Subgroups — C₂×C₅×#5007 #14429814

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#869	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#832	C₂	1	2	yes	maximal
4	C₅×#5007	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#807	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#474	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	—	2	1	no	—
10	C₂²×C₅×Dic₆	—	2	1	no	—
11	C₃×C₄×C₅×D₄	—	2	2	no	—
12	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
19	C₅×#869	—	2	2	no	—
20	C₅×#869	C₂²	1	4	yes	complemented
21	C₅×#832	C₂²	1	8	yes	—
22	C₅×#807	C₂²	1	8	yes	complemented
23	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
24	C₂×#5007	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
26	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
27	C₅×#474	—	3	8	no	—
28	C₂×C₅×#107	—	3	2	no	—
29	C₂×C₅×C₄⋊C₈	—	3	1	no	—
30	C₂×C₅×#102	—	3	2	no	—
31	C₂⁴×C₃×C₅	—	2	1	no	—
32	C₂×C₃×C₅×D₄	—	2	1	no	—
33	C₂×C₃×C₅×D₄	—	2	2	no	—
34	C₂×C₃×C₅×D₄	Q₈	1	4	yes	complemented
35	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	—	4	4	no	—
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₅×Dic₃	—	2	2	no	—
43	C₂×C₅×Dic₆	—	2	4	no	—
44	C₂×C₅×Dic₆	—	4	4	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
47	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
48	C₃×C₄²×C₅	D₄	1	2	yes	—
49	C₃×C₄²×C₅	C₂³	1	2	yes	—
50	C₅×C₄⋊Dic₃	—	2	2	no	—
51	C₅×C₄⋊Dic₃	—	2	4	no	—
52	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
53	C₂×C₅×C₃⋊C₈	—	2	4	no	—
54	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
55	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
56	C₂×#869	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂×#832	C₂×C₅	1	2	yes	—
58	#5007	C₂×C₅	1	8	yes	direct product factor
59	C₂×#807	C₂×C₅	1	2	yes	complemented
60	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂²×C₅×Q₈	—	6	1	no	—
62	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
63	C₂³×C₄×C₅	—	2	1	no	—
64	C₂²×C₅×C₈	—	3	2	no	—
65	C₅×C₄⋊Q₈	—	3	4	no	—
66	C₅×C₄⋊Q₈	—	6	2	no	—
67	C₄×C₅×D₄	—	2	2	no	—
68	C₄×C₅×D₄	C₂×D₃	1	4	yes	—
69	C₂×C₅×C₄⋊C₄	—	3	2	no	—
70	C₂×C₅×C₄⋊C₄	—	6	1	no	—
71	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
72	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
74	C₅×#107	—	3	8	no	—
75	C₅×C₄⋊C₈	—	3	4	no	—
76	C₅×#102	—	3	8	no	—
77	C₂×#474	—	3	1	no	Sylow
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	—	2	2	no	—
80	C₂³×C₃×C₅	—	4	2	no	—
81	C₂³×C₃×C₅	—	4	2	no	—
82	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
83	C₃×C₅×D₄	—	2	4	no	—
84	C₃×C₅×D₄	—	2	2	no	—
85	C₃×C₅×D₄	C₂×Q₈	1	4	yes	complemented
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	4	2	no	—
89	C₂×C₃×C₄×C₅	—	4	8	no	—
90	C₂×C₃×C₄×C₅	D₈	1	4	yes	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
95	C₂×C₃×C₄×C₅	#41	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
97	C₂×C₅×Dic₃	—	2	4	no	—
98	C₂×C₅×Dic₃	—	4	4	no	—
99	C₅×Dic₆	—	4	8	no	—
100	C₅×C₃⋊C₈	—	2	4	no	—
101	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
102	C₂³×C₃×C₄	—	2	1	no	—
103	C₂²×Dic₆	—	2	1	no	—
104	C₃×C₄×D₄	—	2	2	no	—
105	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
107	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
109	C₂×C₄⋊Dic₃	—	2	1	no	—
110	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
111	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
112	#869	—	2	2	no	—
113	#869	C₂²×C₅	1	4	yes	complemented
114	#832	C₂²×C₅	1	8	yes	—
115	#807	C₂²×C₅	1	8	yes	complemented
116	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	4	yes	complemented
117	C₂⁴×C₅	—	2	1	no	—
118	C₂×C₅×Q₈	—	6	4	no	—
119	C₂×C₅×Q₈	—	12	4	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	2	1	no	—
122	C₂×C₅×D₄	Dic₆	1	4	yes	complemented
123	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	—	4	4	no	—
127	C₂²×C₄×C₅	—	6	2	no	—
128	C₂²×C₄×C₅	#67	1	1	yes	characteristic
129	C₂²×C₄×C₅	#67	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
131	C₂×C₅×C₈	—	3	4	no	—
132	C₂×C₅×C₈	—	6	4	no	—
133	C₅×C₄⋊C₄	—	2	1	no	—
134	C₅×C₄⋊C₄	—	3	4	no	—
135	C₅×C₄⋊C₄	—	6	2	no	—
136	C₅×C₄⋊C₄	—	6	4	no	—
137	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
138	C₅×C₂²⋊C₄	—	2	4	no	—
139	C₄²×C₅	#67	1	2	yes	—
140	C₄²×C₅	C₂²×D₃	1	2	yes	—
141	C₂×C₄⋊Q₈	—	3	1	no	—
142	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic
143	#474	—	3	8	no	—
144	C₂×#107	—	3	2	no	—
145	C₂×C₄⋊C₈	—	3	1	no	—
146	C₂×#102	—	3	2	no	—
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	—	4	2	no	—
149	C₂²×C₃×C₅	—	4	2	no	—
150	C₂²×C₃×C₅	—	4	8	no	—
151	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
152	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
153	C₂²×C₃×C₅	#137	1	2	yes	—
154	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	—	4	2	no	—
157	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
158	C₃×C₄×C₅	C₂×D₈	1	4	yes	—
159	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
160	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
161	C₅×Dic₃	—	4	4	no	—
162	C₂⁴×C₃	—	2	1	no	—
163	C₂×C₃×D₄	—	2	1	no	—
164	C₂×C₃×D₄	—	2	2	no	—
165	C₂×C₃×D₄	C₅×Q₈	1	4	yes	complemented
166	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	—	2	4	no	—
169	C₂²×C₃×C₄	—	4	4	no	—
170	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
173	C₂²×Dic₃	—	2	2	no	—
174	C₂×Dic₆	—	2	4	no	—
175	C₂×Dic₆	—	4	4	no	—
176	C₃×C₄⋊C₄	—	2	1	no	—
177	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
178	C₃×C₂²⋊C₄	—	2	4	no	—
179	C₃×C₄²	C₅×D₄	1	2	yes	—
180	C₃×C₄²	C₂³×C₅	1	2	yes	—
181	C₄⋊Dic₃	—	2	2	no	—
182	C₄⋊Dic₃	—	2	4	no	—
183	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
184	C₂×C₃⋊C₈	—	2	4	no	—
185	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
186	C₂³×C₅	—	2	4	no	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	—	4	2	no	—
189	C₂³×C₅	—	4	2	no	—
190	C₂³×C₅	C₂×#67	1	1	yes	characteristic
191	C₅×Q₈	—	12	8	no	—
192	C₅×D₄	—	2	4	no	—
193	C₅×D₄	—	2	2	no	—
194	C₅×D₄	C₂×Dic₆	1	4	yes	complemented
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	8	no	—
199	C₂×C₄×C₅	—	6	4	no	—
200	C₂×C₄×C₅	—	12	4	no	—
201	C₂×C₄×C₅	#213	1	4	yes	—
202	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
203	C₂×C₄×C₅	#235	1	2	yes	—
204	C₂×C₄×C₅	C₂×#67	1	2	yes	—
205	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×#67	1	2	yes	—
207	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
208	C₅×C₈	—	6	4	no	—
209	C₂²×Q₈	—	6	1	no	—
210	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
211	C₂³×C₄	—	2	1	no	—
212	C₂²×C₈	—	3	2	no	—
213	C₄⋊Q₈	—	3	4	no	—
214	C₄⋊Q₈	—	6	2	no	—
215	C₄×D₄	—	2	2	no	—
216	C₄×D₄	C₂×C₅×D₃	1	4	yes	—
217	C₂×C₄⋊C₄	—	3	2	no	—
218	C₂×C₄⋊C₄	—	6	1	no	—
219	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
220	C₂×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
222	#107	—	3	8	no	—
223	C₄⋊C₈	—	3	4	no	—
224	#102	—	3	8	no	—
225	C₂×C₃×C₅	—	4	4	no	—
226	C₂×C₃×C₅	#474	1	4	yes	complemented
227	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
228	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
229	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
230	C₂³×C₃	—	2	4	no	—
231	C₂³×C₃	—	2	2	no	—
232	C₂³×C₃	—	4	2	no	—
233	C₂³×C₃	—	4	2	no	—
234	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
235	C₃×D₄	—	2	4	no	—
236	C₃×D₄	—	2	2	no	—
237	C₃×D₄	C₂×C₅×Q₈	1	4	yes	complemented
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	4	2	no	—
241	C₂×C₃×C₄	—	4	8	no	—
242	C₂×C₃×C₄	C₅×D₈	1	4	yes	—
243	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
244	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
246	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
247	C₂×C₃×C₄	C₅×#41	1	2	yes	—
248	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
249	C₂×Dic₃	—	2	4	no	—
250	C₂×Dic₃	—	4	4	no	—
251	Dic₆	—	4	8	no	—
252	C₃⋊C₈	—	2	4	no	—
253	C₂²×C₅	—	2	4	no	—
254	C₂²×C₅	—	4	8	no	—
255	C₂²×C₅	—	4	2	no	—
256	C₂²×C₅	—	4	2	no	—
257	C₂²×C₅	#924	1	2	yes	—
258	C₂²×C₅	C₂×#213	1	2	yes	—
259	C₂²×C₅	#951	1	2	yes	—
260	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
261	C₄×C₅	—	2	2	no	—
262	C₄×C₅	—	4	2	no	—
263	C₄×C₅	—	12	4	no	—
264	C₄×C₅	#924	1	2	yes	—
265	C₄×C₅	C₂×#213	1	4	yes	—
266	C₄×C₅	C₂²×Dic₆	1	1	yes	characteristic
267	C₄×C₅	C₂×#235	1	1	yes	characteristic
268	C₂⁴	—	2	1	no	—
269	C₂×Q₈	—	6	4	no	—
270	C₂×Q₈	—	12	4	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	C₅×Dic₆	1	4	yes	complemented
274	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	6	2	no	—
279	C₂²×C₄	C₅×#67	1	1	yes	characteristic
280	C₂²×C₄	C₅×#67	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
282	C₂×C₈	—	3	4	no	—
283	C₂×C₈	—	6	4	no	—
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	—	3	4	no	—
286	C₄⋊C₄	—	6	2	no	—
287	C₄⋊C₄	—	6	4	no	—
288	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
289	C₂²⋊C₄	—	2	4	no	—
290	C₄²	C₅×#67	1	2	yes	—
291	C₄²	C₂²×C₅×D₃	1	2	yes	—
292	C₃×C₅	C₂×#474	1	1	yes	characteristic, complemented, Hall
293	C₂²×C₃	—	2	4	no	—
294	C₂²×C₃	—	4	8	no	—
295	C₂²×C₃	—	4	2	no	—
296	C₂²×C₃	—	4	2	no	—
297	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
298	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
299	C₂²×C₃	C₅×#137	1	2	yes	—
300	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	4	2	no	—
303	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
304	C₃×C₄	C₂×C₅×D₈	1	4	yes	—
305	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
306	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
307	Dic₃	—	4	4	no	—
308	C₂×C₅	—	4	4	no	—
309	C₂×C₅	#5007	1	4	yes	direct product factor
310	C₂×C₅	C₂×#924	1	1	yes	characteristic
311	C₂×C₅	C₂²×#213	1	1	yes	characteristic
312	C₂×C₅	C₂×#951	1	1	yes	characteristic
313	C₂³	—	2	4	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₂×C₅×#67	1	1	yes	characteristic
318	Q₈	—	12	8	no	—
319	D₄	—	2	4	no	—
320	D₄	—	2	2	no	—
321	D₄	C₂×C₅×Dic₆	1	4	yes	complemented
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	—	6	4	no	—
327	C₂×C₄	—	12	4	no	—
328	C₂×C₄	C₅×#213	1	4	yes	—
329	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
330	C₂×C₄	C₅×#235	1	2	yes	—
331	C₂×C₄	C₂×C₅×#67	1	2	yes	—
332	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
333	C₂×C₄	C₂×C₅×#67	1	2	yes	—
334	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
335	C₈	—	6	4	no	—
336	C₂×C₃	—	4	4	no	—
337	C₂×C₃	C₅×#474	1	4	yes	complemented
338	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
339	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
340	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
341	C₅	C₂×#5007	1	1	yes	characteristic, direct product factor, Sylow
342	C₂²	—	2	4	no	—
343	C₂²	—	4	8	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	C₅×#924	1	2	yes	—
347	C₂²	C₂×C₅×#213	1	2	yes	—
348	C₂²	C₅×#951	1	2	yes	—
349	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
350	C₄	—	2	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	12	4	no	—
353	C₄	C₅×#924	1	2	yes	—
354	C₄	C₂×C₅×#213	1	4	yes	—
355	C₄	C₂²×C₅×Dic₆	1	1	yes	characteristic
356	C₄	C₂×C₅×#235	1	1	yes	characteristic
357	C₃	C₂×C₅×#474	1	1	yes	characteristic, complemented, Sylow
358	C₂	—	4	4	no	—
359	C₂	C₅×#5007	1	4	yes	direct product factor
360	C₂	C₂×C₅×#924	1	1	yes	characteristic
361	C₂	C₂²×C₅×#213	1	1	yes	characteristic
362	C₂	C₂×C₅×#951	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#474
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#869	C₂	semidirect
4. C₅×#5007	C₂	direct (N × H)
5. C₂×C₅×#807	C₂	semidirect
6. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
20. C₅×#869	C₂²	semidirect
22. C₅×#807	C₂²	semidirect
23. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
24. C₂×#5007	C₅	direct (N × H)
34. C₂×C₃×C₅×D₄	Q₈	semidirect
56. C₂×#869	C₂×C₅	semidirect
58. #5007	C₂×C₅	direct (N × H)
59. C₂×#807	C₂×C₅	semidirect
60. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
85. C₃×C₅×D₄	C₂×Q₈	semidirect
113. #869	C₂²×C₅	semidirect
115. #807	C₂²×C₅	semidirect
116. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
122. C₂×C₅×D₄	Dic₆	semidirect
165. C₂×C₃×D₄	C₅×Q₈	semidirect
194. C₅×D₄	C₂×Dic₆	semidirect
226. C₂×C₃×C₅	#474	semidirect
237. C₃×D₄	C₂×C₅×Q₈	semidirect
273. C₂×D₄	C₅×Dic₆	semidirect
292. C₃×C₅	C₂×#474	semidirect
309. C₂×C₅	#5007	direct (N × H)
321. D₄	C₂×C₅×Dic₆	semidirect
337. C₂×C₃	C₅×#474	semidirect
341. C₅	C₂×#5007	direct (N × H)
357. C₃	C₂×C₅×#474	semidirect
359. C₂	C₅×#5007	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×C₄×C₅×D₄	2
C₂×C₅×#869	2
C₂×C₅×#832	2
C₅×#5007	2
C₂×C₅×#807	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₅×#474	3
C₂×#5007	5

Subgroups — C2×C5×#5007 #14429814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5007 #14429814