Subgroups — C₂×C₅×#5197 #14417928

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 368 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
2	C₂×C₅×#948	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#837	C₂	1	2	yes	maximal, complemented
4	C₅×#5197	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#819	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#444	—	3	1	no	maximal, Hall
8	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
9	C₃×C₅×#135	C₄	1	4	yes	complemented
10	C₃×C₅×#135	C₂²	1	4	yes	—
11	C₂×C₃×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅×SD₁₆	C₄	1	2	yes	complemented
13	C₂×C₃×C₅×D₈	C₄	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#948	—	2	4	no	—
16	C₅×#948	C₂²	1	8	yes	complemented
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×#208	—	2	2	no	—
19	C₂×C₅×#208	C₂²	1	2	yes	—
20	C₂²×C₅×C₃⋊C₈	—	2	2	no	—
21	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₅×#837	C₂²	1	8	yes	complemented
23	C₅×#819	C₂²	1	4	yes	complemented
24	C₅×#815	C₂²	1	4	yes	complemented
25	C₂×#5197	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#135	D₃	1	1	yes	characteristic
27	C₂×C₅×#131	—	3	2	no	—
28	C₅×#444	—	3	8	no	—
29	C₂×C₅×#108	—	3	1	no	—
30	C₂×C₅×#104	—	3	2	no	—
31	C₂×C₅×#97	—	3	1	no	—
32	C₃×C₅×#41	—	2	2	no	—
33	C₃×C₅×#41	—	2	2	no	—
34	C₃×C₅×#41	C₂×C₄	1	4	yes	—
35	C₃×C₅×#41	C₂³	1	4	yes	—
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×Dic₃	—	2	1	no	—
42	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
43	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
44	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
45	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₄×C₅×Dic₃	—	2	1	no	—
50	C₄×C₅×Dic₃	C₂³	1	2	yes	—
51	C₅×#208	—	2	2	no	—
52	C₅×#208	—	2	8	no	—
53	C₅×#208	C₂³	1	4	yes	—
54	C₂×C₅×C₃⋊C₈	—	2	2	no	—
55	C₂×C₅×C₃⋊C₈	—	2	8	no	—
56	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
57	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
59	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic
60	C₂×#948	C₂×C₅	1	2	yes	complemented
61	C₂×#837	C₂×C₅	1	2	yes	complemented
62	#5197	C₂×C₅	1	8	yes	direct product factor
63	C₂×#819	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂×#815	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×C₅×#41	C₂×D₃	1	2	yes	—
66	C₅×#135	Dic₃	1	4	yes	complemented
67	C₅×#135	C₂×D₃	1	4	yes	—
68	C₂×C₅×Q₁₆	Dic₃	1	1	yes	characteristic, complemented
69	C₂×C₅×SD₁₆	Dic₃	1	2	yes	complemented
70	C₂×C₅×D₈	Dic₃	1	1	yes	characteristic, complemented
71	C₅×#131	—	3	8	no	—
72	C₅×#131	—	6	4	no	—
73	C₂×C₅×M₁₆	—	3	2	no	—
74	C₂×C₅×M₁₆	—	6	2	no	—
75	C₂²×C₅×C₈	—	3	1	no	—
76	C₂²×C₅×C₈	—	6	2	no	—
77	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
78	C₂×C₄²×C₅	—	3	1	no	—
79	C₅×#108	—	3	4	no	—
80	C₅×#104	—	3	8	no	—
81	C₅×#97	—	3	4	no	—
82	C₂×#444	—	3	1	no	Sylow
83	C₂³×C₃×C₅	—	2	2	no	—
84	C₂³×C₃×C₅	#41	1	1	yes	characteristic
85	C₃×C₅×Q₈	—	2	2	no	—
86	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
87	C₃×C₅×D₄	—	2	4	no	—
88	C₃×C₅×D₄	—	2	4	no	—
89	C₃×C₅×D₄	—	2	2	no	—
90	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₂×C₅×Dic₃	—	2	2	no	—
101	C₂×C₅×Dic₃	—	4	2	no	—
102	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
103	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
104	C₅×C₃⋊C₈	—	2	4	no	—
105	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
106	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
107	C₃×#135	C₄×C₅	1	4	yes	complemented
108	C₃×#135	C₂²×C₅	1	4	yes	—
109	C₂×C₃×Q₁₆	C₄×C₅	1	1	yes	characteristic, complemented
110	C₂×C₃×SD₁₆	C₄×C₅	1	2	yes	complemented
111	C₂×C₃×D₈	C₄×C₅	1	1	yes	characteristic, complemented
112	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
113	#948	—	2	4	no	—
114	#948	C₂²×C₅	1	8	yes	complemented
115	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
116	C₂×#208	—	2	2	no	—
117	C₂×#208	C₂²×C₅	1	2	yes	—
118	C₂²×C₃⋊C₈	—	2	2	no	—
119	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
120	#837	C₂²×C₅	1	8	yes	complemented
121	#819	C₂²×C₅	1	4	yes	complemented
122	#815	C₂²×C₅	1	4	yes	complemented
123	C₅×#41	—	2	2	no	—
124	C₅×#41	—	2	2	no	—
125	C₅×#41	C₂×Dic₃	1	4	yes	—
126	C₅×#41	C₂²×D₃	1	4	yes	—
127	C₂×C₅×Q₈	C₂×Dic₃	1	2	yes	—
128	C₂×C₅×D₄	—	2	2	no	—
129	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	—	6	1	no	—
132	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₅×Q₁₆	C₂×Dic₃	1	4	yes	complemented
134	C₅×SD₁₆	C₂×Dic₃	1	8	yes	complemented
135	C₅×D₈	C₂×Dic₃	1	4	yes	complemented
136	C₅×M₁₆	—	3	4	no	—
137	C₅×M₁₆	—	6	8	no	—
138	C₅×M₁₆	—	6	2	no	—
139	C₂×C₅×C₈	—	3	2	no	—
140	C₂×C₅×C₈	—	3	2	no	—
141	C₂×C₅×C₈	—	3	2	no	—
142	C₂×C₅×C₈	—	6	8	no	—
143	C₂×C₅×C₈	—	6	2	no	—
144	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
145	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂×Dic₃	1	2	yes	—
147	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
148	C₄²×C₅	—	3	2	no	—
149	C₄²×C₅	—	6	1	no	—
150	C₂×#135	C₅×D₃	1	1	yes	characteristic
151	C₂×#131	—	3	2	no	—
152	#444	—	3	8	no	—
153	C₂×#108	—	3	1	no	—
154	C₂×#104	—	3	2	no	—
155	C₂×#97	—	3	1	no	—
156	C₂²×C₃×C₅	—	2	2	no	—
157	C₂²×C₃×C₅	—	2	4	no	—
158	C₂²×C₃×C₅	—	4	4	no	—
159	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
160	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
162	C₃×C₄×C₅	—	2	4	no	—
163	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
164	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
165	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
167	C₅×Dic₃	—	4	2	no	—
168	C₃×#41	—	2	2	no	—
169	C₃×#41	—	2	2	no	—
170	C₃×#41	C₂×C₄×C₅	1	4	yes	—
171	C₃×#41	C₂³×C₅	1	4	yes	—
172	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
173	C₂×C₃×D₄	—	2	2	no	—
174	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
177	C₂²×Dic₃	—	2	1	no	—
178	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
179	C₃×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
180	C₃×D₈	C₂×C₄×C₅	1	4	yes	complemented
181	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
182	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
183	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
184	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
185	C₄×Dic₃	—	2	1	no	—
186	C₄×Dic₃	C₂³×C₅	1	2	yes	—
187	#208	—	2	2	no	—
188	#208	—	2	8	no	—
189	#208	C₂³×C₅	1	4	yes	—
190	C₂×C₃⋊C₈	—	2	2	no	—
191	C₂×C₃⋊C₈	—	2	8	no	—
192	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
193	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
194	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
195	C₂³×C₅	—	2	2	no	—
196	C₂³×C₅	#237	1	1	yes	characteristic
197	C₅×Q₈	—	2	2	no	—
198	C₅×Q₈	C₂²×Dic₃	1	4	yes	—
199	C₅×D₄	—	2	4	no	—
200	C₅×D₄	—	2	4	no	—
201	C₅×D₄	—	2	2	no	—
202	C₅×D₄	C₂²×Dic₃	1	4	yes	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	6	2	no	—
207	C₂×C₄×C₅	—	12	2	no	—
208	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
210	C₂×C₄×C₅	#237	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
214	C₅×C₈	—	3	4	no	—
215	C₅×C₈	—	6	4	no	—
216	C₅×C₈	C₂²×Dic₃	1	2	yes	—
217	C₅×C₈	C₂²×Dic₃	1	2	yes	—
218	C₂×#41	C₂×C₅×D₃	1	2	yes	—
219	#135	C₅×Dic₃	1	4	yes	complemented
220	#135	C₂×C₅×D₃	1	4	yes	—
221	C₂×Q₁₆	C₅×Dic₃	1	1	yes	characteristic, complemented
222	C₂×SD₁₆	C₅×Dic₃	1	2	yes	complemented
223	C₂×D₈	C₅×Dic₃	1	1	yes	characteristic, complemented
224	#131	—	3	8	no	—
225	#131	—	6	4	no	—
226	C₂×M₁₆	—	3	2	no	—
227	C₂×M₁₆	—	6	2	no	—
228	C₂²×C₈	—	3	1	no	—
229	C₂²×C₈	—	6	2	no	—
230	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
231	C₂×C₄²	—	3	1	no	—
232	#108	—	3	4	no	—
233	#104	—	3	8	no	—
234	#97	—	3	4	no	—
235	C₂×C₃×C₅	—	2	1	no	—
236	C₂×C₃×C₅	—	2	1	no	—
237	C₂×C₃×C₅	—	4	4	no	—
238	C₂×C₃×C₅	#444	1	2	yes	complemented
239	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
240	C₂³×C₃	—	2	2	no	—
241	C₂³×C₃	C₅×#41	1	1	yes	characteristic
242	C₃×Q₈	—	2	2	no	—
243	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
244	C₃×D₄	—	2	4	no	—
245	C₃×D₄	—	2	4	no	—
246	C₃×D₄	—	2	2	no	—
247	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
257	C₂×Dic₃	—	2	2	no	—
258	C₂×Dic₃	—	4	2	no	—
259	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
260	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
261	C₃⋊C₈	—	2	4	no	—
262	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	2	4	no	—
265	C₂²×C₅	—	4	4	no	—
266	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
267	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
268	C₂²×C₅	C₂×#237	1	1	yes	characteristic
269	C₄×C₅	—	2	4	no	—
270	C₄×C₅	—	12	2	no	—
271	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
272	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
273	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
274	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
275	#41	—	2	2	no	—
276	#41	—	2	2	no	—
277	#41	C₂×C₅×Dic₃	1	4	yes	—
278	#41	C₂²×C₅×D₃	1	4	yes	—
279	C₂×Q₈	C₂×C₅×Dic₃	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	6	1	no	—
284	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
285	Q₁₆	C₂×C₅×Dic₃	1	4	yes	complemented
286	SD₁₆	C₂×C₅×Dic₃	1	8	yes	complemented
287	D₈	C₂×C₅×Dic₃	1	4	yes	complemented
288	M₁₆	—	3	4	no	—
289	M₁₆	—	6	8	no	—
290	M₁₆	—	6	2	no	—
291	C₂×C₈	—	3	2	no	—
292	C₂×C₈	—	3	2	no	—
293	C₂×C₈	—	3	2	no	—
294	C₂×C₈	—	6	8	no	—
295	C₂×C₈	—	6	2	no	—
296	C₂×C₈	C₂×C₅×Dic₃	1	1	yes	characteristic
297	C₂×C₈	C₂×C₅×Dic₃	1	1	yes	characteristic
298	C₂×C₈	C₂×C₅×Dic₃	1	2	yes	—
299	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
300	C₄²	—	3	2	no	—
301	C₄²	—	6	1	no	—
302	C₃×C₅	C₂×#444	1	1	yes	characteristic, complemented, Hall
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	4	no	—
305	C₂²×C₃	—	4	4	no	—
306	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
307	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
308	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
311	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
312	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
313	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
314	Dic₃	—	4	2	no	—
315	C₂×C₅	—	2	1	no	—
316	C₂×C₅	—	2	1	no	—
317	C₂×C₅	—	4	4	no	—
318	C₂×C₅	#5197	1	2	yes	direct product factor
319	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
320	C₂³	—	2	2	no	—
321	C₂³	C₅×#237	1	1	yes	characteristic
322	Q₈	—	2	2	no	—
323	Q₈	C₂²×C₅×Dic₃	1	4	yes	—
324	D₄	—	2	4	no	—
325	D₄	—	2	4	no	—
326	D₄	—	2	2	no	—
327	D₄	C₂²×C₅×Dic₃	1	4	yes	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	6	2	no	—
332	C₂×C₄	—	12	2	no	—
333	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
334	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
335	C₂×C₄	C₅×#237	1	1	yes	characteristic
336	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
338	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
339	C₈	—	3	4	no	—
340	C₈	—	6	4	no	—
341	C₈	C₂²×C₅×Dic₃	1	2	yes	—
342	C₈	C₂²×C₅×Dic₃	1	2	yes	—
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	4	4	no	—
346	C₂×C₃	C₅×#444	1	2	yes	complemented
347	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
348	C₅	C₂×#5197	1	1	yes	characteristic, direct product factor, Sylow
349	C₂²	—	2	2	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	4	4	no	—
352	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
353	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
354	C₂²	C₂×C₅×#237	1	1	yes	characteristic
355	C₄	—	2	4	no	—
356	C₄	—	12	2	no	—
357	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
358	C₄	C₅×D₄×Dic₃	1	1	yes	characteristic
359	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
360	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
361	C₃	C₂×C₅×#444	1	1	yes	characteristic, complemented, Sylow
362	C₂	—	2	1	no	—
363	C₂	—	2	1	no	—
364	C₂	—	4	4	no	—
365	C₂	C₅×#5197	1	2	yes	direct product factor
366	C₂	C₂×C₅×D₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₄×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#135	D₃
hypocenter	C₃	C₂×C₅×#444
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#135

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#948	C₂	semidirect
3. C₂×C₅×#837	C₂	semidirect
4. C₅×#5197	C₂	direct (N × H)
5. C₂×C₅×#819	C₂	semidirect
6. C₂×C₅×#815	C₂	semidirect
9. C₃×C₅×#135	C₄	semidirect
11. C₂×C₃×C₅×Q₁₆	C₄	semidirect
12. C₂×C₃×C₅×SD₁₆	C₄	semidirect
13. C₂×C₃×C₅×D₈	C₄	semidirect
16. C₅×#948	C₂²	semidirect
22. C₅×#837	C₂²	semidirect
23. C₅×#819	C₂²	semidirect
24. C₅×#815	C₂²	semidirect
25. C₂×#5197	C₅	direct (N × H)
42. C₃×C₅×Q₁₆	C₂×C₄	semidirect
43. C₃×C₅×SD₁₆	C₂×C₄	semidirect
44. C₃×C₅×D₈	C₂×C₄	semidirect
60. C₂×#948	C₂×C₅	semidirect
61. C₂×#837	C₂×C₅	semidirect
62. #5197	C₂×C₅	direct (N × H)
63. C₂×#819	C₂×C₅	semidirect
64. C₂×#815	C₂×C₅	semidirect
66. C₅×#135	Dic₃	semidirect
68. C₂×C₅×Q₁₆	Dic₃	semidirect
69. C₂×C₅×SD₁₆	Dic₃	semidirect
70. C₂×C₅×D₈	Dic₃	semidirect
107. C₃×#135	C₄×C₅	semidirect
109. C₂×C₃×Q₁₆	C₄×C₅	semidirect
110. C₂×C₃×SD₁₆	C₄×C₅	semidirect
111. C₂×C₃×D₈	C₄×C₅	semidirect
114. #948	C₂²×C₅	semidirect
120. #837	C₂²×C₅	semidirect
121. #819	C₂²×C₅	semidirect
122. #815	C₂²×C₅	semidirect
133. C₅×Q₁₆	C₂×Dic₃	semidirect
134. C₅×SD₁₆	C₂×Dic₃	semidirect
135. C₅×D₈	C₂×Dic₃	semidirect
178. C₃×Q₁₆	C₂×C₄×C₅	semidirect
179. C₃×SD₁₆	C₂×C₄×C₅	semidirect
180. C₃×D₈	C₂×C₄×C₅	semidirect
219. #135	C₅×Dic₃	semidirect
221. C₂×Q₁₆	C₅×Dic₃	semidirect
222. C₂×SD₁₆	C₅×Dic₃	semidirect
223. C₂×D₈	C₅×Dic₃	semidirect
238. C₂×C₃×C₅	#444	semidirect
285. Q₁₆	C₂×C₅×Dic₃	semidirect
286. SD₁₆	C₂×C₅×Dic₃	semidirect
287. D₈	C₂×C₅×Dic₃	semidirect
302. C₃×C₅	C₂×#444	semidirect
318. C₂×C₅	#5197	direct (N × H)
346. C₂×C₃	C₅×#444	semidirect
348. C₅	C₂×#5197	direct (N × H)
361. C₃	C₂×C₅×#444	semidirect
365. C₂	C₅×#5197	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×#948	2
C₂×C₅×#837	2
C₅×#5197	2
C₂×C₅×#819	2
C₂×C₅×#815	2
C₂×C₅×#444	3
C₂×#5197	5

Subgroups — C2×C5×#5197 #14417928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5197 #14417928