Subgroups — C₅×#69933 #14300724

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#821	C₂	1	2	yes	maximal, complemented
5	C₅×#4551	C₂	1	2	yes	maximal, complemented
6	C₅×#1875	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₅×#67	—	2	1	no	—
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₂×C₅×#217	—	2	1	no	—
12	C₅×#930	—	2	2	no	—
13	C₅×#930	C₄	1	4	yes	complemented
14	C₂×C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
15	C₅×#926	—	2	4	no	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂×C₄×C₅×Dic₃	—	2	1	no	—
19	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
20	C₅×#821	—	2	4	no	—
21	#69933	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#121	—	3	1	no	—
23	C₂×C₅×#117	—	3	1	no	—
24	C₂×C₅×#102	—	3	2	no	—
25	C₂×C₅×C₂²⋊C₈	D₃	1	1	yes	characteristic, complemented
26	C₅×#340	—	3	2	no	—
27	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
28	C₂³×C₅×D₃	—	2	1	no	—
29	C₂²×C₃×C₄×C₅	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	—	2	2	no	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₅×#67	—	2	4	no	—
36	C₂×C₅×#67	—	4	4	no	—
37	C₂²×C₅×Dic₃	—	2	2	no	—
38	C₂²×C₅×Dic₃	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	2	no	—
40	C₂×C₅×D₁₂	—	2	2	no	—
41	C₂×C₅×D₁₂	—	2	1	no	—
42	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₅×C₈	—	2	2	no	—
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₅×#217	—	2	4	no	—
47	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
48	C₅×C₄⋊Dic₃	—	2	2	no	—
49	C₅×C₄⋊Dic₃	—	2	1	no	—
50	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
51	C₅×C₄⋊Dic₃	D₄	1	4	yes	complemented
52	C₄×C₅×Dic₃	—	2	4	no	—
53	C₂×#930	C₂×C₅	1	1	yes	characteristic
54	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×#821	C₂×C₅	1	2	yes	complemented
57	#4551	C₂×C₅	1	2	yes	complemented
58	C₂²×C₅×D₄	—	3	1	no	—
59	C₂²×C₅×D₄	—	6	1	no	—
60	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
62	C₅×#121	—	3	4	no	—
63	C₅×#121	—	6	2	no	—
64	C₅×#117	—	6	4	no	—
65	C₂×C₅×C₄⋊C₄	—	3	1	no	—
66	C₂×C₅×C₄⋊C₄	—	3	2	no	—
67	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
68	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
69	C₂×C₄²×C₅	—	6	1	no	—
70	C₅×#102	—	6	4	no	—
71	C₅×C₂²⋊C₈	—	2	2	no	—
72	#1875	—	3	1	no	Sylow
73	C₂³×C₃×C₅	—	2	1	no	—
74	C₂³×C₃×C₅	—	2	1	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	—	2	2	no	—
77	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
78	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₅×D₃	—	2	2	no	—
80	C₂²×C₅×D₃	—	4	1	no	—
81	C₂²×C₅×D₃	—	4	1	no	—
82	C₂²×C₅×D₃	—	4	2	no	—
83	C₂²×C₅×D₃	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	#41	1	2	yes	—
93	C₅×#67	—	4	8	no	—
94	C₂×C₅×Dic₃	—	2	2	no	—
95	C₂×C₅×Dic₃	—	2	4	no	—
96	C₂×C₅×Dic₃	—	4	2	no	—
97	C₂×C₅×Dic₃	—	4	2	no	—
98	C₂×C₅×Dic₃	—	4	2	no	—
99	C₅×D₁₂	—	2	4	no	—
100	C₅×D₁₂	—	4	2	no	—
101	C₃×C₅×C₈	—	4	2	no	—
102	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
103	C₂²×#67	—	2	1	no	—
104	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
105	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
106	C₂×#217	—	2	1	no	—
107	#930	—	2	2	no	—
108	#930	C₄×C₅	1	4	yes	complemented
109	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
110	#926	—	2	4	no	—
111	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
113	C₂×C₄×Dic₃	—	2	1	no	—
114	C₃×C₂²⋊C₈	—	2	2	no	—
115	#821	—	2	4	no	—
116	C₂⁴×C₅	—	6	1	no	—
117	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
118	C₂×C₅×D₄	—	3	2	no	—
119	C₂×C₅×D₄	—	6	4	no	—
120	C₂×C₅×D₄	—	6	2	no	—
121	C₂×C₅×D₄	—	6	2	no	—
122	C₂×C₅×D₄	—	6	1	no	—
123	C₂×C₅×D₄	—	12	4	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	6	2	no	—
127	C₂²×C₄×C₅	—	6	1	no	—
128	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
129	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
130	C₂²×C₄×C₅	#67	1	2	yes	—
131	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₅×C₄⋊C₄	—	3	2	no	—
136	C₅×C₄⋊C₄	—	3	4	no	—
137	C₅×C₄⋊C₄	—	6	2	no	—
138	C₅×C₄⋊C₄	—	6	1	no	—
139	C₅×C₂²⋊C₄	—	6	4	no	—
140	C₅×C₂²⋊C₄	—	6	4	no	—
141	C₄²×C₅	—	6	4	no	—
142	C₂×#121	—	3	1	no	—
143	C₂×#117	—	3	1	no	—
144	C₂×#102	—	3	2	no	—
145	C₂×C₂²⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
146	#340	—	3	2	no	—
147	C₂²×C₃×C₅	—	2	2	no	—
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	—	2	2	no	—
150	C₂²×C₃×C₅	—	4	2	no	—
151	C₂²×C₃×C₅	—	4	2	no	—
152	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₃×C₅	#120	1	1	yes	characteristic
154	C₂²×C₃×C₅	#123	1	1	yes	characteristic
155	C₂²×C₃×C₅	#135	1	2	yes	—
156	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₅×D₃	—	4	2	no	—
158	C₂×C₅×D₃	—	4	2	no	—
159	C₂×C₅×D₃	—	4	2	no	—
160	C₂×C₅×D₃	—	8	2	no	—
161	C₂×C₅×D₃	—	8	2	no	—
162	C₃×C₄×C₅	—	2	2	no	—
163	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
164	C₃×C₄×C₅	#121	1	2	yes	—
165	C₅×Dic₃	—	4	2	no	—
166	C₅×Dic₃	—	4	4	no	—
167	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
168	C₂³×D₃	—	2	1	no	—
169	C₂²×C₃×C₄	—	2	2	no	—
170	C₂²×C₃×C₄	—	2	2	no	—
171	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
172	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
174	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
175	C₂×#67	—	2	4	no	—
176	C₂×#67	—	4	4	no	—
177	C₂²×Dic₃	—	2	2	no	—
178	C₂²×Dic₃	—	2	1	no	—
179	C₂×D₁₂	—	2	2	no	—
180	C₂×D₁₂	—	2	2	no	—
181	C₂×D₁₂	—	2	1	no	—
182	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
183	C₂×C₃×C₈	—	2	2	no	—
184	C₂×C₃×C₈	—	2	2	no	—
185	C₂×C₃×C₈	—	2	2	no	—
186	#217	—	2	4	no	—
187	(C₂×D₃)⋊C₄	—	2	4	no	—
188	C₄⋊Dic₃	—	2	2	no	—
189	C₄⋊Dic₃	—	2	1	no	—
190	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
191	C₄⋊Dic₃	C₅×D₄	1	4	yes	complemented
192	C₄×Dic₃	—	2	4	no	—
193	C₂³×C₅	—	2	1	no	—
194	C₂³×C₅	—	2	1	no	—
195	C₂³×C₅	—	2	2	no	—
196	C₂³×C₅	—	2	2	no	—
197	C₂³×C₅	—	6	2	no	—
198	C₂³×C₅	—	12	1	no	—
199	C₂³×C₅	—	12	1	no	—
200	C₂³×C₅	—	12	2	no	—
201	C₂³×C₅	—	12	2	no	—
202	C₂³×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
203	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
204	C₅×D₄	—	6	4	no	—
205	C₅×D₄	—	12	8	no	—
206	C₅×D₄	—	12	2	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	6	4	no	—
212	C₂×C₄×C₅	—	6	2	no	—
213	C₂×C₄×C₅	—	12	2	no	—
214	C₂×C₄×C₅	—	12	2	no	—
215	C₂×C₄×C₅	—	12	2	no	—
216	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
217	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
218	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
219	C₂×C₄×C₅	#237	1	2	yes	—
220	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
221	C₅×C₈	—	4	2	no	—
222	C₂²×D₄	—	3	1	no	—
223	C₂²×D₄	—	6	1	no	—
224	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
225	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
226	#121	—	3	4	no	—
227	#121	—	6	2	no	—
228	#117	—	6	4	no	—
229	C₂×C₄⋊C₄	—	3	2	no	—
230	C₂×C₄⋊C₄	—	3	1	no	—
231	C₂×C₂²⋊C₄	—	6	1	no	—
232	C₂×C₂²⋊C₄	—	6	1	no	—
233	C₂×C₄²	—	6	1	no	—
234	#102	—	6	4	no	—
235	C₂²⋊C₈	—	2	2	no	—
236	C₂×C₃×C₅	—	4	2	no	—
237	C₂×C₃×C₅	#386	1	1	yes	characteristic
238	C₂×C₃×C₅	#416	1	1	yes	characteristic
239	C₂×C₃×C₅	#418	1	1	yes	characteristic
240	C₂×C₃×C₅	#449	1	2	yes	—
241	C₂×C₃×C₅	#482	1	2	yes	—
242	C₅×D₃	—	8	2	no	—
243	C₂³×C₃	—	2	1	no	—
244	C₂³×C₃	—	2	1	no	—
245	C₂³×C₃	—	2	2	no	—
246	C₂³×C₃	—	2	2	no	—
247	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
248	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
249	C₂²×D₃	—	2	2	no	—
250	C₂²×D₃	—	4	1	no	—
251	C₂²×D₃	—	4	1	no	—
252	C₂²×D₃	—	4	2	no	—
253	C₂²×D₃	—	4	2	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	4	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
259	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
261	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
262	C₂×C₃×C₄	C₅×#41	1	2	yes	—
263	#67	—	4	8	no	—
264	C₂×Dic₃	—	2	2	no	—
265	C₂×Dic₃	—	2	4	no	—
266	C₂×Dic₃	—	4	2	no	—
267	C₂×Dic₃	—	4	2	no	—
268	C₂×Dic₃	—	4	2	no	—
269	D₁₂	—	2	4	no	—
270	D₁₂	—	4	2	no	—
271	C₃×C₈	—	4	2	no	—
272	C₂²×C₅	—	2	2	no	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	2	2	no	—
275	C₂²×C₅	—	4	2	no	—
276	C₂²×C₅	—	4	2	no	—
277	C₂²×C₅	—	12	2	no	—
278	C₂²×C₅	—	12	2	no	—
279	C₂²×C₅	—	12	2	no	—
280	C₂²×C₅	—	24	2	no	—
281	C₂²×C₅	—	24	2	no	—
282	C₂²×C₅	#882	1	1	yes	characteristic
283	C₂²×C₅	#886	1	1	yes	characteristic
284	C₂²×C₅	#904	1	2	yes	—
285	C₂²×C₅	#908	1	2	yes	—
286	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	12	2	no	—
289	C₄×C₅	—	12	4	no	—
290	C₄×C₅	#67⋊C₄	1	2	yes	—
291	C₄×C₅	#939	1	2	yes	—
292	C₂⁴	—	6	1	no	—
293	C₂⁴	C₅×D₁₂	1	1	yes	characteristic
294	C₂×D₄	—	3	2	no	—
295	C₂×D₄	—	6	4	no	—
296	C₂×D₄	—	6	2	no	—
297	C₂×D₄	—	6	2	no	—
298	C₂×D₄	—	6	1	no	—
299	C₂×D₄	—	12	4	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	6	2	no	—
303	C₂²×C₄	—	6	1	no	—
304	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
305	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
306	C₂²×C₄	C₅×#67	1	2	yes	—
307	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₄⋊C₄	—	3	2	no	—
312	C₄⋊C₄	—	3	4	no	—
313	C₄⋊C₄	—	6	2	no	—
314	C₄⋊C₄	—	6	1	no	—
315	C₂²⋊C₄	—	6	4	no	—
316	C₂²⋊C₄	—	6	4	no	—
317	C₄²	—	6	4	no	—
318	C₃×C₅	#1875	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	4	2	no	—
324	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
325	C₂²×C₃	C₅×#120	1	1	yes	characteristic
326	C₂²×C₃	C₅×#123	1	1	yes	characteristic
327	C₂²×C₃	C₅×#135	1	2	yes	—
328	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
329	C₂×D₃	—	4	2	no	—
330	C₂×D₃	—	4	2	no	—
331	C₂×D₃	—	4	2	no	—
332	C₂×D₃	—	8	2	no	—
333	C₂×D₃	—	8	2	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
336	C₃×C₄	C₅×#121	1	2	yes	—
337	Dic₃	—	4	2	no	—
338	Dic₃	—	4	4	no	—
339	C₂×C₅	—	4	2	no	—
340	C₂×C₅	—	24	2	no	—
341	C₂×C₅	#4734	1	2	yes	—
342	C₂×C₅	#4737	1	2	yes	—
343	C₂×C₅	#4958	1	1	yes	characteristic
344	C₂×C₅	#5113	1	1	yes	characteristic
345	C₂×C₅	#5131	1	1	yes	characteristic
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	6	2	no	—
351	C₂³	—	12	1	no	—
352	C₂³	—	12	1	no	—
353	C₂³	—	12	2	no	—
354	C₂³	—	12	2	no	—
355	C₂³	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
356	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
357	D₄	—	6	4	no	—
358	D₄	—	12	8	no	—
359	D₄	—	12	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	6	4	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	—	12	2	no	—
367	C₂×C₄	—	12	2	no	—
368	C₂×C₄	—	12	2	no	—
369	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
370	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
371	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
372	C₂×C₄	C₅×#237	1	2	yes	—
373	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
374	C₈	—	4	2	no	—
375	C₂×C₃	—	4	2	no	—
376	C₂×C₃	C₅×#386	1	1	yes	characteristic
377	C₂×C₃	C₅×#416	1	1	yes	characteristic
378	C₂×C₃	C₅×#418	1	1	yes	characteristic
379	C₂×C₃	C₅×#449	1	2	yes	—
380	C₂×C₃	C₅×#482	1	2	yes	—
381	D₃	—	8	2	no	—
382	C₅	#69933	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	12	2	no	—
389	C₂²	—	12	2	no	—
390	C₂²	—	12	2	no	—
391	C₂²	—	24	2	no	—
392	C₂²	—	24	2	no	—
393	C₂²	C₅×#882	1	1	yes	characteristic
394	C₂²	C₅×#886	1	1	yes	characteristic
395	C₂²	C₅×#904	1	2	yes	—
396	C₂²	C₅×#908	1	2	yes	—
397	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	12	4	no	—
400	C₄	—	12	2	no	—
401	C₄	C₅×#67⋊C₄	1	2	yes	—
402	C₄	C₅×#939	1	2	yes	—
403	C₃	C₅×#1875	1	1	yes	characteristic, complemented, Sylow
404	C₂	—	4	2	no	—
405	C₂	—	24	2	no	—
406	C₂	C₅×#4734	1	2	yes	—
407	C₂	C₅×#4737	1	2	yes	—
408	C₂	C₅×#4958	1	1	yes	characteristic
409	C₂	C₅×#5113	1	1	yes	characteristic
410	C₂	C₅×#5131	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂×C₅×#930	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×C₂²⋊C₈	D₃
hypocenter	C₃	C₅×#1875
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#926	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
4. C₂×C₅×#821	C₂	semidirect
5. C₅×#4551	C₂	semidirect
13. C₅×#930	C₄	semidirect
21. #69933	C₅	direct (N × H)
25. C₂×C₅×C₂²⋊C₈	D₃	semidirect
51. C₅×C₄⋊Dic₃	D₄	semidirect
54. C₂×#926	C₂×C₅	semidirect
55. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
56. C₂×#821	C₂×C₅	semidirect
57. #4551	C₂×C₅	semidirect
108. #930	C₄×C₅	semidirect
145. C₂×C₂²⋊C₈	C₅×D₃	semidirect
191. C₄⋊Dic₃	C₅×D₄	semidirect
318. C₃×C₅	#1875	semidirect
382. C₅	#69933	direct (N × H)
403. C₃	C₅×#1875	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#930	2
C₂×C₅×#926	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₅×#821	2
C₅×#4551	2
C₅×#1875	3
#69933	5

Subgroups — C5×#69933 #14300724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69933 #14300724