
154	C₃×C₅×D₄	—	2	2	no	—
155	C₃×C₅×D₄	—	2	1	no	—
156	C₃×C₅×D₄	—	4	2	no	—
157	C₃×C₅×D₄	—	4	2	no	—
158	C₃×C₅×D₄	—	8	4	no	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	4	2	no	—
161	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
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	2	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
166	C₅×#67	—	4	2	no	—
167	C₂×C₅×Dic₃	—	2	1	no	—
168	C₂×C₅×Dic₃	—	2	2	no	—
169	C₂×C₅×Dic₃	—	4	2	no	—
170	C₅×D₁₂	—	2	1	no	—
171	C₅×D₁₂	—	2	1	no	—
172	C₄×C₅×D₃	—	4	2	no	—
173	C₅×Dic₆	—	2	2	no	—
174	C₅×Dic₆	—	2	1	no	—
175	C₅×Dic₆	—	2	2	no	—
176	C₅×Dic₆	—	2	1	no	—
177	C₅×Dic₆	—	4	2	no	—
178	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
179	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
180	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
181	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
182	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
183	C₂×#235	C₂²×C₅	1	1	yes	characteristic
184	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
185	C₃×#127	C₂²×C₅	1	2	yes	—
186	C₃×#124	C₂²×C₅	1	2	yes	—
187	C₃×#121	—	2	2	no	—
188	C₃×#120	—	2	2	no	—
189	C₃×#117	C₂²×C₅	1	1	yes	characteristic
190	#951	—	2	4	no	—
191	#950	—	2	4	no	—
192	C₂×#216	C₂²×C₅	1	1	yes	characteristic, complemented
193	C₂×#216	C₂²×C₅	1	2	yes	complemented
194	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₂×#214	—	2	4	no	—
196	C₂×#214	C₂²×C₅	1	2	yes	—
197	C₂×#214	C₂²×C₅	1	2	yes	—
198	C₂×#214	C₂²×C₅	1	2	yes	—
199	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
200	C₂×#214	C₂²×C₅	1	2	yes	complemented
201	#932	—	2	4	no	—
202	C₂×#213	C₂²×C₅	1	2	yes	—
203	C₂×#213	C₂²×C₅	1	1	yes	characteristic, complemented
204	C₂×#208	C₂²×C₅	1	1	yes	characteristic
205	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	#897	—	2	2	no	—
207	#886	—	2	2	no	—
208	#875	C₂²×C₅	1	2	yes	complemented
209	#869	C₂²×C₅	1	2	yes	complemented
210	#803	C₂²×C₅	1	2	yes	complemented
211	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
212	C₂⁴×C₅	—	2	1	no	—
213	C₅×#41	—	2	2	no	—
214	C₅×#41	—	2	2	no	—
215	C₅×#41	—	6	2	no	—
216	C₅×#41	—	6	2	no	—
217	C₂×C₅×Q₈	—	3	2	no	—
218	C₂×C₅×Q₈	—	3	1	no	—
219	C₂×C₅×Q₈	—	6	1	no	—
220	C₂×C₅×Q₈	—	6	2	no	—
221	C₂×C₅×Q₈	—	6	2	no	—
222	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
223	C₂×C₅×D₄	—	2	1	no	—
224	C₂×C₅×D₄	—	2	2	no	—
225	C₂×C₅×D₄	—	2	2	no	—
226	C₂×C₅×D₄	—	2	1	no	—
227	C₂×C₅×D₄	—	2	4	no	—
228	C₂×C₅×D₄	—	3	1	no	—
229	C₂×C₅×D₄	—	6	1	no	—
230	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
231	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	—	2	1	no	—
233	C₂²×C₄×C₅	—	6	1	no	—
234	C₂²×C₄×C₅	—	6	1	no	—
235	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
236	C₅×Q₁₆	—	6	2	no	—
237	C₅×Q₁₆	—	6	4	no	—
238	C₅×SD₁₆	—	6	4	no	—
239	C₅×SD₁₆	—	6	4	no	—
240	C₅×SD₁₆	—	6	2	no	—
241	C₅×SD₁₆	—	6	4	no	—
242	C₅×SD₁₆	—	6	4	no	—
243	C₅×SD₁₆	—	6	2	no	—
244	C₅×D₈	—	6	2	no	—
245	C₅×D₈	—	6	4	no	—
246	C₅×M₁₆	—	3	4	no	—
247	C₂×C₅×C₈	—	3	4	no	—
248	C₂×C₅×C₈	—	3	1	no	—
249	C₂×C₅×C₈	—	3	1	no	—
250	C₂×C₅×C₈	—	3	2	no	—
251	C₅×C₄⋊C₄	—	6	4	no	—
252	C₅×C₄⋊C₄	#67	1	2	yes	—
253	C₅×C₂²⋊C₄	—	2	4	no	—
254	C₅×C₂²⋊C₄	—	6	4	no	—
255	C₅×C₂²⋊C₄	#67	1	2	yes	—
256	C₄²×C₅	C₂²×D₃	1	2	yes	—
257	C₂×#137	—	3	1	no	—
258	C₂×AGL(1,ℤ/8)	—	3	1	no	—
259	C₂×#135	—	3	1	no	—
260	C₂²×SD₁₆	—	3	1	no	—
261	#536	—	3	1	no	—
262	#535	C₅×D₃	1	1	yes	characteristic, complemented
263	#497	—	3	2	no	—
264	#496	—	3	2	no	—
265	#495	—	3	2	no	—
266	#492	—	3	2	no	—
267	#405	—	3	1	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	—	4	2	no	—
272	C₂²×C₃×C₅	—	4	4	no	—
273	C₂²×C₃×C₅	—	8	4	no	—
274	C₂²×C₃×C₅	#127	1	2	yes	—
275	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₅×D₃	—	4	1	no	—
277	C₂×C₅×D₃	—	4	2	no	—
278	C₃×C₄×C₅	—	2	4	no	—
279	C₃×C₄×C₅	—	4	1	no	—
280	C₃×C₄×C₅	#127	1	2	yes	—
281	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
283	C₅×Dic₃	—	4	2	no	—
284	C₅×Dic₃	—	4	1	no	—
285	C₂⁴×C₃	—	2	1	no	—
286	C₃×#41	—	2	2	no	—
287	C₃×#41	—	2	2	no	—
288	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₃×D₄	—	2	1	no	—
290	C₂×C₃×D₄	—	2	2	no	—
291	C₂×C₃×D₄	—	2	2	no	—
292	C₂×C₃×D₄	—	2	1	no	—
293	C₂×C₃×D₄	—	2	4	no	—
294	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
295	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
296	C₂²×C₃×C₄	—	2	1	no	—
297	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
298	C₂×#67	—	2	1	no	—
299	C₂²×Dic₃	—	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	—	2	2	no	—
305	C₂×Dic₆	—	2	2	no	—
306	C₂×Dic₆	—	2	1	no	—
307	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
308	C₂×Dic₆	C₂³×C₅	1	2	yes	—
309	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
310	C₃×C₂²⋊C₄	—	2	4	no	—
311	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
312	C₃×C₄²	C₂³×C₅	1	2	yes	—
313	#216	—	2	2	no	—
314	#216	—	2	4	no	—
315	#215	—	2	2	no	—
316	#214	—	2	4	no	—
317	#214	—	2	4	no	—
318	#214	—	2	4	no	—
319	#214	—	2	2	no	—
320	#214	—	2	4	no	—
321	#213	—	2	4	no	—
322	#213	—	2	2	no	—
323	(C₂×D₃)⋊C₄	—	2	4	no	—
324	C₄⋊Dic₃	—	2	4	no	—
325	#208	C₅×D₄	1	4	yes	complemented
326	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	complemented
327	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
328	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
329	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
330	C₂³×C₅	—	2	2	no	—
331	C₂³×C₅	—	2	1	no	—
332	C₂³×C₅	—	4	2	no	—
333	C₂³×C₅	—	6	1	no	—
334	C₂³×C₅	—	8	2	no	—
335	C₂³×C₅	C₂×#67	1	1	yes	characteristic
336	C₅×Q₈	—	2	1	no	—
337	C₅×Q₈	—	2	1	no	—
338	C₅×Q₈	—	6	2	no	—
339	C₅×Q₈	—	6	1	no	—
340	C₅×Q₈	—	6	2	no	—
341	C₅×Q₈	—	6	1	no	—
342	C₅×Q₈	—	12	2	no	—
343	C₅×D₄	—	2	2	no	—
344	C₅×D₄	—	2	1	no	—
345	C₅×D₄	—	2	2	no	—
346	C₅×D₄	—	2	1	no	—
347	C₅×D₄	—	4	2	no	—
348	C₅×D₄	—	4	2	no	—
349	C₅×D₄	—	6	1	no	—
350	C₅×D₄	—	6	1	no	—
351	C₅×D₄	—	8	4	no	—
352	C₅×D₄	—	12	2	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	4	2	no	—
355	C₂×C₄×C₅	—	6	2	no	—
356	C₂×C₄×C₅	—	6	1	no	—
357	C₂×C₄×C₅	—	12	2	no	—
358	C₂×C₄×C₅	—	12	2	no	—
359	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
360	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
361	C₂×C₄×C₅	C₂×#67	1	4	yes	—
362	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
363	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
364	C₅×C₈	—	3	2	no	—
365	C₅×C₈	—	3	2	no	—
366	C₅×C₈	—	3	4	no	—
367	C₂×#41	—	3	1	no	—
368	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
369	C₂²×Q₈	—	3	1	no	—
370	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
371	#137	—	6	4	no	—
372	AGL(1,ℤ/8)	—	6	4	no	—
373	#135	—	6	4	no	—
374	C₂×Q₁₆	—	3	1	no	—
375	C₂×Q₁₆	—	3	2	no	—
376	C₂×SD₁₆	—	3	1	no	—
377	C₂×SD₁₆	—	3	2	no	—
378	C₂×SD₁₆	—	3	2	no	—
379	C₂×SD₁₆	—	3	1	no	—
380	C₂×SD₁₆	—	3	2	no	—
381	C₂×SD₁₆	—	3	2	no	—
382	C₂×SD₁₆	—	6	4	no	—
383	C₂×D₈	—	3	1	no	—
384	C₂×D₈	—	3	2	no	—
385	C₂×M₁₆	—	3	1	no	—
386	C₂²×C₈	—	3	1	no	—
387	C₄⋊Q₈	—	3	2	no	—
388	#127	C₂×C₅×D₃	1	2	yes	—
389	#124	—	3	2	no	—
390	#124	C₂×C₅×D₃	1	2	yes	—
391	#123	—	6	2	no	—
392	C₂²⋊Q₈	—	6	2	no	—
393	#121	—	2	2	no	—
394	#120	—	2	2	no	—
395	#117	C₂×C₅×D₃	1	1	yes	characteristic
396	#97	—	3	2	no	—
397	C₄×C₈	—	3	2	no	—
398	C₂×C₃×C₅	—	2	2	no	—
399	C₂×C₃×C₅	—	8	1	no	—
400	C₂×C₃×C₅	—	8	2	no	—
401	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
402	C₂×C₃×C₅	#577	1	2	yes	—
403	C₅×D₃	—	8	1	no	—
404	C₂³×C₃	—	2	2	no	—
405	C₂³×C₃	—	2	1	no	—
406	C₂³×C₃	—	4	2	no	—
407	C₂³×C₃	—	8	2	no	—
408	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
409	C₂²×D₃	—	2	1	no	—
410	C₃×Q₈	—	2	1	no	—
411	C₃×Q₈	—	2	1	no	—
412	C₃×D₄	—	2	2	no	—
413	C₃×D₄	—	2	1	no	—
414	C₃×D₄	—	2	2	no	—
415	C₃×D₄	—	2	1	no	—
416	C₃×D₄	—	4	2	no	—
417	C₃×D₄	—	4	2	no	—
418	C₃×D₄	—	8	4	no	—
419	C₂×C₃×C₄	—	2	1	no	—
420	C₂×C₃×C₄	—	4	2	no	—
421	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
422	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
423	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
424	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
426	#67	—	4	2	no	—
427	C₂×Dic₃	—	2	1	no	—
428	C₂×Dic₃	—	2	2	no	—
429	C₂×Dic₃	—	4	2	no	—
430	D₁₂	—	2	1	no	—
431	D₁₂	—	2	1	no	—
432	C₄×D₃	—	4	2	no	—
433	Dic₆	—	2	2	no	—
434	Dic₆	—	2	1	no	—
435	Dic₆	—	2	2	no	—
436	Dic₆	—	2	1	no	—
437	Dic₆	—	4	2	no	—
438	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
439	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
440	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	4	1	no	—
443	C₂²×C₅	—	4	2	no	—
444	C₂²×C₅	—	4	2	no	—
445	C₂²×C₅	—	4	4	no	—
446	C₂²×C₅	—	8	4	no	—
447	C₂²×C₅	—	12	1	no	—
448	C₂²×C₅	—	12	2	no	—
449	C₂²×C₅	#940	1	2	yes	—
450	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
451	C₄×C₅	—	2	4	no	—
452	C₄×C₅	—	4	1	no	—
453	C₄×C₅	—	12	1	no	—
454	C₄×C₅	—	12	2	no	—
455	C₄×C₅	#940	1	2	yes	—
456	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
457	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
458	C₂⁴	—	2	1	no	—
459	#41	—	2	2	no	—
460	#41	—	2	2	no	—
461	#41	—	6	2	no	—
462	#41	—	6	2	no	—
463	C₂×Q₈	—	3	2	no	—
464	C₂×Q₈	—	3	1	no	—
465	C₂×Q₈	—	6	1	no	—
466	C₂×Q₈	—	6	2	no	—
467	C₂×Q₈	—	6	2	no	—
468	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	3	1	no	—
475	C₂×D₄	—	6	1	no	—
476	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
477	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	6	1	no	—
480	C₂²×C₄	—	6	1	no	—
481	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
482	Q₁₆	—	6	2	no	—
483	Q₁₆	—	6	4	no	—
484	SD₁₆	—	6	4	no	—
485	SD₁₆	—	6	4	no	—
486	SD₁₆	—	6	2	no	—
487	SD₁₆	—	6	4	no	—
488	SD₁₆	—	6	4	no	—
489	SD₁₆	—	6	2	no	—
490	D₈	—	6	2	no	—
491	D₈	—	6	4	no	—
492	M₁₆	—	3	4	no	—
493	C₂×C₈	—	3	4	no	—
494	C₂×C₈	—	3	1	no	—
495	C₂×C₈	—	3	2	no	—
496	C₂×C₈	—	3	1	no	—
497	C₄⋊C₄	—	6	4	no	—
498	C₄⋊C₄	C₅×#67	1	2	yes	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	6	4	no	—
501	C₂²⋊C₄	C₅×#67	1	2	yes	—
502	C₄²	C₂²×C₅×D₃	1	2	yes	—
503	C₃×C₅	#3154	1	1	yes	characteristic, complemented, Hall
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	4	1	no	—
506	C₂²×C₃	—	4	2	no	—
507	C₂²×C₃	—	4	2	no	—
508	C₂²×C₃	—	4	4	no	—
509	C₂²×C₃	—	8	4	no	—
510	C₂²×C₃	C₅×#127	1	2	yes	—
511	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
512	C₂×D₃	—	4	1	no	—
513	C₂×D₃	—	4	2	no	—
514	C₃×C₄	—	2	4	no	—
515	C₃×C₄	—	4	1	no	—
516	C₃×C₄	C₅×#127	1	2	yes	—
517	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
518	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
519	Dic₃	—	4	2	no	—
520	Dic₃	—	4	1	no	—
521	C₂×C₅	—	2	2	no	—
522	C₂×C₅	—	8	2	no	—
523	C₂×C₅	—	8	1	no	—
524	C₂×C₅	—	24	1	no	—
525	C₂×C₅	C₂×#940	1	1	yes	characteristic
526	C₂×C₅	#5836	1	2	yes	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	6	1	no	—
531	C₂³	—	8	2	no	—
532	C₂³	C₂×C₅×#67	1	1	yes	characteristic
533	Q₈	—	2	1	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	6	2	no	—
536	Q₈	—	6	1	no	—
537	Q₈	—	6	2	no	—
538	Q₈	—	6	1	no	—
539	Q₈	—	12	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	1	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	1	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	6	1	no	—
547	D₄	—	6	1	no	—
548	D₄	—	8	4	no	—
549	D₄	—	12	2	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	6	2	no	—
553	C₂×C₄	—	6	1	no	—
554	C₂×C₄	—	12	2	no	—
555	C₂×C₄	—	12	2	no	—
556	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
557	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
558	C₂×C₄	C₂×C₅×#67	1	4	yes	—
559	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
560	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
561	C₈	—	3	2	no	—
562	C₈	—	3	2	no	—
563	C₈	—	3	4	no	—
564	C₂×C₃	—	2	2	no	—
565	C₂×C₃	—	8	2	no	—
566	C₂×C₃	—	8	1	no	—
567	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
568	C₂×C₃	C₅×#577	1	2	yes	—
569	D₃	—	8	1	no	—
570	C₅	#83381	1	1	yes	characteristic, direct product factor, Sylow
571	C₂²	—	2	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	8	4	no	—
577	C₂²	—	12	1	no	—
578	C₂²	—	12	2	no	—
579	C₂²	C₅×#940	1	2	yes	—
580	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
581	C₄	—	2	4	no	—
582	C₄	—	4	1	no	—
583	C₄	—	12	1	no	—
584	C₄	—	12	2	no	—
585	C₄	C₅×#940	1	2	yes	—
586	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
587	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
588	C₃	C₅×#3154	1	1	yes	characteristic, complemented, Sylow
589	C₂	—	2	2	no	—
590	C₂	—	8	2	no	—
591	C₂	—	8	1	no	—
592	C₂	—	24	1	no	—
593	C₂	C₂×C₅×#940	1	1	yes	characteristic
594	C₂	C₅×#5836	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×#535	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#535	D₃
hypocenter	C₃	C₅×#3154
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#535

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#535	C₂	semidirect
2. C₂×C₅×#951	C₂	semidirect
3. C₂×C₅×#950	C₂	semidirect
4. C₂²×C₅×#214	C₂	semidirect
5. C₂×C₅×#932	C₂	semidirect
6. C₅×#5526	C₂	semidirect
7. C₅×#5076	C₂	semidirect
8. C₅×#5074	C₂	semidirect
9. C₅×#5060	C₂	semidirect
10. C₅×#5059	C₂	semidirect
11. C₅×#4997	C₂	semidirect
24. C₂×C₅×#216	C₂²	semidirect
25. C₂×C₅×#216	C₂²	semidirect
26. C₂×C₅×#215	C₂²	semidirect
31. C₂×C₅×#214	C₂²	semidirect
32. C₂×C₅×#214	C₂²	semidirect
35. C₂×C₅×#213	C₂²	semidirect
40. C₅×#875	C₂²	semidirect
41. C₅×#869	C₂²	semidirect
42. C₅×#803	C₂²	semidirect
43. C₄×C₅×C₃⋊C₈	C₂²	semidirect
44. #83381	C₅	direct (N × H)
50. C₅×#535	D₃	semidirect
96. C₅×#208	D₄	semidirect
97. C₂×C₅×C₃⋊C₈	D₄	semidirect
101. C₃×#535	C₂×C₅	semidirect
102. C₂×#951	C₂×C₅	semidirect
103. C₂×#950	C₂×C₅	semidirect
104. C₂²×#214	C₂×C₅	semidirect
105. C₂×#932	C₂×C₅	semidirect
106. #5526	C₂×C₅	semidirect
107. #5076	C₂×C₅	semidirect
108. #5074	C₂×C₅	semidirect
109. #5060	C₂×C₅	semidirect
110. #5059	C₂×C₅	semidirect
111. #4997	C₂×C₅	semidirect
192. C₂×#216	C₂²×C₅	semidirect
193. C₂×#216	C₂²×C₅	semidirect
194. C₂×#215	C₂²×C₅	semidirect
199. C₂×#214	C₂²×C₅	semidirect
200. C₂×#214	C₂²×C₅	semidirect
203. C₂×#213	C₂²×C₅	semidirect
208. #875	C₂²×C₅	semidirect
209. #869	C₂²×C₅	semidirect
210. #803	C₂²×C₅	semidirect
211. C₄×C₃⋊C₈	C₂²×C₅	semidirect
262. #535	C₅×D₃	semidirect
325. #208	C₅×D₄	semidirect
326. C₂×C₃⋊C₈	C₅×D₄	semidirect
503. C₃×C₅	#3154	semidirect
570. C₅	#83381	direct (N × H)
588. C₃	C₅×#3154	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#535	2
C₂×C₅×#951	2
C₂×C₅×#950	2
C₂²×C₅×#214	2
C₂×C₅×#932	2
C₅×#5526	2
C₅×#5076	2
C₅×#5074	2
C₅×#5060	2
C₅×#5059	2
C₅×#4997	2
C₅×#3154	3
#83381	5

Subgroups — C5×#83381 #14439381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83381 #14439381