Subgroups — C₅×#81207 #14435433

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5691	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5063	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5028	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4889	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4884	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4863	C₂	1	1	yes	maximal, characteristic
9	C₅×#4853	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4845	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4835	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4817	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4809	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4806	C₂	1	1	yes	maximal, characteristic
15	C₅×#4789	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3117	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#125	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₅×#216	C₂²	1	1	yes	characteristic
22	C₂×C₅×#215	C₂²	1	1	yes	characteristic
23	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
24	C₂×C₅×#204	C₂²	1	1	yes	characteristic
25	C₅×#898	—	2	1	no	—
26	C₅×#897	C₂²	1	1	yes	characteristic
27	C₅×#895	C₂²	1	1	yes	characteristic
28	C₅×#894	—	2	1	no	—
29	C₅×#893	—	2	1	no	—
30	C₅×#893	C₂²	1	1	yes	characteristic
31	C₅×#892	—	2	1	no	—
32	C₅×D₃×C₄⋊C₄	—	2	1	no	—
33	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₅×#887	—	2	1	no	—
35	C₅×#887	C₂²	1	1	yes	characteristic
36	C₅×#887	C₂²	1	1	yes	characteristic
37	C₅×#875	C₂²	1	1	yes	characteristic
38	C₄²×C₅×D₃	—	2	1	no	—
39	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
40	C₄×C₅×Dic₆	—	2	1	no	—
41	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
42	C₃×C₅×#107	C₂²	1	1	yes	characteristic
43	C₃×C₅×#106	C₂²	1	1	yes	characteristic
44	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₃×C₅×#103	C₂²	1	1	yes	characteristic
46	C₃×C₅×#103	C₂²	1	1	yes	characteristic
47	C₅×#821	C₂²	1	1	yes	characteristic
48	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
49	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
50	C₅×#816	C₂²	1	1	yes	characteristic
51	C₅×#815	C₂²	1	1	yes	characteristic
52	C₅×#815	C₂²	1	1	yes	characteristic
53	C₅×#810	C₂²	1	1	yes	characteristic
54	C₅×#810	C₂²	1	1	yes	characteristic
55	C₅×#810	C₂²	1	1	yes	characteristic
56	C₅×#809	C₂²	1	1	yes	characteristic
57	C₅×#808	C₂²	1	1	yes	characteristic
58	C₅×#807	C₂²	1	1	yes	characteristic
59	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
60	#81207	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#529	—	3	1	no	—
62	C₂×C₄×C₅×Q₈	—	3	1	no	—
63	C₅×#484	—	3	1	no	—
64	C₅×#481	—	3	1	no	—
65	C₅×#479	—	3	1	no	—
66	C₅×#479	D₃	1	1	yes	characteristic, complemented
67	C₅×#464	—	3	1	no	—
68	C₅×#464	—	3	1	no	—
69	C₅×#451	—	3	1	no	—
70	C₅×#448	—	3	1	no	—
71	C₅×#441	—	3	1	no	—
72	C₅×#441	—	3	1	no	—
73	C₅×#440	—	3	1	no	—
74	C₅×#440	—	3	1	no	—
75	C₅×#432	—	3	1	no	—
76	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₅×D₃×Q₈	—	2	2	no	—
78	C₅×D₃×Q₈	—	2	2	no	—
79	C₂×C₅×D₁₂	—	2	1	no	—
80	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
81	C₂×C₄×C₅×D₃	—	2	1	no	—
82	C₂×C₄×C₅×D₃	—	2	1	no	—
83	C₂×C₄×C₅×D₃	—	2	1	no	—
84	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
85	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
86	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
87	C₂×C₅×Dic₆	—	2	1	no	—
88	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
89	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₃×C₅×C₄⋊C₄	—	2	1	no	—
93	C₃×C₅×C₄⋊C₄	—	2	1	no	—
94	C₃×C₅×C₄⋊C₄	—	2	1	no	—
95	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₃×C₄²×C₅	—	2	1	no	—
99	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₅×#216	—	2	2	no	—
101	C₅×#215	—	2	2	no	—
102	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
103	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
104	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
105	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
106	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
107	C₅×C₄⋊Dic₃	—	2	1	no	—
108	C₅×C₄⋊Dic₃	—	2	1	no	—
109	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
110	C₅×Dic₃⋊C₄	—	2	1	no	—
111	C₅×Dic₃⋊C₄	—	2	1	no	—
112	C₅×Dic₃⋊C₄	—	2	1	no	—
113	C₅×Dic₃⋊C₄	—	2	1	no	—
114	C₄×C₅×Dic₃	—	2	1	no	—
115	C₄×C₅×Dic₃	—	2	1	no	—
116	C₄×C₅×Dic₃	—	2	1	no	—
117	C₄×C₅×Dic₃	—	2	1	no	—
118	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
119	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
120	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
121	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₅×Dic₁₂	—	2	2	no	—
124	C₅×#204	—	2	2	no	—
125	#5691	C₂×C₅	1	1	yes	characteristic
126	C₄×D₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#479	C₂×C₅	1	1	yes	characteristic, complemented
128	#5063	C₂×C₅	1	1	yes	characteristic, complemented
129	#5028	C₂×C₅	1	1	yes	characteristic, complemented
130	#4889	C₂×C₅	1	1	yes	characteristic, complemented
131	#4884	C₂×C₅	1	1	yes	characteristic, complemented
132	#4863	C₂×C₅	1	1	yes	characteristic
133	#4853	C₂×C₅	1	1	yes	characteristic, complemented
134	#4845	C₂×C₅	1	1	yes	characteristic, complemented
135	#4835	C₂×C₅	1	1	yes	characteristic, complemented
136	#4817	C₂×C₅	1	1	yes	characteristic, complemented
137	#4809	C₂×C₅	1	1	yes	characteristic, complemented
138	#4806	C₂×C₅	1	1	yes	characteristic
139	#4789	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂²×C₅×Q₈	—	3	1	no	—
141	C₂×C₅×Q₁₆	—	3	1	no	—
142	C₂×C₅×Q₁₆	—	3	1	no	—
143	C₂×C₅×SD₁₆	—	3	1	no	—
144	C₂×C₅×SD₁₆	—	3	1	no	—
145	C₅×#126	—	6	1	no	—
146	C₅×#125	C₂×D₃	1	1	yes	characteristic
147	C₅×#124	—	3	1	no	—
148	C₅×#123	—	6	1	no	—
149	C₅×C₂²⋊Q₈	—	3	1	no	—
150	C₅×#121	—	3	1	no	—
151	C₄×C₅×Q₈	—	3	1	no	—
152	C₄×C₅×Q₈	—	3	1	no	—
153	C₄×C₅×Q₈	—	3	1	no	—
154	C₄×C₅×Q₈	—	3	1	no	—
155	C₄×C₅×Q₈	—	6	1	no	—
156	C₄×C₅×Q₈	—	6	1	no	—
157	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
158	C₄×C₅×D₄	—	3	1	no	—
159	C₄×C₅×D₄	—	6	1	no	—
160	C₅×#117	—	6	1	no	—
161	C₂×C₅×C₄⋊C₄	—	3	1	no	—
162	C₂×C₅×C₄⋊C₄	—	6	1	no	—
163	C₂×C₄²×C₅	—	3	1	no	—
164	C₂×C₄²×C₅	—	6	1	no	—
165	C₅×#107	—	3	1	no	—
166	C₅×#107	C₂×D₃	1	1	yes	characteristic
167	C₅×#106	—	3	1	no	—
168	C₅×#106	C₂×D₃	1	1	yes	characteristic
169	C₅×C₄⋊C₈	—	3	1	no	—
170	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
171	C₅×#103	—	3	1	no	—
172	C₅×#103	—	3	1	no	—
173	C₅×#103	—	3	1	no	—
174	C₅×#103	—	3	1	no	—
175	C₅×#103	C₂×D₃	1	1	yes	characteristic
176	C₅×#103	C₂×D₃	1	1	yes	characteristic
177	C₅×#102	—	3	1	no	—
178	C₅×#102	—	3	1	no	—
179	C₅×C₂²⋊C₈	—	3	1	no	—
180	C₅×C₂²⋊C₈	—	3	1	no	—
181	C₅×#97	—	3	1	no	—
182	C₅×#97	—	3	1	no	—
183	#3117	—	3	1	no	Sylow
184	C₂²×C₅×D₃	—	2	1	no	—
185	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
186	C₃×C₅×Q₈	—	2	1	no	—
187	C₃×C₅×Q₈	#41	1	2	yes	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
195	C₂×C₅×Dic₃	—	2	1	no	—
196	C₂×C₅×Dic₃	—	2	1	no	—
197	C₂×C₅×Dic₃	—	2	1	no	—
198	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
199	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
200	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
201	C₅×D₁₂	—	2	1	no	—
202	C₅×D₁₂	—	2	1	no	—
203	C₅×D₁₂	—	4	2	no	—
204	C₄×C₅×D₃	—	2	4	no	—
205	C₄×C₅×D₃	—	2	2	no	—
206	C₄×C₅×D₃	—	2	1	no	—
207	C₄×C₅×D₃	—	2	1	no	—
208	C₄×C₅×D₃	—	4	1	no	—
209	C₄×C₅×D₃	—	4	2	no	—
210	C₄×C₅×D₃	—	4	2	no	—
211	C₅×Dic₆	—	2	4	no	—
212	C₅×Dic₆	—	2	1	no	—
213	C₅×Dic₆	—	2	1	no	—
214	C₅×Dic₆	—	2	1	no	—
215	C₅×Dic₆	#41	1	2	yes	—
216	C₃×C₅×C₈	—	2	1	no	—
217	C₃×C₅×C₈	—	2	1	no	—
218	C₅×C₃⋊C₈	—	2	1	no	—
219	C₅×C₃⋊C₈	—	2	1	no	—
220	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
221	C₃×#125	C₂²×C₅	1	1	yes	characteristic
222	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
223	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
224	C₂×#216	C₂²×C₅	1	1	yes	characteristic
225	C₂×#215	C₂²×C₅	1	1	yes	characteristic
226	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
227	C₂×#204	C₂²×C₅	1	1	yes	characteristic
228	#898	—	2	1	no	—
229	#897	C₂²×C₅	1	1	yes	characteristic
230	#895	C₂²×C₅	1	1	yes	characteristic
231	#894	—	2	1	no	—
232	#893	—	2	1	no	—
233	#893	C₂²×C₅	1	1	yes	characteristic
234	#892	—	2	1	no	—
235	D₃×C₄⋊C₄	—	2	1	no	—
236	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	#887	—	2	1	no	—
238	#887	C₂²×C₅	1	1	yes	characteristic
239	#887	C₂²×C₅	1	1	yes	characteristic
240	#875	C₂²×C₅	1	1	yes	characteristic
241	C₄²×D₃	—	2	1	no	—
242	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
243	C₄×Dic₆	—	2	1	no	—
244	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
245	C₃×#107	C₂²×C₅	1	1	yes	characteristic
246	C₃×#106	C₂²×C₅	1	1	yes	characteristic
247	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
248	C₃×#103	C₂²×C₅	1	1	yes	characteristic
249	C₃×#103	C₂²×C₅	1	1	yes	characteristic
250	#821	C₂²×C₅	1	1	yes	characteristic
251	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
253	#816	C₂²×C₅	1	1	yes	characteristic
254	#815	C₂²×C₅	1	1	yes	characteristic
255	#815	C₂²×C₅	1	1	yes	characteristic
256	#810	C₂²×C₅	1	1	yes	characteristic
257	#810	C₂²×C₅	1	1	yes	characteristic
258	#810	C₂²×C₅	1	1	yes	characteristic
259	#809	C₂²×C₅	1	1	yes	characteristic
260	#808	C₂²×C₅	1	1	yes	characteristic
261	#807	C₂²×C₅	1	1	yes	characteristic
262	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₅×Q₈	—	3	1	no	—
264	C₂×C₅×Q₈	—	3	1	no	—
265	C₂×C₅×Q₈	—	6	1	no	—
266	C₂×C₅×Q₈	—	6	2	no	—
267	C₂×C₅×Q₈	—	6	2	no	—
268	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
269	C₂×C₅×D₄	—	3	1	no	—
270	C₂×C₅×D₄	—	6	1	no	—
271	C₂²×C₄×C₅	—	3	1	no	—
272	C₂²×C₄×C₅	—	3	1	no	—
273	C₂²×C₄×C₅	—	3	1	no	—
274	C₂²×C₄×C₅	—	6	1	no	—
275	C₂²×C₄×C₅	—	6	1	no	—
276	C₂²×C₄×C₅	—	6	1	no	—
277	C₅×Q₁₆	—	6	2	no	—
278	C₅×Q₁₆	—	6	2	no	—
279	C₅×SD₁₆	—	6	2	no	—
280	C₅×SD₁₆	—	6	2	no	—
281	C₂×C₅×C₈	—	3	1	no	—
282	C₂×C₅×C₈	—	3	1	no	—
283	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
284	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
285	C₅×C₄⋊C₄	—	2	1	no	—
286	C₅×C₄⋊C₄	—	2	1	no	—
287	C₅×C₄⋊C₄	—	2	1	no	—
288	C₅×C₄⋊C₄	—	3	1	no	—
289	C₅×C₄⋊C₄	—	6	1	no	—
290	C₅×C₄⋊C₄	—	6	1	no	—
291	C₅×C₄⋊C₄	—	6	1	no	—
292	C₅×C₄⋊C₄	—	6	1	no	—
293	C₅×C₄⋊C₄	—	6	1	no	—
294	C₅×C₄⋊C₄	—	6	1	no	—
295	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
296	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
297	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
298	C₅×C₂²⋊C₄	—	6	1	no	—
299	C₅×C₂²⋊C₄	—	6	1	no	—
300	C₅×C₂²⋊C₄	—	6	1	no	—
301	C₅×C₂²⋊C₄	—	6	1	no	—
302	C₅×C₂²⋊C₄	—	6	1	no	—
303	C₄²×C₅	—	2	1	no	—
304	C₄²×C₅	—	3	1	no	—
305	C₄²×C₅	—	3	1	no	—
306	C₄²×C₅	—	3	1	no	—
307	C₄²×C₅	—	6	1	no	—
308	C₄²×C₅	—	6	1	no	—
309	C₄²×C₅	—	6	1	no	—
310	C₄²×C₅	—	6	1	no	—
311	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
312	#529	—	3	1	no	—
313	C₂×C₄×Q₈	—	3	1	no	—
314	#484	—	3	1	no	—
315	#481	—	3	1	no	—
316	#479	—	3	1	no	—
317	#479	C₅×D₃	1	1	yes	characteristic, complemented
318	#464	—	3	1	no	—
319	#464	—	3	1	no	—
320	#451	—	3	1	no	—
321	#448	—	3	1	no	—
322	#441	—	3	1	no	—
323	#441	—	3	1	no	—
324	#440	—	3	1	no	—
325	#440	—	3	1	no	—
326	#432	—	3	1	no	—
327	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₅×D₃	—	2	1	no	—
329	C₂×C₅×D₃	—	2	1	no	—
330	C₂×C₅×D₃	—	4	1	no	—
331	C₂×C₅×D₃	—	4	1	no	—
332	C₂×C₅×D₃	—	4	1	no	—
333	C₂×C₅×D₃	#137	1	2	yes	—
334	C₃×C₄×C₅	—	2	2	no	—
335	C₃×C₄×C₅	—	2	1	no	—
336	C₃×C₄×C₅	—	2	1	no	—
337	C₃×C₄×C₅	—	4	1	no	—
338	C₃×C₄×C₅	—	4	1	no	—
339	C₃×C₄×C₅	—	4	1	no	—
340	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
341	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
342	C₅×Dic₃	—	2	1	no	—
343	C₅×Dic₃	—	2	2	no	—
344	C₅×Dic₃	—	2	1	no	—
345	C₅×Dic₃	—	2	1	no	—
346	C₅×Dic₃	—	4	1	no	—
347	C₅×Dic₃	—	4	1	no	—
348	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
349	D₃×Q₈	—	2	2	no	—
350	D₃×Q₈	—	2	2	no	—
351	C₂×D₁₂	—	2	1	no	—
352	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
353	C₂×C₄×D₃	—	2	1	no	—
354	C₂×C₄×D₃	—	2	1	no	—
355	C₂×C₄×D₃	—	2	1	no	—
356	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
357	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
358	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
359	C₂×Dic₆	—	2	1	no	—
360	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
361	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
364	C₃×C₄⋊C₄	—	2	1	no	—
365	C₃×C₄⋊C₄	—	2	1	no	—
366	C₃×C₄⋊C₄	—	2	1	no	—
367	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
368	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
369	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
370	C₃×C₄²	—	2	1	no	—
371	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
372	#216	—	2	2	no	—
373	#215	—	2	2	no	—
374	(C₂×D₃)⋊C₄	—	2	1	no	—
375	(C₂×D₃)⋊C₄	—	2	1	no	—
376	(C₂×D₃)⋊C₄	—	2	1	no	—
377	(C₂×D₃)⋊C₄	—	2	1	no	—
378	(C₂×D₃)⋊C₄	—	2	1	no	—
379	C₄⋊Dic₃	—	2	1	no	—
380	C₄⋊Dic₃	—	2	1	no	—
381	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
382	Dic₃⋊C₄	—	2	1	no	—
383	Dic₃⋊C₄	—	2	1	no	—
384	Dic₃⋊C₄	—	2	1	no	—
385	Dic₃⋊C₄	—	2	1	no	—
386	C₄×Dic₃	—	2	1	no	—
387	C₄×Dic₃	—	2	1	no	—
388	C₄×Dic₃	—	2	1	no	—
389	C₄×Dic₃	—	2	1	no	—
390	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
391	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
392	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
394	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
395	Dic₁₂	—	2	2	no	—
396	#204	—	2	2	no	—
397	C₂³×C₅	—	3	1	no	—
398	C₂³×C₅	—	6	1	no	—
399	C₅×Q₈	—	2	1	no	—
400	C₅×Q₈	—	3	2	no	—
401	C₅×Q₈	—	6	4	no	—
402	C₅×Q₈	—	6	1	no	—
403	C₅×Q₈	—	6	1	no	—
404	C₅×Q₈	—	6	1	no	—
405	C₅×Q₈	#239	1	2	yes	—
406	C₅×D₄	—	6	1	no	—
407	C₅×D₄	—	6	1	no	—
408	C₅×D₄	—	12	2	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	1	no	—
411	C₂×C₄×C₅	—	2	1	no	—
412	C₂×C₄×C₅	—	2	1	no	—
413	C₂×C₄×C₅	—	3	1	no	—
414	C₂×C₄×C₅	—	3	1	no	—
415	C₂×C₄×C₅	—	3	1	no	—
416	C₂×C₄×C₅	—	6	2	no	—
417	C₂×C₄×C₅	—	6	4	no	—
418	C₂×C₄×C₅	—	6	1	no	—
419	C₂×C₄×C₅	—	6	1	no	—
420	C₂×C₄×C₅	—	6	1	no	—
421	C₂×C₄×C₅	—	6	1	no	—
422	C₂×C₄×C₅	—	6	1	no	—
423	C₂×C₄×C₅	—	12	1	no	—
424	C₂×C₄×C₅	—	12	2	no	—
425	C₂×C₄×C₅	—	12	2	no	—
426	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
427	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
428	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
429	C₅×C₈	—	2	1	no	—
430	C₅×C₈	—	2	1	no	—
431	C₅×C₈	—	6	1	no	—
432	C₅×C₈	—	6	1	no	—
433	C₂²×Q₈	—	3	1	no	—
434	C₂×Q₁₆	—	3	1	no	—
435	C₂×Q₁₆	—	3	1	no	—
436	C₂×SD₁₆	—	3	1	no	—
437	C₂×SD₁₆	—	3	1	no	—
438	#126	—	6	1	no	—
439	#125	C₂×C₅×D₃	1	1	yes	characteristic
440	#124	—	3	1	no	—
441	#123	—	6	1	no	—
442	C₂²⋊Q₈	—	3	1	no	—
443	#121	—	3	1	no	—
444	C₄×Q₈	—	3	1	no	—
445	C₄×Q₈	—	3	1	no	—
446	C₄×Q₈	—	3	1	no	—
447	C₄×Q₈	—	3	1	no	—
448	C₄×Q₈	—	6	1	no	—
449	C₄×Q₈	—	6	1	no	—
450	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
451	C₄×D₄	—	3	1	no	—
452	C₄×D₄	—	6	1	no	—
453	#117	—	6	1	no	—
454	C₂×C₄⋊C₄	—	3	1	no	—
455	C₂×C₄⋊C₄	—	6	1	no	—
456	C₂×C₄²	—	3	1	no	—
457	C₂×C₄²	—	6	1	no	—
458	#107	—	3	1	no	—
459	#107	C₂×C₅×D₃	1	1	yes	characteristic
460	#106	—	3	1	no	—
461	#106	C₂×C₅×D₃	1	1	yes	characteristic
462	C₄⋊C₈	—	3	1	no	—
463	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
464	#103	—	3	1	no	—
465	#103	—	3	1	no	—
466	#103	—	3	1	no	—
467	#103	—	3	1	no	—
468	#103	C₂×C₅×D₃	1	1	yes	characteristic
469	#103	C₂×C₅×D₃	1	1	yes	characteristic
470	#102	—	3	1	no	—
471	#102	—	3	1	no	—
472	C₂²⋊C₈	—	3	1	no	—
473	C₂²⋊C₈	—	3	1	no	—
474	#97	—	3	1	no	—
475	#97	—	3	1	no	—
476	C₂×C₃×C₅	#525	1	1	yes	characteristic
477	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
478	C₂×C₃×C₅	#575	1	1	yes	characteristic
479	C₅×D₃	—	2	2	no	—
480	C₅×D₃	—	8	1	no	—
481	C₂²×D₃	—	2	1	no	—
482	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
483	C₃×Q₈	—	2	1	no	—
484	C₃×Q₈	C₅×#41	1	2	yes	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
491	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
492	C₂×Dic₃	—	2	1	no	—
493	C₂×Dic₃	—	2	1	no	—
494	C₂×Dic₃	—	2	1	no	—
495	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
496	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
497	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
498	D₁₂	—	2	1	no	—
499	D₁₂	—	2	1	no	—
500	D₁₂	—	4	2	no	—
501	C₄×D₃	—	2	4	no	—
502	C₄×D₃	—	2	2	no	—
503	C₄×D₃	—	2	1	no	—
504	C₄×D₃	—	2	1	no	—
505	C₄×D₃	—	4	1	no	—
506	C₄×D₃	—	4	2	no	—
507	C₄×D₃	—	4	2	no	—
508	Dic₆	—	2	4	no	—
509	Dic₆	—	2	1	no	—
510	Dic₆	—	2	1	no	—
511	Dic₆	—	2	1	no	—
512	Dic₆	C₅×#41	1	2	yes	—
513	C₃×C₈	—	2	1	no	—
514	C₃×C₈	—	2	1	no	—
515	C₃⋊C₈	—	2	1	no	—
516	C₃⋊C₈	—	2	1	no	—
517	C₂²×C₅	—	3	2	no	—
518	C₂²×C₅	—	6	1	no	—
519	C₂²×C₅	—	6	1	no	—
520	C₂²×C₅	—	12	1	no	—
521	C₂²×C₅	—	12	1	no	—
522	C₂²×C₅	—	12	1	no	—
523	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
524	C₄×C₅	—	2	1	no	—
525	C₄×C₅	—	2	1	no	—
526	C₄×C₅	—	2	2	no	—
527	C₄×C₅	—	4	1	no	—
528	C₄×C₅	—	4	1	no	—
529	C₄×C₅	—	4	1	no	—
530	C₄×C₅	—	6	1	no	—
531	C₄×C₅	—	6	1	no	—
532	C₄×C₅	—	6	1	no	—
533	C₄×C₅	—	6	2	no	—
534	C₄×C₅	—	12	1	no	—
535	C₄×C₅	—	12	1	no	—
536	C₄×C₅	C₂×#239	1	1	yes	characteristic
537	C₄×C₅	D₃×#41	1	1	yes	characteristic
538	C₂×Q₈	—	3	1	no	—
539	C₂×Q₈	—	3	1	no	—
540	C₂×Q₈	—	6	1	no	—
541	C₂×Q₈	—	6	2	no	—
542	C₂×Q₈	—	6	2	no	—
543	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
544	C₂×D₄	—	3	1	no	—
545	C₂×D₄	—	6	1	no	—
546	C₂²×C₄	—	3	1	no	—
547	C₂²×C₄	—	3	1	no	—
548	C₂²×C₄	—	3	1	no	—
549	C₂²×C₄	—	6	1	no	—
550	C₂²×C₄	—	6	1	no	—
551	C₂²×C₄	—	6	1	no	—
552	Q₁₆	—	6	2	no	—
553	Q₁₆	—	6	2	no	—
554	SD₁₆	—	6	2	no	—
555	SD₁₆	—	6	2	no	—
556	C₂×C₈	—	3	1	no	—
557	C₂×C₈	—	3	1	no	—
558	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
559	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	3	1	no	—
564	C₄⋊C₄	—	6	1	no	—
565	C₄⋊C₄	—	6	1	no	—
566	C₄⋊C₄	—	6	1	no	—
567	C₄⋊C₄	—	6	1	no	—
568	C₄⋊C₄	—	6	1	no	—
569	C₄⋊C₄	—	6	1	no	—
570	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
571	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
572	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
573	C₂²⋊C₄	—	6	1	no	—
574	C₂²⋊C₄	—	6	1	no	—
575	C₂²⋊C₄	—	6	1	no	—
576	C₂²⋊C₄	—	6	1	no	—
577	C₂²⋊C₄	—	6	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	3	1	no	—
580	C₄²	—	3	1	no	—
581	C₄²	—	3	1	no	—
582	C₄²	—	6	1	no	—
583	C₄²	—	6	1	no	—
584	C₄²	—	6	1	no	—
585	C₄²	—	6	1	no	—
586	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
587	C₃×C₅	#3117	1	1	yes	characteristic, complemented, Hall
588	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
589	C₂×D₃	—	2	1	no	—
590	C₂×D₃	—	2	1	no	—
591	C₂×D₃	—	4	1	no	—
592	C₂×D₃	—	4	1	no	—
593	C₂×D₃	—	4	1	no	—
594	C₂×D₃	C₅×#137	1	2	yes	—
595	C₃×C₄	—	2	2	no	—
596	C₃×C₄	—	2	1	no	—
597	C₃×C₄	—	2	1	no	—
598	C₃×C₄	—	4	1	no	—
599	C₃×C₄	—	4	1	no	—
600	C₃×C₄	—	4	1	no	—
601	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
602	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
603	Dic₃	—	2	1	no	—
604	Dic₃	—	2	2	no	—
605	Dic₃	—	2	1	no	—
606	Dic₃	—	2	1	no	—
607	Dic₃	—	4	1	no	—
608	Dic₃	—	4	1	no	—
609	C₂×C₅	—	6	2	no	—
610	C₂×C₅	—	24	1	no	—
611	C₂×C₅	#5627	1	1	yes	characteristic
612	C₂×C₅	#5768	1	1	yes	characteristic
613	C₂×C₅	D₃×#137	1	1	yes	characteristic
614	C₂³	—	3	1	no	—
615	C₂³	—	6	1	no	—
616	Q₈	—	2	1	no	—
617	Q₈	—	3	2	no	—
618	Q₈	—	6	4	no	—
619	Q₈	—	6	1	no	—
620	Q₈	—	6	1	no	—
621	Q₈	—	6	1	no	—
622	Q₈	C₅×#239	1	2	yes	—
623	D₄	—	6	1	no	—
624	D₄	—	6	1	no	—
625	D₄	—	12	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	3	1	no	—
631	C₂×C₄	—	3	1	no	—
632	C₂×C₄	—	3	1	no	—
633	C₂×C₄	—	6	2	no	—
634	C₂×C₄	—	6	4	no	—
635	C₂×C₄	—	6	1	no	—
636	C₂×C₄	—	6	1	no	—
637	C₂×C₄	—	6	1	no	—
638	C₂×C₄	—	6	1	no	—
639	C₂×C₄	—	6	1	no	—
640	C₂×C₄	—	12	1	no	—
641	C₂×C₄	—	12	2	no	—
642	C₂×C₄	—	12	2	no	—
643	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
644	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
645	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
646	C₈	—	2	1	no	—
647	C₈	—	2	1	no	—
648	C₈	—	6	1	no	—
649	C₈	—	6	1	no	—
650	C₂×C₃	C₅×#525	1	1	yes	characteristic
651	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
652	C₂×C₃	C₅×#575	1	1	yes	characteristic
653	D₃	—	2	2	no	—
654	D₃	—	8	1	no	—
655	C₅	#81207	1	1	yes	characteristic, direct product factor, Sylow
656	C₂²	—	3	2	no	—
657	C₂²	—	6	1	no	—
658	C₂²	—	6	1	no	—
659	C₂²	—	12	1	no	—
660	C₂²	—	12	1	no	—
661	C₂²	—	12	1	no	—
662	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	6	1	no	—
670	C₄	—	6	1	no	—
671	C₄	—	6	1	no	—
672	C₄	—	6	2	no	—
673	C₄	—	12	1	no	—
674	C₄	—	12	1	no	—
675	C₄	C₂×C₅×#239	1	1	yes	characteristic
676	C₄	C₅×D₃×#41	1	1	yes	characteristic
677	C₃	C₅×#3117	1	1	yes	characteristic, complemented, Sylow
678	C₂	—	6	2	no	—
679	C₂	—	24	1	no	—
680	C₂	C₅×#5627	1	1	yes	characteristic
681	C₂	C₅×#5768	1	1	yes	characteristic
682	C₂	C₅×D₃×#137	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×#479	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×#895	C₂²
hypercenter	C₅×#479	D₃
hypocenter	C₃	C₅×#3117
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#479

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×D₃×Q₈	C₂	semidirect
3. C₃×C₅×#479	C₂	semidirect
4. C₅×#5063	C₂	semidirect
5. C₅×#5028	C₂	semidirect
6. C₅×#4889	C₂	semidirect
7. C₅×#4884	C₂	semidirect
9. C₅×#4853	C₂	semidirect
10. C₅×#4845	C₂	semidirect
11. C₅×#4835	C₂	semidirect
12. C₅×#4817	C₂	semidirect
13. C₅×#4809	C₂	semidirect
15. C₅×#4789	C₂	semidirect
60. #81207	C₅	direct (N × H)
66. C₅×#479	D₃	semidirect
126. C₄×D₃×Q₈	C₂×C₅	semidirect
127. C₃×#479	C₂×C₅	semidirect
128. #5063	C₂×C₅	semidirect
129. #5028	C₂×C₅	semidirect
130. #4889	C₂×C₅	semidirect
131. #4884	C₂×C₅	semidirect
133. #4853	C₂×C₅	semidirect
134. #4845	C₂×C₅	semidirect
135. #4835	C₂×C₅	semidirect
136. #4817	C₂×C₅	semidirect
137. #4809	C₂×C₅	semidirect
139. #4789	C₂×C₅	semidirect
317. #479	C₅×D₃	semidirect
587. C₃×C₅	#3117	semidirect
655. C₅	#81207	direct (N × H)
677. C₃	C₅×#3117	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5691	2
C₄×C₅×D₃×Q₈	2
C₃×C₅×#479	2
C₅×#5063	2
C₅×#5028	2
C₅×#4889	2
C₅×#4884	2
C₅×#4863	2
C₅×#4853	2
C₅×#4845	2
C₅×#4835	2
C₅×#4817	2
C₅×#4809	2
C₅×#4806	2
C₅×#4789	2
C₅×#3117	3
#81207	5

Subgroups — C5×#81207 #14435433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#81207 #14435433