Subgroups — C₅×#83285 #14438889

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#950	C₂	1	4	yes	maximal, complemented
3	C₅×#5477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5092	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5073	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5059	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3147	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₂×C₅×#235	C₂²	1	2	yes	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#127	C₂²	1	1	yes	characteristic
15	C₃×C₅×#124	C₂²	1	2	yes	—
16	C₃×C₅×#121	—	2	2	no	—
17	C₃×C₄×C₅×D₄	—	2	2	no	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₅×#950	—	2	16	no	—
20	C₂×C₅×#216	C₂²	1	4	yes	—
21	C₂×C₅×#215	C₂²	1	4	yes	—
22	C₂×C₅×#214	C₂²	1	4	yes	—
23	C₂×C₅×#213	C₂²	1	4	yes	—
24	C₅×#930	—	2	2	no	—
25	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
26	C₅×#875	C₂²	1	2	yes	—
27	C₅×#874	C₂²	1	1	yes	characteristic
28	C₄×C₅×D₁₂	—	2	2	no	—
29	C₅×#869	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
31	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
33	#83285	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#135	—	3	4	no	—
35	C₅×#532	—	3	1	no	—
36	C₅×#532	D₃	1	1	yes	characteristic, complemented
37	C₅×#495	—	3	4	no	—
38	C₅×#494	—	3	1	no	—
39	C₅×#493	—	3	1	no	—
40	C₅×#492	—	3	1	no	—
41	C₅×#492	—	3	1	no	—
42	C₂×C₄×C₅×C₈	—	3	1	no	—
43	C₃×C₅×#41	—	2	8	no	—
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	—	2	2	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×#67	—	2	2	no	—
52	C₅×#235	—	2	8	no	—
53	C₂×C₅×D₁₂	—	2	2	no	—
54	C₂×C₅×D₁₂	C₂³	1	2	yes	—
55	C₂×C₄×C₅×D₃	—	2	2	no	—
56	C₂×C₅×Dic₆	C₂³	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	—	2	2	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
59	C₃×C₄²×C₅	D₄	1	2	yes	—
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₅×#216	—	2	8	no	—
63	C₅×#215	—	2	8	no	—
64	C₅×#214	—	2	8	no	—
65	C₅×#213	—	2	8	no	—
66	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
67	C₅×C₄⋊Dic₃	—	2	2	no	—
68	C₂×C₅×C₃⋊C₈	D₄	1	8	yes	complemented
69	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
70	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
71	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#950	C₂×C₅	1	4	yes	complemented
73	#5477	C₂×C₅	1	1	yes	characteristic, complemented
74	#5092	C₂×C₅	1	1	yes	characteristic, complemented
75	#5085	C₂×C₅	1	1	yes	characteristic, complemented
76	#5076	C₂×C₅	1	1	yes	characteristic, complemented
77	#5073	C₂×C₅	1	1	yes	characteristic, complemented
78	#5059	C₂×C₅	1	4	yes	complemented
79	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×C₅×#41	—	3	2	no	—
81	C₂×C₅×#41	C₂×D₃	1	2	yes	—
82	C₅×#135	—	6	16	no	—
83	C₂×C₅×Q₁₆	—	3	4	no	—
84	C₂×C₅×SD₁₆	—	3	4	no	—
85	C₂×C₅×SD₁₆	—	3	4	no	—
86	C₂×C₅×D₈	—	3	4	no	—
87	C₂²×C₅×C₈	—	3	2	no	—
88	C₅×C₄⋊Q₈	—	3	1	no	—
89	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
90	C₅×#127	—	3	1	no	—
91	C₅×#127	C₂×D₃	1	1	yes	characteristic
92	C₅×#124	—	3	2	no	—
93	C₅×#124	C₂×D₃	1	2	yes	—
94	C₅×#121	—	2	2	no	—
95	C₅×#121	—	6	2	no	—
96	C₄×C₅×D₄	—	2	2	no	—
97	C₄×C₅×D₄	—	6	2	no	—
98	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
99	C₄×C₅×C₈	—	3	1	no	—
100	C₄×C₅×C₈	—	3	1	no	—
101	C₄×C₅×C₈	—	3	2	no	—
102	#3147	—	3	1	no	Sylow
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₅×D₃	—	2	2	no	—
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₃×C₅×D₄	—	2	4	no	—
108	C₃×C₅×D₄	—	4	4	no	—
109	C₃×C₅×D₄	—	4	4	no	—
110	C₂×C₃×C₄×C₅	—	2	4	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	4	4	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₅×#67	—	4	4	no	—
119	C₂×C₅×Dic₃	—	2	2	no	—
120	C₅×D₁₂	—	2	4	no	—
121	C₅×D₁₂	—	4	4	no	—
122	C₄×C₅×D₃	—	4	4	no	—
123	C₅×Dic₆	—	2	4	no	—
124	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
125	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
126	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
127	C₂×#235	C₂²×C₅	1	2	yes	—
128	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
129	C₃×#127	C₂²×C₅	1	1	yes	characteristic
130	C₃×#124	C₂²×C₅	1	2	yes	—
131	C₃×#121	—	2	2	no	—
132	C₃×C₄×D₄	—	2	2	no	—
133	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
134	#950	—	2	16	no	—
135	C₂×#216	C₂²×C₅	1	4	yes	—
136	C₂×#215	C₂²×C₅	1	4	yes	—
137	C₂×#214	C₂²×C₅	1	4	yes	—
138	C₂×#213	C₂²×C₅	1	4	yes	—
139	#930	—	2	2	no	—
140	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
141	#875	C₂²×C₅	1	2	yes	—
142	#874	C₂²×C₅	1	1	yes	characteristic
143	C₄×D₁₂	—	2	2	no	—
144	#869	C₂²×C₅	1	1	yes	characteristic
145	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
146	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
147	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
148	C₅×#41	—	2	8	no	—
149	C₅×#41	—	6	8	no	—
150	C₂×C₅×Q₈	—	3	2	no	—
151	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
152	C₂×C₅×D₄	—	2	2	no	—
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	—	3	2	no	—
155	C₂×C₅×D₄	—	6	2	no	—
156	C₂×C₅×D₄	—	6	2	no	—
157	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
158	C₂²×C₄×C₅	—	2	2	no	—
159	C₂²×C₄×C₅	—	6	2	no	—
160	C₂²×C₄×C₅	#67	1	2	yes	—
161	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
162	C₅×Q₁₆	—	6	8	no	—
163	C₅×SD₁₆	—	6	8	no	—
164	C₅×SD₁₆	—	6	8	no	—
165	C₅×D₈	—	6	8	no	—
166	C₂×C₅×C₈	—	3	8	no	—
167	C₂×C₅×C₈	—	3	2	no	—
168	C₂×C₅×C₈	—	3	2	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	—	6	2	no	—
171	C₅×C₂²⋊C₄	—	2	4	no	—
172	C₅×C₂²⋊C₄	—	6	4	no	—
173	C₄²×C₅	#67	1	2	yes	—
174	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
175	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
176	C₂×#135	—	3	4	no	—
177	#532	—	3	1	no	—
178	#532	C₅×D₃	1	1	yes	characteristic, complemented
179	#495	—	3	4	no	—
180	#494	—	3	1	no	—
181	#493	—	3	1	no	—
182	#492	—	3	1	no	—
183	#492	—	3	1	no	—
184	C₂×C₄×C₈	—	3	1	no	—
185	C₂²×C₃×C₅	—	2	2	no	—
186	C₂²×C₃×C₅	—	4	2	no	—
187	C₂²×C₃×C₅	—	4	4	no	—
188	C₂²×C₃×C₅	#127	1	2	yes	—
189	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₅×D₃	—	4	2	no	—
191	C₂×C₅×D₃	—	4	4	no	—
192	C₃×C₄×C₅	—	2	2	no	—
193	C₃×C₄×C₅	—	4	2	no	—
194	C₃×C₄×C₅	#127	1	2	yes	—
195	C₃×C₄×C₅	#135	1	4	yes	complemented
196	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
197	C₅×Dic₃	—	4	2	no	—
198	C₃×#41	—	2	8	no	—
199	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
200	C₂×C₃×D₄	—	2	2	no	—
201	C₂×C₃×D₄	—	2	2	no	—
202	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
203	C₂²×C₃×C₄	—	2	2	no	—
204	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
205	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₂×#67	—	2	2	no	—
207	#235	—	2	8	no	—
208	C₂×D₁₂	—	2	2	no	—
209	C₂×D₁₂	C₂³×C₅	1	2	yes	—
210	C₂×C₄×D₃	—	2	2	no	—
211	C₂×Dic₆	C₂³×C₅	1	2	yes	—
212	C₃×C₄⋊C₄	—	2	2	no	—
213	C₃×C₂²⋊C₄	—	2	4	no	—
214	C₃×C₄²	C₅×D₄	1	2	yes	—
215	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
216	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
217	#216	—	2	8	no	—
218	#215	—	2	8	no	—
219	#214	—	2	8	no	—
220	#213	—	2	8	no	—
221	(C₂×D₃)⋊C₄	—	2	4	no	—
222	C₄⋊Dic₃	—	2	2	no	—
223	C₂×C₃⋊C₈	C₅×D₄	1	8	yes	complemented
224	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
225	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	6	2	no	—
228	C₂³×C₅	C₂×#67	1	1	yes	characteristic
229	C₅×Q₈	—	2	4	no	—
230	C₅×Q₈	—	6	4	no	—
231	C₅×D₄	—	2	4	no	—
232	C₅×D₄	—	4	4	no	—
233	C₅×D₄	—	4	4	no	—
234	C₅×D₄	—	6	4	no	—
235	C₅×D₄	—	12	4	no	—
236	C₅×D₄	—	12	4	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	4	4	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	12	4	no	—
242	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
243	C₂×C₄×C₅	C₂×#67	1	2	yes	—
244	C₂×C₄×C₅	C₂×#67	1	2	yes	—
245	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
247	C₅×C₈	—	3	4	no	—
248	C₅×C₈	—	3	4	no	—
249	C₂×#41	—	3	2	no	—
250	C₂×#41	C₂×C₅×D₃	1	2	yes	—
251	#135	—	6	16	no	—
252	C₂×Q₁₆	—	3	4	no	—
253	C₂×SD₁₆	—	3	4	no	—
254	C₂×SD₁₆	—	3	4	no	—
255	C₂×D₈	—	3	4	no	—
256	C₂²×C₈	—	3	2	no	—
257	C₄⋊Q₈	—	3	1	no	—
258	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
259	#127	—	3	1	no	—
260	#127	C₂×C₅×D₃	1	1	yes	characteristic
261	#124	—	3	2	no	—
262	#124	C₂×C₅×D₃	1	2	yes	—
263	#121	—	2	2	no	—
264	#121	—	6	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	6	2	no	—
267	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
268	C₄×C₈	—	3	1	no	—
269	C₄×C₈	—	3	1	no	—
270	C₄×C₈	—	3	2	no	—
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	—	8	2	no	—
273	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
274	C₂×C₃×C₅	C₂×#135	1	2	yes	—
275	C₅×D₃	—	8	2	no	—
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
278	C₂²×D₃	—	2	2	no	—
279	C₃×Q₈	—	2	4	no	—
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	4	4	no	—
282	C₃×D₄	—	4	4	no	—
283	C₂×C₃×C₄	—	2	4	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	4	4	no	—
286	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
287	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
288	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
290	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
291	#67	—	4	4	no	—
292	C₂×Dic₃	—	2	2	no	—
293	D₁₂	—	2	4	no	—
294	D₁₂	—	4	4	no	—
295	C₄×D₃	—	4	4	no	—
296	Dic₆	—	2	4	no	—
297	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
298	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	4	2	no	—
301	C₂²×C₅	—	4	4	no	—
302	C₂²×C₅	—	12	2	no	—
303	C₂²×C₅	—	12	4	no	—
304	C₂²×C₅	#940	1	2	yes	—
305	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	—	12	2	no	—
309	C₄×C₅	#940	1	2	yes	—
310	C₄×C₅	#950	1	4	yes	complemented
311	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
312	#41	—	2	8	no	—
313	#41	—	6	8	no	—
314	C₂×Q₈	—	3	2	no	—
315	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	3	2	no	—
319	C₂×D₄	—	6	2	no	—
320	C₂×D₄	—	6	2	no	—
321	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	6	2	no	—
324	C₂²×C₄	C₅×#67	1	2	yes	—
325	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
326	Q₁₆	—	6	8	no	—
327	SD₁₆	—	6	8	no	—
328	SD₁₆	—	6	8	no	—
329	D₈	—	6	8	no	—
330	C₂×C₈	—	3	8	no	—
331	C₂×C₈	—	3	2	no	—
332	C₂×C₈	—	3	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	6	2	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	6	4	no	—
337	C₄²	C₅×#67	1	2	yes	—
338	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
339	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
340	C₃×C₅	#3147	1	1	yes	characteristic, complemented, Hall
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	4	2	no	—
343	C₂²×C₃	—	4	4	no	—
344	C₂²×C₃	C₅×#127	1	2	yes	—
345	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
346	C₂×D₃	—	4	2	no	—
347	C₂×D₃	—	4	4	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	4	2	no	—
350	C₃×C₄	C₅×#127	1	2	yes	—
351	C₃×C₄	C₅×#135	1	4	yes	complemented
352	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
353	Dic₃	—	4	2	no	—
354	C₂×C₅	—	2	2	no	—
355	C₂×C₅	—	8	2	no	—
356	C₂×C₅	—	24	2	no	—
357	C₂×C₅	C₂×#940	1	1	yes	characteristic
358	C₂×C₅	C₂×#950	1	2	yes	—
359	C₂³	—	2	2	no	—
360	C₂³	—	6	2	no	—
361	C₂³	C₂×C₅×#67	1	1	yes	characteristic
362	Q₈	—	2	4	no	—
363	Q₈	—	6	4	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	4	4	no	—
367	D₄	—	6	4	no	—
368	D₄	—	12	4	no	—
369	D₄	—	12	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	6	2	no	—
374	C₂×C₄	—	12	4	no	—
375	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
376	C₂×C₄	C₂×C₅×#67	1	2	yes	—
377	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
378	C₂×C₄	C₂×C₅×#67	1	2	yes	—
379	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
380	C₈	—	3	4	no	—
381	C₈	—	3	4	no	—
382	C₂×C₃	—	2	2	no	—
383	C₂×C₃	—	8	2	no	—
384	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
385	C₂×C₃	C₂×C₅×#135	1	2	yes	—
386	D₃	—	8	2	no	—
387	C₅	#83285	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	2	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	12	2	no	—
392	C₂²	—	12	4	no	—
393	C₂²	C₅×#940	1	2	yes	—
394	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	12	2	no	—
398	C₄	C₅×#940	1	2	yes	—
399	C₄	C₅×#950	1	4	yes	complemented
400	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
401	C₃	C₅×#3147	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	8	2	no	—
404	C₂	—	24	2	no	—
405	C₂	C₂×C₅×#940	1	1	yes	characteristic
406	C₂	C₂×C₅×#950	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#532	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#532	D₃
hypocenter	C₃	C₅×#3147
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#532

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₂×C₅×#950	C₂	semidirect
3. C₅×#5477	C₂	semidirect
4. C₅×#5092	C₂	semidirect
5. C₅×#5085	C₂	semidirect
6. C₅×#5076	C₂	semidirect
7. C₅×#5073	C₂	semidirect
8. C₅×#5059	C₂	semidirect
9. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
33. #83285	C₅	direct (N × H)
36. C₅×#532	D₃	semidirect
68. C₂×C₅×C₃⋊C₈	D₄	semidirect
71. C₃×#532	C₂×C₅	semidirect
72. C₂×#950	C₂×C₅	semidirect
73. #5477	C₂×C₅	semidirect
74. #5092	C₂×C₅	semidirect
75. #5085	C₂×C₅	semidirect
76. #5076	C₂×C₅	semidirect
77. #5073	C₂×C₅	semidirect
78. #5059	C₂×C₅	semidirect
79. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
178. #532	C₅×D₃	semidirect
195. C₃×C₄×C₅	#135	semidirect
223. C₂×C₃⋊C₈	C₅×D₄	semidirect
310. C₄×C₅	#950	semidirect
340. C₃×C₅	#3147	semidirect
351. C₃×C₄	C₅×#135	semidirect
387. C₅	#83285	direct (N × H)
399. C₄	C₅×#950	semidirect
401. C₃	C₅×#3147	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#532	2
C₂×C₅×#950	2
C₅×#5477	2
C₅×#5092	2
C₅×#5085	2
C₅×#5076	2
C₅×#5073	2
C₅×#5059	2
C₂×C₄×C₅×C₃⋊C₈	2
C₅×#3147	3
#83285	5

Subgroups — C5×#83285 #14438889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83285 #14438889