Subgroups — C₂×C₅×#5194 #14478266

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 400 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	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5194	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₅×#829	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#828	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#827	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#826	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₅×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#508	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	—	2	1	no	—
11	C₂×C₅×#235	—	2	1	no	—
12	C₃×C₅×#135	—	2	2	no	—
13	C₃×C₅×#135	C₂²	1	4	yes	complemented
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	—	2	1	no	—
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
19	C₅×#904	—	2	2	no	—
20	C₅×#904	C₂²	1	4	yes	complemented
21	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×#204	—	2	1	no	—
23	C₅×#829	C₂²	1	4	yes	complemented
24	C₅×#828	C₂²	1	4	yes	complemented
25	C₅×#827	C₂²	1	4	yes	complemented
26	C₅×#826	C₂²	1	4	yes	complemented
27	C₂×C₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₃⋊C₁₆	C₂²	1	4	yes	complemented
30	C₂×#5194	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	—	3	1	no	—
32	C₂×C₅×#135	D₃	1	1	yes	characteristic, complemented
33	C₅×#508	—	3	8	no	—
34	C₂×C₅×Q₃₂	—	3	1	no	—
35	C₂×C₅×SD₃₂	—	3	1	no	—
36	C₂×C₅×SD₃₂	—	3	1	no	—
37	C₂×C₅×D₁₆	—	3	1	no	—
38	C₂²×C₅×C₁₆	—	3	1	no	—
39	C₃×C₅×#41	—	2	4	no	—
40	C₃×C₅×#41	—	4	2	no	—
41	C₂×C₃×C₅×Q₈	—	2	1	no	—
42	C₂×C₃×C₅×D₄	—	2	1	no	—
43	C₂×C₃×C₅×D₄	—	4	1	no	—
44	C₂²×C₃×C₄×C₅	—	4	1	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂×C₅×#67	—	4	1	no	—
47	C₅×#235	—	2	4	no	—
48	C₅×#235	—	4	2	no	—
49	C₂×C₅×D₁₂	—	2	1	no	—
50	C₂×C₄×C₅×D₃	—	4	1	no	—
51	C₂×C₅×Dic₆	—	2	1	no	—
52	C₃×C₅×Q₁₆	—	2	1	no	—
53	C₃×C₅×Q₁₆	C₂³	1	2	yes	—
54	C₃×C₅×SD₁₆	—	2	4	no	—
55	C₃×C₅×D₈	—	2	1	no	—
56	C₃×C₅×D₈	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
58	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
59	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₅×Dic₁₂	—	2	1	no	—
62	C₅×Dic₁₂	C₂³	1	2	yes	—
63	C₅×D₂₄	—	2	1	no	—
64	C₅×D₂₄	C₂³	1	2	yes	—
65	C₅×#204	—	2	4	no	—
66	C₅×C₃⋊C₁₆	C₂³	1	2	yes	—
67	C₅×C₃⋊C₁₆	C₂³	1	2	yes	—
68	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×#904	C₂×C₅	1	1	yes	characteristic, complemented
70	#5194	C₂×C₅	1	8	yes	direct product factor
71	C₂×#829	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×#828	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#827	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#826	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂²×C₃⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₅×#41	—	2	1	no	—
77	C₂×C₅×#41	—	6	1	no	—
78	C₅×#135	—	2	2	no	—
79	C₅×#135	—	3	4	no	—
80	C₅×#135	—	6	2	no	—
81	C₅×#135	C₂×D₃	1	4	yes	complemented
82	C₂×C₅×Q₁₆	—	3	1	no	—
83	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
84	C₂×C₅×SD₁₆	—	2	1	no	—
85	C₂×C₅×SD₁₆	—	6	1	no	—
86	C₂×C₅×D₈	—	3	1	no	—
87	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
88	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
89	C₅×Q₃₂	—	3	4	no	—
90	C₅×SD₃₂	—	3	4	no	—
91	C₅×SD₃₂	—	3	4	no	—
92	C₅×D₁₆	—	3	4	no	—
93	C₂×C₅×C₁₆	—	3	1	no	—
94	C₂×C₅×C₁₆	—	3	1	no	—
95	C₂×C₅×C₁₆	—	3	4	no	—
96	C₂×#508	—	3	1	no	Sylow
97	C₂³×C₃×C₅	—	4	1	no	—
98	C₂³×C₃×C₅	D₈	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	4	1	no	—
100	C₃×C₅×Q₈	—	2	2	no	—
101	C₃×C₅×Q₈	—	4	1	no	—
102	C₃×C₅×D₄	—	2	2	no	—
103	C₃×C₅×D₄	—	4	4	no	—
104	C₃×C₅×D₄	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	—	4	4	no	—
107	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
108	C₂×C₃×C₄×C₅	D₈	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
111	C₅×#67	—	4	4	no	—
112	C₂×C₅×Dic₃	—	4	1	no	—
113	C₅×D₁₂	—	2	2	no	—
114	C₅×D₁₂	—	4	1	no	—
115	C₄×C₅×D₃	—	4	4	no	—
116	C₅×Dic₆	—	2	2	no	—
117	C₅×Dic₆	—	4	1	no	—
118	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
119	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
121	C₂×C₃×#41	—	2	1	no	—
122	C₂×#235	—	2	1	no	—
123	C₃×#135	—	2	2	no	—
124	C₃×#135	C₂²×C₅	1	4	yes	complemented
125	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×SD₁₆	—	2	1	no	—
127	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
128	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
129	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
130	#904	—	2	2	no	—
131	#904	C₂²×C₅	1	4	yes	complemented
132	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
133	C₂×#204	—	2	1	no	—
134	#829	C₂²×C₅	1	4	yes	complemented
135	#828	C₂²×C₅	1	4	yes	complemented
136	#827	C₂²×C₅	1	4	yes	complemented
137	#826	C₂²×C₅	1	4	yes	complemented
138	C₂×C₃⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₃⋊C₁₆	C₂²×C₅	1	4	yes	complemented
141	C₅×#41	—	2	4	no	—
142	C₅×#41	—	4	2	no	—
143	C₅×#41	—	6	4	no	—
144	C₅×#41	—	12	2	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	—	6	1	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	4	1	no	—
149	C₂×C₅×D₄	—	6	1	no	—
150	C₂×C₅×D₄	—	12	1	no	—
151	C₂²×C₄×C₅	—	4	1	no	—
152	C₂²×C₄×C₅	—	12	1	no	—
153	C₂²×C₄×C₅	#67	1	1	yes	characteristic
154	C₅×Q₁₆	—	2	1	no	—
155	C₅×Q₁₆	—	3	2	no	—
156	C₅×Q₁₆	—	6	1	no	—
157	C₅×Q₁₆	C₂²×D₃	1	2	yes	—
158	C₅×SD₁₆	—	2	4	no	—
159	C₅×SD₁₆	—	6	4	no	—
160	C₅×D₈	—	2	1	no	—
161	C₅×D₈	—	3	2	no	—
162	C₅×D₈	—	6	1	no	—
163	C₅×D₈	C₂²×D₃	1	2	yes	—
164	C₂×C₅×C₈	#67	1	1	yes	characteristic
165	C₂×C₅×C₈	#67	1	2	yes	—
166	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
167	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
168	C₅×C₁₆	—	3	2	no	—
169	C₅×C₁₆	—	3	2	no	—
170	C₂×#135	—	3	1	no	—
171	C₂×#135	C₅×D₃	1	1	yes	characteristic, complemented
172	#508	—	3	8	no	—
173	C₂×Q₃₂	—	3	1	no	—
174	C₂×SD₃₂	—	3	1	no	—
175	C₂×SD₃₂	—	3	1	no	—
176	C₂×D₁₆	—	3	1	no	—
177	C₂²×C₁₆	—	3	1	no	—
178	C₂²×C₃×C₅	—	2	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	8	2	no	—
181	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
182	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
183	C₂×C₅×D₃	—	4	2	no	—
184	C₂×C₅×D₃	—	8	2	no	—
185	C₃×C₄×C₅	—	4	2	no	—
186	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
187	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
188	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₅×Dic₃	—	4	2	no	—
190	C₃×#41	—	2	4	no	—
191	C₃×#41	—	4	2	no	—
192	C₂×C₃×Q₈	—	2	1	no	—
193	C₂×C₃×D₄	—	2	1	no	—
194	C₂×C₃×D₄	—	4	1	no	—
195	C₂²×C₃×C₄	—	4	1	no	—
196	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
197	C₂×#67	—	4	1	no	—
198	#235	—	2	4	no	—
199	#235	—	4	2	no	—
200	C₂×D₁₂	—	2	1	no	—
201	C₂×C₄×D₃	—	4	1	no	—
202	C₂×Dic₆	—	2	1	no	—
203	C₃×Q₁₆	—	2	1	no	—
204	C₃×Q₁₆	C₂³×C₅	1	2	yes	—
205	C₃×SD₁₆	—	2	4	no	—
206	C₃×D₈	—	2	1	no	—
207	C₃×D₈	C₂³×C₅	1	2	yes	—
208	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
209	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
210	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
211	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
212	Dic₁₂	—	2	1	no	—
213	Dic₁₂	C₂³×C₅	1	2	yes	—
214	D₂₄	—	2	1	no	—
215	D₂₄	C₂³×C₅	1	2	yes	—
216	#204	—	2	4	no	—
217	C₃⋊C₁₆	C₂³×C₅	1	2	yes	—
218	C₃⋊C₁₆	C₂³×C₅	1	2	yes	—
219	C₂³×C₅	—	4	1	no	—
220	C₂³×C₅	—	12	1	no	—
221	C₂³×C₅	#213	1	1	yes	characteristic
222	C₅×Q₈	—	2	2	no	—
223	C₅×Q₈	—	4	1	no	—
224	C₅×Q₈	—	6	2	no	—
225	C₅×Q₈	—	12	1	no	—
226	C₅×D₄	—	2	2	no	—
227	C₅×D₄	—	4	4	no	—
228	C₅×D₄	—	4	1	no	—
229	C₅×D₄	—	6	2	no	—
230	C₅×D₄	—	12	4	no	—
231	C₅×D₄	—	12	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	4	no	—
234	C₂×C₄×C₅	—	12	1	no	—
235	C₂×C₄×C₅	—	12	4	no	—
236	C₂×C₄×C₅	#213	1	2	yes	—
237	C₂×C₄×C₅	#213	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×#67	1	2	yes	—
240	C₅×C₈	C₂×#67	1	1	yes	characteristic
241	C₅×C₈	C₂×#67	1	2	yes	—
242	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
243	C₂×#41	—	2	1	no	—
244	C₂×#41	—	6	1	no	—
245	#135	—	2	2	no	—
246	#135	—	3	4	no	—
247	#135	—	6	2	no	—
248	#135	C₂×C₅×D₃	1	4	yes	complemented
249	C₂×Q₁₆	—	3	1	no	—
250	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
251	C₂×SD₁₆	—	2	1	no	—
252	C₂×SD₁₆	—	6	1	no	—
253	C₂×D₈	—	3	1	no	—
254	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
255	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
256	Q₃₂	—	3	4	no	—
257	SD₃₂	—	3	4	no	—
258	SD₃₂	—	3	4	no	—
259	D₁₆	—	3	4	no	—
260	C₂×C₁₆	—	3	1	no	—
261	C₂×C₁₆	—	3	1	no	—
262	C₂×C₁₆	—	3	4	no	—
263	C₂×C₃×C₅	—	2	2	no	—
264	C₂×C₃×C₅	—	8	2	no	—
265	C₂×C₃×C₅	#508	1	2	yes	complemented
266	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
267	C₅×D₃	—	8	2	no	—
268	C₂³×C₃	—	4	1	no	—
269	C₂³×C₃	C₅×D₈	1	1	yes	characteristic
270	C₂²×D₃	—	4	1	no	—
271	C₃×Q₈	—	2	2	no	—
272	C₃×Q₈	—	4	1	no	—
273	C₃×D₄	—	2	2	no	—
274	C₃×D₄	—	4	4	no	—
275	C₃×D₄	—	4	1	no	—
276	C₂×C₃×C₄	—	4	1	no	—
277	C₂×C₃×C₄	—	4	4	no	—
278	C₂×C₃×C₄	C₅×D₈	1	1	yes	characteristic
279	C₂×C₃×C₄	C₅×D₈	1	2	yes	—
280	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
282	#67	—	4	4	no	—
283	C₂×Dic₃	—	4	1	no	—
284	D₁₂	—	2	2	no	—
285	D₁₂	—	4	1	no	—
286	C₄×D₃	—	4	4	no	—
287	Dic₆	—	2	2	no	—
288	Dic₆	—	4	1	no	—
289	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
290	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
291	C₃×C₈	C₂⁴×C₅	1	1	yes	characteristic
292	C₂²×C₅	—	2	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	—	8	2	no	—
295	C₂²×C₅	—	12	2	no	—
296	C₂²×C₅	—	24	2	no	—
297	C₂²×C₅	C₂×#213	1	2	yes	—
298	C₂²×C₅	C₂×#213	1	1	yes	characteristic
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	—	12	2	no	—
301	C₄×C₅	C₂×#213	1	2	yes	—
302	C₄×C₅	C₂×#213	1	1	yes	characteristic
303	C₄×C₅	C₂²×#67	1	1	yes	characteristic
304	#41	—	2	4	no	—
305	#41	—	4	2	no	—
306	#41	—	6	4	no	—
307	#41	—	12	2	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	6	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	6	1	no	—
313	C₂×D₄	—	12	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	12	1	no	—
316	C₂²×C₄	C₅×#67	1	1	yes	characteristic
317	Q₁₆	—	2	1	no	—
318	Q₁₆	—	3	2	no	—
319	Q₁₆	—	6	1	no	—
320	Q₁₆	C₂²×C₅×D₃	1	2	yes	—
321	SD₁₆	—	2	4	no	—
322	SD₁₆	—	6	4	no	—
323	D₈	—	2	1	no	—
324	D₈	—	3	2	no	—
325	D₈	—	6	1	no	—
326	D₈	C₂²×C₅×D₃	1	2	yes	—
327	C₂×C₈	C₅×#67	1	1	yes	characteristic
328	C₂×C₈	C₅×#67	1	2	yes	—
329	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
330	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
331	C₁₆	—	3	2	no	—
332	C₁₆	—	3	2	no	—
333	C₃×C₅	C₂×#508	1	1	yes	characteristic, complemented, Hall
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	4	2	no	—
336	C₂²×C₃	—	8	2	no	—
337	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
338	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
339	C₂×D₃	—	4	2	no	—
340	C₂×D₃	—	8	2	no	—
341	C₃×C₄	—	4	2	no	—
342	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
343	C₃×C₄	C₂×C₅×D₈	1	2	yes	—
344	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
345	Dic₃	—	4	2	no	—
346	C₂×C₅	—	2	2	no	—
347	C₂×C₅	—	8	2	no	—
348	C₂×C₅	—	24	2	no	—
349	C₂×C₅	#5194	1	2	yes	direct product factor
350	C₂×C₅	C₂²×#213	1	1	yes	characteristic
351	C₂³	—	4	1	no	—
352	C₂³	—	12	1	no	—
353	C₂³	C₅×#213	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	6	2	no	—
357	Q₈	—	12	1	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	1	no	—
361	D₄	—	6	2	no	—
362	D₄	—	12	4	no	—
363	D₄	—	12	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	12	1	no	—
367	C₂×C₄	—	12	4	no	—
368	C₂×C₄	C₅×#213	1	1	yes	characteristic
369	C₂×C₄	C₅×#213	1	2	yes	—
370	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
371	C₂×C₄	C₂×C₅×#67	1	2	yes	—
372	C₈	C₂×C₅×#67	1	1	yes	characteristic
373	C₈	C₂×C₅×#67	1	2	yes	—
374	C₈	C₂³×C₅×D₃	1	1	yes	characteristic
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	8	2	no	—
377	C₂×C₃	C₅×#508	1	2	yes	complemented
378	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
379	D₃	—	8	2	no	—
380	C₅	C₂×#5194	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²	—	2	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	12	2	no	—
385	C₂²	—	24	2	no	—
386	C₂²	C₂×C₅×#213	1	2	yes	—
387	C₂²	C₂×C₅×#213	1	1	yes	characteristic
388	C₄	—	4	2	no	—
389	C₄	—	12	2	no	—
390	C₄	C₂×C₅×#213	1	2	yes	—
391	C₄	C₂×C₅×#213	1	1	yes	characteristic
392	C₄	C₂²×C₅×#67	1	1	yes	characteristic
393	C₃	C₂×C₅×#508	1	1	yes	characteristic, complemented, Sylow
394	C₂	—	2	2	no	—
395	C₂	—	8	2	no	—
396	C₂	—	24	2	no	—
397	C₂	C₅×#5194	1	2	yes	direct product factor
398	C₂	C₂²×C₅×#213	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#213
commutator, cosocle	C₃×C₈	C₂⁴×C₅
Frattini	C₈	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂×D₈
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₂×C₅×#508
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ 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. C₂×C₅×#904	C₂	semidirect
3. C₅×#5194	C₂	direct (N × H)
4. C₂×C₅×#829	C₂	semidirect
5. C₂×C₅×#828	C₂	semidirect
6. C₂×C₅×#827	C₂	semidirect
7. C₂×C₅×#826	C₂	semidirect
8. C₂²×C₅×C₃⋊C₁₆	C₂	semidirect
13. C₃×C₅×#135	C₂²	semidirect
20. C₅×#904	C₂²	semidirect
23. C₅×#829	C₂²	semidirect
24. C₅×#828	C₂²	semidirect
25. C₅×#827	C₂²	semidirect
26. C₅×#826	C₂²	semidirect
29. C₂×C₅×C₃⋊C₁₆	C₂²	semidirect
30. C₂×#5194	C₅	direct (N × H)
32. C₂×C₅×#135	D₃	semidirect
68. C₂×C₃×#135	C₂×C₅	semidirect
69. C₂×#904	C₂×C₅	semidirect
70. #5194	C₂×C₅	direct (N × H)
71. C₂×#829	C₂×C₅	semidirect
72. C₂×#828	C₂×C₅	semidirect
73. C₂×#827	C₂×C₅	semidirect
74. C₂×#826	C₂×C₅	semidirect
75. C₂²×C₃⋊C₁₆	C₂×C₅	semidirect
81. C₅×#135	C₂×D₃	semidirect
124. C₃×#135	C₂²×C₅	semidirect
131. #904	C₂²×C₅	semidirect
134. #829	C₂²×C₅	semidirect
135. #828	C₂²×C₅	semidirect
136. #827	C₂²×C₅	semidirect
137. #826	C₂²×C₅	semidirect
140. C₂×C₃⋊C₁₆	C₂²×C₅	semidirect
171. C₂×#135	C₅×D₃	semidirect
248. #135	C₂×C₅×D₃	semidirect
265. C₂×C₃×C₅	#508	semidirect
333. C₃×C₅	C₂×#508	semidirect
349. C₂×C₅	#5194	direct (N × H)
377. C₂×C₃	C₅×#508	semidirect
380. C₅	C₂×#5194	direct (N × H)
393. C₃	C₂×C₅×#508	semidirect
397. C₂	C₅×#5194	direct (N × H)

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
C₂×C₅×#904	2
C₅×#5194	2
C₂×C₅×#829	2
C₂×C₅×#828	2
C₂×C₅×#827	2
C₂×C₅×#826	2
C₂²×C₅×C₃⋊C₁₆	2
C₂×C₅×#508	3
C₂×#5194	5

Subgroups — C2×C5×#5194 #14478266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5194 #14478266