Subgroups — C₂×C₃×#66105 #14510125

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4150	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4097	C₂	1	2	yes	maximal, complemented
4	C₃×#66105	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×D₅×Q₁₆	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#4061	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×#4058	C₂	1	2	yes	maximal, complemented
8	C₂²×C₃×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#66105	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₃×#4150	—	2	8	no	—
13	C₃×#4150	C₂²	1	16	yes	complemented
14	C₂×C₃×Q₈×D₅	C₂²	1	4	yes	—
15	C₂×C₃×#711	—	2	4	no	—
16	C₂×C₃×#711	C₂²	1	4	yes	—
17	C₂×C₃×#709	—	2	2	no	—
18	C₂×C₃×#709	C₂²	1	1	yes	characteristic
19	C₂²×C₃×Dic₁₀	—	2	2	no	—
20	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
21	C₃×C₅×#135	C₂²	1	8	yes	complemented
22	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₃×#4097	C₂²	1	16	yes	complemented
27	C₂×C₃×#689	C₂²	1	4	yes	—
28	C₂×C₃×#687	C₂²	1	4	yes	—
29	C₂×C₃×#681	C₂²	1	1	yes	characteristic
30	C₃×D₅×Q₁₆	C₂²	1	16	yes	complemented
31	C₃×#4061	C₂²	1	32	yes	complemented
32	C₃×#4058	C₂²	1	16	yes	complemented
33	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
34	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
35	C₂×C₃×Dic₂₀	C₂²	1	8	yes	complemented
36	C₃×#4047	C₂²	1	8	yes	complemented
37	C₂×C₃×#676	C₂²	1	2	yes	—
38	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
39	C₂×C₃×#578	—	5	1	no	maximal, Hall
40	C₂×#4150	C₂×C₃	1	2	yes	complemented
41	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×#4097	C₂×C₃	1	2	yes	complemented
43	#66105	C₂×C₃	1	16	yes	direct product factor
44	C₂×D₅×Q₁₆	C₂×C₃	1	2	yes	complemented
45	C₂×#4061	C₂×C₃	1	4	yes	complemented
46	C₂×#4058	C₂×C₃	1	2	yes	complemented
47	C₂²×Dic₂₀	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#4047	C₂×C₃	1	1	yes	characteristic, complemented
49	C₃×C₅×#41	—	2	4	no	—
50	C₃×C₅×#41	C₂³	1	8	yes	—
51	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
57	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
58	C₂²×C₃×Dic₅	—	2	2	no	—
59	C₂²×C₃×Dic₅	—	2	4	no	—
60	C₃×Q₈×D₅	—	2	8	no	—
61	C₃×Q₈×D₅	C₂³	1	16	yes	—
62	C₃×#711	—	2	32	no	—
63	C₃×#711	—	2	8	no	—
64	C₃×#711	C₂³	1	16	yes	—
65	C₃×#709	—	2	16	no	—
66	C₃×#709	D₄	1	4	yes	—
67	C₃×#709	C₂³	1	4	yes	—
68	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₅	—	2	4	no	—
70	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
71	C₂×C₃×Dic₁₀	—	2	2	no	—
72	C₂×C₃×Dic₁₀	—	2	4	no	—
73	C₂×C₃×Dic₁₀	—	2	4	no	—
74	C₂×C₃×Dic₁₀	—	2	16	no	—
75	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
76	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
77	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
78	C₃×C₅×Q₁₆	C₂³	1	4	yes	—
79	C₃×C₅×SD₁₆	C₂³	1	8	yes	—
80	C₃×C₅×D₈	C₂³	1	4	yes	—
81	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
84	C₃×#689	C₂³	1	16	yes	—
85	C₃×#687	C₂³	1	16	yes	—
86	C₃×#681	C₂³	1	4	yes	—
87	C₂×C₃×#168	C₂³	1	2	yes	—
88	C₃×Dic₂₀	C₂³	1	8	yes	—
89	C₃×Dic₂₀	C₂³	1	8	yes	—
90	C₃×#676	C₂³	1	8	yes	—
91	C₃×C₈×D₅	C₂³	1	8	yes	—
92	C₂×C₃×2₋¹⁺⁴	—	5	2	no	—
93	C₃×#578	—	5	16	no	—
94	C₂×C₃×#137	—	5	2	no	—
95	C₂×C₃×#137	—	5	4	no	—
96	C₂×C₃×#135	—	5	2	no	—
97	C₂×C₃×#135	D₅	1	1	yes	characteristic, complemented
98	C₂²×C₃×Q₁₆	—	5	2	no	—
99	C₂²×C₃×Q₁₆	—	5	1	no	—
100	C₂×C₃×#131	—	5	1	no	—
101	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
102	#4150	—	2	8	no	—
103	#4150	C₂²×C₃	1	16	yes	complemented
104	C₂×Q₈×D₅	C₂²×C₃	1	4	yes	—
105	C₂×#711	—	2	4	no	—
106	C₂×#711	C₂²×C₃	1	4	yes	—
107	C₂×#709	—	2	2	no	—
108	C₂×#709	C₂²×C₃	1	1	yes	characteristic
109	C₂²×Dic₁₀	—	2	2	no	—
110	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
111	C₅×#135	C₂²×C₃	1	8	yes	complemented
112	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
114	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
116	#4097	C₂²×C₃	1	16	yes	complemented
117	C₂×#689	C₂²×C₃	1	4	yes	—
118	C₂×#687	C₂²×C₃	1	4	yes	—
119	C₂×#681	C₂²×C₃	1	1	yes	characteristic
120	D₅×Q₁₆	C₂²×C₃	1	16	yes	complemented
121	#4061	C₂²×C₃	1	32	yes	complemented
122	#4058	C₂²×C₃	1	16	yes	complemented
123	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
124	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
125	C₂×Dic₂₀	C₂²×C₃	1	8	yes	complemented
126	#4047	C₂²×C₃	1	8	yes	complemented
127	C₂×#676	C₂²×C₃	1	2	yes	—
128	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
129	C₂×#578	—	5	1	no	Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	C₂⁴	1	4	yes	—
135	C₃×C₅×D₄	—	2	8	no	—
136	C₃×C₅×D₄	—	2	2	no	—
137	C₃×C₅×D₄	C₂⁴	1	4	yes	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	8	no	—
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
144	C₃×C₂²⋊D₅	—	2	16	no	—
145	C₃×C₂²⋊D₅	C₂×D₄	1	8	yes	—
146	C₂×C₃×Dic₅	—	2	4	no	—
147	C₂×C₃×Dic₅	—	2	8	no	—
148	C₂×C₃×Dic₅	—	2	16	no	—
149	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
150	C₃×D₂₀	C₂×D₄	1	4	yes	—
151	C₃×C₄×D₅	—	2	16	no	—
152	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
153	C₃×C₄×D₅	C₂⁴	1	4	yes	—
154	C₃×Dic₁₀	—	2	8	no	—
155	C₃×Dic₁₀	—	2	4	no	—
156	C₃×Dic₁₀	—	2	16	no	—
157	C₃×Dic₁₀	C₂×D₄	1	4	yes	—
158	C₃×Dic₁₀	C₂⁴	1	8	yes	—
159	C₃×C₅×C₈	C₂⁴	1	2	yes	—
160	C₃×C₅×C₈	C₂⁴	1	2	yes	—
161	C₃×#168	C₂⁴	1	4	yes	—
162	C₃×2₋¹⁺⁴	—	5	16	no	—
163	C₃×2₋¹⁺⁴	—	10	8	no	—
164	C₂×C₃×#41	—	5	1	no	—
165	C₂×C₃×#41	—	5	4	no	—
166	C₂×C₃×#41	—	10	2	no	—
167	C₂×C₃×#41	—	10	4	no	—
168	C₂×C₃×#41	C₂×D₅	1	2	yes	—
169	C₂²×C₃×Q₈	—	5	4	no	—
170	C₂²×C₃×Q₈	—	5	2	no	—
171	C₂²×C₃×Q₈	—	10	2	no	—
172	C₃×#137	—	5	16	no	—
173	C₃×#137	—	5	32	no	—
174	C₃×#135	—	5	16	no	—
175	C₃×#135	C₂×D₅	1	8	yes	complemented
176	C₂×C₃×Q₁₆	—	5	4	no	—
177	C₂×C₃×Q₁₆	—	5	16	no	—
178	C₂×C₃×Q₁₆	—	5	2	no	—
179	C₂×C₃×Q₁₆	—	5	2	no	—
180	C₂×C₃×Q₁₆	—	5	8	no	—
181	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
182	C₂×C₃×SD₁₆	—	5	4	no	—
183	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
184	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
185	C₃×#131	—	5	8	no	—
186	C₂×C₃×M₁₆	—	5	1	no	—
187	C₂×C₃×M₁₆	—	5	2	no	—
188	C₂²×C₃×C₈	—	5	2	no	—
189	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
190	C₅×#41	—	2	4	no	—
191	C₅×#41	C₂³×C₃	1	8	yes	—
192	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
193	C₂×C₅×D₄	—	2	2	no	—
194	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₂²⋊D₅	—	2	4	no	—
198	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
199	C₂²×Dic₅	—	2	2	no	—
200	C₂²×Dic₅	—	2	4	no	—
201	Q₈×D₅	—	2	8	no	—
202	Q₈×D₅	C₂³×C₃	1	16	yes	—
203	#711	—	2	32	no	—
204	#711	—	2	8	no	—
205	#711	C₂³×C₃	1	16	yes	—
206	#709	—	2	16	no	—
207	#709	C₃×D₄	1	4	yes	—
208	#709	C₂³×C₃	1	4	yes	—
209	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
210	C₂×C₄×D₅	—	2	4	no	—
211	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
212	C₂×Dic₁₀	—	2	2	no	—
213	C₂×Dic₁₀	—	2	4	no	—
214	C₂×Dic₁₀	—	2	4	no	—
215	C₂×Dic₁₀	—	2	16	no	—
216	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
217	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
218	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
219	C₅×Q₁₆	C₂³×C₃	1	4	yes	—
220	C₅×SD₁₆	C₂³×C₃	1	8	yes	—
221	C₅×D₈	C₂³×C₃	1	4	yes	—
222	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
225	#689	C₂³×C₃	1	16	yes	—
226	#687	C₂³×C₃	1	16	yes	—
227	#681	C₂³×C₃	1	4	yes	—
228	C₂×#168	C₂³×C₃	1	2	yes	—
229	Dic₂₀	C₂³×C₃	1	8	yes	—
230	Dic₂₀	C₂³×C₃	1	8	yes	—
231	#676	C₂³×C₃	1	8	yes	—
232	C₈×D₅	C₂³×C₃	1	8	yes	—
233	C₂×2₋¹⁺⁴	—	5	2	no	—
234	#578	—	5	16	no	—
235	C₂×#137	—	5	2	no	—
236	C₂×#137	—	5	4	no	—
237	C₂×#135	—	5	2	no	—
238	C₂×#135	C₃×D₅	1	1	yes	characteristic, complemented
239	C₂²×Q₁₆	—	5	2	no	—
240	C₂²×Q₁₆	—	5	1	no	—
241	C₂×#131	—	5	1	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	2	4	no	—
244	C₂²×C₃×C₅	—	4	4	no	—
245	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
246	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₃×D₅	—	2	4	no	—
248	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
249	C₃×C₄×C₅	—	2	4	no	—
250	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
251	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
253	C₃×Dic₅	—	2	8	no	—
254	C₃×Dic₅	C₂²×D₄	1	4	yes	—
255	C₃×#41	—	2	4	no	—
256	C₃×#41	—	5	4	no	—
257	C₃×#41	—	5	4	no	—
258	C₃×#41	—	5	16	no	—
259	C₃×#41	—	10	16	no	—
260	C₃×#41	—	10	8	no	—
261	C₃×#41	—	10	32	no	—
262	C₃×#41	C₂²×D₅	1	8	yes	—
263	C₂×C₃×Q₈	—	5	1	no	—
264	C₂×C₃×Q₈	—	5	16	no	—
265	C₂×C₃×Q₈	—	5	4	no	—
266	C₂×C₃×Q₈	—	5	8	no	—
267	C₂×C₃×Q₈	—	10	4	no	—
268	C₂×C₃×Q₈	—	10	16	no	—
269	C₂×C₃×Q₈	—	10	8	no	—
270	C₂×C₃×Q₈	—	10	2	no	—
271	C₂×C₃×Q₈	—	10	4	no	—
272	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
273	C₂×C₃×D₄	—	2	2	no	—
274	C₂×C₃×D₄	—	5	2	no	—
275	C₂×C₃×D₄	—	5	1	no	—
276	C₂×C₃×D₄	—	10	4	no	—
277	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
278	C₂²×C₃×C₄	—	2	2	no	—
279	C₂²×C₃×C₄	—	5	2	no	—
280	C₂²×C₃×C₄	—	10	4	no	—
281	C₂²×C₃×C₄	—	10	4	no	—
282	C₂²×C₃×C₄	—	10	2	no	—
283	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
284	C₃×Q₁₆	—	5	16	no	—
285	C₃×Q₁₆	—	5	8	no	—
286	C₃×Q₁₆	—	5	8	no	—
287	C₃×Q₁₆	C₂²×D₅	1	4	yes	—
288	C₃×SD₁₆	—	5	16	no	—
289	C₃×SD₁₆	C₂²×D₅	1	8	yes	—
290	C₃×D₈	C₂²×D₅	1	4	yes	—
291	C₃×M₁₆	—	5	4	no	—
292	C₃×M₁₆	—	5	8	no	—
293	C₂×C₃×C₈	—	5	2	no	—
294	C₂×C₃×C₈	—	5	8	no	—
295	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
296	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
297	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
298	C₂³×C₅	—	2	2	no	—
299	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
300	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
301	C₅×Q₈	—	2	2	no	—
302	C₅×Q₈	C₂⁴×C₃	1	4	yes	—
303	C₅×D₄	—	2	8	no	—
304	C₅×D₄	—	2	2	no	—
305	C₅×D₄	C₂⁴×C₃	1	4	yes	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	8	no	—
308	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
310	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
312	C₂²⋊D₅	—	2	16	no	—
313	C₂²⋊D₅	C₂×C₃×D₄	1	8	yes	—
314	C₂×Dic₅	—	2	4	no	—
315	C₂×Dic₅	—	2	8	no	—
316	C₂×Dic₅	—	2	16	no	—
317	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
318	D₂₀	C₂×C₃×D₄	1	4	yes	—
319	C₄×D₅	—	2	16	no	—
320	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
321	C₄×D₅	C₂⁴×C₃	1	4	yes	—
322	Dic₁₀	—	2	8	no	—
323	Dic₁₀	—	2	4	no	—
324	Dic₁₀	—	2	16	no	—
325	Dic₁₀	C₂×C₃×D₄	1	4	yes	—
326	Dic₁₀	C₂⁴×C₃	1	8	yes	—
327	C₅×C₈	C₂⁴×C₃	1	2	yes	—
328	C₅×C₈	C₂⁴×C₃	1	2	yes	—
329	#168	C₂⁴×C₃	1	4	yes	—
330	2₋¹⁺⁴	—	5	16	no	—
331	2₋¹⁺⁴	—	10	8	no	—
332	C₂×#41	—	5	1	no	—
333	C₂×#41	—	5	4	no	—
334	C₂×#41	—	10	2	no	—
335	C₂×#41	—	10	4	no	—
336	C₂×#41	C₂×C₃×D₅	1	2	yes	—
337	C₂²×Q₈	—	5	4	no	—
338	C₂²×Q₈	—	5	2	no	—
339	C₂²×Q₈	—	10	2	no	—
340	#137	—	5	16	no	—
341	#137	—	5	32	no	—
342	#135	—	5	16	no	—
343	#135	C₂×C₃×D₅	1	8	yes	complemented
344	C₂×Q₁₆	—	5	4	no	—
345	C₂×Q₁₆	—	5	16	no	—
346	C₂×Q₁₆	—	5	2	no	—
347	C₂×Q₁₆	—	5	2	no	—
348	C₂×Q₁₆	—	5	8	no	—
349	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
350	C₂×SD₁₆	—	5	4	no	—
351	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
352	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
353	#131	—	5	8	no	—
354	C₂×M₁₆	—	5	1	no	—
355	C₂×M₁₆	—	5	2	no	—
356	C₂²×C₈	—	5	2	no	—
357	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
358	C₂×C₃×C₅	—	2	2	no	—
359	C₂×C₃×C₅	—	4	4	no	—
360	C₂×C₃×C₅	#578	1	2	yes	complemented
361	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
362	C₃×D₅	—	2	4	no	—
363	C₂³×C₃	—	2	2	no	—
364	C₂³×C₃	—	5	2	no	—
365	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
366	C₃×Q₈	—	2	2	no	—
367	C₃×Q₈	—	5	4	no	—
368	C₃×Q₈	—	5	8	no	—
369	C₃×Q₈	—	10	16	no	—
370	C₃×Q₈	—	10	8	no	—
371	C₃×Q₈	—	10	4	no	—
372	C₃×Q₈	C₂³×D₅	1	4	yes	—
373	C₃×D₄	—	2	8	no	—
374	C₃×D₄	—	2	2	no	—
375	C₃×D₄	—	5	8	no	—
376	C₃×D₄	—	5	4	no	—
377	C₃×D₄	—	10	16	no	—
378	C₃×D₄	C₂³×D₅	1	4	yes	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	2	8	no	—
381	C₂×C₃×C₄	—	5	2	no	—
382	C₂×C₃×C₄	—	5	4	no	—
383	C₂×C₃×C₄	—	5	4	no	—
384	C₂×C₃×C₄	—	10	16	no	—
385	C₂×C₃×C₄	—	10	16	no	—
386	C₂×C₃×C₄	—	10	8	no	—
387	C₂×C₃×C₄	—	10	4	no	—
388	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
389	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
391	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
392	C₃×C₈	—	5	4	no	—
393	C₃×C₈	C₂³×D₅	1	2	yes	—
394	C₃×C₈	C₂³×D₅	1	2	yes	—
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	—	2	4	no	—
397	C₂²×C₅	—	4	4	no	—
398	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
399	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
400	C₂×D₅	—	2	4	no	—
401	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
402	C₄×C₅	—	2	4	no	—
403	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
404	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
405	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
406	Dic₅	—	2	8	no	—
407	Dic₅	C₂²×C₃×D₄	1	4	yes	—
408	#41	—	2	4	no	—
409	#41	—	5	4	no	—
410	#41	—	5	4	no	—
411	#41	—	5	16	no	—
412	#41	—	10	16	no	—
413	#41	—	10	8	no	—
414	#41	—	10	32	no	—
415	#41	C₂²×C₃×D₅	1	8	yes	—
416	C₂×Q₈	—	5	1	no	—
417	C₂×Q₈	—	5	16	no	—
418	C₂×Q₈	—	5	4	no	—
419	C₂×Q₈	—	5	8	no	—
420	C₂×Q₈	—	10	4	no	—
421	C₂×Q₈	—	10	16	no	—
422	C₂×Q₈	—	10	8	no	—
423	C₂×Q₈	—	10	2	no	—
424	C₂×Q₈	—	10	4	no	—
425	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	5	2	no	—
428	C₂×D₄	—	5	1	no	—
429	C₂×D₄	—	10	4	no	—
430	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	5	2	no	—
433	C₂²×C₄	—	10	4	no	—
434	C₂²×C₄	—	10	4	no	—
435	C₂²×C₄	—	10	2	no	—
436	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
437	Q₁₆	—	5	16	no	—
438	Q₁₆	—	5	8	no	—
439	Q₁₆	—	5	8	no	—
440	Q₁₆	C₂²×C₃×D₅	1	4	yes	—
441	SD₁₆	—	5	16	no	—
442	SD₁₆	C₂²×C₃×D₅	1	8	yes	—
443	D₈	C₂²×C₃×D₅	1	4	yes	—
444	M₁₆	—	5	4	no	—
445	M₁₆	—	5	8	no	—
446	C₂×C₈	—	5	2	no	—
447	C₂×C₈	—	5	8	no	—
448	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
449	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
450	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
451	C₃×C₅	C₂×#578	1	1	yes	characteristic, complemented, Hall
452	C₂²×C₃	—	2	2	no	—
453	C₂²×C₃	—	2	4	no	—
454	C₂²×C₃	—	4	4	no	—
455	C₂²×C₃	—	5	4	no	—
456	C₂²×C₃	—	10	4	no	—
457	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
458	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
459	C₃×C₄	—	2	4	no	—
460	C₃×C₄	—	5	4	no	—
461	C₃×C₄	—	10	8	no	—
462	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
463	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
464	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
465	C₂×C₅	—	2	2	no	—
466	C₂×C₅	—	4	4	no	—
467	C₂×C₅	C₃×#578	1	2	yes	complemented
468	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
469	D₅	—	2	4	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	5	2	no	—
472	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
473	Q₈	—	2	2	no	—
474	Q₈	—	5	4	no	—
475	Q₈	—	5	8	no	—
476	Q₈	—	10	16	no	—
477	Q₈	—	10	8	no	—
478	Q₈	—	10	4	no	—
479	Q₈	C₂³×C₃×D₅	1	4	yes	—
480	D₄	—	2	8	no	—
481	D₄	—	2	2	no	—
482	D₄	—	5	8	no	—
483	D₄	—	5	4	no	—
484	D₄	—	10	16	no	—
485	D₄	C₂³×C₃×D₅	1	4	yes	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	5	2	no	—
489	C₂×C₄	—	5	4	no	—
490	C₂×C₄	—	5	4	no	—
491	C₂×C₄	—	10	16	no	—
492	C₂×C₄	—	10	16	no	—
493	C₂×C₄	—	10	4	no	—
494	C₂×C₄	—	10	8	no	—
495	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
496	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
497	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
498	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
499	C₈	—	5	4	no	—
500	C₈	C₂³×C₃×D₅	1	2	yes	—
501	C₈	C₂³×C₃×D₅	1	2	yes	—
502	C₂×C₃	—	2	2	no	—
503	C₂×C₃	—	4	4	no	—
504	C₂×C₃	—	10	4	no	—
505	C₂×C₃	#66105	1	2	yes	direct product factor
506	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
507	C₅	C₂×C₃×#578	1	1	yes	characteristic, complemented, Sylow
508	C₂²	—	2	2	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	5	4	no	—
512	C₂²	—	10	4	no	—
513	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
514	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
515	C₄	—	2	4	no	—
516	C₄	—	5	4	no	—
517	C₄	—	10	8	no	—
518	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
519	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
520	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
521	C₃	C₂×#66105	1	1	yes	characteristic, direct product factor, Sylow
522	C₂	—	2	2	no	—
523	C₂	—	4	4	no	—
524	C₂	—	10	4	no	—
525	C₂	C₃×#66105	1	2	yes	direct product factor
526	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₄×C₅	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×#135	D₅
hypocenter	C₅	C₂×C₃×#578
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4150	C₂	semidirect
2. C₂×C₃×C₅×#135	C₂	semidirect
3. C₂×C₃×#4097	C₂	semidirect
4. C₃×#66105	C₂	direct (N × H)
5. C₂×C₃×D₅×Q₁₆	C₂	semidirect
6. C₂×C₃×#4061	C₂	semidirect
7. C₂×C₃×#4058	C₂	semidirect
8. C₂²×C₃×Dic₂₀	C₂	semidirect
9. C₂×C₃×#4047	C₂	semidirect
10. C₂×#66105	C₃	direct (N × H)
13. C₃×#4150	C₂²	semidirect
21. C₃×C₅×#135	C₂²	semidirect
26. C₃×#4097	C₂²	semidirect
30. C₃×D₅×Q₁₆	C₂²	semidirect
31. C₃×#4061	C₂²	semidirect
32. C₃×#4058	C₂²	semidirect
35. C₂×C₃×Dic₂₀	C₂²	semidirect
36. C₃×#4047	C₂²	semidirect
40. C₂×#4150	C₂×C₃	semidirect
41. C₂×C₅×#135	C₂×C₃	semidirect
42. C₂×#4097	C₂×C₃	semidirect
43. #66105	C₂×C₃	direct (N × H)
44. C₂×D₅×Q₁₆	C₂×C₃	semidirect
45. C₂×#4061	C₂×C₃	semidirect
46. C₂×#4058	C₂×C₃	semidirect
47. C₂²×Dic₂₀	C₂×C₃	semidirect
48. C₂×#4047	C₂×C₃	semidirect
97. C₂×C₃×#135	D₅	semidirect
103. #4150	C₂²×C₃	semidirect
111. C₅×#135	C₂²×C₃	semidirect
116. #4097	C₂²×C₃	semidirect
120. D₅×Q₁₆	C₂²×C₃	semidirect
121. #4061	C₂²×C₃	semidirect
122. #4058	C₂²×C₃	semidirect
125. C₂×Dic₂₀	C₂²×C₃	semidirect
126. #4047	C₂²×C₃	semidirect
175. C₃×#135	C₂×D₅	semidirect
238. C₂×#135	C₃×D₅	semidirect
343. #135	C₂×C₃×D₅	semidirect
360. C₂×C₃×C₅	#578	semidirect
451. C₃×C₅	C₂×#578	semidirect
467. C₂×C₅	C₃×#578	semidirect
505. C₂×C₃	#66105	direct (N × H)
507. C₅	C₂×C₃×#578	semidirect
521. C₃	C₂×#66105	direct (N × H)
525. C₂	C₃×#66105	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×#4150	2
C₂×C₃×C₅×#135	2
C₂×C₃×#4097	2
C₃×#66105	2
C₂×C₃×D₅×Q₁₆	2
C₂×C₃×#4061	2
C₂×C₃×#4058	2
C₂²×C₃×Dic₂₀	2
C₂×C₃×#4047	2
C₂×#66105	3
C₂×C₃×#578	5

Subgroups — C2×C3×#66105 #14510125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66105 #14510125