Subgroups — C₂×D₅×#626 #13088992

Order 1440.

1078 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅×C₃⋊D₃	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×#67152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#67151	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#626	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×D₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅×#626	C₂	1	8	yes	maximal, direct product factor
9	C₂×D₅×#67	—	3	1	no	maximal
10	C₂×D₅×D₁₂	—	3	1	no	maximal
11	C₂²×C₃⋊D₁₅	C₂²	1	1	yes	characteristic, complemented
12	C₂²×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₃×D₁₅	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₃²×D₅	C₂²	1	1	yes	characteristic
16	C₂×D₅×C₃⋊D₃	—	2	4	no	—
17	C₂×D₅×C₃⋊D₃	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×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
22	#67156	C₂²	1	4	yes	complemented
23	#67152	C₂²	1	4	yes	complemented
24	#67151	C₂²	1	4	yes	complemented
25	C₅×#626	C₂²	1	4	yes	complemented
26	C₃×D₅×Dic₃	C₂²	1	4	yes	complemented
27	C₂²×#626	—	5	1	no	maximal, Hall
28	C₂³×C₃×D₅	—	3	1	no	—
29	C₂²×D₃×D₅	—	3	1	no	—
30	C₂²×D₃×D₅	—	3	1	no	—
31	C₂²×D₃×D₅	—	6	1	no	—
32	C₂²×D₃×D₅	D₃	1	1	yes	characteristic, complemented
33	C₂×#1220	—	3	1	no	—
34	C₂×D₆₀	—	3	1	no	—
35	C₂×C₅×#67	—	3	1	no	—
36	C₂×C₅×D₁₂	—	3	1	no	—
37	C₂×C₃×C₄×D₅	—	3	1	no	—
38	D₅×#67	—	3	8	no	—
39	C₂×#1203	—	3	1	no	—
40	C₂×#1203	—	3	1	no	—
41	C₂×#1202	—	3	1	no	—
42	C₂×#1201	—	3	1	no	—
43	C₂×D₅×Dic₃	D₃	1	1	yes	characteristic, complemented
44	D₅×D₁₂	—	3	8	no	—
45	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃⋊D₁₅	—	2	2	no	—
47	C₂×C₃⋊D₁₅	C₂³	1	2	yes	complemented
48	C₂×C₅×C₃⋊D₃	—	2	2	no	—
49	C₂×C₅×C₃⋊D₃	C₂³	1	2	yes	complemented
50	C₂×C₃×D₁₅	—	2	2	no	—
51	C₂×C₃×D₁₅	C₂³	1	2	yes	complemented
52	C₂×C₃×C₅×D₃	—	2	2	no	—
53	C₂×C₃×C₅×D₃	C₂³	1	2	yes	complemented
54	C₂×C₃²×D₅	D₄	1	4	yes	complemented
55	C₂×C₃²×D₅	C₂³	1	2	yes	—
56	D₅×C₃⋊D₃	—	2	8	no	—
57	C₃×D₃×D₅	—	2	8	no	—
58	C₃×Dic₁₅	C₂³	1	2	yes	complemented
59	C₃×C₅×Dic₃	C₂³	1	2	yes	complemented
60	C₂×D₄×D₅	—	9	1	no	Hall
61	C₂³×C₃⋊D₃	—	5	1	no	—
62	C₂³×C₃×D₃	—	5	1	no	—
63	C₂²×C₃×Dic₃	—	5	1	no	—
64	C₂×#626	—	5	1	no	—
65	C₂×#626	—	5	1	no	—
66	C₂×#626	—	5	1	no	—
67	C₂×#626	—	5	8	no	—
68	C₂×#626	D₅	1	1	yes	characteristic, direct product factor
69	C₂³×C₃×C₅	—	3	1	no	—
70	C₂²×D₁₅	—	3	1	no	—
71	C₂²×D₁₅	—	3	1	no	—
72	C₂²×D₁₅	—	6	1	no	—
73	C₂²×D₁₅	C₂×D₃	1	1	yes	characteristic, complemented
74	C₂²×C₅×D₃	—	3	1	no	—
75	C₂²×C₅×D₃	—	3	1	no	—
76	C₂²×C₅×D₃	—	6	1	no	—
77	C₂²×C₅×D₃	C₂×D₃	1	1	yes	characteristic, complemented
78	C₂²×C₃×D₅	—	2	1	no	—
79	C₂²×C₃×D₅	—	3	1	no	—
80	C₂²×C₃×D₅	—	3	4	no	—
81	C₂²×C₃×D₅	—	6	4	no	—
82	C₂²×C₃×D₅	C₂×D₃	1	1	yes	characteristic
83	C₂²×C₃×D₅	C₂×D₃	1	1	yes	characteristic
84	C₂×D₃×D₅	—	2	4	no	—
85	C₂×D₃×D₅	—	3	4	no	—
86	C₂×D₃×D₅	—	3	4	no	—
87	C₂×D₃×D₅	—	6	4	no	—
88	C₂×D₃×D₅	—	6	8	no	—
89	C₂×D₃×D₅	—	6	4	no	—
90	C₂×D₃×D₅	—	6	4	no	—
91	C₂×D₃×D₅	C₂×D₃	1	4	yes	complemented
92	C₂×C₃×C₄×C₅	—	3	1	no	—
93	#1220	—	3	4	no	—
94	C₂×Dic₁₅	C₂×D₃	1	1	yes	characteristic, complemented
95	D₆₀	—	3	4	no	—
96	C₅×#67	—	3	4	no	—
97	C₂×C₅×Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
98	C₅×D₁₂	—	3	4	no	—
99	C₂×C₃×Dic₅	—	3	1	no	—
100	C₃×C₄×D₅	—	3	4	no	—
101	#1203	—	3	4	no	—
102	#1203	—	3	4	no	—
103	#1202	—	3	4	no	—
104	#1201	—	3	4	no	—
105	D₅×Dic₃	C₂×D₃	1	4	yes	complemented
106	C₂²×#67	—	15	1	no	—
107	C₂²×D₁₂	—	15	1	no	—
108	C₂×C₃²×C₅	C₂×D₄	1	2	yes	complemented
109	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
110	C₃⋊D₁₅	—	2	2	no	—
111	C₅×C₃⋊D₃	—	2	2	no	—
112	C₃×D₁₅	—	2	2	no	—
113	C₃×C₅×D₃	—	2	2	no	—
114	C₃²×D₅	C₂×D₄	1	4	yes	complemented
115	C₂³×D₅	—	3	1	no	—
116	C₂³×D₅	—	9	1	no	—
117	C₂×C₅×D₄	—	9	1	no	—
118	C₂×C₂²⋊D₅	—	9	1	no	—
119	C₂×C₂²⋊D₅	—	9	1	no	—
120	D₄×D₅	—	9	8	no	—
121	C₂×D₂₀	—	9	1	no	—
122	C₂×C₄×D₅	—	3	1	no	—
123	C₂³×C₃²	—	5	1	no	—
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, complemented
128	C₂²×C₃×D₃	—	5	1	no	—
129	C₂²×C₃×D₃	—	5	4	no	—
130	C₂²×C₃×D₃	—	10	4	no	—
131	C₂²×C₃×D₃	C₂×D₅	1	1	yes	characteristic, complemented
132	C₂×C₃×Dic₃	—	5	1	no	—
133	C₂×C₃×Dic₃	—	5	4	no	—
134	C₂×C₃×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
135	#626	—	5	4	no	—
136	#626	—	5	4	no	—
137	#626	—	5	4	no	—
138	#626	C₂×D₅	1	4	yes	direct product factor
139	C₂²×C₃×C₅	—	2	1	no	—
140	C₂²×C₃×C₅	—	3	2	no	—
141	C₂²×C₃×C₅	—	6	2	no	—
142	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₂×D₁₅	—	2	2	no	—
145	C₂×D₁₅	—	3	2	no	—
146	C₂×D₁₅	—	3	2	no	—
147	C₂×D₁₅	—	6	2	no	—
148	C₂×D₁₅	—	6	4	no	—
149	C₂×D₁₅	—	6	2	no	—
150	C₂×D₁₅	—	6	2	no	—
151	C₂×D₁₅	C₂²×D₃	1	2	yes	complemented
152	C₂×C₅×D₃	—	2	2	no	—
153	C₂×C₅×D₃	—	3	2	no	—
154	C₂×C₅×D₃	—	3	2	no	—
155	C₂×C₅×D₃	—	6	2	no	—
156	C₂×C₅×D₃	—	6	4	no	—
157	C₂×C₅×D₃	—	6	2	no	—
158	C₂×C₅×D₃	—	6	2	no	—
159	C₂×C₅×D₃	C₂²×D₃	1	2	yes	complemented
160	C₂×C₃×D₅	—	2	4	no	—
161	C₂×C₃×D₅	—	2	2	no	—
162	C₂×C₃×D₅	—	3	2	no	—
163	C₂×C₃×D₅	—	6	2	no	—
164	C₂×C₃×D₅	—	6	8	no	—
165	C₂×C₃×D₅	D₁₂	1	4	yes	complemented
166	C₂×C₃×D₅	#67	1	4	yes	complemented
167	C₂×C₃×D₅	C₂²×D₃	1	2	yes	—
168	C₂×C₃×D₅	C₂²×D₃	1	2	yes	—
169	D₃×D₅	—	2	8	no	—
170	D₃×D₅	—	6	16	no	—
171	D₃×D₅	—	6	8	no	—
172	D₃×D₅	—	6	8	no	—
173	C₃×C₄×C₅	—	3	2	no	—
174	Dic₁₅	C₂²×D₃	1	2	yes	complemented
175	C₃×Dic₅	—	3	2	no	—
176	C₅×Dic₃	C₂²×D₃	1	2	yes	complemented
177	C₂⁴×C₃	—	15	1	no	—
178	C₂³×D₃	—	5	1	no	—
179	C₂³×D₃	—	15	1	no	—
180	C₂³×D₃	—	15	1	no	—
181	C₂³×D₃	—	30	1	no	—
182	C₂²×C₃×C₄	—	15	1	no	—
183	C₂×#67	—	3	1	no	—
184	C₂×#67	—	15	8	no	—
185	C₂×#67	—	15	1	no	—
186	C₂×#67	—	15	1	no	—
187	C₂×#67	—	15	1	no	—
188	C₂²×Dic₃	—	5	1	no	—
189	C₂×D₁₂	—	3	1	no	—
190	C₂×D₁₂	—	15	8	no	—
191	C₂×D₁₂	—	15	1	no	—
192	C₂×D₁₂	—	15	1	no	—
193	C₂×D₁₂	—	15	1	no	—
194	C₃²×C₅	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
195	C₂³×C₅	—	3	1	no	—
196	C₂³×C₅	—	9	1	no	—
197	C₂²×D₅	—	3	1	no	—
198	C₂²×D₅	—	3	4	no	—
199	C₂²×D₅	—	6	4	no	—
200	C₂²×D₅	—	9	1	no	—
201	C₂²×D₅	—	9	4	no	—
202	C₂²×D₅	—	18	4	no	—
203	C₂²×D₅	D₃²	1	1	yes	characteristic
204	C₅×D₄	—	9	4	no	—
205	C₂×C₄×C₅	—	3	1	no	—
206	C₂²⋊D₅	—	9	4	no	—
207	C₂²⋊D₅	—	9	4	no	—
208	C₂×Dic₅	—	3	1	no	—
209	D₂₀	—	9	4	no	—
210	C₄×D₅	—	3	4	no	—
211	C₂²×C₃²	—	5	4	no	—
212	C₂²×C₃²	—	5	2	no	—
213	C₂²×C₃²	C₂²×D₅	1	1	yes	characteristic
214	C₂×C₃⋊D₃	—	2	2	no	—
215	C₂×C₃⋊D₃	—	5	2	no	—
216	C₂×C₃⋊D₃	—	10	8	no	—
217	C₂×C₃⋊D₃	—	10	2	no	—
218	C₂×C₃⋊D₃	C₂²×D₅	1	2	yes	complemented
219	C₂×C₃×D₃	—	2	2	no	—
220	C₂×C₃×D₃	—	5	2	no	—
221	C₂×C₃×D₃	—	10	8	no	—
222	C₂×C₃×D₃	—	10	2	no	—
223	C₂×C₃×D₃	C₂²×D₅	1	2	yes	complemented
224	C₃×Dic₃	—	5	2	no	—
225	C₃×Dic₃	C₂²×D₅	1	2	yes	complemented
226	C₂²×D₄	—	45	1	no	Sylow
227	C₂×C₃×C₅	—	2	1	no	—
228	C₂×C₃×C₅	—	2	2	no	—
229	C₂×C₃×C₅	—	6	2	no	—
230	C₂×C₃×C₅	C₂×D₁₂	1	2	yes	complemented
231	C₂×C₃×C₅	C₂×#67	1	2	yes	complemented
232	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
234	D₁₅	—	2	2	no	—
235	D₁₅	—	6	4	no	—
236	D₁₅	—	6	2	no	—
237	D₁₅	—	6	2	no	—
238	C₃×D₅	—	2	4	no	—
239	C₃×D₅	—	6	2	no	—
240	C₃×D₅	C₂×D₁₂	1	4	yes	complemented
241	C₃×D₅	C₂×#67	1	4	yes	complemented
242	C₅×D₃	—	2	2	no	—
243	C₅×D₃	—	6	4	no	—
244	C₅×D₃	—	6	2	no	—
245	C₅×D₃	—	6	2	no	—
246	C₂³×C₃	—	3	1	no	—
247	C₂³×C₃	—	5	1	no	—
248	C₂³×C₃	—	5	1	no	—
249	C₂³×C₃	—	10	1	no	—
250	C₂³×C₃	—	15	4	no	—
251	C₂³×C₃	—	15	1	no	—
252	C₂³×C₃	—	30	4	no	—
253	C₂²×D₃	—	3	1	no	—
254	C₂²×D₃	—	3	1	no	—
255	C₂²×D₃	—	5	1	no	—
256	C₂²×D₃	—	5	4	no	—
257	C₂²×D₃	—	6	1	no	—
258	C₂²×D₃	—	10	4	no	—
259	C₂²×D₃	—	15	4	no	—
260	C₂²×D₃	—	15	4	no	—
261	C₂²×D₃	—	15	1	no	—
262	C₂²×D₃	—	15	1	no	—
263	C₂²×D₃	—	30	4	no	—
264	C₂²×D₃	—	30	1	no	—
265	C₂²×D₃	—	30	4	no	—
266	C₂²×D₃	—	30	4	no	—
267	C₂²×D₃	—	30	8	no	—
268	C₂²×D₃	D₃×D₅	1	1	yes	characteristic, complemented
269	C₂×C₃×C₄	—	3	1	no	—
270	C₂×C₃×C₄	—	15	4	no	—
271	C₂×C₃×C₄	—	15	1	no	—
272	#67	—	3	4	no	—
273	#67	—	15	4	no	—
274	#67	—	15	4	no	—
275	#67	—	15	4	no	—
276	C₂×Dic₃	—	5	1	no	—
277	C₂×Dic₃	—	5	4	no	—
278	C₂×Dic₃	D₃×D₅	1	1	yes	characteristic, complemented
279	D₁₂	—	3	4	no	—
280	D₁₂	—	15	4	no	—
281	D₁₂	—	15	4	no	—
282	D₁₂	—	15	4	no	—
283	C₂²×C₅	—	3	2	no	—
284	C₂²×C₅	—	6	2	no	—
285	C₂²×C₅	—	9	2	no	—
286	C₂²×C₅	—	18	2	no	—
287	C₂²×C₅	C₂×D₃²	1	1	yes	characteristic
288	C₂×D₅	—	3	2	no	—
289	C₂×D₅	—	6	2	no	—
290	C₂×D₅	—	6	8	no	—
291	C₂×D₅	—	9	2	no	—
292	C₂×D₅	—	18	2	no	—
293	C₂×D₅	—	18	8	no	—
294	C₂×D₅	#626	1	4	yes	direct product factor
295	C₂×D₅	C₂×D₃²	1	2	yes	—
296	C₄×C₅	—	3	2	no	—
297	Dic₅	—	3	2	no	—
298	C₂×C₃²	—	5	4	no	—
299	C₂×C₃²	D₄×D₅	1	2	yes	complemented
300	C₂×C₃²	C₂³×D₅	1	1	yes	characteristic
301	C₃⋊D₃	—	2	2	no	—
302	C₃⋊D₃	—	10	2	no	—
303	C₃×D₃	—	2	2	no	—
304	C₃×D₃	—	10	2	no	—
305	C₂⁴	—	15	1	no	—
306	C₂⁴	—	45	1	no	—
307	C₂×D₄	—	9	1	no	—
308	C₂×D₄	—	45	1	no	—
309	C₂×D₄	—	45	8	no	—
310	C₂×D₄	—	45	1	no	—
311	C₂×D₄	—	45	1	no	—
312	C₂²×C₄	—	15	1	no	—
313	C₃×C₅	—	2	1	no	—
314	C₃×C₅	C₂²×D₁₂	1	1	yes	characteristic, complemented
315	C₃×C₅	C₂²×#67	1	1	yes	characteristic, complemented
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	3	2	no	—
318	C₂²×C₃	—	5	4	no	—
319	C₂²×C₃	—	5	4	no	—
320	C₂²×C₃	—	5	2	no	—
321	C₂²×C₃	—	5	2	no	—
322	C₂²×C₃	—	6	2	no	—
323	C₂²×C₃	—	10	4	no	—
324	C₂²×C₃	—	10	2	no	—
325	C₂²×C₃	—	15	2	no	—
326	C₂²×C₃	—	30	8	no	—
327	C₂²×C₃	—	30	2	no	—
328	C₂²×C₃	C₂×D₃×D₅	1	1	yes	characteristic
329	C₂²×C₃	C₂×D₃×D₅	1	1	yes	characteristic
330	C₂×D₃	—	2	2	no	—
331	C₂×D₃	—	3	2	no	—
332	C₂×D₃	—	3	2	no	—
333	C₂×D₃	—	5	2	no	—
334	C₂×D₃	—	6	2	no	—
335	C₂×D₃	—	6	4	no	—
336	C₂×D₃	—	6	2	no	—
337	C₂×D₃	—	6	2	no	—
338	C₂×D₃	—	10	8	no	—
339	C₂×D₃	—	10	2	no	—
340	C₂×D₃	—	15	2	no	—
341	C₂×D₃	—	15	2	no	—
342	C₂×D₃	—	30	2	no	—
343	C₂×D₃	—	30	8	no	—
344	C₂×D₃	—	30	8	no	—
345	C₂×D₃	—	30	16	no	—
346	C₂×D₃	—	30	4	no	—
347	C₂×D₃	—	30	2	no	—
348	C₂×D₃	—	30	2	no	—
349	C₂×D₃	C₂×D₃×D₅	1	2	yes	complemented
350	C₃×C₄	—	3	2	no	—
351	C₃×C₄	—	15	2	no	—
352	Dic₃	—	5	2	no	—
353	Dic₃	C₂×D₃×D₅	1	2	yes	complemented
354	C₂×C₅	—	6	2	no	—
355	C₂×C₅	—	18	2	no	—
356	C₂×C₅	C₂×#626	1	2	yes	complemented
357	C₂×C₅	C₂²×D₃²	1	1	yes	characteristic
358	D₅	—	6	2	no	—
359	D₅	—	18	2	no	—
360	D₅	C₂×#626	1	4	yes	direct product factor
361	C₃²	C₂×D₄×D₅	1	1	yes	characteristic, complemented, Sylow
362	C₂³	—	3	1	no	—
363	C₂³	—	5	1	no	—
364	C₂³	—	9	1	no	—
365	C₂³	—	15	4	no	—
366	C₂³	—	15	1	no	—
367	C₂³	—	30	4	no	—
368	C₂³	—	45	4	no	—
369	C₂³	—	45	1	no	—
370	C₂³	—	90	4	no	—
371	D₄	—	9	4	no	—
372	D₄	—	45	4	no	—
373	D₄	—	45	4	no	—
374	D₄	—	45	4	no	—
375	C₂×C₄	—	3	1	no	—
376	C₂×C₄	—	15	4	no	—
377	C₂×C₄	—	15	1	no	—
378	C₂×C₃	—	2	2	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	5	4	no	—
381	C₂×C₃	—	5	4	no	—
382	C₂×C₃	—	6	2	no	—
383	C₂×C₃	—	10	4	no	—
384	C₂×C₃	—	30	2	no	—
385	C₂×C₃	D₅×D₁₂	1	2	yes	complemented
386	C₂×C₃	D₅×#67	1	2	yes	complemented
387	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
388	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
389	D₃	—	2	2	no	—
390	D₃	—	6	4	no	—
391	D₃	—	6	2	no	—
392	D₃	—	6	2	no	—
393	D₃	—	10	2	no	—
394	D₃	—	30	4	no	—
395	D₃	—	30	2	no	—
396	D₃	—	30	2	no	—
397	C₅	C₂²×#626	1	1	yes	characteristic, complemented, Sylow
398	C₂²	—	3	2	no	—
399	C₂²	—	5	4	no	—
400	C₂²	—	5	2	no	—
401	C₂²	—	6	2	no	—
402	C₂²	—	9	2	no	—
403	C₂²	—	15	2	no	—
404	C₂²	—	18	2	no	—
405	C₂²	—	30	8	no	—
406	C₂²	—	30	2	no	—
407	C₂²	—	45	2	no	—
408	C₂²	—	90	8	no	—
409	C₂²	—	90	2	no	—
410	C₂²	D₃²×D₅	1	1	yes	characteristic
411	C₄	—	3	2	no	—
412	C₄	—	15	2	no	—
413	C₃	—	2	1	no	—
414	C₃	C₂×D₅×D₁₂	1	1	yes	characteristic, complemented
415	C₃	C₂×D₅×#67	1	1	yes	characteristic, complemented
416	C₂	—	5	4	no	—
417	C₂	—	6	2	no	—
418	C₂	—	18	2	no	—
419	C₂	—	30	2	no	—
420	C₂	—	90	2	no	—
421	C₂	D₅×#626	1	2	yes	direct product factor
422	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×D₅×C₃⋊D₃	C₂	semidirect
2. C₂²×C₃×D₃×D₅	C₂	semidirect
3. C₂×#67156	C₂	semidirect
4. C₂×#67152	C₂	semidirect
5. C₂×#67151	C₂	semidirect
6. C₂×C₅×#626	C₂	semidirect
7. C₂×C₃×D₅×Dic₃	C₂	semidirect
8. D₅×#626	C₂	direct (N × H)
11. C₂²×C₃⋊D₁₅	C₂²	semidirect
12. C₂²×C₅×C₃⋊D₃	C₂²	semidirect
13. C₂²×C₃×D₁₅	C₂²	semidirect
14. C₂²×C₃×C₅×D₃	C₂²	semidirect
17. C₂×D₅×C₃⋊D₃	C₂²	semidirect
19. C₂×C₃×D₃×D₅	C₂²	semidirect
20. C₂×C₃×Dic₁₅	C₂²	semidirect
21. C₂×C₃×C₅×Dic₃	C₂²	semidirect
22. #67156	C₂²	semidirect
23. #67152	C₂²	semidirect
24. #67151	C₂²	semidirect
25. C₅×#626	C₂²	semidirect
26. C₃×D₅×Dic₃	C₂²	semidirect
32. C₂²×D₃×D₅	D₃	semidirect
43. C₂×D₅×Dic₃	D₃	semidirect
47. C₂×C₃⋊D₁₅	C₂³	semidirect
49. C₂×C₅×C₃⋊D₃	C₂³	semidirect
51. C₂×C₃×D₁₅	C₂³	semidirect
53. C₂×C₃×C₅×D₃	C₂³	semidirect
54. C₂×C₃²×D₅	D₄	semidirect
58. C₃×Dic₁₅	C₂³	semidirect
59. C₃×C₅×Dic₃	C₂³	semidirect
68. C₂×#626	D₅	direct (N × H)
73. C₂²×D₁₅	C₂×D₃	semidirect
77. C₂²×C₅×D₃	C₂×D₃	semidirect
91. C₂×D₃×D₅	C₂×D₃	semidirect
94. C₂×Dic₁₅	C₂×D₃	semidirect
97. C₂×C₅×Dic₃	C₂×D₃	semidirect
105. D₅×Dic₃	C₂×D₃	semidirect
108. C₂×C₃²×C₅	C₂×D₄	semidirect
114. C₃²×D₅	C₂×D₄	semidirect
127. C₂²×C₃⋊D₃	C₂×D₅	semidirect
131. C₂²×C₃×D₃	C₂×D₅	semidirect
134. C₂×C₃×Dic₃	C₂×D₅	semidirect
138. #626	C₂×D₅	direct (N × H)
151. C₂×D₁₅	C₂²×D₃	semidirect
159. C₂×C₅×D₃	C₂²×D₃	semidirect
165. C₂×C₃×D₅	D₁₂	semidirect
166. C₂×C₃×D₅	#67	semidirect
174. Dic₁₅	C₂²×D₃	semidirect
176. C₅×Dic₃	C₂²×D₃	semidirect
194. C₃²×C₅	C₂²×D₄	semidirect
218. C₂×C₃⋊D₃	C₂²×D₅	semidirect
223. C₂×C₃×D₃	C₂²×D₅	semidirect
225. C₃×Dic₃	C₂²×D₅	semidirect
230. C₂×C₃×C₅	C₂×D₁₂	semidirect
231. C₂×C₃×C₅	C₂×#67	semidirect
240. C₃×D₅	C₂×D₁₂	semidirect
241. C₃×D₅	C₂×#67	semidirect
268. C₂²×D₃	D₃×D₅	semidirect
278. C₂×Dic₃	D₃×D₅	semidirect
294. C₂×D₅	#626	direct (N × H)
299. C₂×C₃²	D₄×D₅	semidirect
314. C₃×C₅	C₂²×D₁₂	semidirect
315. C₃×C₅	C₂²×#67	semidirect
349. C₂×D₃	C₂×D₃×D₅	semidirect
353. Dic₃	C₂×D₃×D₅	semidirect
356. C₂×C₅	C₂×#626	semidirect
360. D₅	C₂×#626	direct (N × H)
361. C₃²	C₂×D₄×D₅	semidirect
385. C₂×C₃	D₅×D₁₂	semidirect
386. C₂×C₃	D₅×#67	semidirect
397. C₅	C₂²×#626	semidirect
414. C₃	C₂×D₅×D₁₂	semidirect
415. C₃	C₂×D₅×#67	semidirect
421. C₂	D₅×#626	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×D₅×C₃⋊D₃	2
C₂²×C₃×D₃×D₅	2
C₂×#67156	2
C₂×#67152	2
C₂×#67151	2
C₂×C₅×#626	2
C₂×C₃×D₅×Dic₃	2
D₅×#626	2
C₂×D₅×#67	3
C₂×D₅×D₁₂	3
C₂²×#626	5

Subgroups — C2×D5×#626 #13088992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×#626 #13088992