Subgroups — C₅×#80412 #14436084

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5731	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5546	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5173	C₂	1	1	yes	maximal, characteristic
5	C₅×#5173	C₂	1	1	yes	maximal, characteristic
6	C₅×#5164	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×Dic₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5090	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5009	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4840	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4829	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4811	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4805	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4790	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4789	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3120	—	3	1	no	maximal, Hall
17	C₂×C₅×#237	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₅×#946	C₂²	1	1	yes	characteristic
23	C₅×#946	C₂²	1	1	yes	characteristic
24	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
25	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₅×#216	C₂²	1	1	yes	characteristic
27	C₂×C₅×#216	C₂²	1	1	yes	characteristic
28	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
29	C₄×C₅×#67	—	2	1	no	—
30	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
31	C₅×#898	—	2	1	no	—
32	C₅×#898	—	2	1	no	—
33	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₅×#889	—	2	1	no	—
35	C₅×#889	—	2	1	no	—
36	C₅×#887	C₂²	1	1	yes	characteristic
37	C₅×#67⋊C₄	—	2	1	no	—
38	C₅×#877	—	2	1	no	—
39	C₅×#872	C₂²	1	1	yes	characteristic
40	C₅×#870	C₂²	1	1	yes	characteristic
41	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×C₅×#103	C₂²	1	1	yes	characteristic
44	C₃×C₅×#103	C₂²	1	1	yes	characteristic
45	C₅×#835	C₂²	1	1	yes	characteristic
46	C₅×#835	C₂²	1	1	yes	characteristic
47	C₅×#832	C₂²	1	1	yes	characteristic
48	C₅×#832	C₂²	1	1	yes	characteristic
49	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
50	C₅×(C₂×D₃)⋊C₈	C₂²	1	1	yes	characteristic
51	C₅×#818	C₂²	1	1	yes	characteristic
52	C₅×#817	C₂²	1	1	yes	characteristic
53	C₅×#816	C₂²	1	1	yes	characteristic
54	C₅×#816	C₂²	1	1	yes	characteristic
55	C₅×#815	C₂²	1	1	yes	characteristic
56	C₅×C₈×Dic₃	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	#80412	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#541	—	3	1	no	—
62	C₅×#520	—	3	1	no	—
63	C₅×#484	—	3	1	no	—
64	C₅×#483	—	3	1	no	—
65	C₅×#479	—	3	1	no	—
66	C₅×#478	—	3	1	no	—
67	C₅×#462	—	3	1	no	—
68	C₅×#461	D₃	1	1	yes	characteristic, complemented
69	C₅×#452	—	3	1	no	—
70	C₅×#452	—	3	1	no	—
71	C₅×#441	—	3	1	no	—
72	C₅×#440	—	3	1	no	—
73	C₄×C₅×Q₁₆	—	3	1	no	—
74	C₄×C₅×SD₁₆	—	3	1	no	—
75	C₅×#433	—	3	1	no	—
76	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₅×#67	—	2	1	no	—
81	C₂²×C₅×Dic₃	—	2	1	no	—
82	C₂²×C₅×Dic₃	—	2	1	no	—
83	C₅×#237	—	2	2	no	—
84	C₅×#237	—	2	2	no	—
85	C₂×C₄×C₅×D₃	—	2	1	no	—
86	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
87	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
88	C₃×C₅×SD₁₆	—	2	2	no	—
89	C₃×C₅×SD₁₆	—	2	2	no	—
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	C₂³	1	1	yes	characteristic
95	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
97	C₅×#217	—	2	1	no	—
98	C₅×#216	—	2	2	no	—
99	C₅×#216	—	2	2	no	—
100	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
101	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
102	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
103	C₅×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
104	C₅×C₄⋊Dic₃	—	2	1	no	—
105	C₅×C₄⋊Dic₃	—	2	1	no	—
106	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
107	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
108	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
109	C₅×Dic₃⋊C₄	—	2	1	no	—
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	C₅×Dic₃⋊C₄	—	2	1	no	—
115	C₅×Dic₃⋊C₄	—	2	1	no	—
116	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
117	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
118	C₄×C₅×Dic₃	—	2	1	no	—
119	C₄×C₅×Dic₃	—	2	1	no	—
120	C₄×C₅×Dic₃	—	2	1	no	—
121	C₄×C₅×Dic₃	—	2	1	no	—
122	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
123	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
125	#5731	C₂×C₅	1	1	yes	characteristic, complemented
126	#5546	C₂×C₅	1	1	yes	characteristic
127	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
128	#5173	C₂×C₅	1	1	yes	characteristic
129	#5173	C₂×C₅	1	1	yes	characteristic
130	#5164	C₂×C₅	1	1	yes	characteristic, complemented
131	Dic₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
132	#5090	C₂×C₅	1	1	yes	characteristic, complemented
133	#5009	C₂×C₅	1	1	yes	characteristic, complemented
134	#4840	C₂×C₅	1	1	yes	characteristic, complemented
135	#4829	C₂×C₅	1	1	yes	characteristic, complemented
136	#4811	C₂×C₅	1	1	yes	characteristic, complemented
137	#4805	C₂×C₅	1	1	yes	characteristic, complemented
138	#4790	C₂×C₅	1	1	yes	characteristic, complemented
139	#4789	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₅×#41	—	3	1	no	—
141	C₂×C₅×Q₁₆	—	3	1	no	—
142	C₂×C₅×Q₁₆	—	3	1	no	—
143	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
144	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic
145	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
146	C₅×#126	—	6	1	no	—
147	C₅×#126	—	6	1	no	—
148	C₅×#125	—	3	1	no	—
149	C₅×#125	—	6	1	no	—
150	C₅×#125	—	6	1	no	—
151	C₅×C₂²⋊Q₈	—	3	1	no	—
152	C₅×C₂²⋊Q₈	—	3	1	no	—
153	C₄×C₅×Q₈	—	3	1	no	—
154	C₄×C₅×Q₈	—	3	1	no	—
155	C₄×C₅×Q₈	—	3	1	no	—
156	C₄×C₅×Q₈	—	3	1	no	—
157	C₄×C₅×D₄	—	3	1	no	—
158	C₄×C₅×D₄	—	6	1	no	—
159	C₄×C₅×D₄	—	6	1	no	—
160	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
161	C₅×#117	—	3	1	no	—
162	C₅×#117	—	6	1	no	—
163	C₂×C₅×C₄⋊C₄	—	3	1	no	—
164	C₂×C₅×C₄⋊C₄	—	6	1	no	—
165	C₅×#107	—	3	1	no	—
166	C₅×#107	—	3	1	no	—
167	C₅×#106	—	3	1	no	—
168	C₅×#106	—	3	1	no	—
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	C₄×C₅×C₈	—	3	1	no	—
183	#3120	—	3	1	no	Sylow
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
186	C₃×C₅×Q₈	—	2	1	no	—
187	C₃×C₅×Q₈	—	2	1	no	—
188	C₃×C₅×Q₈	—	2	1	no	—
189	C₃×C₅×Q₈	—	2	1	no	—
190	C₃×C₅×D₄	—	2	1	no	—
191	C₃×C₅×D₄	#41	1	2	yes	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	8	1	no	—
196	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
198	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
199	C₅×#67	—	2	4	no	—
200	C₂×C₅×Dic₃	—	2	4	no	—
201	C₂×C₅×Dic₃	—	2	1	no	—
202	C₂×C₅×Dic₃	—	2	1	no	—
203	C₂×C₅×Dic₃	—	2	1	no	—
204	C₂×C₅×Dic₃	—	2	1	no	—
205	C₂×C₅×Dic₃	—	8	1	no	—
206	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
208	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
209	C₄×C₅×D₃	—	2	1	no	—
210	C₄×C₅×D₃	—	2	1	no	—
211	C₄×C₅×D₃	—	8	1	no	—
212	C₅×Dic₆	—	2	1	no	—
213	C₅×Dic₆	#41	1	2	yes	—
214	C₃×C₅×C₈	—	2	1	no	—
215	C₃×C₅×C₈	—	2	1	no	—
216	C₅×C₃⋊C₈	—	2	1	no	—
217	C₅×C₃⋊C₈	—	2	1	no	—
218	C₂×#237	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
221	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
222	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
223	#946	C₂²×C₅	1	1	yes	characteristic
224	#946	C₂²×C₅	1	1	yes	characteristic
225	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
226	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
227	C₂×#216	C₂²×C₅	1	1	yes	characteristic
228	C₂×#216	C₂²×C₅	1	1	yes	characteristic
229	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
230	C₄×#67	—	2	1	no	—
231	C₂×Dic₃⋊C₄	—	2	1	no	—
232	#898	—	2	1	no	—
233	#898	—	2	1	no	—
234	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	#889	—	2	1	no	—
236	#889	—	2	1	no	—
237	#887	C₂²×C₅	1	1	yes	characteristic
238	#67⋊C₄	—	2	1	no	—
239	#877	—	2	1	no	—
240	#872	C₂²×C₅	1	1	yes	characteristic
241	#870	C₂²×C₅	1	1	yes	characteristic
242	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
243	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
244	C₃×#103	C₂²×C₅	1	1	yes	characteristic
245	C₃×#103	C₂²×C₅	1	1	yes	characteristic
246	#835	C₂²×C₅	1	1	yes	characteristic
247	#835	C₂²×C₅	1	1	yes	characteristic
248	#832	C₂²×C₅	1	1	yes	characteristic
249	#832	C₂²×C₅	1	1	yes	characteristic
250	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
251	(C₂×D₃)⋊C₈	C₂²×C₅	1	1	yes	characteristic
252	#818	C₂²×C₅	1	1	yes	characteristic
253	#817	C₂²×C₅	1	1	yes	characteristic
254	#816	C₂²×C₅	1	1	yes	characteristic
255	#816	C₂²×C₅	1	1	yes	characteristic
256	#815	C₂²×C₅	1	1	yes	characteristic
257	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
258	#808	C₂²×C₅	1	1	yes	characteristic
259	#807	C₂²×C₅	1	1	yes	characteristic
260	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
261	C₅×#41	—	6	2	no	—
262	C₅×#41	—	6	2	no	—
263	C₂×C₅×Q₈	—	3	1	no	—
264	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
265	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
266	C₂×C₅×D₄	—	6	1	no	—
267	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
268	C₂²×C₄×C₅	—	2	1	no	—
269	C₂²×C₄×C₅	—	3	1	no	—
270	C₂²×C₄×C₅	—	6	1	no	—
271	C₂²×C₄×C₅	—	6	1	no	—
272	C₂²×C₄×C₅	—	6	1	no	—
273	C₅×Q₁₆	—	6	2	no	—
274	C₅×Q₁₆	—	6	2	no	—
275	C₅×SD₁₆	—	2	2	no	—
276	C₅×SD₁₆	—	2	2	no	—
277	C₂×C₅×C₈	—	3	1	no	—
278	C₂×C₅×C₈	—	3	1	no	—
279	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
280	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
281	C₅×C₄⋊C₄	—	2	1	no	—
282	C₅×C₄⋊C₄	—	2	1	no	—
283	C₅×C₄⋊C₄	—	3	1	no	—
284	C₅×C₄⋊C₄	—	3	1	no	—
285	C₅×C₄⋊C₄	—	3	1	no	—
286	C₅×C₄⋊C₄	—	3	1	no	—
287	C₅×C₄⋊C₄	—	3	1	no	—
288	C₅×C₄⋊C₄	—	6	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	—	6	1	no	—
296	C₅×C₄⋊C₄	—	6	1	no	—
297	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
298	C₅×C₂²⋊C₄	—	2	1	no	—
299	C₅×C₂²⋊C₄	—	3	1	no	—
300	C₅×C₂²⋊C₄	—	3	1	no	—
301	C₅×C₂²⋊C₄	—	6	1	no	—
302	C₅×C₂²⋊C₄	—	6	1	no	—
303	C₅×C₂²⋊C₄	—	6	1	no	—
304	C₄²×C₅	—	3	1	no	—
305	C₄²×C₅	—	6	1	no	—
306	C₄²×C₅	—	6	1	no	—
307	C₄²×C₅	—	6	1	no	—
308	C₄²×C₅	—	6	1	no	—
309	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
310	#541	—	3	1	no	—
311	#520	—	3	1	no	—
312	#484	—	3	1	no	—
313	#483	—	3	1	no	—
314	#479	—	3	1	no	—
315	#478	—	3	1	no	—
316	#462	—	3	1	no	—
317	#461	C₅×D₃	1	1	yes	characteristic, complemented
318	#452	—	3	1	no	—
319	#452	—	3	1	no	—
320	#441	—	3	1	no	—
321	#440	—	3	1	no	—
322	C₄×Q₁₆	—	3	1	no	—
323	C₄×SD₁₆	—	3	1	no	—
324	#433	—	3	1	no	—
325	C₂²×C₃×C₅	—	2	2	no	—
326	C₂²×C₃×C₅	—	4	1	no	—
327	C₂²×C₃×C₅	—	4	1	no	—
328	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₅×D₃	—	2	1	no	—
330	C₂×C₅×D₃	—	2	1	no	—
331	C₂×C₅×D₃	—	2	1	no	—
332	C₃×C₄×C₅	—	2	1	no	—
333	C₃×C₄×C₅	—	2	1	no	—
334	C₃×C₄×C₅	—	4	1	no	—
335	C₃×C₄×C₅	—	4	1	no	—
336	C₃×C₄×C₅	—	4	1	no	—
337	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
338	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
339	C₅×Dic₃	—	2	2	no	—
340	C₅×Dic₃	—	2	1	no	—
341	C₅×Dic₃	—	2	1	no	—
342	C₅×Dic₃	—	2	1	no	—
343	C₅×Dic₃	—	4	1	no	—
344	C₅×Dic₃	—	4	1	no	—
345	C₅×Dic₃	—	4	1	no	—
346	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
347	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
348	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
349	C₂²×C₃×C₄	—	2	1	no	—
350	C₂×#67	—	2	1	no	—
351	C₂²×Dic₃	—	2	1	no	—
352	C₂²×Dic₃	—	2	1	no	—
353	#237	—	2	2	no	—
354	#237	—	2	2	no	—
355	C₂×C₄×D₃	—	2	1	no	—
356	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
357	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
358	C₃×SD₁₆	—	2	2	no	—
359	C₃×SD₁₆	—	2	2	no	—
360	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
362	C₃×C₄⋊C₄	—	2	1	no	—
363	C₃×C₄⋊C₄	—	2	1	no	—
364	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
365	C₃×C₂²⋊C₄	—	2	1	no	—
366	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
367	#217	—	2	1	no	—
368	#216	—	2	2	no	—
369	#216	—	2	2	no	—
370	(C₂×D₃)⋊C₄	—	2	1	no	—
371	(C₂×D₃)⋊C₄	—	2	1	no	—
372	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
373	(C₂×D₃)⋊C₄	C₅×D₄	1	1	yes	characteristic
374	C₄⋊Dic₃	—	2	1	no	—
375	C₄⋊Dic₃	—	2	1	no	—
376	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
377	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
378	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
379	Dic₃⋊C₄	—	2	1	no	—
380	Dic₃⋊C₄	—	2	1	no	—
381	Dic₃⋊C₄	—	2	1	no	—
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	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
387	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
388	C₄×Dic₃	—	2	1	no	—
389	C₄×Dic₃	—	2	1	no	—
390	C₄×Dic₃	—	2	1	no	—
391	C₄×Dic₃	—	2	1	no	—
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	C₂³×C₅	—	2	1	no	—
396	C₂³×C₅	—	3	1	no	—
397	C₅×Q₈	—	2	1	no	—
398	C₅×Q₈	—	2	1	no	—
399	C₅×Q₈	—	2	1	no	—
400	C₅×Q₈	—	2	1	no	—
401	C₅×Q₈	—	3	2	no	—
402	C₅×Q₈	—	6	1	no	—
403	C₅×D₄	—	2	1	no	—
404	C₅×D₄	—	6	4	no	—
405	C₅×D₄	#237	1	2	yes	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	2	1	no	—
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	3	1	no	—
410	C₂×C₄×C₅	—	3	1	no	—
411	C₂×C₄×C₅	—	3	1	no	—
412	C₂×C₄×C₅	—	6	4	no	—
413	C₂×C₄×C₅	—	6	1	no	—
414	C₂×C₄×C₅	—	6	1	no	—
415	C₂×C₄×C₅	—	6	1	no	—
416	C₂×C₄×C₅	—	6	1	no	—
417	C₂×C₄×C₅	—	6	1	no	—
418	C₂×C₄×C₅	—	6	1	no	—
419	C₂×C₄×C₅	—	8	1	no	—
420	C₂×C₄×C₅	—	24	1	no	—
421	C₂×C₄×C₅	—	24	1	no	—
422	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
423	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
424	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
425	C₅×C₈	—	2	1	no	—
426	C₅×C₈	—	2	1	no	—
427	C₅×C₈	—	6	1	no	—
428	C₅×C₈	—	6	1	no	—
429	C₂×#41	—	3	1	no	—
430	C₂×Q₁₆	—	3	1	no	—
431	C₂×Q₁₆	—	3	1	no	—
432	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
433	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic
434	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
435	#126	—	6	1	no	—
436	#126	—	6	1	no	—
437	#125	—	3	1	no	—
438	#125	—	6	1	no	—
439	#125	—	6	1	no	—
440	C₂²⋊Q₈	—	3	1	no	—
441	C₂²⋊Q₈	—	3	1	no	—
442	C₄×Q₈	—	3	1	no	—
443	C₄×Q₈	—	3	1	no	—
444	C₄×Q₈	—	3	1	no	—
445	C₄×Q₈	—	3	1	no	—
446	C₄×D₄	—	3	1	no	—
447	C₄×D₄	—	6	1	no	—
448	C₄×D₄	—	6	1	no	—
449	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
450	#117	—	3	1	no	—
451	#117	—	6	1	no	—
452	C₂×C₄⋊C₄	—	3	1	no	—
453	C₂×C₄⋊C₄	—	6	1	no	—
454	#107	—	3	1	no	—
455	#107	—	3	1	no	—
456	#106	—	3	1	no	—
457	#106	—	3	1	no	—
458	C₄⋊C₈	—	3	1	no	—
459	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
460	#103	—	3	1	no	—
461	#103	—	3	1	no	—
462	#103	—	3	1	no	—
463	#103	—	3	1	no	—
464	#103	C₂×C₅×D₃	1	1	yes	characteristic
465	#103	C₂×C₅×D₃	1	1	yes	characteristic
466	#102	—	3	1	no	—
467	#102	—	3	1	no	—
468	C₂²⋊C₈	—	3	1	no	—
469	C₂²⋊C₈	—	3	1	no	—
470	#97	—	3	1	no	—
471	C₄×C₈	—	3	1	no	—
472	C₂×C₃×C₅	—	4	2	no	—
473	C₂×C₃×C₅	#525	1	1	yes	characteristic
474	C₂×C₃×C₅	#577	1	1	yes	characteristic
475	C₂×C₃×C₅	#578	1	1	yes	characteristic
476	C₅×D₃	—	4	1	no	—
477	C₂³×C₃	—	2	1	no	—
478	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
479	C₃×Q₈	—	2	1	no	—
480	C₃×Q₈	—	2	1	no	—
481	C₃×Q₈	—	2	1	no	—
482	C₃×Q₈	—	2	1	no	—
483	C₃×D₄	—	2	1	no	—
484	C₃×D₄	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	—	8	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	#67	—	2	4	no	—
493	C₂×Dic₃	—	2	4	no	—
494	C₂×Dic₃	—	2	1	no	—
495	C₂×Dic₃	—	2	1	no	—
496	C₂×Dic₃	—	2	1	no	—
497	C₂×Dic₃	—	2	1	no	—
498	C₂×Dic₃	—	8	1	no	—
499	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
500	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
501	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
502	C₄×D₃	—	2	1	no	—
503	C₄×D₃	—	2	1	no	—
504	C₄×D₃	—	8	1	no	—
505	Dic₆	—	2	1	no	—
506	Dic₆	C₅×#41	1	2	yes	—
507	C₃×C₈	—	2	1	no	—
508	C₃×C₈	—	2	1	no	—
509	C₃⋊C₈	—	2	1	no	—
510	C₃⋊C₈	—	2	1	no	—
511	C₂²×C₅	—	2	2	no	—
512	C₂²×C₅	—	4	1	no	—
513	C₂²×C₅	—	4	1	no	—
514	C₂²×C₅	—	6	1	no	—
515	C₂²×C₅	—	6	1	no	—
516	C₂²×C₅	—	6	1	no	—
517	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
518	C₄×C₅	—	2	1	no	—
519	C₄×C₅	—	2	1	no	—
520	C₄×C₅	—	4	1	no	—
521	C₄×C₅	—	4	1	no	—
522	C₄×C₅	—	4	1	no	—
523	C₄×C₅	—	6	1	no	—
524	C₄×C₅	—	6	1	no	—
525	C₄×C₅	—	6	1	no	—
526	C₄×C₅	—	6	2	no	—
527	C₄×C₅	—	12	1	no	—
528	C₄×C₅	—	12	1	no	—
529	C₄×C₅	—	12	1	no	—
530	C₄×C₅	C₂×#237	1	1	yes	characteristic
531	C₄×C₅	D₃×#41	1	1	yes	characteristic
532	#41	—	6	2	no	—
533	#41	—	6	2	no	—
534	C₂×Q₈	—	3	1	no	—
535	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
536	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
537	C₂×D₄	—	6	1	no	—
538	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	3	1	no	—
541	C₂²×C₄	—	6	1	no	—
542	C₂²×C₄	—	6	1	no	—
543	C₂²×C₄	—	6	1	no	—
544	Q₁₆	—	6	2	no	—
545	Q₁₆	—	6	2	no	—
546	SD₁₆	—	2	2	no	—
547	SD₁₆	—	2	2	no	—
548	C₂×C₈	—	3	1	no	—
549	C₂×C₈	—	3	1	no	—
550	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
551	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	3	1	no	—
555	C₄⋊C₄	—	3	1	no	—
556	C₄⋊C₄	—	3	1	no	—
557	C₄⋊C₄	—	3	1	no	—
558	C₄⋊C₄	—	3	1	no	—
559	C₄⋊C₄	—	6	1	no	—
560	C₄⋊C₄	—	6	1	no	—
561	C₄⋊C₄	—	6	1	no	—
562	C₄⋊C₄	—	6	1	no	—
563	C₄⋊C₄	—	6	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	C₂²×C₅×D₃	1	1	yes	characteristic
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	3	1	no	—
571	C₂²⋊C₄	—	3	1	no	—
572	C₂²⋊C₄	—	6	1	no	—
573	C₂²⋊C₄	—	6	1	no	—
574	C₂²⋊C₄	—	6	1	no	—
575	C₄²	—	3	1	no	—
576	C₄²	—	6	1	no	—
577	C₄²	—	6	1	no	—
578	C₄²	—	6	1	no	—
579	C₄²	—	6	1	no	—
580	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
581	C₃×C₅	#3120	1	1	yes	characteristic, complemented, Hall
582	C₂²×C₃	—	2	2	no	—
583	C₂²×C₃	—	4	1	no	—
584	C₂²×C₃	—	4	1	no	—
585	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
586	C₂×D₃	—	2	1	no	—
587	C₂×D₃	—	2	1	no	—
588	C₂×D₃	—	2	1	no	—
589	C₃×C₄	—	2	1	no	—
590	C₃×C₄	—	2	1	no	—
591	C₃×C₄	—	4	1	no	—
592	C₃×C₄	—	4	1	no	—
593	C₃×C₄	—	4	1	no	—
594	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
595	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
596	Dic₃	—	2	2	no	—
597	Dic₃	—	2	1	no	—
598	Dic₃	—	2	1	no	—
599	Dic₃	—	2	1	no	—
600	Dic₃	—	4	1	no	—
601	Dic₃	—	4	1	no	—
602	Dic₃	—	4	1	no	—
603	C₂×C₅	—	4	2	no	—
604	C₂×C₅	—	12	1	no	—
605	C₂×C₅	#5606	1	1	yes	characteristic
606	C₂×C₅	#5762	1	1	yes	characteristic
607	C₂×C₅	#5779	1	1	yes	characteristic
608	C₂³	—	2	1	no	—
609	C₂³	—	3	1	no	—
610	Q₈	—	2	1	no	—
611	Q₈	—	2	1	no	—
612	Q₈	—	2	1	no	—
613	Q₈	—	2	1	no	—
614	Q₈	—	3	2	no	—
615	Q₈	—	6	1	no	—
616	D₄	—	2	1	no	—
617	D₄	—	6	4	no	—
618	D₄	C₅×#237	1	2	yes	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	3	1	no	—
623	C₂×C₄	—	3	1	no	—
624	C₂×C₄	—	3	1	no	—
625	C₂×C₄	—	6	4	no	—
626	C₂×C₄	—	6	1	no	—
627	C₂×C₄	—	6	1	no	—
628	C₂×C₄	—	6	1	no	—
629	C₂×C₄	—	6	1	no	—
630	C₂×C₄	—	6	1	no	—
631	C₂×C₄	—	6	1	no	—
632	C₂×C₄	—	8	1	no	—
633	C₂×C₄	—	24	1	no	—
634	C₂×C₄	—	24	1	no	—
635	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
636	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
637	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
638	C₈	—	2	1	no	—
639	C₈	—	2	1	no	—
640	C₈	—	6	1	no	—
641	C₈	—	6	1	no	—
642	C₂×C₃	—	4	2	no	—
643	C₂×C₃	C₅×#525	1	1	yes	characteristic
644	C₂×C₃	C₅×#577	1	1	yes	characteristic
645	C₂×C₃	C₅×#578	1	1	yes	characteristic
646	D₃	—	4	1	no	—
647	C₅	#80412	1	1	yes	characteristic, direct product factor, Sylow
648	C₂²	—	2	2	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	6	1	no	—
652	C₂²	—	6	1	no	—
653	C₂²	—	6	1	no	—
654	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	—	6	1	no	—
661	C₄	—	6	1	no	—
662	C₄	—	6	1	no	—
663	C₄	—	6	2	no	—
664	C₄	—	12	1	no	—
665	C₄	—	12	1	no	—
666	C₄	—	12	1	no	—
667	C₄	C₂×C₅×#237	1	1	yes	characteristic
668	C₄	C₅×D₃×#41	1	1	yes	characteristic
669	C₃	C₅×#3120	1	1	yes	characteristic, complemented, Sylow
670	C₂	—	4	2	no	—
671	C₂	—	12	1	no	—
672	C₂	C₅×#5606	1	1	yes	characteristic
673	C₂	C₅×#5762	1	1	yes	characteristic
674	C₂	C₅×#5779	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×#461	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#237	C₂²
hypercenter	C₅×#461	D₃
hypocenter	C₃	C₅×#3120
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#461

Complements

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

N	H ≅ G/N	type
1. C₅×#5731	C₂	semidirect
3. C₃×C₅×#461	C₂	semidirect
6. C₅×#5164	C₂	semidirect
7. C₅×Dic₃×SD₁₆	C₂	semidirect
8. C₅×#5090	C₂	semidirect
9. C₅×#5009	C₂	semidirect
10. C₅×#4840	C₂	semidirect
11. C₅×#4829	C₂	semidirect
12. C₅×#4811	C₂	semidirect
13. C₅×#4805	C₂	semidirect
14. C₅×#4790	C₂	semidirect
15. C₅×#4789	C₂	semidirect
60. #80412	C₅	direct (N × H)
68. C₅×#461	D₃	semidirect
125. #5731	C₂×C₅	semidirect
127. C₃×#461	C₂×C₅	semidirect
130. #5164	C₂×C₅	semidirect
131. Dic₃×SD₁₆	C₂×C₅	semidirect
132. #5090	C₂×C₅	semidirect
133. #5009	C₂×C₅	semidirect
134. #4840	C₂×C₅	semidirect
135. #4829	C₂×C₅	semidirect
136. #4811	C₂×C₅	semidirect
137. #4805	C₂×C₅	semidirect
138. #4790	C₂×C₅	semidirect
139. #4789	C₂×C₅	semidirect
317. #461	C₅×D₃	semidirect
581. C₃×C₅	#3120	semidirect
647. C₅	#80412	direct (N × H)
669. C₃	C₅×#3120	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5731	2
C₅×#5546	2
C₃×C₅×#461	2
C₅×#5173	2
C₅×#5164	2
C₅×Dic₃×SD₁₆	2
C₅×#5090	2
C₅×#5009	2
C₅×#4840	2
C₅×#4829	2
C₅×#4811	2
C₅×#4805	2
C₅×#4790	2
C₅×#4789	2
C₅×#3120	3
#80412	5

Subgroups — C5×#80412 #14436084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#80412 #14436084