Subgroups — C₅×#78565 #14439549

Order 1920.

1192 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	C₂×C₅×#908	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5525	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4712	C₂	1	4	yes	maximal, complemented
7	C₅×#4696	C₂	1	2	yes	maximal, complemented
8	C₅×#4695	C₂	1	2	yes	maximal, complemented
9	C₅×#3155	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	2	yes	—
11	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₅×#908	—	2	8	no	—
16	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
17	C₅×#904	—	2	4	no	—
18	C₂×C₅×D₂₄	—	2	4	no	—
19	C₂×C₅×D₂₄	C₂²	1	2	yes	—
20	C₂×C₅×D₂₄	C₂²	1	2	yes	—
21	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₅×D₂₄	C₂²	1	4	yes	complemented
23	C₂×C₅×#204	C₂²	1	4	yes	complemented
24	C₂×C₅×#204	C₂²	1	2	yes	complemented
25	C₅×#895	—	2	4	no	—
26	C₅×#882	—	2	4	no	—
27	C₅×#875	C₂²	1	4	yes	complemented
28	C₅×#874	C₂²	1	4	yes	complemented
29	C₃×C₅×#97	C₂²	1	2	yes	complemented
30	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
31	#78565	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
33	C₂×C₅×#135	—	3	1	no	—
34	C₂²×C₅×D₈	—	3	1	no	—
35	C₅×#535	—	3	2	no	—
36	C₅×#496	—	3	4	no	—
37	C₅×#495	—	3	2	no	—
38	C₅×#493	—	3	2	no	—
39	C₅×#405	D₃	1	1	yes	characteristic, complemented
40	C₂³×C₅×D₃	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₅×#67	—	2	2	no	—
43	C₅×#235	—	2	4	no	—
44	C₅×#235	—	2	4	no	—
45	C₂×C₅×D₁₂	—	2	4	no	—
46	C₂×C₅×D₁₂	—	2	4	no	—
47	C₂×C₅×D₁₂	—	2	2	no	—
48	C₂×C₅×D₁₂	—	2	8	no	—
49	C₂×C₅×D₁₂	C₂³	1	2	yes	—
50	C₂×C₅×D₁₂	C₂³	1	4	yes	—
51	C₂×C₄×C₅×D₃	—	2	2	no	—
52	C₂×C₅×Dic₆	C₂³	1	2	yes	—
53	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
54	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
55	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
60	C₃×C₄²×C₅	C₂³	1	2	yes	—
61	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
62	C₅×Dic₁₂	—	2	2	no	—
63	C₅×D₂₄	—	2	4	no	—
64	C₅×D₂₄	—	2	4	no	—
65	C₅×D₂₄	—	2	2	no	—
66	C₅×D₂₄	—	2	8	no	—
67	C₅×#204	—	2	4	no	—
68	C₅×#204	—	2	8	no	—
69	C₂×#908	C₂×C₅	1	2	yes	complemented
70	C₂×#904	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂²×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
72	#5525	C₂×C₅	1	2	yes	complemented
73	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
74	#4712	C₂×C₅	1	4	yes	complemented
75	#4696	C₂×C₅	1	2	yes	complemented
76	#4695	C₂×C₅	1	2	yes	complemented
77	C₂×C₅×#41	—	3	2	no	—
78	C₂²×C₅×D₄	—	3	2	no	—
79	C₅×AGL(1,ℤ/8)	—	6	8	no	—
80	C₅×#135	—	6	4	no	—
81	C₂×C₅×Q₁₆	—	3	1	no	—
82	C₂×C₅×SD₁₆	—	3	4	no	—
83	C₂×C₅×SD₁₆	—	3	2	no	—
84	C₂×C₅×D₈	—	3	2	no	—
85	C₂×C₅×D₈	—	3	2	no	—
86	C₂×C₅×D₈	—	3	1	no	—
87	C₂×C₅×D₈	—	3	4	no	—
88	C₂×C₅×D₈	—	6	4	no	—
89	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
91	C₅×#127	—	3	4	no	—
92	C₅×#124	—	3	4	no	—
93	C₅×#121	—	6	4	no	—
94	C₅×#120	—	6	4	no	—
95	C₅×#117	C₂×D₃	1	1	yes	characteristic
96	C₅×#97	C₂×D₃	1	2	yes	complemented
97	C₄×C₅×C₈	C₂×D₃	1	2	yes	complemented
98	#3155	—	3	1	no	Sylow
99	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₅×D₃	—	2	4	no	—
101	C₂²×C₅×D₃	—	2	2	no	—
102	C₂²×C₅×D₃	—	4	4	no	—
103	C₂²×C₅×D₃	—	8	4	no	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
109	C₅×#67	—	4	4	no	—
110	C₂×C₅×Dic₃	—	2	2	no	—
111	C₅×D₁₂	—	2	4	no	—
112	C₅×D₁₂	—	2	2	no	—
113	C₅×D₁₂	—	2	4	no	—
114	C₅×D₁₂	—	2	2	no	—
115	C₅×D₁₂	—	4	4	no	—
116	C₅×D₁₂	—	8	8	no	—
117	C₄×C₅×D₃	—	4	4	no	—
118	C₅×Dic₆	—	2	2	no	—
119	C₅×Dic₆	—	2	2	no	—
120	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
121	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
122	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
123	C₂×#235	C₂²×C₅	1	2	yes	—
124	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
125	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
126	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
127	C₃×#117	C₂²×C₅	1	1	yes	characteristic
128	#908	—	2	8	no	—
129	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
130	#904	—	2	4	no	—
131	C₂×D₂₄	—	2	4	no	—
132	C₂×D₂₄	C₂²×C₅	1	2	yes	—
133	C₂×D₂₄	C₂²×C₅	1	2	yes	—
134	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic, complemented
135	C₂×D₂₄	C₂²×C₅	1	4	yes	complemented
136	C₂×#204	C₂²×C₅	1	4	yes	complemented
137	C₂×#204	C₂²×C₅	1	2	yes	complemented
138	#895	—	2	4	no	—
139	#882	—	2	4	no	—
140	#875	C₂²×C₅	1	4	yes	complemented
141	#874	C₂²×C₅	1	4	yes	complemented
142	C₃×#97	C₂²×C₅	1	2	yes	complemented
143	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
144	C₂⁴×C₅	—	6	2	no	—
145	C₅×#41	—	6	4	no	—
146	C₅×#41	—	6	4	no	—
147	C₂×C₅×Q₈	—	3	2	no	—
148	C₂×C₅×D₄	—	3	4	no	—
149	C₂×C₅×D₄	—	3	2	no	—
150	C₂×C₅×D₄	—	6	2	no	—
151	C₂×C₅×D₄	—	6	4	no	—
152	C₂×C₅×D₄	—	6	4	no	—
153	C₂×C₅×D₄	—	6	2	no	—
154	C₂×C₅×D₄	—	6	8	no	—
155	C₂²×C₄×C₅	—	6	2	no	—
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₅×Q₁₆	—	6	2	no	—
158	C₅×SD₁₆	—	6	4	no	—
159	C₅×SD₁₆	—	6	8	no	—
160	C₅×D₈	—	6	4	no	—
161	C₅×D₈	—	6	4	no	—
162	C₅×D₈	—	6	2	no	—
163	C₅×D₈	—	6	8	no	—
164	C₅×M₁₆	D₁₂	1	4	yes	complemented
165	C₂×C₅×C₈	D₁₂	1	4	yes	complemented
166	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
167	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
168	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
169	C₅×C₄⋊C₄	D₁₂	1	2	yes	—
170	C₅×C₂²⋊C₄	—	6	8	no	—
171	C₅×C₂²⋊C₄	D₁₂	1	2	yes	—
172	C₄²×C₅	C₂²×D₃	1	2	yes	—
173	C₂×AGL(1,ℤ/8)	—	3	2	no	—
174	C₂×#135	—	3	1	no	—
175	C₂²×D₈	—	3	1	no	—
176	#535	—	3	2	no	—
177	#496	—	3	4	no	—
178	#495	—	3	2	no	—
179	#493	—	3	2	no	—
180	#405	C₅×D₃	1	1	yes	characteristic, complemented
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	#127	1	2	yes	—
183	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₅×D₃	—	4	2	no	—
185	C₂×C₅×D₃	—	4	4	no	—
186	C₂×C₅×D₃	—	4	4	no	—
187	C₂×C₅×D₃	—	4	8	no	—
188	C₂×C₅×D₃	—	8	8	no	—
189	C₃×C₄×C₅	—	2	4	no	—
190	C₃×C₄×C₅	#127	1	2	yes	—
191	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₅×Dic₃	—	4	2	no	—
194	C₂³×D₃	—	2	2	no	—
195	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂×#67	—	2	2	no	—
197	#235	—	2	4	no	—
198	#235	—	2	4	no	—
199	C₂×D₁₂	—	2	4	no	—
200	C₂×D₁₂	—	2	4	no	—
201	C₂×D₁₂	—	2	2	no	—
202	C₂×D₁₂	—	2	8	no	—
203	C₂×D₁₂	C₂³×C₅	1	2	yes	—
204	C₂×D₁₂	C₂³×C₅	1	4	yes	—
205	C₂×C₄×D₃	—	2	2	no	—
206	C₂×Dic₆	C₂³×C₅	1	2	yes	—
207	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
208	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
209	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
210	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
211	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
212	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
213	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
214	C₃×C₄²	C₂³×C₅	1	2	yes	—
215	(C₂×D₃)⋊C₄	—	2	8	no	—
216	Dic₁₂	—	2	2	no	—
217	D₂₄	—	2	4	no	—
218	D₂₄	—	2	4	no	—
219	D₂₄	—	2	2	no	—
220	D₂₄	—	2	8	no	—
221	#204	—	2	4	no	—
222	#204	—	2	8	no	—
223	C₂³×C₅	—	6	4	no	—
224	C₂³×C₅	—	6	2	no	—
225	C₂³×C₅	—	12	4	no	—
226	C₂³×C₅	—	24	4	no	—
227	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
228	C₅×Q₈	—	6	2	no	—
229	C₅×Q₈	—	6	2	no	—
230	C₅×D₄	—	6	4	no	—
231	C₅×D₄	—	6	2	no	—
232	C₅×D₄	—	6	4	no	—
233	C₅×D₄	—	6	2	no	—
234	C₅×D₄	—	12	4	no	—
235	C₅×D₄	—	12	4	no	—
236	C₅×D₄	—	24	8	no	—
237	C₂×C₄×C₅	—	6	2	no	—
238	C₂×C₄×C₅	—	12	4	no	—
239	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
240	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
242	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
243	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
244	C₅×C₈	C₂×D₁₂	1	2	yes	—
245	C₅×C₈	C₂×D₁₂	1	2	yes	—
246	C₅×C₈	C₂×D₁₂	1	4	yes	—
247	C₂×#41	—	3	2	no	—
248	C₂²×D₄	—	3	2	no	—
249	AGL(1,ℤ/8)	—	6	8	no	—
250	#135	—	6	4	no	—
251	C₂×Q₁₆	—	3	1	no	—
252	C₂×SD₁₆	—	3	2	no	—
253	C₂×SD₁₆	—	3	4	no	—
254	C₂×D₈	—	3	2	no	—
255	C₂×D₈	—	3	2	no	—
256	C₂×D₈	—	3	1	no	—
257	C₂×D₈	—	3	4	no	—
258	C₂×D₈	—	6	4	no	—
259	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
260	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
261	#127	—	3	4	no	—
262	#124	—	3	4	no	—
263	#121	—	6	4	no	—
264	#120	—	6	4	no	—
265	#117	C₂×C₅×D₃	1	1	yes	characteristic
266	#97	C₂×C₅×D₃	1	2	yes	complemented
267	C₄×C₈	C₂×C₅×D₃	1	2	yes	complemented
268	C₂×C₃×C₅	—	2	2	no	—
269	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
270	C₂×C₃×C₅	#576	1	2	yes	—
271	C₅×D₃	—	8	2	no	—
272	C₅×D₃	—	8	4	no	—
273	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
274	C₂²×D₃	—	2	4	no	—
275	C₂²×D₃	—	2	2	no	—
276	C₂²×D₃	—	4	4	no	—
277	C₂²×D₃	—	8	4	no	—
278	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
279	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
281	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
282	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
283	#67	—	4	4	no	—
284	C₂×Dic₃	—	2	2	no	—
285	D₁₂	—	2	4	no	—
286	D₁₂	—	2	2	no	—
287	D₁₂	—	2	4	no	—
288	D₁₂	—	2	2	no	—
289	D₁₂	—	4	4	no	—
290	D₁₂	—	8	8	no	—
291	C₄×D₃	—	4	4	no	—
292	Dic₆	—	2	2	no	—
293	Dic₆	—	2	2	no	—
294	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
295	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
296	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	12	2	no	—
299	C₂²×C₅	—	12	4	no	—
300	C₂²×C₅	—	12	4	no	—
301	C₂²×C₅	—	12	8	no	—
302	C₂²×C₅	—	24	8	no	—
303	C₂²×C₅	#874	1	2	yes	—
304	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
305	C₄×C₅	—	2	4	no	—
306	C₄×C₅	—	12	2	no	—
307	C₄×C₅	#874	1	2	yes	—
308	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
309	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
310	C₂⁴	—	6	2	no	—
311	#41	—	6	4	no	—
312	#41	—	6	4	no	—
313	C₂×Q₈	—	3	2	no	—
314	C₂×D₄	—	3	4	no	—
315	C₂×D₄	—	3	2	no	—
316	C₂×D₄	—	6	2	no	—
317	C₂×D₄	—	6	4	no	—
318	C₂×D₄	—	6	4	no	—
319	C₂×D₄	—	6	2	no	—
320	C₂×D₄	—	6	8	no	—
321	C₂²×C₄	—	6	2	no	—
322	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
323	Q₁₆	—	6	2	no	—
324	SD₁₆	—	6	4	no	—
325	SD₁₆	—	6	8	no	—
326	D₈	—	6	4	no	—
327	D₈	—	6	4	no	—
328	D₈	—	6	2	no	—
329	D₈	—	6	8	no	—
330	M₁₆	C₅×D₁₂	1	4	yes	complemented
331	C₂×C₈	C₅×D₁₂	1	4	yes	complemented
332	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
333	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
334	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
335	C₄⋊C₄	C₅×D₁₂	1	2	yes	—
336	C₂²⋊C₄	—	6	8	no	—
337	C₂²⋊C₄	C₅×D₁₂	1	2	yes	—
338	C₄²	C₂²×C₅×D₃	1	2	yes	—
339	C₃×C₅	#3155	1	1	yes	characteristic, complemented, Hall
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	C₅×#127	1	2	yes	—
342	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
343	C₂×D₃	—	4	2	no	—
344	C₂×D₃	—	4	4	no	—
345	C₂×D₃	—	4	4	no	—
346	C₂×D₃	—	4	8	no	—
347	C₂×D₃	—	8	8	no	—
348	C₃×C₄	—	2	4	no	—
349	C₃×C₄	C₅×#127	1	2	yes	—
350	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
351	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
352	Dic₃	—	4	2	no	—
353	C₂×C₅	—	2	2	no	—
354	C₂×C₅	—	24	4	no	—
355	C₂×C₅	—	24	2	no	—
356	C₂×C₅	C₂×#874	1	1	yes	characteristic
357	C₂×C₅	#5752	1	2	yes	—
358	C₂³	—	6	4	no	—
359	C₂³	—	6	2	no	—
360	C₂³	—	12	4	no	—
361	C₂³	—	24	4	no	—
362	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
363	Q₈	—	6	2	no	—
364	Q₈	—	6	2	no	—
365	D₄	—	6	4	no	—
366	D₄	—	6	2	no	—
367	D₄	—	6	4	no	—
368	D₄	—	6	2	no	—
369	D₄	—	12	4	no	—
370	D₄	—	12	4	no	—
371	D₄	—	24	8	no	—
372	C₂×C₄	—	6	2	no	—
373	C₂×C₄	—	12	4	no	—
374	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
375	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
376	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
377	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
378	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
379	C₈	C₂×C₅×D₁₂	1	2	yes	—
380	C₈	C₂×C₅×D₁₂	1	2	yes	—
381	C₈	C₂×C₅×D₁₂	1	4	yes	—
382	C₂×C₃	—	2	2	no	—
383	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
384	C₂×C₃	C₅×#576	1	2	yes	—
385	D₃	—	8	4	no	—
386	D₃	—	8	2	no	—
387	C₅	#78565	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	2	2	no	—
389	C₂²	—	12	2	no	—
390	C₂²	—	12	4	no	—
391	C₂²	—	12	4	no	—
392	C₂²	—	12	8	no	—
393	C₂²	—	24	8	no	—
394	C₂²	C₅×#874	1	2	yes	—
395	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
396	C₄	—	2	4	no	—
397	C₄	—	12	2	no	—
398	C₄	C₅×#874	1	2	yes	—
399	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
400	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
401	C₃	C₅×#3155	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	24	4	no	—
404	C₂	—	24	2	no	—
405	C₂	C₂×C₅×#874	1	1	yes	characteristic
406	C₂	C₅×#5752	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#3155
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#405

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#908	C₂	semidirect
2. C₂×C₅×#904	C₂	semidirect
3. C₂²×C₅×D₂₄	C₂	semidirect
4. C₅×#5525	C₂	semidirect
5. C₃×C₅×#405	C₂	semidirect
6. C₅×#4712	C₂	semidirect
7. C₅×#4696	C₂	semidirect
8. C₅×#4695	C₂	semidirect
16. C₂×C₅×Dic₁₂	C₂²	semidirect
21. C₂×C₅×D₂₄	C₂²	semidirect
22. C₂×C₅×D₂₄	C₂²	semidirect
23. C₂×C₅×#204	C₂²	semidirect
24. C₂×C₅×#204	C₂²	semidirect
27. C₅×#875	C₂²	semidirect
28. C₅×#874	C₂²	semidirect
29. C₃×C₅×#97	C₂²	semidirect
30. C₃×C₄×C₅×C₈	C₂²	semidirect
31. #78565	C₅	direct (N × H)
39. C₅×#405	D₃	semidirect
53. C₃×C₅×M₁₆	D₄	semidirect
54. C₂×C₃×C₅×C₈	D₄	semidirect
69. C₂×#908	C₂×C₅	semidirect
70. C₂×#904	C₂×C₅	semidirect
71. C₂²×D₂₄	C₂×C₅	semidirect
72. #5525	C₂×C₅	semidirect
73. C₃×#405	C₂×C₅	semidirect
74. #4712	C₂×C₅	semidirect
75. #4696	C₂×C₅	semidirect
76. #4695	C₂×C₅	semidirect
96. C₅×#97	C₂×D₃	semidirect
97. C₄×C₅×C₈	C₂×D₃	semidirect
129. C₂×Dic₁₂	C₂²×C₅	semidirect
134. C₂×D₂₄	C₂²×C₅	semidirect
135. C₂×D₂₄	C₂²×C₅	semidirect
136. C₂×#204	C₂²×C₅	semidirect
137. C₂×#204	C₂²×C₅	semidirect
140. #875	C₂²×C₅	semidirect
141. #874	C₂²×C₅	semidirect
142. C₃×#97	C₂²×C₅	semidirect
143. C₃×C₄×C₈	C₂²×C₅	semidirect
164. C₅×M₁₆	D₁₂	semidirect
165. C₂×C₅×C₈	D₁₂	semidirect
180. #405	C₅×D₃	semidirect
207. C₃×M₁₆	C₅×D₄	semidirect
208. C₂×C₃×C₈	C₅×D₄	semidirect
266. #97	C₂×C₅×D₃	semidirect
267. C₄×C₈	C₂×C₅×D₃	semidirect
330. M₁₆	C₅×D₁₂	semidirect
331. C₂×C₈	C₅×D₁₂	semidirect
339. C₃×C₅	#3155	semidirect
387. C₅	#78565	direct (N × H)
401. C₃	C₅×#3155	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#908	2
C₂×C₅×#904	2
C₂²×C₅×D₂₄	2
C₅×#5525	2
C₃×C₅×#405	2
C₅×#4712	2
C₅×#4696	2
C₅×#4695	2
C₅×#3155	3
#78565	5

Subgroups — C5×#78565 #14439549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78565 #14439549