Subgroups — C₂×C₃×#66103 #14509955

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4149	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4095	C₂	1	2	yes	maximal, complemented
4	C₃×#66103	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃×#4065	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#4060	C₂	1	4	yes	maximal, complemented
7	C₂×C₃×D₅×D₈	C₂	1	2	yes	maximal, complemented
8	C₂²×C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#66103	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
12	C₃×#4149	—	2	8	no	—
13	C₃×#4149	C₂²	1	16	yes	complemented
14	C₂×C₃×#713	C₂²	1	4	yes	complemented
15	C₂×C₃×D₄×D₅	—	2	4	no	—
16	C₂×C₃×D₄×D₅	C₂²	1	4	yes	complemented
17	C₂×C₃×#709	—	2	2	no	—
18	C₂×C₃×#709	C₂²	1	1	yes	characteristic
19	C₂²×C₃×D₂₀	—	2	2	no	—
20	C₂²×C₃×D₂₀	C₂²	1	2	yes	complemented
21	C₃×C₅×#135	C₂²	1	8	yes	complemented
22	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×#4095	C₂²	1	16	yes	complemented
27	C₂×C₃×#688	C₂²	1	4	yes	complemented
28	C₂×C₃×#686	C₂²	1	4	yes	complemented
29	C₂×C₃×#681	C₂²	1	1	yes	characteristic, complemented
30	C₃×#4065	C₂²	1	16	yes	complemented
31	C₃×#4060	C₂²	1	32	yes	complemented
32	C₃×D₅×D₈	C₂²	1	16	yes	complemented
33	C₂×C₃×D₄₀	C₂²	1	2	yes	complemented
34	C₂×C₃×D₄₀	C₂²	1	2	yes	complemented
35	C₂×C₃×D₄₀	C₂²	1	8	yes	complemented
36	C₃×#4047	C₂²	1	8	yes	complemented
37	C₂×C₃×#676	C₂²	1	2	yes	complemented
38	C₂×C₃×C₈×D₅	C₂²	1	2	yes	complemented
39	C₂×C₃×#576	—	5	1	no	maximal, Hall
40	C₂×#4149	C₂×C₃	1	2	yes	complemented
41	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×#4095	C₂×C₃	1	2	yes	complemented
43	#66103	C₂×C₃	1	16	yes	direct product factor
44	C₂×#4065	C₂×C₃	1	2	yes	complemented
45	C₂×#4060	C₂×C₃	1	4	yes	complemented
46	C₂×D₅×D₈	C₂×C₃	1	2	yes	complemented
47	C₂²×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×#4047	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂³×C₃×D₅	—	2	2	no	—
50	C₂³×C₃×D₅	—	2	4	no	—
51	C₃×C₅×#41	—	2	4	no	—
52	C₃×C₅×#41	C₂³	1	8	yes	complemented
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	—	2	2	no	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
59	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
60	C₃×#713	—	2	8	no	—
61	C₃×#713	C₂³	1	16	yes	complemented
62	C₃×D₄×D₅	—	2	32	no	—
63	C₃×D₄×D₅	—	2	8	no	—
64	C₃×D₄×D₅	C₂³	1	16	yes	complemented
65	C₃×#709	—	2	16	no	—
66	C₃×#709	D₄	1	4	yes	—
67	C₃×#709	C₂³	1	4	yes	—
68	C₂×C₃×D₂₀	—	2	4	no	—
69	C₂×C₃×D₂₀	—	2	2	no	—
70	C₂×C₃×D₂₀	—	2	4	no	—
71	C₂×C₃×D₂₀	—	2	16	no	—
72	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
73	C₂×C₃×D₂₀	C₂³	1	4	yes	—
74	C₂×C₃×D₂₀	C₂³	1	8	yes	complemented
75	C₂×C₃×C₄×D₅	—	2	4	no	—
76	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
77	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
78	C₃×C₅×Q₁₆	C₂³	1	4	yes	complemented
79	C₃×C₅×SD₁₆	C₂³	1	8	yes	complemented
80	C₃×C₅×D₈	C₂³	1	4	yes	complemented
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	complemented
84	C₃×#688	C₂³	1	16	yes	complemented
85	C₃×#686	C₂³	1	16	yes	complemented
86	C₃×#681	C₂³	1	4	yes	complemented
87	C₂×C₃×#168	C₂³	1	2	yes	—
88	C₃×D₄₀	C₂³	1	8	yes	complemented
89	C₃×D₄₀	C₂³	1	8	yes	complemented
90	C₃×#676	C₂³	1	8	yes	complemented
91	C₃×C₈×D₅	C₂³	1	8	yes	complemented
92	C₂×C₃×H(5,𝔽₂)	—	5	2	no	—
93	C₃×#576	—	5	16	no	—
94	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
95	C₂×C₃×AGL(1,ℤ/8)	—	5	4	no	—
96	C₂×C₃×#135	—	5	2	no	—
97	C₂×C₃×#135	D₅	1	1	yes	characteristic, complemented
98	C₂²×C₃×D₈	—	5	2	no	—
99	C₂²×C₃×D₈	—	5	1	no	—
100	C₂×C₃×#131	—	5	1	no	—
101	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
102	#4149	—	2	8	no	—
103	#4149	C₂²×C₃	1	16	yes	complemented
104	C₂×#713	C₂²×C₃	1	4	yes	complemented
105	C₂×D₄×D₅	—	2	4	no	—
106	C₂×D₄×D₅	C₂²×C₃	1	4	yes	complemented
107	C₂×#709	—	2	2	no	—
108	C₂×#709	C₂²×C₃	1	1	yes	characteristic
109	C₂²×D₂₀	—	2	2	no	—
110	C₂²×D₂₀	C₂²×C₃	1	2	yes	complemented
111	C₅×#135	C₂²×C₃	1	8	yes	complemented
112	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
114	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
116	#4095	C₂²×C₃	1	16	yes	complemented
117	C₂×#688	C₂²×C₃	1	4	yes	complemented
118	C₂×#686	C₂²×C₃	1	4	yes	complemented
119	C₂×#681	C₂²×C₃	1	1	yes	characteristic, complemented
120	#4065	C₂²×C₃	1	16	yes	complemented
121	#4060	C₂²×C₃	1	32	yes	complemented
122	D₅×D₈	C₂²×C₃	1	16	yes	complemented
123	C₂×D₄₀	C₂²×C₃	1	2	yes	complemented
124	C₂×D₄₀	C₂²×C₃	1	2	yes	complemented
125	C₂×D₄₀	C₂²×C₃	1	8	yes	complemented
126	#4047	C₂²×C₃	1	8	yes	complemented
127	C₂×#676	C₂²×C₃	1	2	yes	complemented
128	C₂×C₈×D₅	C₂²×C₃	1	2	yes	complemented
129	C₂×#576	—	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	—	2	4	no	—
133	C₂²×C₃×D₅	—	2	8	no	—
134	C₂²×C₃×D₅	—	2	16	no	—
135	C₂²×C₃×D₅	—	8	8	no	—
136	C₂²×C₃×D₅	—	8	4	no	—
137	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	C₂⁴	1	4	yes	—
140	C₃×C₅×D₄	—	2	8	no	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₃×C₅×D₄	C₂⁴	1	4	yes	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	8	no	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
149	C₃×C₂²⋊D₅	—	2	16	no	—
150	C₃×C₂²⋊D₅	C₂×D₄	1	8	yes	—
151	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
152	C₃×D₂₀	—	2	16	no	—
153	C₃×D₂₀	—	2	8	no	—
154	C₃×D₂₀	—	2	4	no	—
155	C₃×D₂₀	C₂×D₄	1	4	yes	—
156	C₃×D₂₀	C₂⁴	1	8	yes	—
157	C₃×C₄×D₅	—	2	16	no	—
158	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
159	C₃×C₄×D₅	C₂⁴	1	4	yes	—
160	C₃×Dic₁₀	C₂×D₄	1	4	yes	—
161	C₃×C₅×C₈	C₂⁴	1	2	yes	—
162	C₃×C₅×C₈	C₂⁴	1	2	yes	—
163	C₃×#168	C₂⁴	1	4	yes	—
164	C₃×H(5,𝔽₂)	—	5	16	no	—
165	C₃×H(5,𝔽₂)	—	10	8	no	—
166	C₂×C₃×#41	—	5	1	no	—
167	C₂×C₃×#41	—	5	4	no	—
168	C₂×C₃×#41	—	10	2	no	—
169	C₂×C₃×#41	C₂×D₅	1	2	yes	complemented
170	C₂²×C₃×D₄	—	5	4	no	—
171	C₂²×C₃×D₄	—	5	2	no	—
172	C₂²×C₃×D₄	—	10	2	no	—
173	C₂²×C₃×D₄	—	10	4	no	—
174	C₃×AGL(1,ℤ/8)	—	5	16	no	—
175	C₃×AGL(1,ℤ/8)	—	5	32	no	—
176	C₃×#135	—	5	16	no	—
177	C₃×#135	C₂×D₅	1	8	yes	complemented
178	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
179	C₂×C₃×SD₁₆	—	5	4	no	—
180	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
181	C₂×C₃×D₈	—	5	4	no	—
182	C₂×C₃×D₈	—	5	16	no	—
183	C₂×C₃×D₈	—	5	2	no	—
184	C₂×C₃×D₈	—	5	2	no	—
185	C₂×C₃×D₈	—	5	8	no	—
186	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
187	C₃×#131	—	5	8	no	—
188	C₂×C₃×M₁₆	—	5	1	no	—
189	C₂×C₃×M₁₆	—	5	2	no	—
190	C₂²×C₃×C₈	—	5	2	no	—
191	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
192	C₂³×D₅	—	2	2	no	—
193	C₂³×D₅	—	2	4	no	—
194	C₅×#41	—	2	4	no	—
195	C₅×#41	C₂³×C₃	1	8	yes	complemented
196	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
197	C₂×C₅×D₄	—	2	2	no	—
198	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
199	C₂²×C₄×C₅	—	2	2	no	—
200	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₂²⋊D₅	—	2	4	no	—
202	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
203	#713	—	2	8	no	—
204	#713	C₂³×C₃	1	16	yes	complemented
205	D₄×D₅	—	2	32	no	—
206	D₄×D₅	—	2	8	no	—
207	D₄×D₅	C₂³×C₃	1	16	yes	complemented
208	#709	—	2	16	no	—
209	#709	C₃×D₄	1	4	yes	—
210	#709	C₂³×C₃	1	4	yes	—
211	C₂×D₂₀	—	2	4	no	—
212	C₂×D₂₀	—	2	2	no	—
213	C₂×D₂₀	—	2	4	no	—
214	C₂×D₂₀	—	2	16	no	—
215	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
216	C₂×D₂₀	C₂³×C₃	1	4	yes	—
217	C₂×D₂₀	C₂³×C₃	1	8	yes	complemented
218	C₂×C₄×D₅	—	2	4	no	—
219	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
220	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
221	C₅×Q₁₆	C₂³×C₃	1	4	yes	complemented
222	C₅×SD₁₆	C₂³×C₃	1	8	yes	complemented
223	C₅×D₈	C₂³×C₃	1	4	yes	complemented
224	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
225	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
226	C₂×C₅×C₈	C₂³×C₃	1	4	yes	complemented
227	#688	C₂³×C₃	1	16	yes	complemented
228	#686	C₂³×C₃	1	16	yes	complemented
229	#681	C₂³×C₃	1	4	yes	complemented
230	C₂×#168	C₂³×C₃	1	2	yes	—
231	D₄₀	C₂³×C₃	1	8	yes	complemented
232	D₄₀	C₂³×C₃	1	8	yes	complemented
233	#676	C₂³×C₃	1	8	yes	complemented
234	C₈×D₅	C₂³×C₃	1	8	yes	complemented
235	C₂×H(5,𝔽₂)	—	5	2	no	—
236	#576	—	5	16	no	—
237	C₂×AGL(1,ℤ/8)	—	5	2	no	—
238	C₂×AGL(1,ℤ/8)	—	5	4	no	—
239	C₂×#135	—	5	2	no	—
240	C₂×#135	C₃×D₅	1	1	yes	characteristic, complemented
241	C₂²×D₈	—	5	2	no	—
242	C₂²×D₈	—	5	1	no	—
243	C₂×#131	—	5	1	no	—
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	—	2	4	no	—
246	C₂²×C₃×C₅	—	4	4	no	—
247	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
248	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₃×D₅	—	2	4	no	—
250	C₂×C₃×D₅	—	2	8	no	—
251	C₂×C₃×D₅	—	4	8	no	—
252	C₂×C₃×D₅	—	8	16	no	—
253	C₂×C₃×D₅	—	8	8	no	—
254	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
255	C₃×C₄×C₅	—	2	4	no	—
256	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
257	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
258	C₃×C₄×C₅	C₂⁵	1	1	yes	characteristic
259	C₃×Dic₅	C₂²×D₄	1	4	yes	—
260	C₂⁴×C₃	—	10	4	no	—
261	C₂⁴×C₃	—	10	2	no	—
262	C₃×#41	—	2	4	no	—
263	C₃×#41	—	5	4	no	—
264	C₃×#41	—	5	4	no	—
265	C₃×#41	—	5	16	no	—
266	C₃×#41	—	10	16	no	—
267	C₃×#41	—	10	8	no	—
268	C₃×#41	C₂²×D₅	1	8	yes	complemented
269	C₂×C₃×Q₈	—	5	1	no	—
270	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
271	C₂×C₃×D₄	—	2	2	no	—
272	C₂×C₃×D₄	—	5	2	no	—
273	C₂×C₃×D₄	—	5	16	no	—
274	C₂×C₃×D₄	—	5	1	no	—
275	C₂×C₃×D₄	—	5	4	no	—
276	C₂×C₃×D₄	—	5	8	no	—
277	C₂×C₃×D₄	—	10	16	no	—
278	C₂×C₃×D₄	—	10	4	no	—
279	C₂×C₃×D₄	—	10	8	no	—
280	C₂×C₃×D₄	—	10	4	no	—
281	C₂×C₃×D₄	—	10	32	no	—
282	C₂×C₃×D₄	—	10	2	no	—
283	C₂×C₃×D₄	—	10	4	no	—
284	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
285	C₂²×C₃×C₄	—	2	2	no	—
286	C₂²×C₃×C₄	—	5	2	no	—
287	C₂²×C₃×C₄	—	10	4	no	—
288	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
289	C₃×Q₁₆	C₂²×D₅	1	4	yes	complemented
290	C₃×SD₁₆	—	5	16	no	—
291	C₃×SD₁₆	C₂²×D₅	1	8	yes	complemented
292	C₃×D₈	—	5	16	no	—
293	C₃×D₈	—	5	8	no	—
294	C₃×D₈	—	5	8	no	—
295	C₃×D₈	C₂²×D₅	1	4	yes	complemented
296	C₃×M₁₆	—	5	4	no	—
297	C₃×M₁₆	—	5	8	no	—
298	C₂×C₃×C₈	—	5	2	no	—
299	C₂×C₃×C₈	—	5	8	no	—
300	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
301	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
302	C₂×C₃×C₈	C₂²×D₅	1	4	yes	complemented
303	C₂³×C₅	—	2	2	no	—
304	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
305	C₂²×D₅	—	2	4	no	—
306	C₂²×D₅	—	2	8	no	—
307	C₂²×D₅	—	2	16	no	—
308	C₂²×D₅	—	8	8	no	—
309	C₂²×D₅	—	8	4	no	—
310	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
311	C₅×Q₈	—	2	2	no	—
312	C₅×Q₈	C₂⁴×C₃	1	4	yes	—
313	C₅×D₄	—	2	8	no	—
314	C₅×D₄	—	2	2	no	—
315	C₅×D₄	C₂⁴×C₃	1	4	yes	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	8	no	—
318	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
320	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
322	C₂²⋊D₅	—	2	16	no	—
323	C₂²⋊D₅	C₂×C₃×D₄	1	8	yes	—
324	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
325	D₂₀	—	2	16	no	—
326	D₂₀	—	2	8	no	—
327	D₂₀	—	2	4	no	—
328	D₂₀	C₂×C₃×D₄	1	4	yes	—
329	D₂₀	C₂⁴×C₃	1	8	yes	—
330	C₄×D₅	—	2	16	no	—
331	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
332	C₄×D₅	C₂⁴×C₃	1	4	yes	—
333	Dic₁₀	C₂×C₃×D₄	1	4	yes	—
334	C₅×C₈	C₂⁴×C₃	1	2	yes	—
335	C₅×C₈	C₂⁴×C₃	1	2	yes	—
336	#168	C₂⁴×C₃	1	4	yes	—
337	H(5,𝔽₂)	—	5	16	no	—
338	H(5,𝔽₂)	—	10	8	no	—
339	C₂×#41	—	5	1	no	—
340	C₂×#41	—	5	4	no	—
341	C₂×#41	—	10	2	no	—
342	C₂×#41	C₂×C₃×D₅	1	2	yes	complemented
343	C₂²×D₄	—	5	4	no	—
344	C₂²×D₄	—	5	2	no	—
345	C₂²×D₄	—	10	2	no	—
346	C₂²×D₄	—	10	4	no	—
347	AGL(1,ℤ/8)	—	5	16	no	—
348	AGL(1,ℤ/8)	—	5	32	no	—
349	#135	—	5	16	no	—
350	#135	C₂×C₃×D₅	1	8	yes	complemented
351	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
352	C₂×SD₁₆	—	5	4	no	—
353	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
354	C₂×D₈	—	5	4	no	—
355	C₂×D₈	—	5	16	no	—
356	C₂×D₈	—	5	2	no	—
357	C₂×D₈	—	5	2	no	—
358	C₂×D₈	—	5	8	no	—
359	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
360	#131	—	5	8	no	—
361	C₂×M₁₆	—	5	1	no	—
362	C₂×M₁₆	—	5	2	no	—
363	C₂²×C₈	—	5	2	no	—
364	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
365	C₂×C₃×C₅	—	2	2	no	—
366	C₂×C₃×C₅	—	4	4	no	—
367	C₂×C₃×C₅	#576	1	2	yes	complemented
368	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
369	C₃×D₅	—	2	4	no	—
370	C₃×D₅	—	4	8	no	—
371	C₂³×C₃	—	2	2	no	—
372	C₂³×C₃	—	5	2	no	—
373	C₂³×C₃	—	10	16	no	—
374	C₂³×C₃	—	10	4	no	—
375	C₂³×C₃	—	10	8	no	—
376	C₂³×C₃	—	40	4	no	—
377	C₂³×C₃	—	40	8	no	—
378	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
379	C₃×Q₈	—	2	2	no	—
380	C₃×Q₈	—	5	4	no	—
381	C₃×Q₈	C₂³×D₅	1	4	yes	—
382	C₃×D₄	—	2	8	no	—
383	C₃×D₄	—	2	2	no	—
384	C₃×D₄	—	5	8	no	—
385	C₃×D₄	—	5	4	no	—
386	C₃×D₄	—	5	8	no	—
387	C₃×D₄	—	10	16	no	—
388	C₃×D₄	—	10	16	no	—
389	C₃×D₄	—	10	8	no	—
390	C₃×D₄	—	10	4	no	—
391	C₃×D₄	C₂³×D₅	1	4	yes	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	8	no	—
394	C₂×C₃×C₄	—	5	2	no	—
395	C₂×C₃×C₄	—	5	4	no	—
396	C₂×C₃×C₄	—	5	4	no	—
397	C₂×C₃×C₄	—	10	16	no	—
398	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
399	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
401	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
402	C₃×C₈	—	5	4	no	—
403	C₃×C₈	C₂³×D₅	1	2	yes	—
404	C₃×C₈	C₂³×D₅	1	2	yes	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	2	4	no	—
407	C₂²×C₅	—	4	4	no	—
408	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
409	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
410	C₂×D₅	—	2	4	no	—
411	C₂×D₅	—	2	8	no	—
412	C₂×D₅	—	4	8	no	—
413	C₂×D₅	—	8	16	no	—
414	C₂×D₅	—	8	8	no	—
415	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
416	C₄×C₅	—	2	4	no	—
417	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
418	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
419	C₄×C₅	C₂⁵×C₃	1	1	yes	characteristic
420	Dic₅	C₂²×C₃×D₄	1	4	yes	—
421	C₂⁴	—	10	4	no	—
422	C₂⁴	—	10	2	no	—
423	#41	—	2	4	no	—
424	#41	—	5	4	no	—
425	#41	—	5	4	no	—
426	#41	—	5	16	no	—
427	#41	—	10	16	no	—
428	#41	—	10	8	no	—
429	#41	C₂²×C₃×D₅	1	8	yes	complemented
430	C₂×Q₈	—	5	1	no	—
431	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	5	2	no	—
434	C₂×D₄	—	5	16	no	—
435	C₂×D₄	—	5	1	no	—
436	C₂×D₄	—	5	4	no	—
437	C₂×D₄	—	5	8	no	—
438	C₂×D₄	—	10	16	no	—
439	C₂×D₄	—	10	4	no	—
440	C₂×D₄	—	10	8	no	—
441	C₂×D₄	—	10	4	no	—
442	C₂×D₄	—	10	32	no	—
443	C₂×D₄	—	10	2	no	—
444	C₂×D₄	—	10	4	no	—
445	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	5	2	no	—
448	C₂²×C₄	—	10	4	no	—
449	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
450	Q₁₆	C₂²×C₃×D₅	1	4	yes	complemented
451	SD₁₆	—	5	16	no	—
452	SD₁₆	C₂²×C₃×D₅	1	8	yes	complemented
453	D₈	—	5	16	no	—
454	D₈	—	5	8	no	—
455	D₈	—	5	8	no	—
456	D₈	C₂²×C₃×D₅	1	4	yes	complemented
457	M₁₆	—	5	4	no	—
458	M₁₆	—	5	8	no	—
459	C₂×C₈	—	5	2	no	—
460	C₂×C₈	—	5	8	no	—
461	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
462	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
463	C₂×C₈	C₂²×C₃×D₅	1	4	yes	complemented
464	C₃×C₅	C₂×#576	1	1	yes	characteristic, complemented, Hall
465	C₂²×C₃	—	2	2	no	—
466	C₂²×C₃	—	2	4	no	—
467	C₂²×C₃	—	4	4	no	—
468	C₂²×C₃	—	5	4	no	—
469	C₂²×C₃	—	10	4	no	—
470	C₂²×C₃	—	10	8	no	—
471	C₂²×C₃	—	20	8	no	—
472	C₂²×C₃	—	40	8	no	—
473	C₂²×C₃	—	40	16	no	—
474	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
475	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
476	C₃×C₄	—	2	4	no	—
477	C₃×C₄	—	5	4	no	—
478	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
479	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
480	C₃×C₄	C₂⁴×D₅	1	1	yes	characteristic
481	C₂×C₅	—	2	2	no	—
482	C₂×C₅	—	4	4	no	—
483	C₂×C₅	C₃×#576	1	2	yes	complemented
484	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
485	D₅	—	2	4	no	—
486	D₅	—	4	8	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	5	2	no	—
489	C₂³	—	10	16	no	—
490	C₂³	—	10	4	no	—
491	C₂³	—	10	8	no	—
492	C₂³	—	40	4	no	—
493	C₂³	—	40	8	no	—
494	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
495	Q₈	—	2	2	no	—
496	Q₈	—	5	4	no	—
497	Q₈	C₂³×C₃×D₅	1	4	yes	—
498	D₄	—	2	8	no	—
499	D₄	—	2	2	no	—
500	D₄	—	5	8	no	—
501	D₄	—	5	4	no	—
502	D₄	—	5	8	no	—
503	D₄	—	10	16	no	—
504	D₄	—	10	16	no	—
505	D₄	—	10	8	no	—
506	D₄	—	10	4	no	—
507	D₄	C₂³×C₃×D₅	1	4	yes	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	5	2	no	—
511	C₂×C₄	—	5	4	no	—
512	C₂×C₄	—	5	4	no	—
513	C₂×C₄	—	10	16	no	—
514	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
515	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
516	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
517	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
518	C₈	—	5	4	no	—
519	C₈	C₂³×C₃×D₅	1	2	yes	—
520	C₈	C₂³×C₃×D₅	1	2	yes	—
521	C₂×C₃	—	2	2	no	—
522	C₂×C₃	—	4	4	no	—
523	C₂×C₃	—	10	4	no	—
524	C₂×C₃	—	20	8	no	—
525	C₂×C₃	#66103	1	2	yes	direct product factor
526	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
527	C₅	C₂×C₃×#576	1	1	yes	characteristic, complemented, Sylow
528	C₂²	—	2	2	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	5	4	no	—
532	C₂²	—	10	4	no	—
533	C₂²	—	10	8	no	—
534	C₂²	—	20	8	no	—
535	C₂²	—	40	8	no	—
536	C₂²	—	40	16	no	—
537	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
538	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
539	C₄	—	2	4	no	—
540	C₄	—	5	4	no	—
541	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
542	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
543	C₄	C₂⁴×C₃×D₅	1	1	yes	characteristic
544	C₃	C₂×#66103	1	1	yes	characteristic, direct product factor, Sylow
545	C₂	—	2	2	no	—
546	C₂	—	4	4	no	—
547	C₂	—	10	4	no	—
548	C₂	—	20	8	no	—
549	C₂	C₃×#66103	1	2	yes	direct product factor
550	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×#576
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×#4149	C₂	semidirect
2. C₂×C₃×C₅×#135	C₂	semidirect
3. C₂×C₃×#4095	C₂	semidirect
4. C₃×#66103	C₂	direct (N × H)
5. C₂×C₃×#4065	C₂	semidirect
6. C₂×C₃×#4060	C₂	semidirect
7. C₂×C₃×D₅×D₈	C₂	semidirect
8. C₂²×C₃×D₄₀	C₂	semidirect
9. C₂×C₃×#4047	C₂	semidirect
10. C₂×#66103	C₃	direct (N × H)
11. C₂×C₃×C₅×#41	C₂²	semidirect
13. C₃×#4149	C₂²	semidirect
14. C₂×C₃×#713	C₂²	semidirect
16. C₂×C₃×D₄×D₅	C₂²	semidirect
20. C₂²×C₃×D₂₀	C₂²	semidirect
21. C₃×C₅×#135	C₂²	semidirect
22. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
23. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
24. C₂×C₃×C₅×D₈	C₂²	semidirect
25. C₂²×C₃×C₅×C₈	C₂²	semidirect
26. C₃×#4095	C₂²	semidirect
27. C₂×C₃×#688	C₂²	semidirect
28. C₂×C₃×#686	C₂²	semidirect
29. C₂×C₃×#681	C₂²	semidirect
30. C₃×#4065	C₂²	semidirect
31. C₃×#4060	C₂²	semidirect
32. C₃×D₅×D₈	C₂²	semidirect
33. C₂×C₃×D₄₀	C₂²	semidirect
34. C₂×C₃×D₄₀	C₂²	semidirect
35. C₂×C₃×D₄₀	C₂²	semidirect
36. C₃×#4047	C₂²	semidirect
37. C₂×C₃×#676	C₂²	semidirect
38. C₂×C₃×C₈×D₅	C₂²	semidirect
40. C₂×#4149	C₂×C₃	semidirect
41. C₂×C₅×#135	C₂×C₃	semidirect
42. C₂×#4095	C₂×C₃	semidirect
43. #66103	C₂×C₃	direct (N × H)
44. C₂×#4065	C₂×C₃	semidirect
45. C₂×#4060	C₂×C₃	semidirect
46. C₂×D₅×D₈	C₂×C₃	semidirect
47. C₂²×D₄₀	C₂×C₃	semidirect
48. C₂×#4047	C₂×C₃	semidirect
52. C₃×C₅×#41	C₂³	semidirect
61. C₃×#713	C₂³	semidirect
64. C₃×D₄×D₅	C₂³	semidirect
74. C₂×C₃×D₂₀	C₂³	semidirect
78. C₃×C₅×Q₁₆	C₂³	semidirect
79. C₃×C₅×SD₁₆	C₂³	semidirect
80. C₃×C₅×D₈	C₂³	semidirect
83. C₂×C₃×C₅×C₈	C₂³	semidirect
84. C₃×#688	C₂³	semidirect
85. C₃×#686	C₂³	semidirect
86. C₃×#681	C₂³	semidirect
88. C₃×D₄₀	C₂³	semidirect
89. C₃×D₄₀	C₂³	semidirect
90. C₃×#676	C₂³	semidirect
91. C₃×C₈×D₅	C₂³	semidirect
97. C₂×C₃×#135	D₅	semidirect
101. C₂×C₅×#41	C₂²×C₃	semidirect
103. #4149	C₂²×C₃	semidirect
104. C₂×#713	C₂²×C₃	semidirect
106. C₂×D₄×D₅	C₂²×C₃	semidirect
110. C₂²×D₂₀	C₂²×C₃	semidirect
111. C₅×#135	C₂²×C₃	semidirect
112. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
113. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
114. C₂×C₅×D₈	C₂²×C₃	semidirect
115. C₂²×C₅×C₈	C₂²×C₃	semidirect
116. #4095	C₂²×C₃	semidirect
117. C₂×#688	C₂²×C₃	semidirect
118. C₂×#686	C₂²×C₃	semidirect
119. C₂×#681	C₂²×C₃	semidirect
120. #4065	C₂²×C₃	semidirect
121. #4060	C₂²×C₃	semidirect
122. D₅×D₈	C₂²×C₃	semidirect
123. C₂×D₄₀	C₂²×C₃	semidirect
124. C₂×D₄₀	C₂²×C₃	semidirect
125. C₂×D₄₀	C₂²×C₃	semidirect
126. #4047	C₂²×C₃	semidirect
127. C₂×#676	C₂²×C₃	semidirect
128. C₂×C₈×D₅	C₂²×C₃	semidirect
169. C₂×C₃×#41	C₂×D₅	semidirect
177. C₃×#135	C₂×D₅	semidirect
178. C₂×C₃×Q₁₆	C₂×D₅	semidirect
180. C₂×C₃×SD₁₆	C₂×D₅	semidirect
186. C₂×C₃×D₈	C₂×D₅	semidirect
191. C₂²×C₃×C₈	C₂×D₅	semidirect
195. C₅×#41	C₂³×C₃	semidirect
204. #713	C₂³×C₃	semidirect
207. D₄×D₅	C₂³×C₃	semidirect
217. C₂×D₂₀	C₂³×C₃	semidirect
221. C₅×Q₁₆	C₂³×C₃	semidirect
222. C₅×SD₁₆	C₂³×C₃	semidirect
223. C₅×D₈	C₂³×C₃	semidirect
226. C₂×C₅×C₈	C₂³×C₃	semidirect
227. #688	C₂³×C₃	semidirect
228. #686	C₂³×C₃	semidirect
229. #681	C₂³×C₃	semidirect
231. D₄₀	C₂³×C₃	semidirect
232. D₄₀	C₂³×C₃	semidirect
233. #676	C₂³×C₃	semidirect
234. C₈×D₅	C₂³×C₃	semidirect
240. C₂×#135	C₃×D₅	semidirect
268. C₃×#41	C₂²×D₅	semidirect
289. C₃×Q₁₆	C₂²×D₅	semidirect
291. C₃×SD₁₆	C₂²×D₅	semidirect
295. C₃×D₈	C₂²×D₅	semidirect
302. C₂×C₃×C₈	C₂²×D₅	semidirect
342. C₂×#41	C₂×C₃×D₅	semidirect
350. #135	C₂×C₃×D₅	semidirect
351. C₂×Q₁₆	C₂×C₃×D₅	semidirect
353. C₂×SD₁₆	C₂×C₃×D₅	semidirect
359. C₂×D₈	C₂×C₃×D₅	semidirect
364. C₂²×C₈	C₂×C₃×D₅	semidirect
367. C₂×C₃×C₅	#576	semidirect
429. #41	C₂²×C₃×D₅	semidirect
450. Q₁₆	C₂²×C₃×D₅	semidirect
452. SD₁₆	C₂²×C₃×D₅	semidirect
456. D₈	C₂²×C₃×D₅	semidirect
463. C₂×C₈	C₂²×C₃×D₅	semidirect
464. C₃×C₅	C₂×#576	semidirect
483. C₂×C₅	C₃×#576	semidirect
525. C₂×C₃	#66103	direct (N × H)
527. C₅	C₂×C₃×#576	semidirect
544. C₃	C₂×#66103	direct (N × H)
549. C₂	C₃×#66103	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×#4149	2
C₂×C₃×C₅×#135	2
C₂×C₃×#4095	2
C₃×#66103	2
C₂×C₃×#4065	2
C₂×C₃×#4060	2
C₂×C₃×D₅×D₈	2
C₂²×C₃×D₄₀	2
C₂×C₃×#4047	2
C₂×#66103	3
C₂×C₃×#576	5

Subgroups — C2×C3×#66103 #14509955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66103 #14509955