Subgroups — C₅×#79241 #14430684

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5522	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#890	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5133	C₂	1	1	yes	maximal, characteristic
5	C₅×#5118	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4995	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4966	C₂	1	1	yes	maximal, characteristic
8	C₅×#4891	C₂	1	2	yes	maximal, complemented
9	C₅×#4877	C₂	1	2	yes	maximal, complemented
10	C₅×#4871	C₂	1	2	yes	maximal, complemented
11	C₅×#4857	C₂	1	2	yes	maximal, complemented
12	C₅×#3080	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
20	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×#208	C₂²	1	1	yes	characteristic
22	C₅×#893	C₂²	1	1	yes	characteristic
23	C₅×#893	C₂²	1	1	yes	characteristic
24	C₅×#890	—	2	1	no	—
25	C₅×#890	—	2	1	no	—
26	C₅×#890	C₂²	1	2	yes	—
27	C₅×#890	C₂²	1	2	yes	—
28	C₅×#887	C₂²	1	1	yes	characteristic
29	C₅×#887	C₂²	1	1	yes	characteristic
30	C₅×#67⋊C₄	—	2	1	no	—
31	C₅×#67⋊C₄	—	2	1	no	—
32	C₅×#872	—	2	1	no	—
33	C₄²×C₅×D₃	—	2	1	no	—
34	C₃×C₅×#107	C₂²	1	2	yes	—
35	C₃×C₅×#106	C₂²	1	2	yes	—
36	C₅×#821	C₂²	1	2	yes	—
37	C₅×#816	C₂²	1	2	yes	—
38	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
39	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
40	C₅×#810	C₂²	1	2	yes	—
41	C₅×#809	C₂²	1	2	yes	—
42	C₅×#808	C₂²	1	2	yes	—
43	C₅×#807	C₂²	1	2	yes	—
44	#79241	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#125	—	3	1	no	—
46	C₄×C₅×#41	—	3	1	no	—
47	C₅×#479	—	3	2	no	—
48	C₅×#479	—	3	2	no	—
49	C₅×#478	—	3	2	no	—
50	C₅×#478	—	3	2	no	—
51	C₅×#428	—	3	1	no	—
52	C₅×#428	D₃	1	1	yes	characteristic, complemented
53	C₅×#423	—	3	1	no	—
54	C₅×#417	—	3	1	no	—
55	C₅×#417	—	3	1	no	—
56	C₂²×C₃×C₄×C₅	—	2	1	no	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₅×#67	—	2	1	no	—
59	C₂²×C₅×Dic₃	—	2	1	no	—
60	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₅×#235	—	2	2	no	—
63	C₅×#235	Q₈	1	4	yes	—
64	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
65	C₂×C₄×C₅×D₃	—	2	1	no	—
66	C₂×C₄×C₅×D₃	—	2	1	no	—
67	C₂×C₄×C₅×D₃	—	2	1	no	—
68	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
69	C₃×C₅×M₁₆	—	2	2	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₃×C₄²×C₅	—	2	1	no	—
77	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
78	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
79	C₅×C₄⋊Dic₃	—	2	1	no	—
80	C₅×C₄⋊Dic₃	—	2	2	no	—
81	C₅×C₄⋊Dic₃	—	2	2	no	—
82	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
83	C₅×Dic₃⋊C₄	—	2	1	no	—
84	C₅×Dic₃⋊C₄	—	2	1	no	—
85	C₅×Dic₃⋊C₄	—	2	2	no	—
86	C₅×Dic₃⋊C₄	—	2	2	no	—
87	C₄×C₅×Dic₃	—	2	1	no	—
88	C₄×C₅×Dic₃	—	2	1	no	—
89	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
90	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
91	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
93	C₅×#208	—	2	2	no	—
94	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
95	#5522	C₂×C₅	1	1	yes	characteristic
96	C₂×#890	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#428	C₂×C₅	1	1	yes	characteristic, complemented
98	#5133	C₂×C₅	1	1	yes	characteristic
99	#5118	C₂×C₅	1	1	yes	characteristic, complemented
100	#4995	C₂×C₅	1	1	yes	characteristic, complemented
101	#4966	C₂×C₅	1	1	yes	characteristic
102	#4891	C₂×C₅	1	2	yes	complemented
103	#4877	C₂×C₅	1	2	yes	complemented
104	#4871	C₂×C₅	1	2	yes	complemented
105	#4857	C₂×C₅	1	2	yes	complemented
106	C₂×C₅×#41	—	3	1	no	—
107	C₂×C₅×M₁₆	—	3	1	no	—
108	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
109	C₅×#125	—	3	2	no	—
110	C₅×#125	—	3	2	no	—
111	C₅×#125	—	6	1	no	—
112	C₅×#125	—	6	1	no	—
113	C₄×C₅×Q₈	—	3	1	no	—
114	C₄×C₅×Q₈	—	3	1	no	—
115	C₄×C₅×D₄	—	3	1	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	6	1	no	—
118	C₄×C₅×D₄	—	6	1	no	—
119	C₅×#117	—	6	1	no	—
120	C₅×#117	C₂×D₃	1	1	yes	characteristic
121	C₂×C₅×C₄⋊C₄	—	3	1	no	—
122	C₂×C₅×C₄⋊C₄	—	6	1	no	—
123	C₂×C₅×C₄⋊C₄	—	6	1	no	—
124	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
125	C₂×C₄²×C₅	—	3	1	no	—
126	C₂×C₄²×C₅	—	6	1	no	—
127	C₅×#107	—	3	2	no	—
128	C₅×#107	C₂×D₃	1	2	yes	—
129	C₅×#106	—	3	2	no	—
130	C₅×#106	C₂×D₃	1	2	yes	—
131	C₅×C₄⋊C₈	—	3	2	no	—
132	C₅×C₄⋊C₈	—	3	2	no	—
133	C₅×#103	—	3	2	no	—
134	C₅×#103	—	3	2	no	—
135	C₅×#102	—	3	2	no	—
136	C₅×#102	—	3	2	no	—
137	#3080	—	3	1	no	Sylow
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₅×D₃	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	4	2	no	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
146	C₂×C₃×C₄×C₅	#41	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₅×#67	—	2	4	no	—
149	C₂×C₅×Dic₃	—	2	1	no	—
150	C₂×C₅×Dic₃	—	2	2	no	—
151	C₂×C₅×Dic₃	—	4	1	no	—
152	C₂×C₅×Dic₃	—	4	1	no	—
153	C₂×C₅×Dic₃	—	4	2	no	—
154	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
158	C₅×D₁₂	—	2	1	no	—
159	C₅×D₁₂	C₂×Q₈	1	2	yes	—
160	C₄×C₅×D₃	—	2	4	no	—
161	C₄×C₅×D₃	—	4	2	no	—
162	C₄×C₅×D₃	—	4	2	no	—
163	C₅×Dic₆	—	2	1	no	—
164	C₅×Dic₆	C₂×Q₈	1	2	yes	—
165	C₃×C₅×C₈	—	2	2	no	—
166	C₅×C₃⋊C₈	—	2	2	no	—
167	C₂×#235	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
169	C₃×#117	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₄⋊Dic₃	—	2	1	no	—
172	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
173	C₂×Dic₃⋊C₄	—	2	1	no	—
174	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
175	C₂×#208	C₂²×C₅	1	1	yes	characteristic
176	#893	C₂²×C₅	1	1	yes	characteristic
177	#893	C₂²×C₅	1	1	yes	characteristic
178	#890	—	2	1	no	—
179	#890	—	2	1	no	—
180	#890	C₂²×C₅	1	2	yes	—
181	#890	C₂²×C₅	1	2	yes	—
182	#887	C₂²×C₅	1	1	yes	characteristic
183	#887	C₂²×C₅	1	1	yes	characteristic
184	#67⋊C₄	—	2	1	no	—
185	#67⋊C₄	—	2	1	no	—
186	#872	—	2	1	no	—
187	C₄²×D₃	—	2	1	no	—
188	C₃×#107	C₂²×C₅	1	2	yes	—
189	C₃×#106	C₂²×C₅	1	2	yes	—
190	#821	C₂²×C₅	1	2	yes	—
191	#816	C₂²×C₅	1	2	yes	—
192	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
193	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
194	#810	C₂²×C₅	1	2	yes	—
195	#809	C₂²×C₅	1	2	yes	—
196	#808	C₂²×C₅	1	2	yes	—
197	#807	C₂²×C₅	1	2	yes	—
198	C₅×#41	—	3	4	no	—
199	C₅×#41	—	6	2	no	—
200	C₂×C₅×Q₈	—	3	1	no	—
201	C₂×C₅×D₄	—	3	1	no	—
202	C₂×C₅×D₄	—	6	1	no	—
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	3	1	no	—
205	C₂²×C₄×C₅	—	3	1	no	—
206	C₂²×C₄×C₅	—	6	1	no	—
207	C₂²×C₄×C₅	—	6	1	no	—
208	C₂²×C₄×C₅	—	6	1	no	—
209	C₂²×C₄×C₅	—	6	1	no	—
210	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
211	C₅×M₁₆	—	2	2	no	—
212	C₅×M₁₆	—	6	2	no	—
213	C₂×C₅×C₈	—	3	2	no	—
214	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	3	2	no	—
217	C₅×C₄⋊C₄	—	6	2	no	—
218	C₅×C₄⋊C₄	—	6	2	no	—
219	C₅×C₄⋊C₄	—	6	2	no	—
220	C₅×C₄⋊C₄	—	6	2	no	—
221	C₅×C₄⋊C₄	—	6	1	no	—
222	C₅×C₄⋊C₄	—	6	1	no	—
223	C₅×C₄⋊C₄	—	6	1	no	—
224	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
225	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
226	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
227	C₅×C₂²⋊C₄	—	2	1	no	—
228	C₅×C₂²⋊C₄	—	6	1	no	—
229	C₅×C₂²⋊C₄	—	6	1	no	—
230	C₄²×C₅	—	2	1	no	—
231	C₄²×C₅	—	3	1	no	—
232	C₄²×C₅	—	3	1	no	—
233	C₄²×C₅	—	3	1	no	—
234	C₄²×C₅	—	3	1	no	—
235	C₄²×C₅	—	6	1	no	—
236	C₄²×C₅	—	6	1	no	—
237	C₂×#125	—	3	1	no	—
238	C₄×#41	—	3	1	no	—
239	#479	—	3	2	no	—
240	#479	—	3	2	no	—
241	#478	—	3	2	no	—
242	#478	—	3	2	no	—
243	#428	—	3	1	no	—
244	#428	C₅×D₃	1	1	yes	characteristic, complemented
245	#423	—	3	1	no	—
246	#417	—	3	1	no	—
247	#417	—	3	1	no	—
248	C₂²×C₃×C₅	—	2	1	no	—
249	C₂²×C₃×C₅	—	2	1	no	—
250	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
251	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₅×D₃	—	2	2	no	—
253	C₂×C₅×D₃	—	4	1	no	—
254	C₂×C₅×D₃	—	4	1	no	—
255	C₃×C₄×C₅	—	4	1	no	—
256	C₃×C₄×C₅	—	4	1	no	—
257	C₃×C₄×C₅	—	4	2	no	—
258	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
259	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
260	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₅×Dic₃	—	2	2	no	—
262	C₅×Dic₃	—	2	1	no	—
263	C₅×Dic₃	—	2	1	no	—
264	C₅×Dic₃	—	2	1	no	—
265	C₅×Dic₃	—	2	1	no	—
266	C₅×Dic₃	—	4	2	no	—
267	C₂²×C₃×C₄	—	2	1	no	—
268	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
269	C₂×#67	—	2	1	no	—
270	C₂²×Dic₃	—	2	1	no	—
271	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
272	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
273	#235	—	2	2	no	—
274	#235	C₅×Q₈	1	4	yes	—
275	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₄×D₃	—	2	1	no	—
277	C₂×C₄×D₃	—	2	1	no	—
278	C₂×C₄×D₃	—	2	1	no	—
279	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
280	C₃×M₁₆	—	2	2	no	—
281	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
282	C₃×C₄⋊C₄	—	2	1	no	—
283	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
284	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
285	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
286	C₃×C₂²⋊C₄	—	2	1	no	—
287	C₃×C₄²	—	2	1	no	—
288	(C₂×D₃)⋊C₄	—	2	1	no	—
289	(C₂×D₃)⋊C₄	—	2	1	no	—
290	C₄⋊Dic₃	—	2	1	no	—
291	C₄⋊Dic₃	—	2	2	no	—
292	C₄⋊Dic₃	—	2	2	no	—
293	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
294	Dic₃⋊C₄	—	2	1	no	—
295	Dic₃⋊C₄	—	2	1	no	—
296	Dic₃⋊C₄	—	2	2	no	—
297	Dic₃⋊C₄	—	2	2	no	—
298	C₄×Dic₃	—	2	1	no	—
299	C₄×Dic₃	—	2	1	no	—
300	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
301	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
302	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
303	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
304	#208	—	2	2	no	—
305	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
306	C₂³×C₅	—	6	1	no	—
307	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
308	C₅×Q₈	—	3	2	no	—
309	C₅×Q₈	—	6	1	no	—
310	C₅×D₄	—	3	2	no	—
311	C₅×D₄	—	6	4	no	—
312	C₅×D₄	—	6	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	3	1	no	—
317	C₂×C₄×C₅	—	3	1	no	—
318	C₂×C₄×C₅	—	3	1	no	—
319	C₂×C₄×C₅	—	3	1	no	—
320	C₂×C₄×C₅	—	4	2	no	—
321	C₂×C₄×C₅	—	6	1	no	—
322	C₂×C₄×C₅	—	6	4	no	—
323	C₂×C₄×C₅	—	6	2	no	—
324	C₂×C₄×C₅	—	12	2	no	—
325	C₂×C₄×C₅	—	12	2	no	—
326	C₂×C₄×C₅	—	12	1	no	—
327	C₂×C₄×C₅	—	12	1	no	—
328	C₂×C₄×C₅	—	12	2	no	—
329	C₂×C₄×C₅	#235	1	2	yes	—
330	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
332	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
333	C₅×C₈	—	2	2	no	—
334	C₅×C₈	—	6	2	no	—
335	C₂×#41	—	3	1	no	—
336	C₂×M₁₆	—	3	1	no	—
337	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
338	#125	—	3	2	no	—
339	#125	—	3	2	no	—
340	#125	—	6	1	no	—
341	#125	—	6	1	no	—
342	C₄×Q₈	—	3	1	no	—
343	C₄×Q₈	—	3	1	no	—
344	C₄×D₄	—	3	1	no	—
345	C₄×D₄	—	3	1	no	—
346	C₄×D₄	—	6	1	no	—
347	C₄×D₄	—	6	1	no	—
348	#117	—	6	1	no	—
349	#117	C₂×C₅×D₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	—	3	1	no	—
351	C₂×C₄⋊C₄	—	6	1	no	—
352	C₂×C₄⋊C₄	—	6	1	no	—
353	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
354	C₂×C₄²	—	3	1	no	—
355	C₂×C₄²	—	6	1	no	—
356	#107	—	3	2	no	—
357	#107	C₂×C₅×D₃	1	2	yes	—
358	#106	—	3	2	no	—
359	#106	C₂×C₅×D₃	1	2	yes	—
360	C₄⋊C₈	—	3	2	no	—
361	C₄⋊C₈	—	3	2	no	—
362	#103	—	3	2	no	—
363	#103	—	3	2	no	—
364	#102	—	3	2	no	—
365	#102	—	3	2	no	—
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
368	C₂×C₃×C₅	#575	1	1	yes	characteristic
369	C₂×C₃×C₅	#575	1	1	yes	characteristic
370	C₅×D₃	—	4	2	no	—
371	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂²×D₃	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	4	2	no	—
377	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
379	C₂×C₃×C₄	C₅×#41	1	2	yes	—
380	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
381	#67	—	2	4	no	—
382	C₂×Dic₃	—	2	1	no	—
383	C₂×Dic₃	—	2	2	no	—
384	C₂×Dic₃	—	4	1	no	—
385	C₂×Dic₃	—	4	1	no	—
386	C₂×Dic₃	—	4	2	no	—
387	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
388	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
391	D₁₂	—	2	1	no	—
392	D₁₂	C₂×C₅×Q₈	1	2	yes	—
393	C₄×D₃	—	2	4	no	—
394	C₄×D₃	—	4	2	no	—
395	C₄×D₃	—	4	2	no	—
396	Dic₆	—	2	1	no	—
397	Dic₆	C₂×C₅×Q₈	1	2	yes	—
398	C₃×C₈	—	2	2	no	—
399	C₃⋊C₈	—	2	2	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	6	2	no	—
403	C₂²×C₅	—	12	1	no	—
404	C₂²×C₅	—	12	1	no	—
405	C₂²×C₅	#896	1	2	yes	—
406	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
407	C₄×C₅	—	4	2	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	1	no	—
410	C₄×C₅	—	6	2	no	—
411	C₄×C₅	—	6	1	no	—
412	C₄×C₅	—	6	1	no	—
413	C₄×C₅	—	6	1	no	—
414	C₄×C₅	—	6	1	no	—
415	C₄×C₅	—	12	2	no	—
416	C₄×C₅	#896	1	2	yes	—
417	C₄×C₅	C₂×#235	1	1	yes	characteristic
418	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
419	#41	—	3	4	no	—
420	#41	—	6	2	no	—
421	C₂×Q₈	—	3	1	no	—
422	C₂×D₄	—	3	1	no	—
423	C₂×D₄	—	6	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	3	1	no	—
426	C₂²×C₄	—	3	1	no	—
427	C₂²×C₄	—	6	1	no	—
428	C₂²×C₄	—	6	1	no	—
429	C₂²×C₄	—	6	1	no	—
430	C₂²×C₄	—	6	1	no	—
431	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
432	M₁₆	—	2	2	no	—
433	M₁₆	—	6	2	no	—
434	C₂×C₈	—	3	2	no	—
435	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	3	2	no	—
438	C₄⋊C₄	—	6	2	no	—
439	C₄⋊C₄	—	6	2	no	—
440	C₄⋊C₄	—	6	2	no	—
441	C₄⋊C₄	—	6	2	no	—
442	C₄⋊C₄	—	6	1	no	—
443	C₄⋊C₄	—	6	1	no	—
444	C₄⋊C₄	—	6	1	no	—
445	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
446	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
447	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	6	1	no	—
450	C₂²⋊C₄	—	6	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	3	1	no	—
453	C₄²	—	3	1	no	—
454	C₄²	—	3	1	no	—
455	C₄²	—	3	1	no	—
456	C₄²	—	6	1	no	—
457	C₄²	—	6	1	no	—
458	C₃×C₅	#3080	1	1	yes	characteristic, complemented, Hall
459	C₂²×C₃	—	2	1	no	—
460	C₂²×C₃	—	2	1	no	—
461	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
462	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
463	C₂×D₃	—	2	2	no	—
464	C₂×D₃	—	4	1	no	—
465	C₂×D₃	—	4	1	no	—
466	C₃×C₄	—	4	1	no	—
467	C₃×C₄	—	4	1	no	—
468	C₃×C₄	—	4	2	no	—
469	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
470	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
471	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
472	Dic₃	—	2	2	no	—
473	Dic₃	—	2	1	no	—
474	Dic₃	—	2	1	no	—
475	Dic₃	—	2	1	no	—
476	Dic₃	—	2	1	no	—
477	Dic₃	—	4	2	no	—
478	C₂×C₅	—	2	2	no	—
479	C₂×C₅	—	12	2	no	—
480	C₂×C₅	C₂×#896	1	1	yes	characteristic
481	C₂×C₅	#5773	1	1	yes	characteristic
482	C₂×C₅	#5777	1	1	yes	characteristic
483	C₂³	—	6	1	no	—
484	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
485	Q₈	—	3	2	no	—
486	Q₈	—	6	1	no	—
487	D₄	—	3	2	no	—
488	D₄	—	6	4	no	—
489	D₄	—	6	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	3	1	no	—
494	C₂×C₄	—	3	1	no	—
495	C₂×C₄	—	3	1	no	—
496	C₂×C₄	—	3	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	6	1	no	—
499	C₂×C₄	—	6	4	no	—
500	C₂×C₄	—	6	2	no	—
501	C₂×C₄	—	12	2	no	—
502	C₂×C₄	—	12	2	no	—
503	C₂×C₄	—	12	1	no	—
504	C₂×C₄	—	12	1	no	—
505	C₂×C₄	—	12	2	no	—
506	C₂×C₄	C₅×#235	1	2	yes	—
507	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
508	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
509	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
510	C₈	—	2	2	no	—
511	C₈	—	6	2	no	—
512	C₂×C₃	—	2	2	no	—
513	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
514	C₂×C₃	C₅×#575	1	1	yes	characteristic
515	C₂×C₃	C₅×#575	1	1	yes	characteristic
516	D₃	—	4	2	no	—
517	C₅	#79241	1	1	yes	characteristic, direct product factor, Sylow
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	6	2	no	—
521	C₂²	—	12	1	no	—
522	C₂²	—	12	1	no	—
523	C₂²	C₅×#896	1	2	yes	—
524	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
525	C₄	—	4	2	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	6	2	no	—
529	C₄	—	6	1	no	—
530	C₄	—	6	1	no	—
531	C₄	—	6	1	no	—
532	C₄	—	6	1	no	—
533	C₄	—	12	2	no	—
534	C₄	C₅×#896	1	2	yes	—
535	C₄	C₂×C₅×#235	1	1	yes	characteristic
536	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
537	C₃	C₅×#3080	1	1	yes	characteristic, complemented, Sylow
538	C₂	—	2	2	no	—
539	C₂	—	12	2	no	—
540	C₂	C₂×C₅×#896	1	1	yes	characteristic
541	C₂	C₅×#5773	1	1	yes	characteristic
542	C₂	C₅×#5777	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#428	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#235	C₂²
hypercenter	C₅×#428	D₃
hypocenter	C₃	C₅×#3080
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#428

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#890	C₂	semidirect
3. C₃×C₅×#428	C₂	semidirect
5. C₅×#5118	C₂	semidirect
6. C₅×#4995	C₂	semidirect
8. C₅×#4891	C₂	semidirect
9. C₅×#4877	C₂	semidirect
10. C₅×#4871	C₂	semidirect
11. C₅×#4857	C₂	semidirect
44. #79241	C₅	direct (N × H)
52. C₅×#428	D₃	semidirect
96. C₂×#890	C₂×C₅	semidirect
97. C₃×#428	C₂×C₅	semidirect
99. #5118	C₂×C₅	semidirect
100. #4995	C₂×C₅	semidirect
102. #4891	C₂×C₅	semidirect
103. #4877	C₂×C₅	semidirect
104. #4871	C₂×C₅	semidirect
105. #4857	C₂×C₅	semidirect
244. #428	C₅×D₃	semidirect
458. C₃×C₅	#3080	semidirect
517. C₅	#79241	direct (N × H)
537. C₃	C₅×#3080	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5522	2
C₂×C₅×#890	2
C₃×C₅×#428	2
C₅×#5133	2
C₅×#5118	2
C₅×#4995	2
C₅×#4966	2
C₅×#4891	2
C₅×#4877	2
C₅×#4871	2
C₅×#4857	2
C₅×#3080	3
#79241	5

Subgroups — C5×#79241 #14430684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79241 #14430684