Subgroups — C₅×#79208 #14413398

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₅×D₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5121	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4995	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4964	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4881	C₂	1	2	yes	maximal, complemented
9	C₅×#4880	C₂	1	2	yes	maximal, complemented
10	C₅×#4861	C₂	1	2	yes	maximal, complemented
11	C₅×#4860	C₂	1	2	yes	maximal, complemented
12	C₅×#2911	—	3	1	no	maximal, Hall
13	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
18	C₅×#926	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Dic₃	—	2	1	no	—
21	C₂×C₅×#208	C₂²	1	1	yes	characteristic
22	C₅×D₃×M₁₆	C₄	1	8	yes	complemented
23	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
24	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
25	C₅×#892	—	2	1	no	—
26	C₅×#892	—	2	1	no	—
27	C₅×#892	C₂²	1	2	yes	—
28	C₅×#892	C₂²	1	2	yes	—
29	C₅×#892	C₂²	1	1	yes	characteristic
30	C₅×#892	C₂²	1	1	yes	characteristic
31	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
34	C₅×#877	—	2	1	no	—
35	C₅×#872	—	2	1	no	—
36	C₄²×C₅×D₃	—	2	1	no	—
37	C₃×C₅×#107	C₂²	1	2	yes	complemented
38	C₃×C₅×#106	C₂²	1	2	yes	complemented
39	C₅×#818	C₂²	1	2	yes	complemented
40	C₅×#817	C₂²	1	2	yes	complemented
41	C₅×#808	C₂²	1	2	yes	complemented
42	C₅×#808	C₂²	1	2	yes	complemented
43	C₅×#807	C₂²	1	2	yes	complemented
44	C₅×#807	C₂²	1	2	yes	complemented
45	#79208	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂²×C₅×M₁₆	—	3	1	no	—
47	C₂×C₅×#117	—	3	1	no	—
48	C₂×C₅×#117	—	3	1	no	—
49	C₅×#428	—	3	2	no	—
50	C₅×#428	—	3	2	no	—
51	C₅×#428	—	3	1	no	—
52	C₅×#428	—	3	1	no	—
53	C₅×#428	—	3	1	no	—
54	C₅×#428	D₃	1	1	yes	characteristic, complemented
55	C₅×#427	—	3	2	no	—
56	C₅×#427	—	3	2	no	—
57	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	—	2	1	no	—
59	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₂²×C₅×Dic₃	—	2	1	no	—
61	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	—	2	1	no	—
63	C₂×C₄×C₅×D₃	—	2	1	no	—
64	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
65	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
66	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
67	C₂×C₄×C₅×D₃	Q₈	1	4	yes	—
68	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
69	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
77	C₃×C₄²×C₅	—	2	1	no	—
78	C₅×#217	—	2	1	no	—
79	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
80	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
81	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
82	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
83	C₅×C₄⋊Dic₃	—	2	1	no	—
84	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
87	C₅×Dic₃⋊C₄	—	2	1	no	—
88	C₅×Dic₃⋊C₄	—	2	1	no	—
89	C₄×C₅×Dic₃	—	2	1	no	—
90	C₄×C₅×Dic₃	—	2	1	no	—
91	C₄×C₅×Dic₃	—	2	1	no	—
92	C₄×C₅×Dic₃	—	2	2	no	—
93	C₄×C₅×Dic₃	—	2	2	no	—
94	C₅×#208	C₂×C₄	1	4	yes	complemented
95	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
96	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	complemented
97	C₅×D₃×C₈	C₂×C₄	1	8	yes	complemented
98	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic
99	D₃×#117	C₂×C₅	1	1	yes	characteristic
100	C₂×#892	C₂×C₅	1	1	yes	characteristic
101	C₃×#428	C₂×C₅	1	1	yes	characteristic, complemented
102	#5121	C₂×C₅	1	1	yes	characteristic, complemented
103	#4995	C₂×C₅	1	1	yes	characteristic, complemented
104	#4964	C₂×C₅	1	1	yes	characteristic, complemented
105	#4881	C₂×C₅	1	2	yes	complemented
106	#4880	C₂×C₅	1	2	yes	complemented
107	#4861	C₂×C₅	1	2	yes	complemented
108	#4860	C₂×C₅	1	2	yes	complemented
109	C₂³×C₄×C₅	—	3	1	no	—
110	C₂×C₅×M₁₆	—	3	1	no	—
111	C₂×C₅×M₁₆	—	3	8	no	—
112	C₂×C₅×M₁₆	—	3	2	no	—
113	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
114	C₂²×C₅×C₈	—	3	2	no	—
115	C₅×#117	—	3	1	no	—
116	C₅×#117	—	3	1	no	—
117	C₅×#117	—	3	1	no	—
118	C₅×#117	—	3	2	no	—
119	C₅×#117	—	3	2	no	—
120	C₅×#117	—	6	1	no	—
121	C₅×#117	—	6	1	no	—
122	C₅×#117	—	6	1	no	—
123	C₅×#117	—	6	1	no	—
124	C₅×#117	C₂×D₃	1	1	yes	characteristic
125	C₂×C₅×C₄⋊C₄	—	3	1	no	—
126	C₂×C₅×C₄⋊C₄	—	3	1	no	—
127	C₂×C₅×C₄⋊C₄	—	3	1	no	—
128	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
129	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
130	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
131	C₂×C₄²×C₅	—	6	1	no	—
132	C₂×C₄²×C₅	—	6	1	no	—
133	C₅×#107	—	3	2	no	—
134	C₅×#107	—	3	2	no	—
135	C₅×#107	—	3	2	no	—
136	C₅×#107	C₂×D₃	1	2	yes	complemented
137	C₅×#106	—	3	2	no	—
138	C₅×#106	—	3	2	no	—
139	C₅×#106	—	3	2	no	—
140	C₅×#106	C₂×D₃	1	2	yes	complemented
141	#2911	—	3	1	no	Sylow
142	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₅×D₃	—	4	1	no	—
144	C₂²×C₅×D₃	—	4	1	no	—
145	C₂²×C₅×D₃	C₄⋊C₄	1	4	yes	—
146	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	4	2	no	—
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₂×C₅×Dic₃	—	2	1	no	—
157	C₂×C₅×Dic₃	—	2	1	no	—
158	C₂×C₅×Dic₃	—	2	2	no	—
159	C₂×C₅×Dic₃	—	4	2	no	—
160	C₂×C₅×Dic₃	C₄⋊C₄	1	4	yes	—
161	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
163	C₄×C₅×D₃	—	4	2	no	—
164	C₄×C₅×D₃	—	4	2	no	—
165	C₄×C₅×D₃	C₄⋊C₄	1	4	yes	—
166	C₄×C₅×D₃	C₄⋊C₄	1	4	yes	—
167	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
168	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
169	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
170	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
171	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
172	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
175	C₃×#117	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
178	#926	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄×Dic₃	—	2	1	no	—
181	C₂×#208	C₂²×C₅	1	1	yes	characteristic
182	D₃×M₁₆	C₄×C₅	1	8	yes	complemented
183	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
184	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
185	#892	—	2	1	no	—
186	#892	—	2	1	no	—
187	#892	C₂²×C₅	1	1	yes	characteristic
188	#892	C₂²×C₅	1	2	yes	—
189	#892	C₂²×C₅	1	2	yes	—
190	#892	C₂²×C₅	1	1	yes	characteristic
191	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
193	D₃×C₂²⋊C₄	—	2	1	no	—
194	#877	—	2	1	no	—
195	#872	—	2	1	no	—
196	C₄²×D₃	—	2	1	no	—
197	C₃×#107	C₂²×C₅	1	2	yes	complemented
198	C₃×#106	C₂²×C₅	1	2	yes	complemented
199	#818	C₂²×C₅	1	2	yes	complemented
200	#817	C₂²×C₅	1	2	yes	complemented
201	#808	C₂²×C₅	1	2	yes	complemented
202	#808	C₂²×C₅	1	2	yes	complemented
203	#807	C₂²×C₅	1	2	yes	complemented
204	#807	C₂²×C₅	1	2	yes	complemented
205	C₂⁴×C₅	—	3	1	no	—
206	C₂²×C₄×C₅	—	2	1	no	—
207	C₂²×C₄×C₅	—	3	1	no	—
208	C₂²×C₄×C₅	—	3	4	no	—
209	C₂²×C₄×C₅	—	3	1	no	—
210	C₂²×C₄×C₅	—	3	1	no	—
211	C₂²×C₄×C₅	—	3	4	no	—
212	C₂²×C₄×C₅	—	3	1	no	—
213	C₂²×C₄×C₅	—	3	1	no	—
214	C₂²×C₄×C₅	—	6	1	no	—
215	C₂²×C₄×C₅	—	6	1	no	—
216	C₂²×C₄×C₅	—	6	1	no	—
217	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
218	C₅×M₁₆	—	3	4	no	—
219	C₅×M₁₆	—	3	8	no	—
220	C₅×M₁₆	C₄×D₃	1	4	yes	complemented
221	C₂×C₅×C₈	—	3	2	no	—
222	C₂×C₅×C₈	—	3	8	no	—
223	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	3	2	no	—
226	C₅×C₄⋊C₄	—	3	1	no	—
227	C₅×C₄⋊C₄	—	3	1	no	—
228	C₅×C₄⋊C₄	—	6	1	no	—
229	C₅×C₄⋊C₄	—	6	1	no	—
230	C₅×C₄⋊C₄	—	6	1	no	—
231	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
232	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
233	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
234	C₅×C₂²⋊C₄	—	2	1	no	—
235	C₅×C₂²⋊C₄	—	6	1	no	—
236	C₅×C₂²⋊C₄	—	6	1	no	—
237	C₅×C₂²⋊C₄	—	6	2	no	—
238	C₅×C₂²⋊C₄	—	6	2	no	—
239	C₅×C₂²⋊C₄	—	6	1	no	—
240	C₄²×C₅	—	2	1	no	—
241	C₄²×C₅	—	6	1	no	—
242	C₄²×C₅	—	6	1	no	—
243	C₄²×C₅	—	6	2	no	—
244	C₄²×C₅	—	6	2	no	—
245	C₄²×C₅	—	6	1	no	—
246	C₂²×M₁₆	—	3	1	no	—
247	C₂×#117	—	3	1	no	—
248	C₂×#117	—	3	1	no	—
249	#428	—	3	1	no	—
250	#428	—	3	1	no	—
251	#428	—	3	1	no	—
252	#428	—	3	2	no	—
253	#428	—	3	2	no	—
254	#428	C₅×D₃	1	1	yes	characteristic, complemented
255	#427	—	3	2	no	—
256	#427	—	3	2	no	—
257	C₂²×C₃×C₅	—	2	1	no	—
258	C₂²×C₃×C₅	—	2	1	no	—
259	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
260	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₅×D₃	—	2	1	no	—
262	C₂×C₅×D₃	—	2	1	no	—
263	C₂×C₅×D₃	—	2	1	no	—
264	C₂×C₅×D₃	—	2	1	no	—
265	C₂×C₅×D₃	—	4	4	no	—
266	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
267	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
268	C₃×C₄×C₅	—	4	1	no	—
269	C₃×C₄×C₅	—	4	1	no	—
270	C₃×C₄×C₅	—	4	2	no	—
271	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
272	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
273	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
274	C₅×Dic₃	—	4	1	no	—
275	C₅×Dic₃	—	4	1	no	—
276	C₅×Dic₃	—	4	2	no	—
277	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
278	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
279	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
280	C₂²×C₃×C₄	—	2	1	no	—
281	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
282	C₂²×Dic₃	—	2	1	no	—
283	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
284	C₂×C₄×D₃	—	2	1	no	—
285	C₂×C₄×D₃	—	2	1	no	—
286	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
287	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
288	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
289	C₂×C₄×D₃	C₅×Q₈	1	4	yes	—
290	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
292	C₃×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
293	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
294	C₃×C₄⋊C₄	—	2	1	no	—
295	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
296	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
297	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
298	C₃×C₂²⋊C₄	—	2	1	no	—
299	C₃×C₄²	—	2	1	no	—
300	#217	—	2	1	no	—
301	(C₂×D₃)⋊C₄	—	2	1	no	—
302	(C₂×D₃)⋊C₄	—	2	1	no	—
303	(C₂×D₃)⋊C₄	—	2	2	no	—
304	(C₂×D₃)⋊C₄	—	2	2	no	—
305	C₄⋊Dic₃	—	2	1	no	—
306	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
307	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
308	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
309	Dic₃⋊C₄	—	2	1	no	—
310	Dic₃⋊C₄	—	2	1	no	—
311	C₄×Dic₃	—	2	1	no	—
312	C₄×Dic₃	—	2	1	no	—
313	C₄×Dic₃	—	2	1	no	—
314	C₄×Dic₃	—	2	2	no	—
315	C₄×Dic₃	—	2	2	no	—
316	#208	C₂×C₄×C₅	1	4	yes	complemented
317	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
318	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	8	yes	complemented
319	D₃×C₈	C₂×C₄×C₅	1	8	yes	complemented
320	C₂³×C₅	—	3	1	no	—
321	C₂³×C₅	—	3	1	no	—
322	C₂³×C₅	—	3	4	no	—
323	C₂³×C₅	—	12	1	no	—
324	C₂³×C₅	—	12	1	no	—
325	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	3	4	no	—
330	C₂×C₄×C₅	—	3	1	no	—
331	C₂×C₄×C₅	—	3	1	no	—
332	C₂×C₄×C₅	—	3	4	no	—
333	C₂×C₄×C₅	—	3	4	no	—
334	C₂×C₄×C₅	—	3	2	no	—
335	C₂×C₄×C₅	—	3	2	no	—
336	C₂×C₄×C₅	—	3	2	no	—
337	C₂×C₄×C₅	—	3	2	no	—
338	C₂×C₄×C₅	—	4	2	no	—
339	C₂×C₄×C₅	—	6	1	no	—
340	C₂×C₄×C₅	—	6	2	no	—
341	C₂×C₄×C₅	—	6	1	no	—
342	C₂×C₄×C₅	—	12	2	no	—
343	C₂×C₄×C₅	—	12	2	no	—
344	C₂×C₄×C₅	—	12	2	no	—
345	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
346	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
347	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
348	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
349	C₅×C₈	—	3	4	no	—
350	C₅×C₈	C₂×C₄×D₃	1	4	yes	—
351	C₂³×C₄	—	3	1	no	—
352	C₂×M₁₆	—	3	1	no	—
353	C₂×M₁₆	—	3	8	no	—
354	C₂×M₁₆	—	3	2	no	—
355	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
356	C₂²×C₈	—	3	2	no	—
357	#117	—	3	1	no	—
358	#117	—	3	1	no	—
359	#117	—	3	2	no	—
360	#117	—	3	1	no	—
361	#117	—	3	2	no	—
362	#117	—	6	1	no	—
363	#117	—	6	1	no	—
364	#117	—	6	1	no	—
365	#117	—	6	1	no	—
366	#117	C₂×C₅×D₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	—	3	1	no	—
368	C₂×C₄⋊C₄	—	3	1	no	—
369	C₂×C₄⋊C₄	—	3	1	no	—
370	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	—	6	1	no	—
372	C₂×C₂²⋊C₄	—	6	1	no	—
373	C₂×C₄²	—	6	1	no	—
374	C₂×C₄²	—	6	1	no	—
375	#107	—	3	2	no	—
376	#107	—	3	2	no	—
377	#107	—	3	2	no	—
378	#107	C₂×C₅×D₃	1	2	yes	complemented
379	#106	—	3	2	no	—
380	#106	—	3	2	no	—
381	#106	—	3	2	no	—
382	#106	C₂×C₅×D₃	1	2	yes	complemented
383	C₂×C₃×C₅	—	2	2	no	—
384	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
385	C₂×C₃×C₅	#575	1	1	yes	characteristic
386	C₂×C₃×C₅	#575	1	1	yes	characteristic
387	C₅×D₃	—	2	2	no	—
388	C₅×D₃	—	2	2	no	—
389	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂²×D₃	—	4	1	no	—
391	C₂²×D₃	—	4	1	no	—
392	C₂²×D₃	C₅×C₄⋊C₄	1	4	yes	—
393	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
394	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	4	2	no	—
399	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
400	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
402	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
403	C₂×Dic₃	—	2	1	no	—
404	C₂×Dic₃	—	2	1	no	—
405	C₂×Dic₃	—	2	2	no	—
406	C₂×Dic₃	—	4	2	no	—
407	C₂×Dic₃	C₅×C₄⋊C₄	1	4	yes	—
408	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
409	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
410	C₄×D₃	—	4	2	no	—
411	C₄×D₃	—	4	2	no	—
412	C₄×D₃	C₅×C₄⋊C₄	1	4	yes	—
413	C₄×D₃	C₅×C₄⋊C₄	1	4	yes	—
414	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
415	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
416	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
417	C₄×D₃	C₂×C₅×Q₈	1	2	yes	—
418	C₃×C₈	C₂²×C₄×C₅	1	4	yes	—
419	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	3	2	no	—
423	C₂²×C₅	—	3	2	no	—
424	C₂²×C₅	—	6	1	no	—
425	C₂²×C₅	—	6	1	no	—
426	C₂²×C₅	—	6	1	no	—
427	C₂²×C₅	—	6	1	no	—
428	C₂²×C₅	—	12	4	no	—
429	C₂²×C₅	D₃×C₄⋊C₄	1	2	yes	—
430	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
431	C₄×C₅	—	3	2	no	—
432	C₄×C₅	—	3	2	no	—
433	C₄×C₅	—	4	2	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	12	1	no	—
437	C₄×C₅	—	12	1	no	—
438	C₄×C₅	—	12	2	no	—
439	C₄×C₅	D₃×C₄⋊C₄	1	2	yes	—
440	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
441	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
442	C₂⁴	—	3	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	3	1	no	—
445	C₂²×C₄	—	3	4	no	—
446	C₂²×C₄	—	3	1	no	—
447	C₂²×C₄	—	3	1	no	—
448	C₂²×C₄	—	3	4	no	—
449	C₂²×C₄	—	3	1	no	—
450	C₂²×C₄	—	3	1	no	—
451	C₂²×C₄	—	6	1	no	—
452	C₂²×C₄	—	6	1	no	—
453	C₂²×C₄	—	6	1	no	—
454	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
455	M₁₆	—	3	4	no	—
456	M₁₆	—	3	8	no	—
457	M₁₆	C₄×C₅×D₃	1	4	yes	complemented
458	C₂×C₈	—	3	2	no	—
459	C₂×C₈	—	3	8	no	—
460	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	3	1	no	—
463	C₄⋊C₄	—	3	2	no	—
464	C₄⋊C₄	—	3	1	no	—
465	C₄⋊C₄	—	6	1	no	—
466	C₄⋊C₄	—	6	1	no	—
467	C₄⋊C₄	—	6	1	no	—
468	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
470	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	6	1	no	—
473	C₂²⋊C₄	—	6	1	no	—
474	C₂²⋊C₄	—	6	2	no	—
475	C₂²⋊C₄	—	6	2	no	—
476	C₂²⋊C₄	—	6	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	6	1	no	—
479	C₄²	—	6	1	no	—
480	C₄²	—	6	2	no	—
481	C₄²	—	6	2	no	—
482	C₄²	—	6	1	no	—
483	C₃×C₅	#2911	1	1	yes	characteristic, complemented, Hall
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
487	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
488	C₂×D₃	—	2	1	no	—
489	C₂×D₃	—	2	1	no	—
490	C₂×D₃	—	2	1	no	—
491	C₂×D₃	—	2	1	no	—
492	C₂×D₃	—	4	4	no	—
493	C₂×D₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
494	C₂×D₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
495	C₃×C₄	—	4	1	no	—
496	C₃×C₄	—	4	1	no	—
497	C₃×C₄	—	4	2	no	—
498	C₃×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
499	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
500	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
501	Dic₃	—	4	1	no	—
502	Dic₃	—	4	1	no	—
503	Dic₃	—	4	2	no	—
504	Dic₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
505	Dic₃	C₂×C₅×C₄⋊C₄	1	2	yes	—
506	C₂×C₅	—	2	2	no	—
507	C₂×C₅	—	6	2	no	—
508	C₂×C₅	—	6	2	no	—
509	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
510	C₂×C₅	#5773	1	1	yes	characteristic
511	C₂×C₅	#5777	1	1	yes	characteristic
512	C₂³	—	3	1	no	—
513	C₂³	—	3	1	no	—
514	C₂³	—	3	4	no	—
515	C₂³	—	12	1	no	—
516	C₂³	—	12	1	no	—
517	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	3	4	no	—
522	C₂×C₄	—	3	1	no	—
523	C₂×C₄	—	3	1	no	—
524	C₂×C₄	—	3	4	no	—
525	C₂×C₄	—	3	4	no	—
526	C₂×C₄	—	3	2	no	—
527	C₂×C₄	—	3	2	no	—
528	C₂×C₄	—	3	2	no	—
529	C₂×C₄	—	3	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	6	1	no	—
532	C₂×C₄	—	6	2	no	—
533	C₂×C₄	—	6	1	no	—
534	C₂×C₄	—	12	2	no	—
535	C₂×C₄	—	12	2	no	—
536	C₂×C₄	—	12	2	no	—
537	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
538	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
539	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
540	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
541	C₈	—	3	4	no	—
542	C₈	C₂×C₄×C₅×D₃	1	4	yes	—
543	C₂×C₃	—	2	2	no	—
544	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
545	C₂×C₃	C₅×#575	1	1	yes	characteristic
546	C₂×C₃	C₅×#575	1	1	yes	characteristic
547	D₃	—	2	2	no	—
548	D₃	—	2	2	no	—
549	C₅	#79208	1	1	yes	characteristic, direct product factor, Sylow
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	3	2	no	—
553	C₂²	—	3	2	no	—
554	C₂²	—	6	1	no	—
555	C₂²	—	6	1	no	—
556	C₂²	—	6	1	no	—
557	C₂²	—	6	1	no	—
558	C₂²	—	12	4	no	—
559	C₂²	C₅×D₃×C₄⋊C₄	1	2	yes	—
560	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
561	C₄	—	3	2	no	—
562	C₄	—	3	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	12	1	no	—
567	C₄	—	12	1	no	—
568	C₄	—	12	2	no	—
569	C₄	C₅×D₃×C₄⋊C₄	1	2	yes	—
570	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
571	C₄	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
572	C₃	C₅×#2911	1	1	yes	characteristic, complemented, Sylow
573	C₂	—	2	2	no	—
574	C₂	—	6	2	no	—
575	C₂	—	6	2	no	—
576	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
577	C₂	C₅×#5773	1	1	yes	characteristic
578	C₂	C₅×#5777	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#428	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂³×C₅×D₃	D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#428	D₃
hypocenter	C₃	C₅×#2911
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#428

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#428	C₂	semidirect
5. C₅×#5121	C₂	semidirect
6. C₅×#4995	C₂	semidirect
7. C₅×#4964	C₂	semidirect
8. C₅×#4881	C₂	semidirect
9. C₅×#4880	C₂	semidirect
10. C₅×#4861	C₂	semidirect
11. C₅×#4860	C₂	semidirect
22. C₅×D₃×M₁₆	C₄	semidirect
37. C₃×C₅×#107	C₂²	semidirect
38. C₃×C₅×#106	C₂²	semidirect
39. C₅×#818	C₂²	semidirect
40. C₅×#817	C₂²	semidirect
41. C₅×#808	C₂²	semidirect
42. C₅×#808	C₂²	semidirect
43. C₅×#807	C₂²	semidirect
44. C₅×#807	C₂²	semidirect
45. #79208	C₅	direct (N × H)
54. C₅×#428	D₃	semidirect
70. C₃×C₅×M₁₆	C₂×C₄	semidirect
94. C₅×#208	C₂×C₄	semidirect
96. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
97. C₅×D₃×C₈	C₂×C₄	semidirect
101. C₃×#428	C₂×C₅	semidirect
102. #5121	C₂×C₅	semidirect
103. #4995	C₂×C₅	semidirect
104. #4964	C₂×C₅	semidirect
105. #4881	C₂×C₅	semidirect
106. #4880	C₂×C₅	semidirect
107. #4861	C₂×C₅	semidirect
108. #4860	C₂×C₅	semidirect
136. C₅×#107	C₂×D₃	semidirect
140. C₅×#106	C₂×D₃	semidirect
182. D₃×M₁₆	C₄×C₅	semidirect
197. C₃×#107	C₂²×C₅	semidirect
198. C₃×#106	C₂²×C₅	semidirect
199. #818	C₂²×C₅	semidirect
200. #817	C₂²×C₅	semidirect
201. #808	C₂²×C₅	semidirect
202. #808	C₂²×C₅	semidirect
203. #807	C₂²×C₅	semidirect
204. #807	C₂²×C₅	semidirect
220. C₅×M₁₆	C₄×D₃	semidirect
254. #428	C₅×D₃	semidirect
292. C₃×M₁₆	C₂×C₄×C₅	semidirect
316. #208	C₂×C₄×C₅	semidirect
318. ΓL(1,𝔽₂₅)	C₂×C₄×C₅	semidirect
319. D₃×C₈	C₂×C₄×C₅	semidirect
378. #107	C₂×C₅×D₃	semidirect
382. #106	C₂×C₅×D₃	semidirect
457. M₁₆	C₄×C₅×D₃	semidirect
483. C₃×C₅	#2911	semidirect
549. C₅	#79208	direct (N × H)
572. C₃	C₅×#2911	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₃×M₁₆	2
C₅×D₃×#117	2
C₂×C₅×#892	2
C₃×C₅×#428	2
C₅×#5121	2
C₅×#4995	2
C₅×#4964	2
C₅×#4881	2
C₅×#4880	2
C₅×#4861	2
C₅×#4860	2
C₅×#2911	3
#79208	5

Subgroups — C5×#79208 #14413398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79208 #14413398