Subgroups — C₅×#78871 #14430681

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Dic₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#890	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic
4	C₅×#5232	C₂	1	1	yes	maximal, characteristic
5	C₅×#5121	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5118	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4964	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4799	C₂	1	2	yes	maximal, complemented
9	C₅×#4796	C₂	1	2	yes	maximal, complemented
10	C₅×#4766	C₂	1	2	yes	maximal, complemented
11	C₅×#4763	C₂	1	2	yes	maximal, complemented
12	C₅×#3080	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
17	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
18	C₅×D₄×Dic₃	—	2	1	no	—
19	C₅×D₄×Dic₃	—	2	1	no	—
20	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
21	C₅×D₄×Dic₃	C₂²	1	1	yes	characteristic
22	C₅×#926	—	2	1	no	—
23	C₅×#926	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
25	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
27	C₂×C₄×C₅×Dic₃	—	2	1	no	—
28	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
29	C₂×C₅×#208	C₂²	1	1	yes	characteristic
30	C₅×#890	—	2	1	no	—
31	C₅×#890	—	2	1	no	—
32	C₅×#890	C₂²	1	2	yes	—
33	C₅×#890	C₂²	1	2	yes	—
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#102	C₂²	1	2	yes	—
36	C₅×#835	C₂²	1	2	yes	—
37	C₅×#832	C₂²	1	2	yes	—
38	C₅×#818	C₂²	1	2	yes	—
39	C₅×#817	C₂²	1	2	yes	—
40	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
41	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
42	C₅×#808	C₂²	1	2	yes	—
43	C₅×#807	C₂²	1	2	yes	—
44	#78871	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#125	—	3	1	no	—
46	C₄×C₅×#41	—	3	1	no	—
47	C₅×#479	—	3	2	no	—
48	C₅×#479	—	3	2	no	—
49	C₅×#478	—	3	2	no	—
50	C₅×#478	—	3	2	no	—
51	C₅×#428	—	3	1	no	—
52	C₅×#428	—	3	1	no	—
53	C₅×#423	—	3	1	no	—
54	C₅×#417	—	3	1	no	—
55	C₅×#417	D₃	1	1	yes	characteristic
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	Q₈	1	4	yes	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₅×Dic₃	—	2	1	no	—
65	C₂²×C₅×Dic₃	—	2	1	no	—
66	C₂²×C₅×Dic₃	—	2	1	no	—
67	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
68	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
69	C₃×C₅×M₁₆	—	2	2	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	—	2	1	no	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₅×#217	—	2	1	no	—
74	C₅×#217	—	2	1	no	—
75	C₅×#217	—	2	1	no	—
76	C₅×C₄⋊Dic₃	—	2	1	no	—
77	C₅×C₄⋊Dic₃	—	2	2	no	—
78	C₅×C₄⋊Dic₃	—	2	2	no	—
79	C₅×C₄⋊Dic₃	—	2	1	no	—
80	C₅×C₄⋊Dic₃	—	2	1	no	—
81	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
82	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
84	C₅×Dic₃⋊C₄	—	2	2	no	—
85	C₅×Dic₃⋊C₄	—	2	2	no	—
86	C₄×C₅×Dic₃	—	2	1	no	—
87	C₄×C₅×Dic₃	—	2	1	no	—
88	C₄×C₅×Dic₃	—	2	1	no	—
89	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
90	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
91	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
93	C₅×#208	—	2	2	no	—
94	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
95	Dic₃×#41	C₂×C₅	1	1	yes	characteristic
96	C₂×#890	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#417	C₂×C₅	1	1	yes	characteristic
98	#5232	C₂×C₅	1	1	yes	characteristic
99	#5121	C₂×C₅	1	1	yes	characteristic, complemented
100	#5118	C₂×C₅	1	1	yes	characteristic, complemented
101	#4964	C₂×C₅	1	1	yes	characteristic, complemented
102	#4799	C₂×C₅	1	2	yes	complemented
103	#4796	C₂×C₅	1	2	yes	complemented
104	#4766	C₂×C₅	1	2	yes	complemented
105	#4763	C₂×C₅	1	2	yes	complemented
106	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
107	C₂×C₅×M₁₆	—	3	1	no	—
108	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
109	C₅×#125	—	3	2	no	—
110	C₅×#125	—	3	2	no	—
111	C₅×#125	—	6	1	no	—
112	C₅×#125	—	6	1	no	—
113	C₄×C₅×Q₈	—	3	1	no	—
114	C₄×C₅×Q₈	—	3	1	no	—
115	C₄×C₅×D₄	—	3	1	no	—
116	C₄×C₅×D₄	—	3	1	no	—
117	C₄×C₅×D₄	—	6	1	no	—
118	C₄×C₅×D₄	—	6	1	no	—
119	C₅×#117	—	3	1	no	—
120	C₅×#117	—	6	1	no	—
121	C₂×C₅×C₄⋊C₄	—	3	1	no	—
122	C₂×C₅×C₄⋊C₄	—	6	1	no	—
123	C₂×C₅×C₄⋊C₄	—	6	1	no	—
124	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
125	C₂×C₄²×C₅	—	3	1	no	—
126	C₂×C₄²×C₅	—	6	1	no	—
127	C₅×#107	—	3	2	no	—
128	C₅×#107	—	3	2	no	—
129	C₅×#106	—	3	2	no	—
130	C₅×#106	—	3	2	no	—
131	C₅×C₄⋊C₈	—	3	2	no	—
132	C₅×C₄⋊C₈	—	3	2	no	—
133	C₅×#103	—	3	2	no	—
134	C₅×#103	C₂×D₃	1	2	yes	—
135	C₅×#102	—	3	2	no	—
136	C₅×#102	C₂×D₃	1	2	yes	—
137	#3080	—	3	1	no	Sylow
138	C₂³×C₃×C₅	—	2	1	no	—
139	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
140	C₃×C₅×Q₈	—	2	1	no	—
141	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	—
142	C₃×C₅×D₄	—	2	4	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	4	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	4	2	no	—
149	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₂×C₅×Dic₃	—	2	1	no	—
154	C₂×C₅×Dic₃	—	2	1	no	—
155	C₂×C₅×Dic₃	—	2	2	no	—
156	C₂×C₅×Dic₃	—	4	1	no	—
157	C₂×C₅×Dic₃	—	4	1	no	—
158	C₂×C₅×Dic₃	—	4	2	no	—
159	C₂×C₅×Dic₃	—	4	2	no	—
160	C₂×C₅×Dic₃	—	4	2	no	—
161	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
164	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
165	C₃×C₅×C₈	—	2	2	no	—
166	C₅×C₃⋊C₈	—	2	2	no	—
167	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
170	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
171	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
172	D₄×Dic₃	—	2	1	no	—
173	D₄×Dic₃	—	2	1	no	—
174	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
175	D₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
176	#926	—	2	1	no	—
177	#926	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₄⋊Dic₃	—	2	1	no	—
179	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
180	C₂×Dic₃⋊C₄	—	2	1	no	—
181	C₂×C₄×Dic₃	—	2	1	no	—
182	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
183	C₂×#208	C₂²×C₅	1	1	yes	characteristic
184	#890	—	2	1	no	—
185	#890	—	2	1	no	—
186	#890	C₂²×C₅	1	2	yes	—
187	#890	C₂²×C₅	1	2	yes	—
188	C₃×#103	C₂²×C₅	1	2	yes	—
189	C₃×#102	C₂²×C₅	1	2	yes	—
190	#835	C₂²×C₅	1	2	yes	—
191	#832	C₂²×C₅	1	2	yes	—
192	#818	C₂²×C₅	1	2	yes	—
193	#817	C₂²×C₅	1	2	yes	—
194	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
195	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
196	#808	C₂²×C₅	1	2	yes	—
197	#807	C₂²×C₅	1	2	yes	—
198	C₅×#41	—	2	2	no	—
199	C₅×#41	Dic₆	1	4	yes	—
200	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	3	1	no	—
206	C₂²×C₄×C₅	—	3	1	no	—
207	C₂²×C₄×C₅	—	6	1	no	—
208	C₂²×C₄×C₅	—	6	1	no	—
209	C₂²×C₄×C₅	—	6	1	no	—
210	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
211	C₅×M₁₆	—	2	2	no	—
212	C₅×M₁₆	—	6	2	no	—
213	C₂×C₅×C₈	—	3	2	no	—
214	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	3	2	no	—
217	C₅×C₄⋊C₄	—	3	1	no	—
218	C₅×C₄⋊C₄	—	3	1	no	—
219	C₅×C₄⋊C₄	—	6	2	no	—
220	C₅×C₄⋊C₄	—	6	2	no	—
221	C₅×C₄⋊C₄	—	6	2	no	—
222	C₅×C₄⋊C₄	—	6	2	no	—
223	C₅×C₄⋊C₄	—	6	1	no	—
224	C₅×C₄⋊C₄	—	6	1	no	—
225	C₅×C₄⋊C₄	—	6	1	no	—
226	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
227	C₅×C₂²⋊C₄	—	6	1	no	—
228	C₅×C₂²⋊C₄	—	6	1	no	—
229	C₅×C₂²⋊C₄	—	6	1	no	—
230	C₄²×C₅	—	3	1	no	—
231	C₄²×C₅	—	3	1	no	—
232	C₄²×C₅	—	3	1	no	—
233	C₄²×C₅	—	3	1	no	—
234	C₄²×C₅	—	6	1	no	—
235	C₄²×C₅	—	6	1	no	—
236	C₄²×C₅	—	6	1	no	—
237	C₂×#125	—	3	1	no	—
238	C₄×#41	—	3	1	no	—
239	#479	—	3	2	no	—
240	#479	—	3	2	no	—
241	#478	—	3	2	no	—
242	#478	—	3	2	no	—
243	#428	—	3	1	no	—
244	#428	—	3	1	no	—
245	#423	—	3	1	no	—
246	#417	—	3	1	no	—
247	#417	C₅×D₃	1	1	yes	characteristic
248	C₂²×C₃×C₅	—	2	1	no	—
249	C₂²×C₃×C₅	—	2	1	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	4	1	no	—
252	C₂²×C₃×C₅	—	4	1	no	—
253	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
254	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
255	C₃×C₄×C₅	—	2	2	no	—
256	C₃×C₄×C₅	—	4	2	no	—
257	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
258	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
259	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₅×Dic₃	—	2	1	no	—
261	C₅×Dic₃	—	2	1	no	—
262	C₅×Dic₃	—	2	1	no	—
263	C₅×Dic₃	—	2	1	no	—
264	C₅×Dic₃	—	4	1	no	—
265	C₅×Dic₃	—	4	1	no	—
266	C₅×Dic₃	—	4	2	no	—
267	C₃×#41	—	2	2	no	—
268	C₃×#41	C₅×Q₈	1	4	yes	—
269	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	—	2	1	no	—
273	C₂²×C₃×C₄	—	2	1	no	—
274	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂²×Dic₃	—	2	1	no	—
276	C₂²×Dic₃	—	2	1	no	—
277	C₂²×Dic₃	—	2	1	no	—
278	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
279	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
280	C₃×M₁₆	—	2	2	no	—
281	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
282	C₃×C₄⋊C₄	—	2	1	no	—
283	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
284	#217	—	2	1	no	—
285	#217	—	2	1	no	—
286	#217	—	2	1	no	—
287	C₄⋊Dic₃	—	2	1	no	—
288	C₄⋊Dic₃	—	2	2	no	—
289	C₄⋊Dic₃	—	2	2	no	—
290	C₄⋊Dic₃	—	2	1	no	—
291	C₄⋊Dic₃	—	2	1	no	—
292	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
293	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
294	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
295	Dic₃⋊C₄	—	2	2	no	—
296	Dic₃⋊C₄	—	2	2	no	—
297	C₄×Dic₃	—	2	1	no	—
298	C₄×Dic₃	—	2	1	no	—
299	C₄×Dic₃	—	2	1	no	—
300	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
301	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
302	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
303	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
304	#208	—	2	2	no	—
305	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
306	C₂³×C₅	—	2	1	no	—
307	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
308	C₅×Q₈	—	2	1	no	—
309	C₅×Q₈	C₂×Dic₆	1	2	yes	—
310	C₅×D₄	—	2	4	no	—
311	C₅×D₄	—	2	1	no	—
312	C₅×D₄	C₂×Dic₆	1	2	yes	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	4	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	3	1	no	—
317	C₂×C₄×C₅	—	3	1	no	—
318	C₂×C₄×C₅	—	3	1	no	—
319	C₂×C₄×C₅	—	3	1	no	—
320	C₂×C₄×C₅	—	4	2	no	—
321	C₂×C₄×C₅	—	6	1	no	—
322	C₂×C₄×C₅	—	6	1	no	—
323	C₂×C₄×C₅	—	6	2	no	—
324	C₂×C₄×C₅	—	12	1	no	—
325	C₂×C₄×C₅	—	12	1	no	—
326	C₂×C₄×C₅	—	12	2	no	—
327	C₂×C₄×C₅	—	12	2	no	—
328	C₂×C₄×C₅	—	12	2	no	—
329	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
330	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅	#237	1	2	yes	—
332	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
333	C₅×C₈	—	2	2	no	—
334	C₅×C₈	—	6	2	no	—
335	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
336	C₂×M₁₆	—	3	1	no	—
337	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
338	#125	—	3	2	no	—
339	#125	—	3	2	no	—
340	#125	—	6	1	no	—
341	#125	—	6	1	no	—
342	C₄×Q₈	—	3	1	no	—
343	C₄×Q₈	—	3	1	no	—
344	C₄×D₄	—	3	1	no	—
345	C₄×D₄	—	3	1	no	—
346	C₄×D₄	—	6	1	no	—
347	C₄×D₄	—	6	1	no	—
348	#117	—	3	1	no	—
349	#117	—	6	1	no	—
350	C₂×C₄⋊C₄	—	3	1	no	—
351	C₂×C₄⋊C₄	—	6	1	no	—
352	C₂×C₄⋊C₄	—	6	1	no	—
353	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
354	C₂×C₄²	—	3	1	no	—
355	C₂×C₄²	—	6	1	no	—
356	#107	—	3	2	no	—
357	#107	—	3	2	no	—
358	#106	—	3	2	no	—
359	#106	—	3	2	no	—
360	C₄⋊C₈	—	3	2	no	—
361	C₄⋊C₈	—	3	2	no	—
362	#103	—	3	2	no	—
363	#103	C₂×C₅×D₃	1	2	yes	—
364	#102	—	3	2	no	—
365	#102	C₂×C₅×D₃	1	2	yes	—
366	C₂×C₃×C₅	—	2	2	no	—
367	C₂×C₃×C₅	—	4	2	no	—
368	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
369	C₂×C₃×C₅	#575	1	1	yes	characteristic
370	C₂×C₃×C₅	#575	1	1	yes	characteristic
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
373	C₃×Q₈	—	2	1	no	—
374	C₃×Q₈	C₂×C₅×Q₈	1	2	yes	—
375	C₃×D₄	—	2	4	no	—
376	C₃×D₄	—	2	1	no	—
377	C₃×D₄	C₂×C₅×Q₈	1	2	yes	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	4	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	4	2	no	—
382	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
384	C₂×C₃×C₄	C₅×#41	1	2	yes	—
385	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
386	C₂×Dic₃	—	2	1	no	—
387	C₂×Dic₃	—	2	1	no	—
388	C₂×Dic₃	—	2	2	no	—
389	C₂×Dic₃	—	4	1	no	—
390	C₂×Dic₃	—	4	1	no	—
391	C₂×Dic₃	—	4	2	no	—
392	C₂×Dic₃	—	4	2	no	—
393	C₂×Dic₃	—	4	2	no	—
394	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
395	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
396	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
397	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
398	C₃×C₈	—	2	2	no	—
399	C₃⋊C₈	—	2	2	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	4	1	no	—
404	C₂²×C₅	—	4	1	no	—
405	C₂²×C₅	#878	1	2	yes	—
406	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	4	2	no	—
409	C₄×C₅	—	6	1	no	—
410	C₄×C₅	—	6	1	no	—
411	C₄×C₅	—	6	1	no	—
412	C₄×C₅	—	6	1	no	—
413	C₄×C₅	—	12	1	no	—
414	C₄×C₅	—	12	1	no	—
415	C₄×C₅	—	12	2	no	—
416	C₄×C₅	#878	1	2	yes	—
417	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
418	C₄×C₅	C₂×#237	1	1	yes	characteristic
419	#41	—	2	2	no	—
420	#41	C₅×Dic₆	1	4	yes	—
421	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	3	1	no	—
427	C₂²×C₄	—	3	1	no	—
428	C₂²×C₄	—	6	1	no	—
429	C₂²×C₄	—	6	1	no	—
430	C₂²×C₄	—	6	1	no	—
431	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
432	M₁₆	—	2	2	no	—
433	M₁₆	—	6	2	no	—
434	C₂×C₈	—	3	2	no	—
435	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	3	2	no	—
438	C₄⋊C₄	—	3	1	no	—
439	C₄⋊C₄	—	3	1	no	—
440	C₄⋊C₄	—	6	2	no	—
441	C₄⋊C₄	—	6	2	no	—
442	C₄⋊C₄	—	6	2	no	—
443	C₄⋊C₄	—	6	2	no	—
444	C₄⋊C₄	—	6	1	no	—
445	C₄⋊C₄	—	6	1	no	—
446	C₄⋊C₄	—	6	1	no	—
447	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
448	C₂²⋊C₄	—	6	1	no	—
449	C₂²⋊C₄	—	6	1	no	—
450	C₂²⋊C₄	—	6	1	no	—
451	C₄²	—	3	1	no	—
452	C₄²	—	3	1	no	—
453	C₄²	—	3	1	no	—
454	C₄²	—	3	1	no	—
455	C₄²	—	6	1	no	—
456	C₄²	—	6	1	no	—
457	C₄²	—	6	1	no	—
458	C₃×C₅	#3080	1	1	yes	characteristic, complemented, Hall
459	C₂²×C₃	—	2	1	no	—
460	C₂²×C₃	—	2	1	no	—
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	4	1	no	—
463	C₂²×C₃	—	4	1	no	—
464	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
465	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
466	C₃×C₄	—	2	2	no	—
467	C₃×C₄	—	4	2	no	—
468	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
469	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
470	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
471	Dic₃	—	2	1	no	—
472	Dic₃	—	2	1	no	—
473	Dic₃	—	2	1	no	—
474	Dic₃	—	2	1	no	—
475	Dic₃	—	4	1	no	—
476	Dic₃	—	4	1	no	—
477	Dic₃	—	4	2	no	—
478	C₂×C₅	—	2	2	no	—
479	C₂×C₅	—	4	2	no	—
480	C₂×C₅	C₂×#878	1	1	yes	characteristic
481	C₂×C₅	#5773	1	1	yes	characteristic
482	C₂×C₅	#5777	1	1	yes	characteristic
483	C₂³	—	2	1	no	—
484	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
485	Q₈	—	2	1	no	—
486	Q₈	C₂×C₅×Dic₆	1	2	yes	—
487	D₄	—	2	4	no	—
488	D₄	—	2	1	no	—
489	D₄	C₂×C₅×Dic₆	1	2	yes	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	3	1	no	—
494	C₂×C₄	—	3	1	no	—
495	C₂×C₄	—	3	1	no	—
496	C₂×C₄	—	3	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	6	1	no	—
499	C₂×C₄	—	6	1	no	—
500	C₂×C₄	—	6	2	no	—
501	C₂×C₄	—	12	1	no	—
502	C₂×C₄	—	12	1	no	—
503	C₂×C₄	—	12	2	no	—
504	C₂×C₄	—	12	2	no	—
505	C₂×C₄	—	12	2	no	—
506	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
507	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
508	C₂×C₄	C₅×#237	1	2	yes	—
509	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
510	C₈	—	2	2	no	—
511	C₈	—	6	2	no	—
512	C₂×C₃	—	2	2	no	—
513	C₂×C₃	—	4	2	no	—
514	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
515	C₂×C₃	C₅×#575	1	1	yes	characteristic
516	C₂×C₃	C₅×#575	1	1	yes	characteristic
517	C₅	#78871	1	1	yes	characteristic, direct product factor, Sylow
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	C₅×#878	1	2	yes	—
524	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	6	1	no	—
528	C₄	—	6	1	no	—
529	C₄	—	6	1	no	—
530	C₄	—	6	1	no	—
531	C₄	—	12	1	no	—
532	C₄	—	12	1	no	—
533	C₄	—	12	2	no	—
534	C₄	C₅×#878	1	2	yes	—
535	C₄	C₂²×C₅×Dic₆	1	1	yes	characteristic
536	C₄	C₂×C₅×#237	1	1	yes	characteristic
537	C₃	C₅×#3080	1	1	yes	characteristic, complemented, Sylow
538	C₂	—	2	2	no	—
539	C₂	—	4	2	no	—
540	C₂	C₂×C₅×#878	1	1	yes	characteristic
541	C₂	C₅×#5773	1	1	yes	characteristic
542	C₂	C₅×#5777	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×#417	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
hypercenter	C₅×#417	D₃
hypocenter	C₃	C₅×#3080
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#417

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#890	C₂	semidirect
5. C₅×#5121	C₂	semidirect
6. C₅×#5118	C₂	semidirect
7. C₅×#4964	C₂	semidirect
8. C₅×#4799	C₂	semidirect
9. C₅×#4796	C₂	semidirect
10. C₅×#4766	C₂	semidirect
11. C₅×#4763	C₂	semidirect
44. #78871	C₅	direct (N × H)
96. C₂×#890	C₂×C₅	semidirect
99. #5121	C₂×C₅	semidirect
100. #5118	C₂×C₅	semidirect
101. #4964	C₂×C₅	semidirect
102. #4799	C₂×C₅	semidirect
103. #4796	C₂×C₅	semidirect
104. #4766	C₂×C₅	semidirect
105. #4763	C₂×C₅	semidirect
458. C₃×C₅	#3080	semidirect
517. C₅	#78871	direct (N × H)
537. C₃	C₅×#3080	semidirect

Maximal subgroups

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

subgroup	index
C₅×Dic₃×#41	2
C₂×C₅×#890	2
C₃×C₅×#417	2
C₅×#5232	2
C₅×#5121	2
C₅×#5118	2
C₅×#4964	2
C₅×#4799	2
C₅×#4796	2
C₅×#4766	2
C₅×#4763	2
C₅×#3080	3
#78871	5

Subgroups — C5×#78871 #14430681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78871 #14430681