Subgroups — C₅×#78640 #14424114

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#909	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#407	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5133	C₂	1	2	yes	maximal, complemented
6	C₅×#4739	C₂	1	2	yes	maximal, complemented
7	C₅×#4733	C₂	1	4	yes	maximal, complemented
8	C₅×#4731	C₂	1	2	yes	maximal, complemented
9	C₅×#3007	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	—	2	1	no	—
12	C₂×C₅×#235	—	2	1	no	—
13	C₂×C₅×#235	—	2	1	no	—
14	C₂×C₅×#235	—	2	8	no	—
15	C₂×C₅×#235	C₂²	1	2	yes	—
16	C₂×C₅×#235	C₂²	1	2	yes	—
17	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₅×D₃	—	2	1	no	—
19	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
22	C₂×C₅×#217	—	2	1	no	—
23	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
24	C₅×#924	—	2	1	no	—
25	C₅×#924	—	2	1	no	—
26	C₅×#924	C₂²	1	2	yes	—
27	C₅×#924	C₂²	1	2	yes	complemented
28	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
29	C₅×#909	—	2	8	no	—
30	C₂×C₅×Dic₁₂	C₂²	1	4	yes	complemented
31	C₂×C₅×#204	C₂²	1	4	yes	complemented
32	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
34	C₅×#821	C₂²	1	4	yes	complemented
35	C₅×#816	C₂²	1	4	yes	complemented
36	#78640	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂²×C₅×#41	—	3	1	no	—
38	C₂×C₅×#137	—	3	2	no	—
39	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
40	C₅×#452	—	3	4	no	—
41	C₅×#451	—	3	2	no	—
42	C₅×#450	—	3	2	no	—
43	C₅×#417	—	3	2	no	—
44	C₅×#407	D₃	1	1	yes	characteristic, complemented
45	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
46	C₂³×C₅×D₃	—	2	1	no	—
47	C₂²×C₃×C₄×C₅	—	2	4	no	—
48	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₅×#67	—	2	8	no	—
55	C₂×C₅×#67	—	2	2	no	—
56	C₂×C₅×#67	—	2	2	no	—
57	C₂²×C₅×Dic₃	—	2	1	no	—
58	C₂²×C₅×Dic₃	—	2	1	no	—
59	C₂²×C₅×Dic₃	—	2	1	no	—
60	C₅×#235	—	2	8	no	—
61	C₅×#235	—	2	8	no	—
62	C₅×#235	—	2	4	no	—
63	C₅×#235	—	2	4	no	—
64	C₅×#235	—	2	4	no	—
65	C₅×#235	D₄	1	8	yes	—
66	C₂×C₅×D₁₂	—	2	1	no	—
67	C₂×C₅×D₁₂	—	2	4	no	—
68	C₂×C₅×D₁₂	C₂³	1	2	yes	—
69	C₂×C₄×C₅×D₃	—	2	8	no	—
70	C₂×C₄×C₅×D₃	—	2	2	no	—
71	C₂×C₄×C₅×D₃	—	2	2	no	—
72	C₂×C₅×Dic₆	—	2	1	no	—
73	C₂×C₅×Dic₆	—	2	4	no	—
74	C₂×C₅×Dic₆	—	2	4	no	—
75	C₂×C₅×Dic₆	—	2	1	no	—
76	C₂×C₅×Dic₆	C₂³	1	2	yes	—
77	C₂×C₅×Dic₆	C₂³	1	2	yes	—
78	C₃×C₅×M₁₆	—	2	4	no	—
79	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
80	C₅×#217	—	2	2	no	—
81	C₅×#217	—	2	2	no	—
82	C₅×C₄⋊Dic₃	—	2	1	no	—
83	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
84	C₅×Dic₃⋊C₄	—	2	2	no	—
85	C₅×Dic₃⋊C₄	—	2	2	no	—
86	C₅×Dic₁₂	—	2	8	no	—
87	C₅×#204	—	2	8	no	—
88	C₂²×#235	C₂×C₅	1	1	yes	characteristic
89	C₂×#924	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×#909	C₂×C₅	1	2	yes	complemented
91	C₃×#407	C₂×C₅	1	1	yes	characteristic, complemented
92	#5133	C₂×C₅	1	2	yes	complemented
93	#4739	C₂×C₅	1	2	yes	complemented
94	#4733	C₂×C₅	1	4	yes	complemented
95	#4731	C₂×C₅	1	2	yes	complemented
96	C₂×C₅×#41	—	3	2	no	—
97	C₂×C₅×#41	—	3	2	no	—
98	C₂×C₅×#41	—	6	8	no	—
99	C₂×C₅×#41	—	6	1	no	—
100	C₂×C₅×#41	—	6	1	no	—
101	C₂²×C₅×Q₈	—	3	1	no	—
102	C₂²×C₅×Q₈	—	3	1	no	—
103	C₂²×C₅×D₄	—	3	1	no	—
104	C₂²×C₅×D₄	—	6	1	no	—
105	C₂³×C₄×C₅	—	6	1	no	—
106	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
107	C₅×#137	—	6	8	no	—
108	C₂×C₅×Q₁₆	—	3	4	no	—
109	C₂×C₅×SD₁₆	—	3	4	no	—
110	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	complemented
111	C₅×C₂²⋊Q₈	—	3	2	no	—
112	C₅×C₂²⋊Q₈	—	3	2	no	—
113	C₅×C₂²⋊Q₈	—	6	1	no	—
114	C₅×C₂²⋊Q₈	—	6	1	no	—
115	C₂×C₅×C₄⋊C₄	—	3	1	no	—
116	C₂×C₅×C₄⋊C₄	—	6	1	no	—
117	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
118	C₅×#103	—	3	4	no	—
119	C₅×#102	—	3	4	no	—
120	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
121	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	complemented
122	#3007	—	3	1	no	Sylow
123	C₂³×C₃×C₅	—	2	2	no	—
124	C₂³×C₃×C₅	—	2	2	no	—
125	C₂³×C₃×C₅	—	4	1	no	—
126	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₅×D₃	—	2	4	no	—
130	C₂²×C₅×D₃	—	2	2	no	—
131	C₂²×C₅×D₃	—	4	2	no	—
132	C₂²×C₅×D₃	—	4	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₅×#67	—	2	8	no	—
144	C₅×#67	—	2	8	no	—
145	C₂×C₅×Dic₃	—	2	4	no	—
146	C₂×C₅×Dic₃	—	2	2	no	—
147	C₂×C₅×Dic₃	—	2	2	no	—
148	C₂×C₅×Dic₃	—	2	2	no	—
149	C₂×C₅×Dic₃	—	4	2	no	—
150	C₂×C₅×Dic₃	—	4	2	no	—
151	C₅×D₁₂	—	2	4	no	—
152	C₅×D₁₂	—	2	2	no	—
153	C₅×D₁₂	C₂×D₄	1	4	yes	—
154	C₄×C₅×D₃	—	2	8	no	—
155	C₄×C₅×D₃	—	2	8	no	—
156	C₅×Dic₆	—	2	4	no	—
157	C₅×Dic₆	—	2	2	no	—
158	C₅×Dic₆	—	2	4	no	—
159	C₅×Dic₆	—	4	2	no	—
160	C₅×Dic₆	C₂×D₄	1	4	yes	—
161	C₃×C₅×C₈	—	2	4	no	—
162	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
163	C₂²×#67	—	2	1	no	—
164	C₂×#235	—	2	1	no	—
165	C₂×#235	—	2	1	no	—
166	C₂×#235	—	2	8	no	—
167	C₂×#235	C₂²×C₅	1	2	yes	—
168	C₂×#235	C₂²×C₅	1	2	yes	—
169	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
170	C₂²×C₄×D₃	—	2	1	no	—
171	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
172	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
173	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
174	C₂×#217	—	2	1	no	—
175	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
176	#924	—	2	1	no	—
177	#924	—	2	1	no	—
178	#924	C₂²×C₅	1	2	yes	—
179	#924	C₂²×C₅	1	2	yes	complemented
180	C₂×Dic₃⋊C₄	—	2	1	no	—
181	#909	—	2	8	no	—
182	C₂×Dic₁₂	C₂²×C₅	1	4	yes	complemented
183	C₂×#204	C₂²×C₅	1	4	yes	complemented
184	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
185	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
186	#821	C₂²×C₅	1	4	yes	complemented
187	#816	C₂²×C₅	1	4	yes	complemented
188	C₂⁴×C₅	—	6	1	no	—
189	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
190	C₅×#41	—	3	8	no	—
191	C₅×#41	—	6	4	no	—
192	C₅×#41	—	6	4	no	—
193	C₅×#41	—	6	8	no	—
194	C₅×#41	—	6	8	no	—
195	C₅×#41	—	6	4	no	—
196	C₂×C₅×Q₈	—	3	2	no	—
197	C₂×C₅×Q₈	—	3	2	no	—
198	C₂×C₅×Q₈	—	6	4	no	—
199	C₂×C₅×Q₈	—	6	1	no	—
200	C₂×C₅×Q₈	—	6	1	no	—
201	C₂×C₅×Q₈	—	6	4	no	—
202	C₂×C₅×D₄	—	3	2	no	—
203	C₂×C₅×D₄	—	6	4	no	—
204	C₂×C₅×D₄	—	6	8	no	—
205	C₂×C₅×D₄	—	6	2	no	—
206	C₂×C₅×D₄	—	6	2	no	—
207	C₂×C₅×D₄	—	6	1	no	—
208	C₂²×C₄×C₅	—	2	4	no	—
209	C₂²×C₄×C₅	—	6	8	no	—
210	C₂²×C₄×C₅	—	6	1	no	—
211	C₂²×C₄×C₅	—	6	2	no	—
212	C₂²×C₄×C₅	—	6	2	no	—
213	C₂²×C₄×C₅	—	6	1	no	—
214	C₂²×C₄×C₅	—	6	1	no	—
215	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
216	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
217	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
221	C₅×Q₁₆	—	6	8	no	—
222	C₅×SD₁₆	—	6	8	no	—
223	C₅×M₁₆	—	2	4	no	—
224	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
225	C₅×C₄⋊C₄	—	3	2	no	—
226	C₅×C₄⋊C₄	—	6	1	no	—
227	C₅×C₄⋊C₄	—	6	2	no	—
228	C₅×C₄⋊C₄	—	6	2	no	—
229	C₅×C₂²⋊C₄	—	6	2	no	—
230	C₅×C₂²⋊C₄	—	6	2	no	—
231	C₂²×#41	—	3	1	no	—
232	C₂×#137	—	3	2	no	—
233	C₂×C₂²⋊Q₈	—	3	1	no	—
234	#452	—	3	4	no	—
235	#451	—	3	2	no	—
236	#450	—	3	2	no	—
237	#417	—	3	2	no	—
238	#407	C₅×D₃	1	1	yes	characteristic, complemented
239	C₂²×C₃×C₅	—	2	1	no	—
240	C₂²×C₃×C₅	—	2	1	no	—
241	C₂²×C₃×C₅	—	2	1	no	—
242	C₂²×C₃×C₅	—	2	1	no	—
243	C₂²×C₃×C₅	—	2	1	no	—
244	C₂²×C₃×C₅	—	2	1	no	—
245	C₂²×C₃×C₅	—	2	1	no	—
246	C₂²×C₃×C₅	—	4	4	no	—
247	C₂²×C₃×C₅	#120	1	2	yes	—
248	C₂²×C₃×C₅	#137	1	2	yes	complemented
249	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₅×D₃	—	2	4	no	—
251	C₂×C₅×D₃	—	4	8	no	—
252	C₂×C₅×D₃	—	4	2	no	—
253	C₂×C₅×D₃	—	4	2	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	#120	1	2	yes	—
257	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
258	C₅×Dic₃	—	2	4	no	—
259	C₅×Dic₃	—	4	2	no	—
260	C₅×Dic₃	—	4	2	no	—
261	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
262	C₂³×D₃	—	2	1	no	—
263	C₂²×C₃×C₄	—	2	4	no	—
264	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
265	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
269	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
270	C₂×#67	—	2	8	no	—
271	C₂×#67	—	2	2	no	—
272	C₂×#67	—	2	2	no	—
273	C₂²×Dic₃	—	2	1	no	—
274	C₂²×Dic₃	—	2	1	no	—
275	C₂²×Dic₃	—	2	1	no	—
276	#235	—	2	8	no	—
277	#235	—	2	8	no	—
278	#235	—	2	4	no	—
279	#235	—	2	4	no	—
280	#235	—	2	4	no	—
281	#235	C₅×D₄	1	8	yes	—
282	C₂×D₁₂	—	2	1	no	—
283	C₂×D₁₂	—	2	4	no	—
284	C₂×D₁₂	C₂³×C₅	1	2	yes	—
285	C₂×C₄×D₃	—	2	8	no	—
286	C₂×C₄×D₃	—	2	2	no	—
287	C₂×C₄×D₃	—	2	2	no	—
288	C₂×Dic₆	—	2	1	no	—
289	C₂×Dic₆	—	2	4	no	—
290	C₂×Dic₆	—	2	4	no	—
291	C₂×Dic₆	—	2	1	no	—
292	C₂×Dic₆	C₂³×C₅	1	2	yes	—
293	C₂×Dic₆	C₂³×C₅	1	2	yes	—
294	C₃×M₁₆	—	2	4	no	—
295	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
296	#217	—	2	2	no	—
297	#217	—	2	2	no	—
298	C₄⋊Dic₃	—	2	1	no	—
299	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
300	Dic₃⋊C₄	—	2	2	no	—
301	Dic₃⋊C₄	—	2	2	no	—
302	Dic₁₂	—	2	8	no	—
303	#204	—	2	8	no	—
304	C₂³×C₅	—	2	2	no	—
305	C₂³×C₅	—	2	2	no	—
306	C₂³×C₅	—	4	1	no	—
307	C₂³×C₅	—	6	4	no	—
308	C₂³×C₅	—	6	2	no	—
309	C₂³×C₅	—	12	2	no	—
310	C₂³×C₅	—	12	2	no	—
311	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
312	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
313	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
314	C₅×Q₈	—	3	4	no	—
315	C₅×Q₈	—	6	4	no	—
316	C₅×Q₈	—	6	2	no	—
317	C₅×Q₈	—	6	4	no	—
318	C₅×Q₈	—	12	2	no	—
319	C₅×D₄	—	3	4	no	—
320	C₅×D₄	—	6	4	no	—
321	C₅×D₄	—	6	8	no	—
322	C₅×D₄	—	6	8	no	—
323	C₅×D₄	—	6	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	2	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	6	8	no	—
330	C₂×C₄×C₅	—	6	4	no	—
331	C₂×C₄×C₅	—	6	2	no	—
332	C₂×C₄×C₅	—	6	8	no	—
333	C₂×C₄×C₅	—	6	2	no	—
334	C₂×C₄×C₅	—	6	2	no	—
335	C₂×C₄×C₅	—	12	2	no	—
336	C₂×C₄×C₅	—	12	2	no	—
337	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
338	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
339	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
340	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
341	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
342	C₅×C₈	—	2	4	no	—
343	C₂×#41	—	3	2	no	—
344	C₂×#41	—	3	2	no	—
345	C₂×#41	—	6	8	no	—
346	C₂×#41	—	6	1	no	—
347	C₂×#41	—	6	1	no	—
348	C₂²×Q₈	—	3	1	no	—
349	C₂²×Q₈	—	3	1	no	—
350	C₂²×D₄	—	3	1	no	—
351	C₂²×D₄	—	6	1	no	—
352	C₂³×C₄	—	6	1	no	—
353	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
354	#137	—	6	8	no	—
355	C₂×Q₁₆	—	3	4	no	—
356	C₂×SD₁₆	—	3	4	no	—
357	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	complemented
358	C₂²⋊Q₈	—	3	2	no	—
359	C₂²⋊Q₈	—	3	2	no	—
360	C₂²⋊Q₈	—	6	1	no	—
361	C₂²⋊Q₈	—	6	1	no	—
362	C₂×C₄⋊C₄	—	3	1	no	—
363	C₂×C₄⋊C₄	—	6	1	no	—
364	C₂×C₂²⋊C₄	—	6	1	no	—
365	#103	—	3	4	no	—
366	#102	—	3	4	no	—
367	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	—
368	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	complemented
369	C₂×C₃×C₅	—	2	2	no	—
370	C₂×C₃×C₅	—	2	2	no	—
371	C₂×C₃×C₅	—	4	1	no	—
372	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
373	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
374	C₂×C₃×C₅	#575	1	1	yes	characteristic
375	C₅×D₃	—	4	4	no	—
376	C₂³×C₃	—	2	2	no	—
377	C₂³×C₃	—	2	2	no	—
378	C₂³×C₃	—	4	1	no	—
379	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂²×D₃	—	2	4	no	—
383	C₂²×D₃	—	2	2	no	—
384	C₂²×D₃	—	4	2	no	—
385	C₂²×D₃	—	4	2	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
392	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
395	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
396	#67	—	2	8	no	—
397	#67	—	2	8	no	—
398	C₂×Dic₃	—	2	4	no	—
399	C₂×Dic₃	—	2	2	no	—
400	C₂×Dic₃	—	2	2	no	—
401	C₂×Dic₃	—	2	2	no	—
402	C₂×Dic₃	—	4	2	no	—
403	C₂×Dic₃	—	4	2	no	—
404	D₁₂	—	2	4	no	—
405	D₁₂	—	2	2	no	—
406	D₁₂	C₂×C₅×D₄	1	4	yes	—
407	C₄×D₃	—	2	8	no	—
408	C₄×D₃	—	2	8	no	—
409	Dic₆	—	2	4	no	—
410	Dic₆	—	2	2	no	—
411	Dic₆	—	2	4	no	—
412	Dic₆	—	4	2	no	—
413	Dic₆	C₂×C₅×D₄	1	4	yes	—
414	C₃×C₈	—	2	4	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	2	1	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	4	4	no	—
423	C₂²×C₅	—	6	4	no	—
424	C₂²×C₅	—	12	8	no	—
425	C₂²×C₅	—	12	2	no	—
426	C₂²×C₅	—	12	2	no	—
427	C₂²×C₅	#882	1	2	yes	—
428	C₂²×C₅	#909	1	2	yes	complemented
429	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
430	C₄×C₅	—	2	1	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	6	4	no	—
433	C₄×C₅	—	12	2	no	—
434	C₄×C₅	—	12	2	no	—
435	C₄×C₅	#882	1	2	yes	—
436	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
437	C₂⁴	—	6	1	no	—
438	C₂⁴	C₅×D₁₂	1	1	yes	characteristic
439	#41	—	3	8	no	—
440	#41	—	6	4	no	—
441	#41	—	6	4	no	—
442	#41	—	6	8	no	—
443	#41	—	6	8	no	—
444	#41	—	6	4	no	—
445	C₂×Q₈	—	3	2	no	—
446	C₂×Q₈	—	3	2	no	—
447	C₂×Q₈	—	6	4	no	—
448	C₂×Q₈	—	6	1	no	—
449	C₂×Q₈	—	6	1	no	—
450	C₂×Q₈	—	6	4	no	—
451	C₂×D₄	—	3	2	no	—
452	C₂×D₄	—	6	4	no	—
453	C₂×D₄	—	6	8	no	—
454	C₂×D₄	—	6	2	no	—
455	C₂×D₄	—	6	2	no	—
456	C₂×D₄	—	6	1	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	6	8	no	—
459	C₂²×C₄	—	6	1	no	—
460	C₂²×C₄	—	6	2	no	—
461	C₂²×C₄	—	6	2	no	—
462	C₂²×C₄	—	6	1	no	—
463	C₂²×C₄	—	6	1	no	—
464	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
465	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
466	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
468	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
469	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
470	Q₁₆	—	6	8	no	—
471	SD₁₆	—	6	8	no	—
472	M₁₆	—	2	4	no	—
473	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
474	C₄⋊C₄	—	3	2	no	—
475	C₄⋊C₄	—	6	1	no	—
476	C₄⋊C₄	—	6	2	no	—
477	C₄⋊C₄	—	6	2	no	—
478	C₂²⋊C₄	—	6	2	no	—
479	C₂²⋊C₄	—	6	2	no	—
480	C₃×C₅	#3007	1	1	yes	characteristic, complemented, Hall
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	2	1	no	—
487	C₂²×C₃	—	2	1	no	—
488	C₂²×C₃	—	4	4	no	—
489	C₂²×C₃	C₅×#120	1	2	yes	—
490	C₂²×C₃	C₅×#137	1	2	yes	complemented
491	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
492	C₂×D₃	—	2	4	no	—
493	C₂×D₃	—	4	8	no	—
494	C₂×D₃	—	4	2	no	—
495	C₂×D₃	—	4	2	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	C₅×#120	1	2	yes	—
499	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
500	Dic₃	—	2	4	no	—
501	Dic₃	—	4	2	no	—
502	Dic₃	—	4	2	no	—
503	C₂×C₅	—	2	2	no	—
504	C₂×C₅	—	2	2	no	—
505	C₂×C₅	—	4	1	no	—
506	C₂×C₅	—	12	4	no	—
507	C₂×C₅	C₂×#882	1	1	yes	characteristic
508	C₂×C₅	C₂×#909	1	1	yes	characteristic
509	C₂×C₅	#5748	1	1	yes	characteristic
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	6	4	no	—
514	C₂³	—	6	2	no	—
515	C₂³	—	12	2	no	—
516	C₂³	—	12	2	no	—
517	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
518	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
519	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
520	Q₈	—	3	4	no	—
521	Q₈	—	6	4	no	—
522	Q₈	—	6	2	no	—
523	Q₈	—	6	4	no	—
524	Q₈	—	12	2	no	—
525	D₄	—	3	4	no	—
526	D₄	—	6	4	no	—
527	D₄	—	6	8	no	—
528	D₄	—	6	8	no	—
529	D₄	—	6	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	6	8	no	—
536	C₂×C₄	—	6	4	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	6	8	no	—
539	C₂×C₄	—	6	2	no	—
540	C₂×C₄	—	6	2	no	—
541	C₂×C₄	—	12	2	no	—
542	C₂×C₄	—	12	2	no	—
543	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
544	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
545	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
546	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
547	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
548	C₈	—	2	4	no	—
549	C₂×C₃	—	2	2	no	—
550	C₂×C₃	—	2	2	no	—
551	C₂×C₃	—	4	1	no	—
552	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
553	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
554	C₂×C₃	C₅×#575	1	1	yes	characteristic
555	D₃	—	4	4	no	—
556	C₅	#78640	1	1	yes	characteristic, direct product factor, Sylow
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	6	4	no	—
566	C₂²	—	12	8	no	—
567	C₂²	—	12	2	no	—
568	C₂²	—	12	2	no	—
569	C₂²	C₅×#882	1	2	yes	—
570	C₂²	C₅×#909	1	2	yes	complemented
571	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	6	4	no	—
575	C₄	—	12	2	no	—
576	C₄	—	12	2	no	—
577	C₄	C₅×#882	1	2	yes	—
578	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
579	C₃	C₅×#3007	1	1	yes	characteristic, complemented, Sylow
580	C₂	—	2	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	4	1	no	—
583	C₂	—	12	4	no	—
584	C₂	C₂×C₅×#882	1	1	yes	characteristic
585	C₂	C₂×C₅×#909	1	1	yes	characteristic
586	C₂	C₅×#5748	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#407	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×#235	C₂
hypercenter	C₅×#407	D₃
hypocenter	C₃	C₅×#3007
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₅×#407

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#924	C₂	semidirect
3. C₂×C₅×#909	C₂	semidirect
4. C₃×C₅×#407	C₂	semidirect
5. C₅×#5133	C₂	semidirect
6. C₅×#4739	C₂	semidirect
7. C₅×#4733	C₂	semidirect
8. C₅×#4731	C₂	semidirect
20. C₂²×C₅×Dic₆	C₂²	semidirect
21. C₂×C₃×C₅×M₁₆	C₂²	semidirect
23. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
27. C₅×#924	C₂²	semidirect
30. C₂×C₅×Dic₁₂	C₂²	semidirect
31. C₂×C₅×#204	C₂²	semidirect
33. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
34. C₅×#821	C₂²	semidirect
35. C₅×#816	C₂²	semidirect
36. #78640	C₅	direct (N × H)
44. C₅×#407	D₃	semidirect
89. C₂×#924	C₂×C₅	semidirect
90. C₂×#909	C₂×C₅	semidirect
91. C₃×#407	C₂×C₅	semidirect
92. #5133	C₂×C₅	semidirect
93. #4739	C₂×C₅	semidirect
94. #4733	C₂×C₅	semidirect
95. #4731	C₂×C₅	semidirect
110. C₂×C₅×M₁₆	C₂×D₃	semidirect
121. C₅×C₂²⋊C₈	C₂×D₃	semidirect
172. C₂²×Dic₆	C₂²×C₅	semidirect
173. C₂×C₃×M₁₆	C₂²×C₅	semidirect
175. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
179. #924	C₂²×C₅	semidirect
182. C₂×Dic₁₂	C₂²×C₅	semidirect
183. C₂×#204	C₂²×C₅	semidirect
185. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
186. #821	C₂²×C₅	semidirect
187. #816	C₂²×C₅	semidirect
238. #407	C₅×D₃	semidirect
248. C₂²×C₃×C₅	#137	semidirect
357. C₂×M₁₆	C₂×C₅×D₃	semidirect
368. C₂²⋊C₈	C₂×C₅×D₃	semidirect
428. C₂²×C₅	#909	semidirect
480. C₃×C₅	#3007	semidirect
490. C₂²×C₃	C₅×#137	semidirect
556. C₅	#78640	direct (N × H)
570. C₂²	C₅×#909	semidirect
579. C₃	C₅×#3007	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#235	2
C₂×C₅×#924	2
C₂×C₅×#909	2
C₃×C₅×#407	2
C₅×#5133	2
C₅×#4739	2
C₅×#4733	2
C₅×#4731	2
C₅×#3007	3
#78640	5

Subgroups — C5×#78640 #14424114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78640 #14424114