Subgroups — C₂×D₃×#1201 #13088997

Order 1440.

998 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#67156	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#67150	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#67138	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#1201	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×#1201	C₂	1	8	yes	maximal, direct product factor
9	C₂×D₃×C₂²⋊D₅	—	3	1	no	maximal
10	C₂²×#1201	—	3	1	no	maximal
11	C₂²×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
12	C₂²×C₃×D₁₅	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃²×D₅	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₅×D₃²	—	2	4	no	—
17	C₂×C₅×D₃²	C₂²	1	4	yes	complemented
18	C₂×C₃×D₃×D₅	—	2	4	no	—
19	C₂×C₃×D₃×D₅	C₂²	1	4	yes	complemented
20	C₂×C₃⋊Dic₁₅	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
22	#67156	C₂²	1	4	yes	complemented
23	#67150	C₂²	1	4	yes	complemented
24	D₃×Dic₁₅	C₂²	1	4	yes	complemented
25	#67138	C₂²	1	4	yes	complemented
26	C₃×#1201	C₂²	1	4	yes	complemented
27	C₂×D₃×#67	—	5	1	no	maximal, Hall
28	C₂³×C₅×D₃	—	3	1	no	—
29	C₂³×C₅×D₃	—	3	1	no	—
30	C₂³×C₃×D₅	—	3	1	no	—
31	C₂²×D₃×D₅	D₃	1	1	yes	characteristic, complemented
32	C₂×#1220	—	3	1	no	—
33	C₂²×Dic₁₅	—	3	1	no	—
34	C₂×C₃×C₂²⋊D₅	—	3	1	no	—
35	D₃×C₂²⋊D₅	—	3	8	no	—
36	C₂×#1203	—	3	1	no	—
37	C₂×#1201	—	3	1	no	—
38	C₂×#1201	—	3	1	no	—
39	C₂×#1201	—	3	1	no	—
40	C₂×#1201	—	3	1	no	—
41	C₂×#1201	—	3	8	no	—
42	C₂×#1201	—	6	1	no	—
43	C₂×#1201	D₃	1	1	yes	characteristic, direct product factor
44	C₂×D₃×Dic₅	—	3	1	no	—
45	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₅×C₃⋊D₃	—	2	2	no	—
47	C₂×C₅×C₃⋊D₃	C₂³	1	2	yes	complemented
48	C₂×C₃×D₁₅	—	2	2	no	—
49	C₂×C₃×D₁₅	C₂³	1	2	yes	complemented
50	C₂×C₃×C₅×D₃	—	2	2	no	—
51	C₂×C₃×C₅×D₃	D₄	1	4	yes	complemented
52	C₂×C₃×C₅×D₃	C₂³	1	2	yes	—
53	C₂×C₃×C₅×D₃	C₂³	1	2	yes	complemented
54	C₂×C₃²×D₅	—	2	2	no	—
55	C₂×C₃²×D₅	C₂³	1	2	yes	complemented
56	C₅×D₃²	—	2	8	no	—
57	C₃×D₃×D₅	—	2	8	no	—
58	C₃⋊Dic₁₅	C₂³	1	2	yes	complemented
59	C₃×Dic₁₅	C₂³	1	2	yes	complemented
60	C₂²×C₂²⋊D₅	—	9	1	no	Hall
61	C₂³×C₃×D₃	—	5	1	no	—
62	C₂²×D₃²	D₅	1	1	yes	characteristic, complemented
63	C₂×#638	—	5	1	no	—
64	C₂×C₃×#67	—	5	1	no	—
65	D₃×#67	—	5	8	no	—
66	C₂×#626	—	5	1	no	—
67	C₂×#625	—	5	1	no	—
68	C₂×D₃×Dic₃	—	5	1	no	—
69	C₂³×C₃×C₅	—	3	1	no	—
70	C₂³×C₃×C₅	—	3	1	no	—
71	C₂²×D₁₅	C₂×D₃	1	1	yes	characteristic, complemented
72	C₂²×C₅×D₃	—	3	1	no	—
73	C₂²×C₅×D₃	—	3	1	no	—
74	C₂²×C₅×D₃	—	3	4	no	—
75	C₂²×C₅×D₃	—	3	4	no	—
76	C₂²×C₅×D₃	—	6	4	no	—
77	C₂²×C₅×D₃	—	6	4	no	—
78	C₂²×C₅×D₃	—	6	1	no	—
79	C₂²×C₅×D₃	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₅×D₃	C₂×D₃	1	1	yes	characteristic, complemented
81	C₂²×C₃×D₅	—	2	1	no	—
82	C₂²×C₃×D₅	—	3	1	no	—
83	C₂²×C₃×D₅	—	3	4	no	—
84	C₂²×C₃×D₅	—	6	4	no	—
85	C₂²×C₃×D₅	C₂×D₃	1	1	yes	characteristic, complemented
86	C₂²×C₃×D₅	C₂×D₃	1	1	yes	characteristic, complemented
87	C₂×D₃×D₅	—	2	4	no	—
88	C₂×D₃×D₅	C₂×D₃	1	4	yes	complemented
89	#1220	—	3	4	no	—
90	C₂×Dic₁₅	—	3	1	no	—
91	C₂×Dic₁₅	—	3	1	no	—
92	C₂×Dic₁₅	—	3	4	no	—
93	C₂×Dic₁₅	—	6	1	no	—
94	C₂×Dic₁₅	C₂×D₃	1	1	yes	characteristic, complemented
95	C₃×C₂²⋊D₅	—	3	4	no	—
96	C₂×C₃×Dic₅	—	3	1	no	—
97	#1203	—	3	4	no	—
98	#1201	—	3	4	no	—
99	#1201	—	3	4	no	—
100	#1201	—	3	4	no	—
101	#1201	—	3	4	no	—
102	#1201	—	6	4	no	—
103	#1201	C₂×D₃	1	4	yes	direct product factor
104	D₃×Dic₅	—	3	4	no	—
105	C₂²×#67	—	15	1	no	—
106	C₂×D₃×D₄	—	15	1	no	—
107	C₂×C₃²×C₅	C₂×D₄	1	2	yes	complemented
108	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
109	C₅×C₃⋊D₃	—	2	2	no	—
110	C₃×D₁₅	—	2	2	no	—
111	C₃×C₅×D₃	—	2	2	no	—
112	C₃×C₅×D₃	C₂×D₄	1	4	yes	complemented
113	C₃²×D₅	—	2	2	no	—
114	C₂⁴×C₅	—	9	1	no	—
115	C₂³×D₅	—	3	1	no	—
116	C₂×C₂²⋊D₅	—	3	1	no	—
117	C₂×C₂²⋊D₅	—	9	1	no	—
118	C₂×C₂²⋊D₅	—	9	8	no	—
119	C₂×C₂²⋊D₅	—	9	1	no	—
120	C₂×C₂²⋊D₅	—	9	1	no	—
121	C₂²×Dic₅	—	9	1	no	—
122	C₂³×C₃²	—	5	1	no	—
123	C₂²×C₃⋊D₃	C₂×D₅	1	1	yes	characteristic, complemented
124	C₂²×C₃×D₃	—	5	1	no	—
125	C₂²×C₃×D₃	—	5	4	no	—
126	C₂²×C₃×D₃	—	10	4	no	—
127	C₂²×C₃×D₃	C₂×D₅	1	1	yes	characteristic
128	C₂²×C₃×D₃	C₂×D₅	1	1	yes	characteristic, complemented
129	C₂×D₃²	—	2	4	no	—
130	C₂×D₃²	C₂×D₅	1	4	yes	complemented
131	#638	—	5	4	no	—
132	C₂×C₃⋊Dic₃	—	5	1	no	—
133	C₃×#67	—	5	4	no	—
134	C₂×C₃×Dic₃	—	5	1	no	—
135	#626	—	5	4	no	—
136	#625	—	5	4	no	—
137	D₃×Dic₃	—	5	4	no	—
138	C₂²×C₃×C₅	—	2	1	no	—
139	C₂²×C₃×C₅	—	3	4	no	—
140	C₂²×C₃×C₅	—	3	2	no	—
141	C₂²×C₃×C₅	—	3	2	no	—
142	C₂²×C₃×C₅	—	6	2	no	—
143	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
145	C₂×D₁₅	—	2	2	no	—
146	C₂×D₁₅	C₂²×D₃	1	2	yes	complemented
147	C₂×C₅×D₃	—	2	2	no	—
148	C₂×C₅×D₃	—	3	2	no	—
149	C₂×C₅×D₃	—	3	2	no	—
150	C₂×C₅×D₃	—	6	2	no	—
151	C₂×C₅×D₃	—	6	8	no	—
152	C₂×C₅×D₃	—	6	2	no	—
153	C₂×C₅×D₃	—	6	2	no	—
154	C₂×C₅×D₃	—	6	8	no	—
155	C₂×C₅×D₃	—	12	2	no	—
156	C₂×C₅×D₃	#67	1	4	yes	complemented
157	C₂×C₅×D₃	C₂²×D₃	1	2	yes	—
158	C₂×C₅×D₃	C₂²×D₃	1	2	yes	complemented
159	C₂×C₃×D₅	—	2	2	no	—
160	C₂×C₃×D₅	—	2	2	no	—
161	C₂×C₃×D₅	—	2	2	no	—
162	C₂×C₃×D₅	—	3	2	no	—
163	C₂×C₃×D₅	—	4	2	no	—
164	C₂×C₃×D₅	—	6	8	no	—
165	C₂×C₃×D₅	—	6	2	no	—
166	C₂×C₃×D₅	C₂²×D₃	1	2	yes	complemented
167	C₂×C₃×D₅	C₂²×D₃	1	2	yes	complemented
168	D₃×D₅	—	2	8	no	—
169	Dic₁₅	—	3	2	no	—
170	Dic₁₅	—	3	2	no	—
171	Dic₁₅	—	6	2	no	—
172	Dic₁₅	C₂²×D₃	1	2	yes	complemented
173	C₃×Dic₅	—	3	2	no	—
174	C₂⁴×C₃	—	15	1	no	—
175	C₂³×D₃	—	3	1	no	—
176	C₂³×D₃	—	3	1	no	—
177	C₂³×D₃	—	5	1	no	—
178	C₂×C₃×D₄	—	15	1	no	—
179	C₂×#67	—	5	1	no	—
180	C₂×#67	—	15	1	no	—
181	C₂×#67	—	15	8	no	—
182	C₂×#67	—	15	1	no	—
183	C₂×#67	—	15	1	no	—
184	C₂×#67	—	15	1	no	—
185	C₂×#67	—	15	1	no	—
186	C₂×#67	—	30	1	no	—
187	C₂²×Dic₃	—	15	1	no	—
188	D₃×D₄	—	15	8	no	—
189	C₂×D₁₂	—	15	1	no	—
190	C₂×C₄×D₃	—	15	1	no	—
191	C₃²×C₅	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
192	C₂³×C₅	—	3	1	no	—
193	C₂³×C₅	—	3	1	no	—
194	C₂³×C₅	—	9	4	no	—
195	C₂³×C₅	—	9	1	no	—
196	C₂³×C₅	—	18	4	no	—
197	C₂²×D₅	—	3	1	no	—
198	C₂²×D₅	—	3	4	no	—
199	C₂²×D₅	—	6	4	no	—
200	C₂²×D₅	D₃²	1	1	yes	characteristic, complemented
201	C₂²⋊D₅	—	3	4	no	—
202	C₂²⋊D₅	—	9	4	no	—
203	C₂²⋊D₅	—	9	4	no	—
204	C₂²⋊D₅	—	9	4	no	—
205	C₂×Dic₅	—	3	1	no	—
206	C₂×Dic₅	—	9	4	no	—
207	C₂×Dic₅	—	9	1	no	—
208	C₂²×C₃²	—	5	2	no	—
209	C₂²×C₃²	—	10	2	no	—
210	C₂²×C₃²	C₂²×D₅	1	1	yes	characteristic
211	C₂×C₃⋊D₃	—	2	2	no	—
212	C₂×C₃⋊D₃	C₂²×D₅	1	2	yes	complemented
213	C₂×C₃×D₃	—	2	2	no	—
214	C₂×C₃×D₃	—	5	2	no	—
215	C₂×C₃×D₃	—	10	2	no	—
216	C₂×C₃×D₃	—	10	8	no	—
217	C₂×C₃×D₃	C₂²⋊D₅	1	4	yes	complemented
218	C₂×C₃×D₃	C₂²×D₅	1	2	yes	—
219	C₂×C₃×D₃	C₂²×D₅	1	2	yes	complemented
220	D₃²	—	2	8	no	—
221	C₃⋊Dic₃	—	5	2	no	—
222	C₃×Dic₃	—	5	2	no	—
223	C₂²×D₄	—	45	1	no	Sylow
224	C₂×C₃×C₅	—	2	1	no	—
225	C₂×C₃×C₅	—	2	2	no	—
226	C₂×C₃×C₅	—	3	4	no	—
227	C₂×C₃×C₅	—	6	2	no	—
228	C₂×C₃×C₅	D₃×D₄	1	2	yes	complemented
229	C₂×C₃×C₅	C₂×#67	1	2	yes	complemented
230	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
231	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
232	D₁₅	—	2	2	no	—
233	C₃×D₅	—	2	2	no	—
234	C₃×D₅	—	2	2	no	—
235	C₃×D₅	—	4	2	no	—
236	C₃×D₅	—	6	2	no	—
237	C₅×D₃	—	2	2	no	—
238	C₅×D₃	—	6	2	no	—
239	C₅×D₃	—	6	2	no	—
240	C₅×D₃	—	12	2	no	—
241	C₅×D₃	C₂×#67	1	4	yes	complemented
242	C₂³×C₃	—	3	1	no	—
243	C₂³×C₃	—	3	1	no	—
244	C₂³×C₃	—	5	1	no	—
245	C₂³×C₃	—	5	1	no	—
246	C₂³×C₃	—	10	1	no	—
247	C₂³×C₃	—	15	4	no	—
248	C₂³×C₃	—	15	1	no	—
249	C₂³×C₃	—	30	4	no	—
250	C₂²×D₃	—	3	1	no	—
251	C₂²×D₃	—	3	1	no	—
252	C₂²×D₃	—	3	4	no	—
253	C₂²×D₃	—	3	4	no	—
254	C₂²×D₃	—	5	1	no	—
255	C₂²×D₃	—	5	4	no	—
256	C₂²×D₃	—	6	1	no	—
257	C₂²×D₃	—	6	4	no	—
258	C₂²×D₃	—	6	4	no	—
259	C₂²×D₃	—	10	4	no	—
260	C₂²×D₃	D₃×D₅	1	1	yes	characteristic
261	C₂²×D₃	D₃×D₅	1	1	yes	characteristic, complemented
262	C₃×D₄	—	15	4	no	—
263	C₂×C₃×C₄	—	15	1	no	—
264	#67	—	5	4	no	—
265	#67	—	15	4	no	—
266	#67	—	15	4	no	—
267	#67	—	15	4	no	—
268	#67	—	15	4	no	—
269	#67	—	15	4	no	—
270	#67	—	30	4	no	—
271	C₂×Dic₃	—	5	1	no	—
272	C₂×Dic₃	—	15	4	no	—
273	C₂×Dic₃	—	15	1	no	—
274	C₂×Dic₃	—	15	1	no	—
275	C₂×Dic₃	—	30	1	no	—
276	D₁₂	—	15	4	no	—
277	C₄×D₃	—	15	4	no	—
278	C₂²×C₅	—	3	2	no	—
279	C₂²×C₅	—	3	4	no	—
280	C₂²×C₅	—	3	2	no	—
281	C₂²×C₅	—	6	2	no	—
282	C₂²×C₅	—	9	2	no	—
283	C₂²×C₅	—	18	8	no	—
284	C₂²×C₅	—	18	2	no	—
285	C₂²×C₅	C₂×D₃²	1	1	yes	characteristic
286	C₂×D₅	—	2	2	no	—
287	C₂×D₅	—	3	2	no	—
288	C₂×D₅	—	6	8	no	—
289	C₂×D₅	—	6	2	no	—
290	C₂×D₅	C₂×D₃²	1	2	yes	complemented
291	Dic₅	—	3	2	no	—
292	Dic₅	—	9	2	no	—
293	C₂×C₃²	—	10	2	no	—
294	C₂×C₃²	C₂×C₂²⋊D₅	1	2	yes	complemented
295	C₂×C₃²	C₂³×D₅	1	1	yes	characteristic
296	C₃⋊D₃	—	2	2	no	—
297	C₃×D₃	—	2	2	no	—
298	C₃×D₃	—	10	2	no	—
299	C₃×D₃	C₂×C₂²⋊D₅	1	4	yes	complemented
300	C₂⁴	—	9	1	no	—
301	C₂⁴	—	15	1	no	—
302	C₂×D₄	—	15	1	no	—
303	C₂×D₄	—	45	1	no	—
304	C₂×D₄	—	45	8	no	—
305	C₂×D₄	—	45	1	no	—
306	C₂×D₄	—	45	1	no	—
307	C₂²×C₄	—	45	1	no	—
308	C₃×C₅	—	2	1	no	—
309	C₃×C₅	C₂×D₃×D₄	1	1	yes	characteristic, complemented
310	C₃×C₅	C₂²×#67	1	1	yes	characteristic, complemented
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	3	4	no	—
313	C₂²×C₃	—	3	2	no	—
314	C₂²×C₃	—	3	2	no	—
315	C₂²×C₃	—	5	2	no	—
316	C₂²×C₃	—	5	2	no	—
317	C₂²×C₃	—	6	2	no	—
318	C₂²×C₃	—	10	2	no	—
319	C₂²×C₃	—	10	2	no	—
320	C₂²×C₃	—	10	2	no	—
321	C₂²×C₃	—	15	2	no	—
322	C₂²×C₃	—	20	2	no	—
323	C₂²×C₃	—	30	8	no	—
324	C₂²×C₃	—	30	2	no	—
325	C₂²×C₃	C₂×D₃×D₅	1	1	yes	characteristic
326	C₂²×C₃	C₂×D₃×D₅	1	1	yes	characteristic
327	C₂×D₃	—	2	2	no	—
328	C₂×D₃	—	3	2	no	—
329	C₂×D₃	—	3	2	no	—
330	C₂×D₃	—	5	2	no	—
331	C₂×D₃	—	6	2	no	—
332	C₂×D₃	—	6	8	no	—
333	C₂×D₃	—	6	2	no	—
334	C₂×D₃	—	6	2	no	—
335	C₂×D₃	—	6	8	no	—
336	C₂×D₃	—	10	2	no	—
337	C₂×D₃	—	10	8	no	—
338	C₂×D₃	—	12	2	no	—
339	C₂×D₃	#1201	1	4	yes	direct product factor
340	C₂×D₃	C₂×D₃×D₅	1	2	yes	—
341	C₂×D₃	C₂×D₃×D₅	1	2	yes	complemented
342	C₃×C₄	—	15	2	no	—
343	Dic₃	—	5	2	no	—
344	Dic₃	—	15	2	no	—
345	Dic₃	—	15	2	no	—
346	Dic₃	—	30	2	no	—
347	C₂×C₅	—	3	4	no	—
348	C₂×C₅	—	6	2	no	—
349	C₂×C₅	—	18	2	no	—
350	C₂×C₅	D₃×#67	1	2	yes	complemented
351	C₂×C₅	C₂²×D₃²	1	1	yes	characteristic
352	D₅	—	2	2	no	—
353	D₅	—	6	2	no	—
354	C₃²	C₂²×C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
355	C₂³	—	3	1	no	—
356	C₂³	—	3	1	no	—
357	C₂³	—	5	1	no	—
358	C₂³	—	9	4	no	—
359	C₂³	—	9	1	no	—
360	C₂³	—	15	4	no	—
361	C₂³	—	15	1	no	—
362	C₂³	—	18	4	no	—
363	C₂³	—	30	4	no	—
364	D₄	—	15	4	no	—
365	D₄	—	45	4	no	—
366	D₄	—	45	4	no	—
367	D₄	—	45	4	no	—
368	C₂×C₄	—	15	1	no	—
369	C₂×C₄	—	45	4	no	—
370	C₂×C₄	—	45	1	no	—
371	C₂×C₃	—	2	2	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	3	4	no	—
374	C₂×C₃	—	6	2	no	—
375	C₂×C₃	—	10	2	no	—
376	C₂×C₃	—	10	2	no	—
377	C₂×C₃	—	20	2	no	—
378	C₂×C₃	—	30	2	no	—
379	C₂×C₃	C₂×#1201	1	2	yes	complemented
380	C₂×C₃	D₃×C₂²⋊D₅	1	2	yes	complemented
381	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
382	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
383	D₃	—	2	2	no	—
384	D₃	—	6	2	no	—
385	D₃	—	6	2	no	—
386	D₃	—	10	2	no	—
387	D₃	—	12	2	no	—
388	D₃	C₂×#1201	1	4	yes	direct product factor
389	C₅	C₂×D₃×#67	1	1	yes	characteristic, complemented, Sylow
390	C₂²	—	3	4	no	—
391	C₂²	—	3	2	no	—
392	C₂²	—	3	2	no	—
393	C₂²	—	5	2	no	—
394	C₂²	—	6	2	no	—
395	C₂²	—	9	2	no	—
396	C₂²	—	10	2	no	—
397	C₂²	—	15	2	no	—
398	C₂²	—	18	8	no	—
399	C₂²	—	18	2	no	—
400	C₂²	—	30	8	no	—
401	C₂²	—	30	2	no	—
402	C₂²	D₃²×D₅	1	1	yes	characteristic
403	C₄	—	15	2	no	—
404	C₄	—	45	2	no	—
405	C₃	—	2	1	no	—
406	C₃	C₂²×#1201	1	1	yes	characteristic, complemented
407	C₃	C₂×D₃×C₂²⋊D₅	1	1	yes	characteristic, complemented
408	C₂	—	3	4	no	—
409	C₂	—	6	2	no	—
410	C₂	—	10	2	no	—
411	C₂	—	18	2	no	—
412	C₂	—	30	2	no	—
413	C₂	D₃×#1201	1	2	yes	direct product factor
414	C₂	C₂×D₃²×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃²×D₅
commutator, cosocle	C₂×C₃²×C₅	C₂⁴
Frattini	C₂	C₂×D₃²×D₅
Fitting, socle	C₂²×C₃²×C₅	C₂³
hypocenter	C₃²×C₅	C₂²×D₄
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃²	C₂	semidirect
2. C₂²×C₃×D₃×D₅	C₂	semidirect
3. C₂×#67156	C₂	semidirect
4. C₂×#67150	C₂	semidirect
5. C₂×D₃×Dic₁₅	C₂	semidirect
6. C₂×#67138	C₂	semidirect
7. C₂×C₃×#1201	C₂	semidirect
8. D₃×#1201	C₂	direct (N × H)
11. C₂²×C₅×C₃⋊D₃	C₂²	semidirect
12. C₂²×C₃×D₁₅	C₂²	semidirect
14. C₂²×C₃×C₅×D₃	C₂²	semidirect
15. C₂²×C₃²×D₅	C₂²	semidirect
17. C₂×C₅×D₃²	C₂²	semidirect
19. C₂×C₃×D₃×D₅	C₂²	semidirect
20. C₂×C₃⋊Dic₁₅	C₂²	semidirect
21. C₂×C₃×Dic₁₅	C₂²	semidirect
22. #67156	C₂²	semidirect
23. #67150	C₂²	semidirect
24. D₃×Dic₁₅	C₂²	semidirect
25. #67138	C₂²	semidirect
26. C₃×#1201	C₂²	semidirect
31. C₂²×D₃×D₅	D₃	semidirect
43. C₂×#1201	D₃	direct (N × H)
47. C₂×C₅×C₃⋊D₃	C₂³	semidirect
49. C₂×C₃×D₁₅	C₂³	semidirect
51. C₂×C₃×C₅×D₃	D₄	semidirect
53. C₂×C₃×C₅×D₃	C₂³	semidirect
55. C₂×C₃²×D₅	C₂³	semidirect
58. C₃⋊Dic₁₅	C₂³	semidirect
59. C₃×Dic₁₅	C₂³	semidirect
62. C₂²×D₃²	D₅	semidirect
71. C₂²×D₁₅	C₂×D₃	semidirect
80. C₂²×C₅×D₃	C₂×D₃	semidirect
85. C₂²×C₃×D₅	C₂×D₃	semidirect
86. C₂²×C₃×D₅	C₂×D₃	semidirect
88. C₂×D₃×D₅	C₂×D₃	semidirect
94. C₂×Dic₁₅	C₂×D₃	semidirect
103. #1201	C₂×D₃	direct (N × H)
107. C₂×C₃²×C₅	C₂×D₄	semidirect
112. C₃×C₅×D₃	C₂×D₄	semidirect
123. C₂²×C₃⋊D₃	C₂×D₅	semidirect
128. C₂²×C₃×D₃	C₂×D₅	semidirect
130. C₂×D₃²	C₂×D₅	semidirect
146. C₂×D₁₅	C₂²×D₃	semidirect
156. C₂×C₅×D₃	#67	semidirect
158. C₂×C₅×D₃	C₂²×D₃	semidirect
166. C₂×C₃×D₅	C₂²×D₃	semidirect
167. C₂×C₃×D₅	C₂²×D₃	semidirect
172. Dic₁₅	C₂²×D₃	semidirect
191. C₃²×C₅	C₂²×D₄	semidirect
200. C₂²×D₅	D₃²	semidirect
212. C₂×C₃⋊D₃	C₂²×D₅	semidirect
217. C₂×C₃×D₃	C₂²⋊D₅	semidirect
219. C₂×C₃×D₃	C₂²×D₅	semidirect
228. C₂×C₃×C₅	D₃×D₄	semidirect
229. C₂×C₃×C₅	C₂×#67	semidirect
241. C₅×D₃	C₂×#67	semidirect
261. C₂²×D₃	D₃×D₅	semidirect
290. C₂×D₅	C₂×D₃²	semidirect
294. C₂×C₃²	C₂×C₂²⋊D₅	semidirect
299. C₃×D₃	C₂×C₂²⋊D₅	semidirect
309. C₃×C₅	C₂×D₃×D₄	semidirect
310. C₃×C₅	C₂²×#67	semidirect
339. C₂×D₃	#1201	direct (N × H)
341. C₂×D₃	C₂×D₃×D₅	semidirect
350. C₂×C₅	D₃×#67	semidirect
354. C₃²	C₂²×C₂²⋊D₅	semidirect
379. C₂×C₃	C₂×#1201	semidirect
380. C₂×C₃	D₃×C₂²⋊D₅	semidirect
388. D₃	C₂×#1201	direct (N × H)
389. C₅	C₂×D₃×#67	semidirect
406. C₃	C₂²×#1201	semidirect
407. C₃	C₂×D₃×C₂²⋊D₅	semidirect
413. C₂	D₃×#1201	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₃²	2
C₂²×C₃×D₃×D₅	2
C₂×#67156	2
C₂×#67150	2
C₂×D₃×Dic₁₅	2
C₂×#67138	2
C₂×C₃×#1201	2
D₃×#1201	2
C₂×D₃×C₂²⋊D₅	3
C₂²×#1201	3
C₂×D₃×#67	5

Subgroups — C2×D3×#1201 #13088997

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×#1201 #13088997