Subgroups — C₅×#83906 #14439552

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×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5830	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#949	C₂	1	2	yes	maximal, complemented
4	C₂²×C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5191	C₂	1	2	yes	maximal, complemented
6	C₅×#5176	C₂	1	4	yes	maximal, complemented
7	C₅×#5151	C₂	1	2	yes	maximal, complemented
8	C₅×#5101	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3155	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
12	C₃×C₅×#135	—	2	4	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₅×#949	—	2	8	no	—
18	C₅×#947	C₂²	1	4	yes	complemented
19	C₂×C₅×#215	C₂²	1	4	yes	complemented
20	C₅×#940	C₂²	1	4	yes	complemented
21	C₅×#937	—	2	4	no	—
22	C₂×C₅×#213	C₂²	1	4	yes	complemented
23	C₅×#930	—	2	4	no	—
24	C₅×#926	C₂²	1	1	yes	characteristic
25	C₂×C₅×#208	C₂²	1	1	yes	characteristic
26	C₂×C₅×D₂₄	—	2	4	no	—
27	C₂×C₅×D₂₄	C₂²	1	2	yes	—
28	C₂×C₅×D₂₄	C₂²	1	2	yes	—
29	C₅×#815	C₂²	1	2	yes	complemented
30	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
31	#83906	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
33	C₂×C₅×#135	D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
40	C₂³×C₅×D₃	—	2	2	no	—
41	C₃×C₅×#41	—	2	4	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	—	2	2	no	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₅×#67	—	2	8	no	—
49	C₂×C₅×D₁₂	—	2	4	no	—
50	C₂×C₅×D₁₂	—	2	4	no	—
51	C₂×C₅×D₁₂	—	2	2	no	—
52	C₂×C₅×D₁₂	C₂³	1	4	yes	—
53	C₃×C₅×Q₁₆	—	2	2	no	—
54	C₃×C₅×SD₁₆	—	2	4	no	—
55	C₃×C₅×D₈	—	2	2	no	—
56	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
57	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₅×#217	D₄	1	2	yes	—
60	C₅×#215	—	2	8	no	—
61	C₅×#213	—	2	8	no	—
62	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
63	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
64	C₄×C₅×Dic₃	C₂³	1	2	yes	—
65	C₅×#208	D₄	1	4	yes	complemented
66	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
67	C₅×D₂₄	—	2	4	no	—
68	C₅×D₂₄	—	2	4	no	—
69	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
70	#5830	C₂×C₅	1	2	yes	complemented
71	C₂×#949	C₂×C₅	1	2	yes	complemented
72	C₂²×D₂₄	C₂×C₅	1	1	yes	characteristic, complemented
73	#5191	C₂×C₅	1	2	yes	complemented
74	#5176	C₂×C₅	1	4	yes	complemented
75	#5151	C₂×C₅	1	2	yes	complemented
76	#5101	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×C₅×#41	C₂×D₃	1	2	yes	—
78	C₂²×C₅×D₄	—	3	2	no	—
79	C₅×AGL(1,ℤ/8)	—	6	8	no	—
80	C₅×#135	—	2	4	no	—
81	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic, complemented
82	C₂×C₅×SD₁₆	—	3	4	no	—
83	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	complemented
84	C₂×C₅×D₈	—	3	4	no	—
85	C₂×C₅×D₈	—	3	2	no	—
86	C₂×C₅×D₈	—	3	2	no	—
87	C₂×C₅×D₈	—	6	4	no	—
88	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic, complemented
89	C₂×C₅×M₁₆	—	3	1	no	—
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	—	3	1	no	—
96	C₅×#97	—	3	2	no	—
97	C₄×C₅×C₈	—	3	2	no	—
98	#3155	—	3	1	no	Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₅×D₃	—	2	4	no	—
102	C₂²×C₅×D₃	—	4	4	no	—
103	C₂²×C₅×D₃	—	8	4	no	—
104	C₃×C₅×Q₈	—	2	2	no	—
105	C₃×C₅×Q₈	—	2	2	no	—
106	C₃×C₅×D₄	—	2	2	no	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	—	4	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	4	4	no	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₅×#67	—	8	8	no	—
116	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
117	C₅×D₁₂	—	2	4	no	—
118	C₅×D₁₂	—	2	4	no	—
119	C₅×D₁₂	—	4	4	no	—
120	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
121	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
122	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
123	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
124	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
125	C₃×#135	—	2	4	no	—
126	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
127	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
128	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
129	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
130	#949	—	2	8	no	—
131	#947	C₂²×C₅	1	4	yes	complemented
132	C₂×#215	C₂²×C₅	1	4	yes	complemented
133	#940	C₂²×C₅	1	4	yes	complemented
134	#937	—	2	4	no	—
135	C₂×#213	C₂²×C₅	1	4	yes	complemented
136	#930	—	2	4	no	—
137	#926	C₂²×C₅	1	1	yes	characteristic
138	C₂×#208	C₂²×C₅	1	1	yes	characteristic
139	C₂×D₂₄	—	2	4	no	—
140	C₂×D₂₄	C₂²×C₅	1	2	yes	—
141	C₂×D₂₄	C₂²×C₅	1	2	yes	—
142	#815	C₂²×C₅	1	2	yes	complemented
143	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
144	C₂⁴×C₅	—	6	2	no	—
145	C₅×#41	—	2	4	no	—
146	C₅×#41	—	2	4	no	—
147	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	—	3	4	no	—
150	C₂×C₅×D₄	—	6	8	no	—
151	C₂×C₅×D₄	—	6	4	no	—
152	C₂×C₅×D₄	—	6	2	no	—
153	C₂×C₅×D₄	—	6	4	no	—
154	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₅×Q₁₆	—	2	2	no	—
158	C₅×SD₁₆	—	2	4	no	—
159	C₅×SD₁₆	—	6	8	no	—
160	C₅×D₈	—	2	2	no	—
161	C₅×D₈	—	6	8	no	—
162	C₅×D₈	—	6	4	no	—
163	C₅×D₈	—	6	4	no	—
164	C₅×M₁₆	—	3	4	no	—
165	C₂×C₅×C₈	—	3	2	no	—
166	C₂×C₅×C₈	#67	1	4	yes	complemented
167	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
168	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
169	C₅×C₄⋊C₄	—	3	2	no	—
170	C₅×C₂²⋊C₄	—	3	2	no	—
171	C₅×C₂²⋊C₄	—	6	8	no	—
172	C₄²×C₅	—	3	2	no	—
173	C₂×AGL(1,ℤ/8)	—	3	2	no	—
174	C₂×#135	C₅×D₃	1	1	yes	characteristic, complemented
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	—	3	1	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	—	4	4	no	—
184	C₂²×C₃×C₅	#127	1	2	yes	—
185	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
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	—	4	2	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	—	2	4	no	—
194	C₂³×D₃	—	2	2	no	—
195	C₃×#41	—	2	4	no	—
196	C₃×#41	—	2	4	no	—
197	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
198	C₂×C₃×D₄	—	2	2	no	—
199	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
200	C₂²×C₃×C₄	—	2	2	no	—
201	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
202	C₂×#67	—	2	8	no	—
203	C₂×D₁₂	—	2	4	no	—
204	C₂×D₁₂	—	2	4	no	—
205	C₂×D₁₂	—	2	2	no	—
206	C₂×D₁₂	C₂³×C₅	1	4	yes	—
207	C₃×Q₁₆	—	2	2	no	—
208	C₃×SD₁₆	—	2	4	no	—
209	C₃×D₈	—	2	2	no	—
210	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
211	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
212	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
213	#217	C₅×D₄	1	2	yes	—
214	#215	—	2	8	no	—
215	#213	—	2	8	no	—
216	(C₂×D₃)⋊C₄	—	2	8	no	—
217	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
218	C₄×Dic₃	C₂³×C₅	1	2	yes	—
219	#208	C₅×D₄	1	4	yes	complemented
220	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
221	D₂₄	—	2	4	no	—
222	D₂₄	—	2	4	no	—
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	—	6	4	no	—
225	C₂³×C₅	—	12	4	no	—
226	C₂³×C₅	—	24	4	no	—
227	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
228	C₅×Q₈	—	2	2	no	—
229	C₅×Q₈	—	2	2	no	—
230	C₅×D₄	—	2	2	no	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	—	4	4	no	—
233	C₅×D₄	—	6	4	no	—
234	C₅×D₄	—	6	4	no	—
235	C₅×D₄	—	12	4	no	—
236	C₅×D₄	—	24	8	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	3	4	no	—
239	C₂×C₄×C₅	—	4	4	no	—
240	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
242	C₂×C₄×C₅	C₂×#67	1	2	yes	—
243	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
244	C₅×C₈	—	3	4	no	—
245	C₅×C₈	C₂×#67	1	2	yes	—
246	C₅×C₈	C₂×#67	1	2	yes	—
247	C₂×#41	C₂×C₅×D₃	1	2	yes	—
248	C₂²×D₄	—	3	2	no	—
249	AGL(1,ℤ/8)	—	6	8	no	—
250	#135	—	2	4	no	—
251	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
252	C₂×SD₁₆	—	3	4	no	—
253	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	complemented
254	C₂×D₈	—	3	4	no	—
255	C₂×D₈	—	3	2	no	—
256	C₂×D₈	—	3	2	no	—
257	C₂×D₈	—	6	4	no	—
258	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
259	C₂×M₁₆	—	3	1	no	—
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	—	3	1	no	—
266	#97	—	3	2	no	—
267	C₄×C₈	—	3	2	no	—
268	C₂×C₃×C₅	—	2	2	no	—
269	C₂×C₃×C₅	—	8	2	no	—
270	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
271	C₂×C₃×C₅	#576	1	2	yes	—
272	C₅×D₃	—	8	4	no	—
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂²×D₃	—	2	4	no	—
276	C₂²×D₃	—	4	4	no	—
277	C₂²×D₃	—	8	4	no	—
278	C₃×Q₈	—	2	2	no	—
279	C₃×Q₈	—	2	2	no	—
280	C₃×D₄	—	2	2	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	4	4	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	4	4	no	—
285	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
287	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
288	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
289	#67	—	8	8	no	—
290	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
291	D₁₂	—	2	4	no	—
292	D₁₂	—	2	4	no	—
293	D₁₂	—	4	4	no	—
294	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
295	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
296	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	4	4	no	—
299	C₂²×C₅	—	4	2	no	—
300	C₂²×C₅	—	12	8	no	—
301	C₂²×C₅	—	12	4	no	—
302	C₂²×C₅	—	24	8	no	—
303	C₂²×C₅	#940	1	2	yes	—
304	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	6	4	no	—
307	C₄×C₅	#940	1	2	yes	—
308	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
309	C₄×C₅	C₂²×#67	1	1	yes	characteristic
310	C₂⁴	—	6	2	no	—
311	#41	—	2	4	no	—
312	#41	—	2	4	no	—
313	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	3	4	no	—
316	C₂×D₄	—	6	8	no	—
317	C₂×D₄	—	6	4	no	—
318	C₂×D₄	—	6	2	no	—
319	C₂×D₄	—	6	4	no	—
320	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
323	Q₁₆	—	2	2	no	—
324	SD₁₆	—	2	4	no	—
325	SD₁₆	—	6	8	no	—
326	D₈	—	2	2	no	—
327	D₈	—	6	8	no	—
328	D₈	—	6	4	no	—
329	D₈	—	6	4	no	—
330	M₁₆	—	3	4	no	—
331	C₂×C₈	—	3	2	no	—
332	C₂×C₈	C₅×#67	1	4	yes	complemented
333	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
334	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
335	C₄⋊C₄	—	3	2	no	—
336	C₂²⋊C₄	—	3	2	no	—
337	C₂²⋊C₄	—	6	8	no	—
338	C₄²	—	3	2	no	—
339	C₃×C₅	#3155	1	1	yes	characteristic, complemented, Hall
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	4	2	no	—
342	C₂²×C₃	—	4	4	no	—
343	C₂²×C₃	C₅×#127	1	2	yes	—
344	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
345	C₂×D₃	—	4	4	no	—
346	C₂×D₃	—	4	8	no	—
347	C₂×D₃	—	8	8	no	—
348	C₃×C₄	—	4	2	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	—	2	4	no	—
353	C₂×C₅	—	2	2	no	—
354	C₂×C₅	—	8	2	no	—
355	C₂×C₅	—	24	4	no	—
356	C₂×C₅	#5769	1	2	yes	—
357	C₂×C₅	C₂×#940	1	1	yes	characteristic
358	C₂³	—	2	2	no	—
359	C₂³	—	6	4	no	—
360	C₂³	—	12	4	no	—
361	C₂³	—	24	4	no	—
362	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	4	no	—
368	D₄	—	6	4	no	—
369	D₄	—	6	4	no	—
370	D₄	—	12	4	no	—
371	D₄	—	24	8	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	3	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
376	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
377	C₂×C₄	C₂×C₅×#67	1	2	yes	—
378	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
379	C₈	—	3	4	no	—
380	C₈	C₂×C₅×#67	1	2	yes	—
381	C₈	C₂×C₅×#67	1	2	yes	—
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	C₅×#576	1	2	yes	—
386	D₃	—	8	4	no	—
387	C₅	#83906	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	2	2	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	12	8	no	—
392	C₂²	—	12	4	no	—
393	C₂²	—	24	8	no	—
394	C₂²	C₅×#940	1	2	yes	—
395	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
396	C₄	—	4	2	no	—
397	C₄	—	6	4	no	—
398	C₄	C₅×#940	1	2	yes	—
399	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
400	C₄	C₂²×C₅×#67	1	1	yes	characteristic
401	C₃	C₅×#3155	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	8	2	no	—
404	C₂	—	24	4	no	—
405	C₂	C₅×#5769	1	2	yes	—
406	C₂	C₂×C₅×#940	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	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₅×#3155
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₅×#5830	C₂	semidirect
3. C₂×C₅×#949	C₂	semidirect
4. C₂²×C₅×D₂₄	C₂	semidirect
5. C₅×#5191	C₂	semidirect
6. C₅×#5176	C₂	semidirect
7. C₅×#5151	C₂	semidirect
8. C₅×#5101	C₂	semidirect
13. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
14. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
15. C₂×C₃×C₅×D₈	C₂²	semidirect
18. C₅×#947	C₂²	semidirect
19. C₂×C₅×#215	C₂²	semidirect
20. C₅×#940	C₂²	semidirect
22. C₂×C₅×#213	C₂²	semidirect
29. C₅×#815	C₂²	semidirect
30. C₅×C₈×Dic₃	C₂²	semidirect
31. #83906	C₅	direct (N × H)
33. C₂×C₅×#135	D₃	semidirect
56. C₂×C₃×C₅×C₈	D₄	semidirect
65. C₅×#208	D₄	semidirect
69. C₂×C₃×#135	C₂×C₅	semidirect
70. #5830	C₂×C₅	semidirect
71. C₂×#949	C₂×C₅	semidirect
72. C₂²×D₂₄	C₂×C₅	semidirect
73. #5191	C₂×C₅	semidirect
74. #5176	C₂×C₅	semidirect
75. #5151	C₂×C₅	semidirect
76. #5101	C₂×C₅	semidirect
81. C₂×C₅×Q₁₆	C₂×D₃	semidirect
83. C₂×C₅×SD₁₆	C₂×D₃	semidirect
88. C₂×C₅×D₈	C₂×D₃	semidirect
126. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
127. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
128. C₂×C₃×D₈	C₂²×C₅	semidirect
131. #947	C₂²×C₅	semidirect
132. C₂×#215	C₂²×C₅	semidirect
133. #940	C₂²×C₅	semidirect
135. C₂×#213	C₂²×C₅	semidirect
142. #815	C₂²×C₅	semidirect
143. C₈×Dic₃	C₂²×C₅	semidirect
166. C₂×C₅×C₈	#67	semidirect
174. C₂×#135	C₅×D₃	semidirect
210. C₂×C₃×C₈	C₅×D₄	semidirect
219. #208	C₅×D₄	semidirect
251. C₂×Q₁₆	C₂×C₅×D₃	semidirect
253. C₂×SD₁₆	C₂×C₅×D₃	semidirect
258. C₂×D₈	C₂×C₅×D₃	semidirect
332. C₂×C₈	C₅×#67	semidirect
339. C₃×C₅	#3155	semidirect
387. C₅	#83906	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×C₃×C₅×#135	2
C₅×#5830	2
C₂×C₅×#949	2
C₂²×C₅×D₂₄	2
C₅×#5191	2
C₅×#5176	2
C₅×#5151	2
C₅×#5101	2
C₅×#3155	3
#83906	5

Subgroups — C5×#83906 #14439552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83906 #14439552