Subgroups — C₅×#78731 #14430768

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5798	C₂	1	1	yes	maximal, characteristic
2	C₅×#5500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic
4	C₅×#5215	C₂	1	1	yes	maximal, characteristic
5	C₅×#5106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4964	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4766	C₂	1	2	yes	maximal, complemented
9	C₅×#4763	C₂	1	2	yes	maximal, complemented
10	C₅×#4761	C₂	1	2	yes	maximal, complemented
11	C₅×#4759	C₂	1	2	yes	maximal, complemented
12	C₅×#3081	—	3	1	no	maximal, Hall
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₅×#217	—	2	2	no	—
17	C₅×D₄×Dic₃	—	2	1	no	—
18	C₅×D₄×Dic₃	—	2	1	no	—
19	C₅×D₄×Dic₃	C₂²	1	2	yes	—
20	C₅×D₄×Dic₃	C₂²	1	2	yes	—
21	C₅×#926	C₂²	1	1	yes	characteristic
22	C₅×#926	C₂²	1	1	yes	characteristic
23	C₅×#926	C₂²	1	1	yes	characteristic
24	C₅×#924	—	2	2	no	—
25	C₂×C₅×#208	C₂²	1	1	yes	characteristic
26	C₅×#890	—	2	1	no	—
27	C₅×#890	C₂²	1	2	yes	complemented
28	C₅×#888	—	2	1	no	—
29	C₅×#888	C₂²	1	2	yes	complemented
30	C₃×C₅×#102	C₂²	1	2	yes	—
31	C₃×C₅×#102	C₂²	1	2	yes	—
32	C₅×#832	C₂²	1	2	yes	—
33	C₅×#832	C₂²	1	2	yes	—
34	C₅×#818	C₂²	1	1	yes	characteristic, complemented
35	C₅×#818	C₂²	1	1	yes	characteristic, complemented
36	C₅×#817	C₂²	1	1	yes	characteristic, complemented
37	C₅×#817	C₂²	1	1	yes	characteristic, complemented
38	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
39	C₅×Dic₃⋊C₈	C₂²	1	2	yes	complemented
40	C₅×#808	C₂²	1	2	yes	complemented
41	C₅×#807	C₂²	1	2	yes	complemented
42	#78731	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#544	—	3	1	no	—
44	C₅×#518	—	3	1	no	—
45	C₅×#478	—	3	2	no	—
46	C₅×#478	—	3	2	no	—
47	C₅×#476	—	3	2	no	—
48	C₅×#474	—	3	2	no	—
49	C₅×#428	—	3	1	no	—
50	C₅×#427	—	3	1	no	—
51	C₅×#424	—	3	1	no	—
52	C₅×#418	—	3	1	no	—
53	C₂×C₅×#102	D₃	1	1	yes	characteristic
54	C₂⁴×C₃×C₅	—	2	1	no	—
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	Q₈	1	4	yes	complemented
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₅×Dic₃	—	2	2	no	—
62	C₂²×C₅×Dic₃	—	2	2	no	—
63	C₂×C₅×Dic₆	—	2	2	no	—
64	C₂×C₃×C₅×C₈	—	2	2	no	—
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₅×#217	—	2	1	no	—
70	C₅×#217	—	2	1	no	—
71	C₅×#217	—	2	2	no	—
72	C₅×#217	—	2	2	no	—
73	C₅×#217	D₄	1	2	yes	—
74	C₅×C₄⋊Dic₃	—	2	2	no	—
75	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
76	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
77	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
78	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
79	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
80	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
81	C₅×Dic₃⋊C₄	—	2	2	no	—
82	C₅×Dic₃⋊C₄	—	2	2	no	—
83	C₄×C₅×Dic₃	—	2	1	no	—
84	C₄×C₅×Dic₃	—	2	1	no	—
85	C₄×C₅×Dic₃	C₂³	1	2	yes	—
86	C₅×#208	—	2	2	no	—
87	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
88	#5798	C₂×C₅	1	1	yes	characteristic
89	#5500	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic
91	#5215	C₂×C₅	1	1	yes	characteristic
92	#5106	C₂×C₅	1	1	yes	characteristic, complemented
93	#5102	C₂×C₅	1	1	yes	characteristic, complemented
94	#4964	C₂×C₅	1	1	yes	characteristic, complemented
95	#4766	C₂×C₅	1	2	yes	complemented
96	#4763	C₂×C₅	1	2	yes	complemented
97	#4761	C₂×C₅	1	2	yes	complemented
98	#4759	C₂×C₅	1	2	yes	complemented
99	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
100	C₂×C₅×M₁₆	—	3	1	no	—
101	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
102	C₅×C₄⋊Q₈	—	3	2	no	—
103	C₅×C₄⋊Q₈	—	6	1	no	—
104	C₅×#125	—	3	2	no	—
105	C₅×#125	—	6	1	no	—
106	C₅×C₂²⋊Q₈	—	6	2	no	—
107	C₄×C₅×D₄	—	3	2	no	—
108	C₄×C₅×D₄	—	3	2	no	—
109	C₄×C₅×D₄	—	6	1	no	—
110	C₄×C₅×D₄	—	6	1	no	—
111	C₅×#117	—	3	1	no	—
112	C₅×#117	—	3	1	no	—
113	C₅×#117	—	3	1	no	—
114	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
115	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
116	C₅×#107	—	3	1	no	—
117	C₅×#107	—	3	1	no	—
118	C₅×#107	—	3	2	no	—
119	C₅×#106	—	3	1	no	—
120	C₅×#106	—	3	1	no	—
121	C₅×#106	—	3	2	no	—
122	C₅×C₄⋊C₈	—	3	2	no	—
123	C₅×C₄⋊C₈	—	3	2	no	—
124	C₅×#102	—	3	2	no	—
125	C₅×#102	—	3	2	no	—
126	C₅×#102	C₂×D₃	1	2	yes	—
127	C₅×#102	C₂×D₃	1	2	yes	—
128	#3081	—	3	1	no	Sylow
129	C₂³×C₃×C₅	—	2	2	no	—
130	C₂³×C₃×C₅	—	2	4	no	—
131	C₂³×C₃×C₅	—	8	1	no	—
132	C₂³×C₃×C₅	—	8	1	no	—
133	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
134	C₃×C₅×D₄	—	2	4	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	C₂×Q₈	1	4	yes	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	8	1	no	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
141	C₂×C₃×C₄×C₅	#41	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₂×C₅×Dic₃	—	2	1	no	—
144	C₂×C₅×Dic₃	—	2	1	no	—
145	C₂×C₅×Dic₃	—	2	1	no	—
146	C₂×C₅×Dic₃	—	2	1	no	—
147	C₂×C₅×Dic₃	—	8	2	no	—
148	C₂×C₅×Dic₃	—	8	2	no	—
149	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
150	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
151	C₅×Dic₆	—	8	2	no	—
152	C₃×C₅×C₈	—	2	1	no	—
153	C₃×C₅×C₈	—	2	1	no	—
154	C₅×C₃⋊C₈	—	2	2	no	—
155	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
156	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
158	C₂×#217	—	2	2	no	—
159	D₄×Dic₃	—	2	1	no	—
160	D₄×Dic₃	—	2	1	no	—
161	D₄×Dic₃	C₂²×C₅	1	2	yes	—
162	D₄×Dic₃	C₂²×C₅	1	2	yes	—
163	#926	C₂²×C₅	1	1	yes	characteristic
164	#926	C₂²×C₅	1	1	yes	characteristic
165	#926	C₂²×C₅	1	1	yes	characteristic
166	#924	—	2	2	no	—
167	C₂×#208	C₂²×C₅	1	1	yes	characteristic
168	#890	—	2	1	no	—
169	#890	C₂²×C₅	1	2	yes	complemented
170	#888	—	2	1	no	—
171	#888	C₂²×C₅	1	2	yes	complemented
172	C₃×#102	C₂²×C₅	1	2	yes	—
173	C₃×#102	C₂²×C₅	1	2	yes	—
174	#832	C₂²×C₅	1	2	yes	—
175	#832	C₂²×C₅	1	2	yes	—
176	#818	C₂²×C₅	1	1	yes	characteristic, complemented
177	#818	C₂²×C₅	1	1	yes	characteristic, complemented
178	#817	C₂²×C₅	1	1	yes	characteristic, complemented
179	#817	C₂²×C₅	1	1	yes	characteristic, complemented
180	Dic₃⋊C₈	C₂²×C₅	1	2	yes	complemented
181	Dic₃⋊C₈	C₂²×C₅	1	2	yes	complemented
182	#808	C₂²×C₅	1	2	yes	complemented
183	#807	C₂²×C₅	1	2	yes	complemented
184	C₂⁴×C₅	—	2	1	no	—
185	C₂×C₅×Q₈	—	6	2	no	—
186	C₂×C₅×D₄	—	2	1	no	—
187	C₂×C₅×D₄	—	2	2	no	—
188	C₂×C₅×D₄	Dic₆	1	4	yes	complemented
189	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	6	2	no	—
192	C₂²×C₄×C₅	—	6	2	no	—
193	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
194	C₅×M₁₆	—	6	2	no	—
195	C₂×C₅×C₈	—	2	2	no	—
196	C₂×C₅×C₈	—	3	2	no	—
197	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	3	1	no	—
201	C₅×C₄⋊C₄	—	3	1	no	—
202	C₅×C₄⋊C₄	—	3	1	no	—
203	C₅×C₄⋊C₄	—	3	1	no	—
204	C₅×C₄⋊C₄	—	3	1	no	—
205	C₅×C₄⋊C₄	—	3	1	no	—
206	C₅×C₄⋊C₄	—	6	2	no	—
207	C₅×C₄⋊C₄	—	6	2	no	—
208	C₅×C₄⋊C₄	—	6	2	no	—
209	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
210	C₅×C₂²⋊C₄	—	3	2	no	—
211	C₅×C₂²⋊C₄	—	6	2	no	—
212	C₅×C₂²⋊C₄	—	6	2	no	—
213	C₅×C₂²⋊C₄	—	6	1	no	—
214	C₅×C₂²⋊C₄	—	6	1	no	—
215	C₄²×C₅	—	3	2	no	—
216	C₄²×C₅	—	6	1	no	—
217	C₄²×C₅	—	6	1	no	—
218	#544	—	3	1	no	—
219	#518	—	3	1	no	—
220	#478	—	3	2	no	—
221	#478	—	3	2	no	—
222	#476	—	3	2	no	—
223	#474	—	3	2	no	—
224	#428	—	3	1	no	—
225	#427	—	3	1	no	—
226	#424	—	3	1	no	—
227	#418	—	3	1	no	—
228	C₂×#102	C₅×D₃	1	1	yes	characteristic
229	C₂²×C₃×C₅	—	2	1	no	—
230	C₂²×C₃×C₅	—	2	1	no	—
231	C₂²×C₃×C₅	—	2	4	no	—
232	C₂²×C₃×C₅	—	4	2	no	—
233	C₂²×C₃×C₅	—	4	2	no	—
234	C₂²×C₃×C₅	—	8	4	no	—
235	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
236	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
237	C₃×C₄×C₅	—	4	2	no	—
238	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
239	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₅×Dic₃	—	2	2	no	—
242	C₅×Dic₃	—	2	2	no	—
243	C₅×Dic₃	—	4	1	no	—
244	C₅×Dic₃	—	4	1	no	—
245	C₅×Dic₃	—	4	1	no	—
246	C₅×Dic₃	—	4	1	no	—
247	C₂⁴×C₃	—	2	1	no	—
248	C₂×C₃×D₄	—	2	1	no	—
249	C₂×C₃×D₄	—	2	2	no	—
250	C₂×C₃×D₄	C₅×Q₈	1	4	yes	complemented
251	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
252	C₂²×C₃×C₄	—	2	1	no	—
253	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
254	C₂²×Dic₃	—	2	2	no	—
255	C₂²×Dic₃	—	2	2	no	—
256	C₂×Dic₆	—	2	2	no	—
257	C₂×C₃×C₈	—	2	2	no	—
258	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
260	C₃×C₄⋊C₄	—	2	1	no	—
261	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
262	#217	—	2	1	no	—
263	#217	—	2	1	no	—
264	#217	—	2	2	no	—
265	#217	—	2	2	no	—
266	#217	C₅×D₄	1	2	yes	—
267	C₄⋊Dic₃	—	2	2	no	—
268	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
269	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
270	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
271	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
272	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
273	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
274	Dic₃⋊C₄	—	2	2	no	—
275	Dic₃⋊C₄	—	2	2	no	—
276	C₄×Dic₃	—	2	1	no	—
277	C₄×Dic₃	—	2	1	no	—
278	C₄×Dic₃	C₂³×C₅	1	2	yes	—
279	#208	—	2	2	no	—
280	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
281	C₂³×C₅	—	2	2	no	—
282	C₂³×C₅	—	2	4	no	—
283	C₂³×C₅	—	8	1	no	—
284	C₂³×C₅	—	8	1	no	—
285	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
286	C₅×Q₈	—	24	2	no	—
287	C₅×D₄	—	2	4	no	—
288	C₅×D₄	—	2	2	no	—
289	C₅×D₄	C₂×Dic₆	1	4	yes	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	3	2	no	—
292	C₂×C₄×C₅	—	3	2	no	—
293	C₂×C₄×C₅	—	6	1	no	—
294	C₂×C₄×C₅	—	6	1	no	—
295	C₂×C₄×C₅	—	6	1	no	—
296	C₂×C₄×C₅	—	6	1	no	—
297	C₂×C₄×C₅	—	8	1	no	—
298	C₂×C₄×C₅	—	24	2	no	—
299	C₂×C₄×C₅	—	24	2	no	—
300	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
301	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
302	C₂×C₄×C₅	#237	1	2	yes	—
303	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
304	C₅×C₈	—	2	1	no	—
305	C₅×C₈	—	2	1	no	—
306	C₅×C₈	—	6	2	no	—
307	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
308	C₂×M₁₆	—	3	1	no	—
309	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
310	C₄⋊Q₈	—	3	2	no	—
311	C₄⋊Q₈	—	6	1	no	—
312	#125	—	3	2	no	—
313	#125	—	6	1	no	—
314	C₂²⋊Q₈	—	6	2	no	—
315	C₄×D₄	—	3	2	no	—
316	C₄×D₄	—	3	2	no	—
317	C₄×D₄	—	6	1	no	—
318	C₄×D₄	—	6	1	no	—
319	#117	—	3	1	no	—
320	#117	—	3	1	no	—
321	#117	—	3	1	no	—
322	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	6	2	no	—
324	#107	—	3	1	no	—
325	#107	—	3	1	no	—
326	#107	—	3	2	no	—
327	#106	—	3	1	no	—
328	#106	—	3	1	no	—
329	#106	—	3	2	no	—
330	C₄⋊C₈	—	3	2	no	—
331	C₄⋊C₈	—	3	2	no	—
332	#102	—	3	2	no	—
333	#102	—	3	2	no	—
334	#102	C₂×C₅×D₃	1	2	yes	—
335	#102	C₂×C₅×D₃	1	2	yes	—
336	C₂×C₃×C₅	—	2	2	no	—
337	C₂×C₃×C₅	—	4	4	no	—
338	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
339	C₂×C₃×C₅	#576	1	1	yes	characteristic
340	C₂×C₃×C₅	#577	1	1	yes	characteristic
341	C₂³×C₃	—	2	2	no	—
342	C₂³×C₃	—	2	4	no	—
343	C₂³×C₃	—	8	1	no	—
344	C₂³×C₃	—	8	1	no	—
345	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
346	C₃×D₄	—	2	4	no	—
347	C₃×D₄	—	2	2	no	—
348	C₃×D₄	C₂×C₅×Q₈	1	4	yes	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	8	1	no	—
351	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
353	C₂×C₃×C₄	C₅×#41	1	2	yes	—
354	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
355	C₂×Dic₃	—	2	1	no	—
356	C₂×Dic₃	—	2	1	no	—
357	C₂×Dic₃	—	2	1	no	—
358	C₂×Dic₃	—	2	1	no	—
359	C₂×Dic₃	—	8	2	no	—
360	C₂×Dic₃	—	8	2	no	—
361	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
362	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
363	Dic₆	—	8	2	no	—
364	C₃×C₈	—	2	1	no	—
365	C₃×C₈	—	2	1	no	—
366	C₃⋊C₈	—	2	2	no	—
367	C₂²×C₅	—	2	1	no	—
368	C₂²×C₅	—	2	1	no	—
369	C₂²×C₅	—	2	4	no	—
370	C₂²×C₅	—	4	2	no	—
371	C₂²×C₅	—	4	2	no	—
372	C₂²×C₅	—	8	4	no	—
373	C₂²×C₅	#878	1	2	yes	—
374	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
375	C₄×C₅	—	4	2	no	—
376	C₄×C₅	—	6	2	no	—
377	C₄×C₅	—	6	2	no	—
378	C₄×C₅	—	12	1	no	—
379	C₄×C₅	—	12	1	no	—
380	C₄×C₅	—	12	1	no	—
381	C₄×C₅	—	12	1	no	—
382	C₄×C₅	#878	1	2	yes	—
383	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
384	C₄×C₅	C₂×#237	1	1	yes	characteristic
385	C₂⁴	—	2	1	no	—
386	C₂×Q₈	—	6	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	C₅×Dic₆	1	4	yes	complemented
390	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	6	2	no	—
393	C₂²×C₄	—	6	2	no	—
394	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
395	M₁₆	—	6	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	3	2	no	—
398	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
399	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	3	1	no	—
402	C₄⋊C₄	—	3	1	no	—
403	C₄⋊C₄	—	3	1	no	—
404	C₄⋊C₄	—	3	1	no	—
405	C₄⋊C₄	—	3	1	no	—
406	C₄⋊C₄	—	3	1	no	—
407	C₄⋊C₄	—	6	2	no	—
408	C₄⋊C₄	—	6	2	no	—
409	C₄⋊C₄	—	6	2	no	—
410	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
411	C₂²⋊C₄	—	3	2	no	—
412	C₂²⋊C₄	—	6	2	no	—
413	C₂²⋊C₄	—	6	2	no	—
414	C₂²⋊C₄	—	6	1	no	—
415	C₂²⋊C₄	—	6	1	no	—
416	C₄²	—	3	2	no	—
417	C₄²	—	6	1	no	—
418	C₄²	—	6	1	no	—
419	C₃×C₅	#3081	1	1	yes	characteristic, complemented, Hall
420	C₂²×C₃	—	2	1	no	—
421	C₂²×C₃	—	2	1	no	—
422	C₂²×C₃	—	2	4	no	—
423	C₂²×C₃	—	4	2	no	—
424	C₂²×C₃	—	4	2	no	—
425	C₂²×C₃	—	8	4	no	—
426	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
427	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
428	C₃×C₄	—	4	2	no	—
429	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
430	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
431	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
432	Dic₃	—	2	2	no	—
433	Dic₃	—	2	2	no	—
434	Dic₃	—	4	1	no	—
435	Dic₃	—	4	1	no	—
436	Dic₃	—	4	1	no	—
437	Dic₃	—	4	1	no	—
438	C₂×C₅	—	2	2	no	—
439	C₂×C₅	—	4	4	no	—
440	C₂×C₅	C₂×#878	1	1	yes	characteristic
441	C₂×C₅	#5757	1	1	yes	characteristic
442	C₂×C₅	#5762	1	1	yes	characteristic
443	C₂³	—	2	2	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	8	1	no	—
446	C₂³	—	8	1	no	—
447	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
448	Q₈	—	24	2	no	—
449	D₄	—	2	4	no	—
450	D₄	—	2	2	no	—
451	D₄	C₂×C₅×Dic₆	1	4	yes	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	3	2	no	—
455	C₂×C₄	—	6	1	no	—
456	C₂×C₄	—	6	1	no	—
457	C₂×C₄	—	6	1	no	—
458	C₂×C₄	—	6	1	no	—
459	C₂×C₄	—	8	1	no	—
460	C₂×C₄	—	24	2	no	—
461	C₂×C₄	—	24	2	no	—
462	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
463	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
464	C₂×C₄	C₅×#237	1	2	yes	—
465	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
466	C₈	—	2	1	no	—
467	C₈	—	2	1	no	—
468	C₈	—	6	2	no	—
469	C₂×C₃	—	2	2	no	—
470	C₂×C₃	—	4	4	no	—
471	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
472	C₂×C₃	C₅×#576	1	1	yes	characteristic
473	C₂×C₃	C₅×#577	1	1	yes	characteristic
474	C₅	#78731	1	1	yes	characteristic, direct product factor, Sylow
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	8	4	no	—
481	C₂²	C₅×#878	1	2	yes	—
482	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
483	C₄	—	4	2	no	—
484	C₄	—	6	2	no	—
485	C₄	—	6	2	no	—
486	C₄	—	12	1	no	—
487	C₄	—	12	1	no	—
488	C₄	—	12	1	no	—
489	C₄	—	12	1	no	—
490	C₄	C₅×#878	1	2	yes	—
491	C₄	C₂²×C₅×Dic₆	1	1	yes	characteristic
492	C₄	C₂×C₅×#237	1	1	yes	characteristic
493	C₃	C₅×#3081	1	1	yes	characteristic, complemented, Sylow
494	C₂	—	2	2	no	—
495	C₂	—	4	4	no	—
496	C₂	C₂×C₅×#878	1	1	yes	characteristic
497	C₂	C₅×#5757	1	1	yes	characteristic
498	C₂	C₅×#5762	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	C₂×C₃×C₅×#102	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂×C₅×#102	D₃
hypocenter	C₃	C₅×#3081
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#102

Complements

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

N	H ≅ G/N	type
2. C₅×#5500	C₂	semidirect
5. C₅×#5106	C₂	semidirect
6. C₅×#5102	C₂	semidirect
7. C₅×#4964	C₂	semidirect
8. C₅×#4766	C₂	semidirect
9. C₅×#4763	C₂	semidirect
10. C₅×#4761	C₂	semidirect
11. C₅×#4759	C₂	semidirect
27. C₅×#890	C₂²	semidirect
29. C₅×#888	C₂²	semidirect
34. C₅×#818	C₂²	semidirect
35. C₅×#818	C₂²	semidirect
36. C₅×#817	C₂²	semidirect
37. C₅×#817	C₂²	semidirect
38. C₅×Dic₃⋊C₈	C₂²	semidirect
39. C₅×Dic₃⋊C₈	C₂²	semidirect
40. C₅×#808	C₂²	semidirect
41. C₅×#807	C₂²	semidirect
42. #78731	C₅	direct (N × H)
57. C₂×C₃×C₅×D₄	Q₈	semidirect
89. #5500	C₂×C₅	semidirect
92. #5106	C₂×C₅	semidirect
93. #5102	C₂×C₅	semidirect
94. #4964	C₂×C₅	semidirect
95. #4766	C₂×C₅	semidirect
96. #4763	C₂×C₅	semidirect
97. #4761	C₂×C₅	semidirect
98. #4759	C₂×C₅	semidirect
169. #890	C₂²×C₅	semidirect
171. #888	C₂²×C₅	semidirect
176. #818	C₂²×C₅	semidirect
177. #818	C₂²×C₅	semidirect
178. #817	C₂²×C₅	semidirect
179. #817	C₂²×C₅	semidirect
180. Dic₃⋊C₈	C₂²×C₅	semidirect
181. Dic₃⋊C₈	C₂²×C₅	semidirect
182. #808	C₂²×C₅	semidirect
183. #807	C₂²×C₅	semidirect
188. C₂×C₅×D₄	Dic₆	semidirect
250. C₂×C₃×D₄	C₅×Q₈	semidirect
389. C₂×D₄	C₅×Dic₆	semidirect
419. C₃×C₅	#3081	semidirect
474. C₅	#78731	direct (N × H)
493. C₃	C₅×#3081	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5798	2
C₅×#5500	2
C₂×C₃×C₅×#102	2
C₅×#5215	2
C₅×#5106	2
C₅×#5102	2
C₅×#4964	2
C₅×#4766	2
C₅×#4763	2
C₅×#4761	2
C₅×#4759	2
C₅×#3081	3
#78731	5

Subgroups — C5×#78731 #14430768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78731 #14430768