Subgroups — C₅×#83664 #14459931

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5551	C₂	1	1	yes	maximal, characteristic
3	C₅×#5093	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5051	C₂	1	2	yes	maximal, complemented
6	C₅×#5047	C₂	1	2	yes	maximal, complemented
7	C₅×#5031	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×#215	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5002	C₂	1	2	yes	maximal, complemented
11	C₅×#4996	C₂	1	2	yes	maximal, complemented
12	C₅×#3302	—	3	1	no	maximal, Hall
13	C₂×C₅×#235	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#126	—	2	2	no	—
16	C₃×C₅×#124	—	2	1	no	—
17	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₃×C₄×C₅×Q₈	—	2	1	no	—
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₃×C₅×#117	C₂²	1	2	yes	—
22	C₂×C₅×#216	C₂²	1	2	yes	—
23	C₂×C₅×#215	C₂²	1	1	yes	characteristic
24	C₅×#938	—	2	1	no	—
25	C₅×#924	C₂²	1	2	yes	—
26	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
27	C₅×D₃×C₄⋊C₄	—	2	1	no	—
28	C₅×#883	—	2	2	no	—
29	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
30	C₅×#869	C₂²	1	1	yes	characteristic
31	C₅×#835	C₂²	1	1	yes	characteristic
32	C₅×#830	C₂²	1	2	yes	—
33	C₅×#810	C₂²	1	2	yes	—
34	C₅×#810	C₂²	1	2	yes	—
35	C₅×#810	C₂²	1	2	yes	—
36	C₅×#809	C₂²	1	1	yes	characteristic
37	C₅×#809	C₂²	1	2	yes	—
38	C₅×#808	C₂²	1	1	yes	characteristic
39	C₅×#807	C₂²	1	2	yes	—
40	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	#83664	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#556	D₃	1	1	yes	characteristic, complemented
44	C₅×#547	—	3	1	no	—
45	C₅×#487	—	3	1	no	—
46	C₅×#485	—	3	2	no	—
47	C₅×#474	—	3	1	no	—
48	C₅×#467	—	3	2	no	—
49	C₅×#462	—	3	1	no	—
50	C₅×#452	—	3	2	no	—
51	C₄×C₅×SD₁₆	—	3	1	no	—
52	C₅×C₈×D₄	—	3	1	no	—
53	C₅×#416	—	3	2	no	—
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂×C₅×#67	—	2	2	no	—
59	C₅×#235	—	2	4	no	—
60	C₅×#235	—	4	2	no	—
61	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	—	2	1	no	—
63	C₂×C₄×C₅×D₃	—	2	2	no	—
64	C₂×C₅×Dic₆	C₂³	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	—	2	2	no	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
74	C₃×C₄²×C₅	—	2	2	no	—
75	C₃×C₄²×C₅	—	2	1	no	—
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#217	—	2	2	no	—
78	C₅×#216	—	4	2	no	—
79	C₅×#215	—	2	2	no	—
80	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
81	C₅×C₄⋊Dic₃	—	2	1	no	—
82	C₅×C₄⋊Dic₃	—	2	1	no	—
83	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
84	C₅×Dic₃⋊C₄	—	2	2	no	—
85	C₂×C₅×C₃⋊C₈	—	4	2	no	—
86	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
88	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
90	#5551	C₂×C₅	1	1	yes	characteristic
91	#5093	C₂×C₅	1	1	yes	characteristic, complemented
92	#5087	C₂×C₅	1	1	yes	characteristic, complemented
93	#5051	C₂×C₅	1	2	yes	complemented
94	#5047	C₂×C₅	1	2	yes	complemented
95	#5031	C₂×C₅	1	1	yes	characteristic, complemented
96	C₄×#215	C₂×C₅	1	1	yes	characteristic, complemented
97	D₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
98	#5002	C₂×C₅	1	2	yes	complemented
99	#4996	C₂×C₅	1	2	yes	complemented
100	C₂×C₅×#41	—	3	2	no	—
101	C₂×C₅×Q₁₆	—	3	2	no	—
102	C₂×C₅×SD₁₆	—	3	1	no	—
103	C₂²×C₅×C₈	—	3	2	no	—
104	C₅×C₄⋊Q₈	—	3	1	no	—
105	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
106	C₅×#126	—	2	2	no	—
107	C₅×#124	—	2	1	no	—
108	C₅×#123	—	6	2	no	—
109	C₅×C₂²⋊Q₈	—	3	2	no	—
110	C₅×C₂²⋊Q₈	C₂×D₃	1	2	yes	—
111	C₅×#121	—	6	1	no	—
112	C₄×C₅×Q₈	—	2	1	no	—
113	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
114	C₄×C₅×D₄	—	3	1	no	—
115	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
116	C₅×#117	C₂×D₃	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	—	6	1	no	—
118	C₅×#107	—	3	2	no	—
119	C₅×#106	—	3	1	no	—
120	C₅×C₄⋊C₈	—	3	1	no	—
121	C₅×#103	—	3	1	no	—
122	C₅×#103	—	3	2	no	—
123	C₅×#103	—	3	2	no	—
124	C₅×#103	—	3	2	no	—
125	C₅×#102	—	3	1	no	—
126	C₅×#102	—	3	2	no	—
127	C₅×C₂²⋊C₈	—	3	2	no	—
128	C₄×C₅×C₈	—	3	1	no	—
129	#3302	—	3	1	no	Sylow
130	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
131	C₂²×C₅×D₃	—	2	1	no	—
132	C₃×C₅×Q₈	—	2	1	no	—
133	C₃×C₅×Q₈	—	2	1	no	—
134	C₃×C₅×Q₈	—	4	2	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₅×#67	—	4	4	no	—
146	C₂×C₅×Dic₃	—	2	1	no	—
147	C₂×C₅×Dic₃	—	2	2	no	—
148	C₅×D₁₂	—	2	1	no	—
149	C₅×D₁₂	#41	1	2	yes	—
150	C₄×C₅×D₃	—	4	4	no	—
151	C₄×C₅×D₃	—	4	2	no	—
152	C₅×Dic₆	—	2	2	no	—
153	C₅×Dic₆	—	2	2	no	—
154	C₅×C₃⋊C₈	—	2	1	no	—
155	C₅×C₃⋊C₈	—	2	1	no	—
156	C₅×C₃⋊C₈	—	2	2	no	—
157	C₂×#235	C₂²×C₅	1	2	yes	—
158	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
159	C₃×#126	—	2	2	no	—
160	C₃×#124	—	2	1	no	—
161	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
162	C₃×C₄×Q₈	—	2	1	no	—
163	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
164	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
165	C₃×#117	C₂²×C₅	1	2	yes	—
166	C₂×#216	C₂²×C₅	1	2	yes	—
167	C₂×#215	C₂²×C₅	1	1	yes	characteristic
168	#938	—	2	1	no	—
169	#924	C₂²×C₅	1	2	yes	—
170	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
171	D₃×C₄⋊C₄	—	2	1	no	—
172	#883	—	2	2	no	—
173	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
174	#869	C₂²×C₅	1	1	yes	characteristic
175	#835	C₂²×C₅	1	1	yes	characteristic
176	#830	C₂²×C₅	1	2	yes	—
177	#810	C₂²×C₅	1	2	yes	—
178	#810	C₂²×C₅	1	2	yes	—
179	#810	C₂²×C₅	1	2	yes	—
180	#809	C₂²×C₅	1	1	yes	characteristic
181	#809	C₂²×C₅	1	2	yes	—
182	#808	C₂²×C₅	1	1	yes	characteristic
183	#807	C₂²×C₅	1	2	yes	—
184	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
185	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
186	C₅×#41	—	6	4	no	—
187	C₅×#41	—	12	2	no	—
188	C₂×C₅×Q₈	—	2	1	no	—
189	C₂×C₅×Q₈	—	3	2	no	—
190	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
191	C₂×C₅×D₄	—	3	1	no	—
192	C₂×C₅×D₄	—	6	2	no	—
193	C₂×C₅×D₄	#67	1	1	yes	characteristic
194	C₂²×C₄×C₅	—	6	1	no	—
195	C₂²×C₄×C₅	—	6	2	no	—
196	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
197	C₅×Q₁₆	—	12	2	no	—
198	C₅×SD₁₆	—	6	2	no	—
199	C₂×C₅×C₈	—	3	1	no	—
200	C₂×C₅×C₈	—	3	2	no	—
201	C₂×C₅×C₈	—	3	1	no	—
202	C₂×C₅×C₈	—	12	2	no	—
203	C₅×C₄⋊C₄	—	2	2	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	3	1	no	—
207	C₅×C₄⋊C₄	—	6	1	no	—
208	C₅×C₄⋊C₄	—	6	2	no	—
209	C₅×C₄⋊C₄	—	6	1	no	—
210	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
211	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
212	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
213	C₅×C₂²⋊C₄	—	2	2	no	—
214	C₅×C₂²⋊C₄	—	2	2	no	—
215	C₅×C₂²⋊C₄	—	6	2	no	—
216	C₅×C₂²⋊C₄	—	6	1	no	—
217	C₅×C₂²⋊C₄	#67	1	2	yes	—
218	C₄²×C₅	—	2	2	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
221	#556	C₅×D₃	1	1	yes	characteristic, complemented
222	#547	—	3	1	no	—
223	#487	—	3	1	no	—
224	#485	—	3	2	no	—
225	#474	—	3	1	no	—
226	#467	—	3	2	no	—
227	#462	—	3	1	no	—
228	#452	—	3	2	no	—
229	C₄×SD₁₆	—	3	1	no	—
230	C₈×D₄	—	3	1	no	—
231	#416	—	3	2	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	—	2	2	no	—
234	C₂²×C₃×C₅	—	2	2	no	—
235	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	—	4	1	no	—
238	C₂×C₅×D₃	—	4	1	no	—
239	C₃×C₄×C₅	—	2	2	no	—
240	C₃×C₄×C₅	—	2	1	no	—
241	C₃×C₄×C₅	—	4	1	no	—
242	C₃×C₄×C₅	—	4	2	no	—
243	C₃×C₄×C₅	—	4	1	no	—
244	C₃×C₄×C₅	#135	1	2	yes	—
245	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
246	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
247	C₅×Dic₃	—	4	2	no	—
248	C₅×Dic₃	—	4	1	no	—
249	C₂×C₃×Q₈	—	2	1	no	—
250	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
253	C₂×#67	—	2	2	no	—
254	#235	—	2	4	no	—
255	#235	—	4	2	no	—
256	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄×D₃	—	2	1	no	—
258	C₂×C₄×D₃	—	2	2	no	—
259	C₂×Dic₆	C₂³×C₅	1	2	yes	—
260	C₃×C₄⋊C₄	—	2	2	no	—
261	C₃×C₄⋊C₄	—	2	1	no	—
262	C₃×C₄⋊C₄	—	2	1	no	—
263	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
264	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
265	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
266	C₃×C₂²⋊C₄	—	2	2	no	—
267	C₃×C₂²⋊C₄	—	2	2	no	—
268	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
269	C₃×C₄²	—	2	2	no	—
270	C₃×C₄²	—	2	1	no	—
271	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
272	#217	—	2	2	no	—
273	#216	—	4	2	no	—
274	#215	—	2	2	no	—
275	(C₂×D₃)⋊C₄	—	2	1	no	—
276	C₄⋊Dic₃	—	2	1	no	—
277	C₄⋊Dic₃	—	2	1	no	—
278	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
279	Dic₃⋊C₄	—	2	2	no	—
280	C₂×C₃⋊C₈	—	4	2	no	—
281	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
282	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
283	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
284	C₂³×C₅	—	6	1	no	—
285	C₂³×C₅	C₂×#67	1	2	yes	—
286	C₅×Q₈	—	2	1	no	—
287	C₅×Q₈	—	2	1	no	—
288	C₅×Q₈	—	4	2	no	—
289	C₅×Q₈	—	6	2	no	—
290	C₅×Q₈	—	6	2	no	—
291	C₅×D₄	—	2	2	no	—
292	C₅×D₄	—	3	2	no	—
293	C₅×D₄	—	6	1	no	—
294	C₅×D₄	—	12	4	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	6	1	no	—
301	C₂×C₄×C₅	—	6	2	no	—
302	C₂×C₄×C₅	—	12	4	no	—
303	C₂×C₄×C₅	—	12	2	no	—
304	C₂×C₄×C₅	C₂×#67	1	2	yes	—
305	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
308	C₅×C₈	—	6	1	no	—
309	C₅×C₈	—	6	1	no	—
310	C₅×C₈	—	6	2	no	—
311	C₂×#41	—	3	2	no	—
312	C₂×Q₁₆	—	3	2	no	—
313	C₂×SD₁₆	—	3	1	no	—
314	C₂²×C₈	—	3	2	no	—
315	C₄⋊Q₈	—	3	1	no	—
316	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
317	#126	—	2	2	no	—
318	#124	—	2	1	no	—
319	#123	—	6	2	no	—
320	C₂²⋊Q₈	—	3	2	no	—
321	C₂²⋊Q₈	C₂×C₅×D₃	1	2	yes	—
322	#121	—	6	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
325	C₄×D₄	—	3	1	no	—
326	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
327	#117	C₂×C₅×D₃	1	2	yes	—
328	C₂×C₄⋊C₄	—	6	1	no	—
329	#107	—	3	2	no	—
330	#106	—	3	1	no	—
331	C₄⋊C₈	—	3	1	no	—
332	#103	—	3	1	no	—
333	#103	—	3	2	no	—
334	#103	—	3	2	no	—
335	#103	—	3	2	no	—
336	#102	—	3	1	no	—
337	#102	—	3	2	no	—
338	C₂²⋊C₈	—	3	2	no	—
339	C₄×C₈	—	3	1	no	—
340	C₂×C₃×C₅	—	4	2	no	—
341	C₂×C₃×C₅	#546	1	1	yes	characteristic
342	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
343	C₂×C₃×C₅	#578	1	1	yes	characteristic
344	C₅×D₃	—	4	2	no	—
345	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
346	C₂²×D₃	—	2	1	no	—
347	C₃×Q₈	—	2	1	no	—
348	C₃×Q₈	—	2	1	no	—
349	C₃×Q₈	—	4	2	no	—
350	C₃×D₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
357	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
360	#67	—	4	4	no	—
361	C₂×Dic₃	—	2	1	no	—
362	C₂×Dic₃	—	2	2	no	—
363	D₁₂	—	2	1	no	—
364	D₁₂	C₅×#41	1	2	yes	—
365	C₄×D₃	—	4	4	no	—
366	C₄×D₃	—	4	2	no	—
367	Dic₆	—	2	2	no	—
368	Dic₆	—	2	2	no	—
369	C₃⋊C₈	—	2	1	no	—
370	C₃⋊C₈	—	2	1	no	—
371	C₃⋊C₈	—	2	2	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	2	no	—
375	C₂²×C₅	—	6	2	no	—
376	C₂²×C₅	—	12	1	no	—
377	C₂²×C₅	—	12	1	no	—
378	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	2	1	no	—
381	C₄×C₅	—	4	2	no	—
382	C₄×C₅	—	4	1	no	—
383	C₄×C₅	—	4	1	no	—
384	C₄×C₅	—	12	1	no	—
385	C₄×C₅	—	12	2	no	—
386	C₄×C₅	#950	1	2	yes	—
387	C₄×C₅	D₃×#41	1	1	yes	characteristic
388	C₄×C₅	#1009	1	1	yes	characteristic
389	#41	—	6	4	no	—
390	#41	—	12	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	3	2	no	—
393	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
394	C₂×D₄	—	3	1	no	—
395	C₂×D₄	—	6	2	no	—
396	C₂×D₄	C₅×#67	1	1	yes	characteristic
397	C₂²×C₄	—	6	1	no	—
398	C₂²×C₄	—	6	2	no	—
399	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
400	Q₁₆	—	12	2	no	—
401	SD₁₆	—	6	2	no	—
402	C₂×C₈	—	3	1	no	—
403	C₂×C₈	—	3	1	no	—
404	C₂×C₈	—	3	2	no	—
405	C₂×C₈	—	12	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	3	1	no	—
410	C₄⋊C₄	—	6	1	no	—
411	C₄⋊C₄	—	6	2	no	—
412	C₄⋊C₄	—	6	1	no	—
413	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
414	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
415	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	6	2	no	—
419	C₂²⋊C₄	—	6	1	no	—
420	C₂²⋊C₄	C₅×#67	1	2	yes	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
424	C₃×C₅	#3302	1	1	yes	characteristic, complemented, Hall
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	—	2	2	no	—
427	C₂²×C₃	—	2	2	no	—
428	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
429	C₂×D₃	—	2	2	no	—
430	C₂×D₃	—	4	1	no	—
431	C₂×D₃	—	4	1	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	1	no	—
434	C₃×C₄	—	4	1	no	—
435	C₃×C₄	—	4	2	no	—
436	C₃×C₄	—	4	1	no	—
437	C₃×C₄	C₅×#135	1	2	yes	—
438	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
439	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
440	Dic₃	—	4	2	no	—
441	Dic₃	—	4	1	no	—
442	C₂×C₅	—	4	2	no	—
443	C₂×C₅	—	12	2	no	—
444	C₂×C₅	C₂×#950	1	1	yes	characteristic
445	C₂×C₅	#5829	1	1	yes	characteristic
446	C₂×C₅	#5838	1	1	yes	characteristic
447	C₂³	—	6	1	no	—
448	C₂³	C₂×C₅×#67	1	2	yes	—
449	Q₈	—	2	1	no	—
450	Q₈	—	2	1	no	—
451	Q₈	—	4	2	no	—
452	Q₈	—	6	2	no	—
453	Q₈	—	6	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	3	2	no	—
456	D₄	—	6	1	no	—
457	D₄	—	12	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	6	1	no	—
464	C₂×C₄	—	6	2	no	—
465	C₂×C₄	—	12	4	no	—
466	C₂×C₄	—	12	2	no	—
467	C₂×C₄	C₂×C₅×#67	1	2	yes	—
468	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
469	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
470	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
471	C₈	—	6	1	no	—
472	C₈	—	6	1	no	—
473	C₈	—	6	2	no	—
474	C₂×C₃	—	4	2	no	—
475	C₂×C₃	C₅×#546	1	1	yes	characteristic
476	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
477	C₂×C₃	C₅×#578	1	1	yes	characteristic
478	D₃	—	4	2	no	—
479	C₅	#83664	1	1	yes	characteristic, direct product factor, Sylow
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	6	2	no	—
484	C₂²	—	12	1	no	—
485	C₂²	—	12	1	no	—
486	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	12	1	no	—
493	C₄	—	12	2	no	—
494	C₄	C₅×#950	1	2	yes	—
495	C₄	C₅×D₃×#41	1	1	yes	characteristic
496	C₄	C₅×#1009	1	1	yes	characteristic
497	C₃	C₅×#3302	1	1	yes	characteristic, complemented, Sylow
498	C₂	—	4	2	no	—
499	C₂	—	12	2	no	—
500	C₂	C₂×C₅×#950	1	1	yes	characteristic
501	C₂	C₅×#5829	1	1	yes	characteristic
502	C₂	C₅×#5838	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×#556	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#5551	C₂
hypercenter	C₅×#556	D₃
hypocenter	C₃	C₅×#3302
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×#556

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#556	C₂	semidirect
3. C₅×#5093	C₂	semidirect
4. C₅×#5087	C₂	semidirect
5. C₅×#5051	C₂	semidirect
6. C₅×#5047	C₂	semidirect
7. C₅×#5031	C₂	semidirect
8. C₄×C₅×#215	C₂	semidirect
9. C₅×D₄×C₃⋊C₈	C₂	semidirect
10. C₅×#5002	C₂	semidirect
11. C₅×#4996	C₂	semidirect
42. #83664	C₅	direct (N × H)
43. C₅×#556	D₃	semidirect
89. C₃×#556	C₂×C₅	semidirect
91. #5093	C₂×C₅	semidirect
92. #5087	C₂×C₅	semidirect
93. #5051	C₂×C₅	semidirect
94. #5047	C₂×C₅	semidirect
95. #5031	C₂×C₅	semidirect
96. C₄×#215	C₂×C₅	semidirect
97. D₄×C₃⋊C₈	C₂×C₅	semidirect
98. #5002	C₂×C₅	semidirect
99. #4996	C₂×C₅	semidirect
221. #556	C₅×D₃	semidirect
424. C₃×C₅	#3302	semidirect
479. C₅	#83664	direct (N × H)
497. C₃	C₅×#3302	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#556	2
C₅×#5551	2
C₅×#5093	2
C₅×#5087	2
C₅×#5051	2
C₅×#5047	2
C₅×#5031	2
C₄×C₅×#215	2
C₅×D₄×C₃⋊C₈	2
C₅×#5002	2
C₅×#4996	2
C₅×#3302	3
#83664	5

Subgroups — C5×#83664 #14459931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83664 #14459931