Subgroups — C₂×C₃×#65335 #14423236

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#688	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65335	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#3941	C₂	1	2	yes	maximal, complemented
7	C₂×#65335	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₃×D₅	—	2	1	no	—
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×D₂₀	—	2	1	no	—
12	C₂²×C₃×D₂₀	—	2	2	no	—
13	C₂²×C₃×D₂₀	—	2	8	no	—
14	C₂²×C₃×D₂₀	C₂²	1	4	yes	—
15	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
16	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
17	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
18	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
21	C₂×C₃×#688	—	2	8	no	—
22	C₂×C₃×#688	C₂²	1	8	yes	complemented
23	C₂²×C₃×#168	C₂²	1	2	yes	complemented
24	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
25	C₃×#3941	C₂²	1	8	yes	complemented
26	C₂×C₃×#450	—	5	1	no	maximal, Hall
27	C₂³×D₂₀	C₂×C₃	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
29	C₂²×#688	C₂×C₃	1	2	yes	complemented
30	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
31	#65335	C₂×C₃	1	8	yes	direct product factor
32	C₂×#3941	C₂×C₃	1	2	yes	complemented
33	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
34	C₂³×C₃×D₅	—	2	8	no	—
35	C₂³×C₃×D₅	—	2	4	no	—
36	C₂³×C₃×D₅	—	2	2	no	—
37	C₂³×C₃×D₅	—	4	4	no	—
38	C₂³×C₃×D₅	—	4	4	no	—
39	C₂×C₃×C₅×Q₈	—	2	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	4	no	—
41	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	complemented
42	C₂²×C₃×C₄×C₅	—	2	4	no	—
43	C₂²×C₃×C₄×C₅	—	2	1	no	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₃×D₂₀	—	2	8	no	—
50	C₂×C₃×D₂₀	—	2	16	no	—
51	C₂×C₃×D₂₀	—	2	4	no	—
52	C₂×C₃×D₂₀	—	2	2	no	—
53	C₂×C₃×D₂₀	—	2	4	no	—
54	C₂×C₃×D₂₀	—	2	16	no	—
55	C₂×C₃×D₂₀	D₄	1	8	yes	—
56	C₂×C₃×D₂₀	C₂³	1	4	yes	—
57	C₃×C₅×C₄⋊C₄	—	2	4	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	complemented
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×#688	—	2	16	no	—
62	C₂×C₃×#168	—	2	4	no	—
63	C₂×C₃×#168	C₂³	1	4	yes	complemented
64	C₂³×C₃×D₄	—	5	1	no	—
65	C₂²×C₃×SD₁₆	—	5	2	no	—
66	C₂×C₃×C₂²⋊Q₈	D₅	1	1	yes	characteristic, complemented
67	C₃×#450	—	5	8	no	—
68	C₂×C₃×#102	—	5	2	no	—
69	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
70	C₂⁴×D₅	—	2	1	no	—
71	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
72	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂²×D₂₀	—	2	1	no	—
74	C₂²×D₂₀	—	2	2	no	—
75	C₂²×D₂₀	—	2	8	no	—
76	C₂²×D₂₀	C₂²×C₃	1	4	yes	—
77	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
78	C₅×C₂²⋊Q₈	—	2	2	no	—
79	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₂×#688	—	2	8	no	—
84	C₂×#688	C₂²×C₃	1	8	yes	complemented
85	C₂²×#168	C₂²×C₃	1	2	yes	complemented
86	C₂²⋊#168	C₂²×C₃	1	4	yes	complemented
87	#3941	C₂²×C₃	1	8	yes	complemented
88	C₂×#450	—	5	1	no	Sylow
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	SD₁₆	1	4	yes	complemented
92	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
93	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₃×D₅	—	2	16	no	—
95	C₂²×C₃×D₅	—	2	8	no	—
96	C₂²×C₃×D₅	—	2	4	no	—
97	C₂²×C₃×D₅	—	4	8	no	—
98	C₂²×C₃×D₅	—	4	32	no	—
99	C₂²×C₃×D₅	—	4	4	no	—
100	C₂²×C₃×D₅	—	4	8	no	—
101	C₂²×C₃×D₅	—	4	4	no	—
102	C₃×C₅×Q₈	—	2	4	no	—
103	C₃×C₅×Q₈	—	4	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	4	2	no	—
110	C₂×C₃×C₄×C₅	—	4	2	no	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₃×D₂₀	—	2	16	no	—
116	C₃×D₂₀	—	2	8	no	—
117	C₃×D₂₀	—	2	4	no	—
118	C₃×D₂₀	C₂×D₄	1	8	yes	—
119	C₃×#168	—	2	4	no	—
120	C₂⁵×C₃	—	10	1	no	—
121	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
122	C₂²×C₃×D₄	—	5	2	no	—
123	C₂²×C₃×D₄	—	5	4	no	—
124	C₂²×C₃×D₄	—	10	8	no	—
125	C₂²×C₃×D₄	—	10	2	no	—
126	C₂²×C₃×D₄	—	10	1	no	—
127	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
128	C₂×C₃×SD₁₆	—	5	8	no	—
129	C₂×C₃×SD₁₆	—	10	8	no	—
130	C₂²×C₃×C₈	—	5	2	no	—
131	C₃×C₂²⋊Q₈	—	2	2	no	—
132	C₃×C₂²⋊Q₈	C₂×D₅	1	4	yes	complemented
133	C₂×C₃×C₄⋊C₄	—	2	1	no	—
134	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
135	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
136	C₃×#102	—	5	8	no	—
137	C₃×C₂²⋊C₈	—	5	4	no	—
138	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
139	C₂³×D₅	—	2	8	no	—
140	C₂³×D₅	—	2	4	no	—
141	C₂³×D₅	—	2	2	no	—
142	C₂³×D₅	—	4	4	no	—
143	C₂³×D₅	—	4	4	no	—
144	C₂×C₅×Q₈	—	2	1	no	—
145	C₂×C₅×Q₈	—	2	4	no	—
146	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	complemented
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
153	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
154	C₂×D₂₀	—	2	8	no	—
155	C₂×D₂₀	—	2	16	no	—
156	C₂×D₂₀	—	2	4	no	—
157	C₂×D₂₀	—	2	4	no	—
158	C₂×D₂₀	—	2	2	no	—
159	C₂×D₂₀	—	2	16	no	—
160	C₂×D₂₀	C₃×D₄	1	8	yes	—
161	C₂×D₂₀	C₂³×C₃	1	4	yes	—
162	C₅×C₄⋊C₄	—	2	4	no	—
163	C₅×C₄⋊C₄	—	2	1	no	—
164	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	complemented
165	C₅×C₂²⋊C₄	—	2	4	no	—
166	#688	—	2	16	no	—
167	C₂×#168	—	2	4	no	—
168	C₂×#168	C₂³×C₃	1	4	yes	complemented
169	C₂³×D₄	—	5	1	no	—
170	C₂²×SD₁₆	—	5	2	no	—
171	C₂×C₂²⋊Q₈	C₃×D₅	1	1	yes	characteristic, complemented
172	#450	—	5	8	no	—
173	C₂×#102	—	5	2	no	—
174	C₂×C₂²⋊C₈	—	5	1	no	—
175	C₂²×C₃×C₅	—	2	2	no	—
176	C₂²×C₃×C₅	—	2	2	no	—
177	C₂²×C₃×C₅	—	2	8	no	—
178	C₂²×C₃×C₅	#120	1	2	yes	—
179	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
180	C₂²×C₃×C₅	C₂×SD₁₆	1	4	yes	complemented
181	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
182	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₃×D₅	—	2	8	no	—
184	C₂×C₃×D₅	—	4	32	no	—
185	C₂×C₃×D₅	—	4	4	no	—
186	C₂×C₃×D₅	—	4	4	no	—
187	C₂×C₃×D₅	—	4	16	no	—
188	C₃×C₄×C₅	—	2	2	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	#120	1	2	yes	—
192	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
193	C₂⁴×C₃	—	10	8	no	—
194	C₂⁴×C₃	—	10	4	no	—
195	C₂⁴×C₃	—	10	2	no	—
196	C₂⁴×C₃	—	20	4	no	—
197	C₂⁴×C₃	—	20	4	no	—
198	C₂⁴×C₃	C₂²⋊D₅	1	1	yes	characteristic
199	C₂×C₃×Q₈	—	2	1	no	—
200	C₂×C₃×Q₈	—	2	4	no	—
201	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	complemented
202	C₂×C₃×D₄	—	5	8	no	—
203	C₂×C₃×D₄	—	5	4	no	—
204	C₂×C₃×D₄	—	10	16	no	—
205	C₂×C₃×D₄	—	10	8	no	—
206	C₂×C₃×D₄	—	10	16	no	—
207	C₂×C₃×D₄	—	10	4	no	—
208	C₂×C₃×D₄	—	10	4	no	—
209	C₂×C₃×D₄	—	10	2	no	—
210	C₂²×C₃×C₄	—	2	4	no	—
211	C₂²×C₃×C₄	—	2	1	no	—
212	C₂²×C₃×C₄	—	2	1	no	—
213	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
214	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
216	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
217	C₃×SD₁₆	—	10	16	no	—
218	C₂×C₃×C₈	—	5	4	no	—
219	C₂×C₃×C₈	—	10	4	no	—
220	C₃×C₄⋊C₄	—	2	4	no	—
221	C₃×C₄⋊C₄	—	2	1	no	—
222	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	complemented
223	C₃×C₂²⋊C₄	—	2	4	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	C₃×SD₁₆	1	4	yes	complemented
227	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
228	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
229	C₂²×D₅	—	2	16	no	—
230	C₂²×D₅	—	2	8	no	—
231	C₂²×D₅	—	2	4	no	—
232	C₂²×D₅	—	4	8	no	—
233	C₂²×D₅	—	4	32	no	—
234	C₂²×D₅	—	4	4	no	—
235	C₂²×D₅	—	4	8	no	—
236	C₂²×D₅	—	4	4	no	—
237	C₅×Q₈	—	2	4	no	—
238	C₅×Q₈	—	4	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	2	4	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	4	2	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
247	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
248	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
250	D₂₀	—	2	16	no	—
251	D₂₀	—	2	8	no	—
252	D₂₀	—	2	4	no	—
253	D₂₀	C₂×C₃×D₄	1	8	yes	—
254	#168	—	2	4	no	—
255	C₂⁵	—	10	1	no	—
256	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
257	C₂²×D₄	—	5	2	no	—
258	C₂²×D₄	—	5	4	no	—
259	C₂²×D₄	—	10	8	no	—
260	C₂²×D₄	—	10	1	no	—
261	C₂²×D₄	—	10	2	no	—
262	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
263	C₂×SD₁₆	—	5	8	no	—
264	C₂×SD₁₆	—	10	8	no	—
265	C₂²×C₈	—	5	2	no	—
266	C₂²⋊Q₈	—	2	2	no	—
267	C₂²⋊Q₈	C₂×C₃×D₅	1	4	yes	complemented
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	#102	—	5	8	no	—
272	C₂²⋊C₈	—	5	4	no	—
273	C₂×C₃×C₅	—	2	4	no	—
274	C₂×C₃×C₅	#450	1	4	yes	complemented
275	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
278	C₃×D₅	—	4	8	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	—	10	16	no	—
282	C₂³×C₃	—	10	4	no	—
283	C₂³×C₃	—	10	8	no	—
284	C₂³×C₃	—	20	32	no	—
285	C₂³×C₃	—	20	8	no	—
286	C₂³×C₃	—	20	4	no	—
287	C₂³×C₃	—	20	8	no	—
288	C₂³×C₃	—	20	4	no	—
289	C₂³×C₃	#688	1	4	yes	complemented
290	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
291	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
292	C₃×Q₈	—	2	4	no	—
293	C₃×Q₈	—	4	2	no	—
294	C₃×D₄	—	5	8	no	—
295	C₃×D₄	—	10	16	no	—
296	C₃×D₄	—	10	4	no	—
297	C₃×D₄	—	10	8	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	4	no	—
300	C₂×C₃×C₄	—	2	4	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	4	2	no	—
304	C₂×C₃×C₄	—	4	2	no	—
305	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
306	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
307	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
309	C₃×C₈	—	10	4	no	—
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	—	2	8	no	—
312	C₂²×C₅	—	2	2	no	—
313	C₂²×C₅	C₃×#120	1	2	yes	—
314	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
315	C₂²×C₅	C₂×C₃×SD₁₆	1	4	yes	complemented
316	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
317	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
318	C₂×D₅	—	2	8	no	—
319	C₂×D₅	—	4	32	no	—
320	C₂×D₅	—	4	4	no	—
321	C₂×D₅	—	4	4	no	—
322	C₂×D₅	—	4	16	no	—
323	C₄×C₅	—	2	2	no	—
324	C₄×C₅	—	4	2	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	C₃×#120	1	2	yes	—
327	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
328	C₂⁴	—	10	8	no	—
329	C₂⁴	—	10	4	no	—
330	C₂⁴	—	10	2	no	—
331	C₂⁴	—	20	4	no	—
332	C₂⁴	—	20	4	no	—
333	C₂⁴	C₃×C₂²⋊D₅	1	1	yes	characteristic
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	complemented
337	C₂×D₄	—	5	8	no	—
338	C₂×D₄	—	5	4	no	—
339	C₂×D₄	—	10	16	no	—
340	C₂×D₄	—	10	8	no	—
341	C₂×D₄	—	10	16	no	—
342	C₂×D₄	—	10	4	no	—
343	C₂×D₄	—	10	4	no	—
344	C₂×D₄	—	10	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
349	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
350	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
351	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
352	SD₁₆	—	10	16	no	—
353	C₂×C₈	—	5	4	no	—
354	C₂×C₈	—	10	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	complemented
358	C₂²⋊C₄	—	2	4	no	—
359	C₃×C₅	C₂×#450	1	1	yes	characteristic, complemented, Hall
360	C₂²×C₃	—	2	8	no	—
361	C₂²×C₃	—	2	2	no	—
362	C₂²×C₃	—	2	2	no	—
363	C₂²×C₃	—	10	8	no	—
364	C₂²×C₃	—	20	32	no	—
365	C₂²×C₃	—	20	16	no	—
366	C₂²×C₃	—	20	4	no	—
367	C₂²×C₃	—	20	4	no	—
368	C₂²×C₃	#4083	1	2	yes	—
369	C₂²×C₃	C₂×#688	1	2	yes	—
370	C₂²×C₃	C₂×#688	1	4	yes	complemented
371	C₂²×C₃	#4095	1	2	yes	—
372	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
373	C₃×C₄	—	2	2	no	—
374	C₃×C₄	—	4	2	no	—
375	C₃×C₄	—	4	2	no	—
376	C₃×C₄	#4083	1	2	yes	—
377	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
378	C₂×C₅	—	2	4	no	—
379	C₂×C₅	C₃×#450	1	4	yes	complemented
380	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
381	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
382	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
383	D₅	—	4	8	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	10	16	no	—
387	C₂³	—	10	8	no	—
388	C₂³	—	10	4	no	—
389	C₂³	—	20	32	no	—
390	C₂³	—	20	8	no	—
391	C₂³	—	20	4	no	—
392	C₂³	—	20	8	no	—
393	C₂³	—	20	4	no	—
394	C₂³	C₃×#688	1	4	yes	complemented
395	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
396	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
397	Q₈	—	2	4	no	—
398	Q₈	—	4	2	no	—
399	D₄	—	5	8	no	—
400	D₄	—	10	16	no	—
401	D₄	—	10	8	no	—
402	D₄	—	10	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
411	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
412	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
413	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
414	C₈	—	10	4	no	—
415	C₂×C₃	—	2	4	no	—
416	C₂×C₃	—	20	8	no	—
417	C₂×C₃	#65335	1	4	yes	direct product factor
418	C₂×C₃	C₂×#4083	1	1	yes	characteristic
419	C₂×C₃	C₂²×#688	1	1	yes	characteristic
420	C₂×C₃	C₂×#4095	1	1	yes	characteristic
421	C₅	C₂×C₃×#450	1	1	yes	characteristic, complemented, Sylow
422	C₂²	—	2	2	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	10	8	no	—
426	C₂²	—	20	32	no	—
427	C₂²	—	20	4	no	—
428	C₂²	—	20	16	no	—
429	C₂²	—	20	4	no	—
430	C₂²	C₃×#4083	1	2	yes	—
431	C₂²	C₂×C₃×#688	1	2	yes	—
432	C₂²	C₂×C₃×#688	1	4	yes	complemented
433	C₂²	C₃×#4095	1	2	yes	—
434	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	C₃×#4083	1	2	yes	—
439	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
440	C₃	C₂×#65335	1	1	yes	characteristic, direct product factor, Sylow
441	C₂	—	2	4	no	—
442	C₂	—	20	8	no	—
443	C₂	C₃×#65335	1	4	yes	direct product factor
444	C₂	C₂×C₃×#4083	1	1	yes	characteristic
445	C₂	C₂²×C₃×#688	1	1	yes	characteristic
446	C₂	C₂×C₃×#4095	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×C₂²⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×C₃×D₂₀	C₂
hypercenter	C₂×C₃×C₂²⋊Q₈	D₅
hypocenter	C₅	C₂×C₃×#450
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂×C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₂²×C₃×#688	C₂	semidirect
4. C₂×C₃×C₂²⋊#168	C₂	semidirect
5. C₃×#65335	C₂	direct (N × H)
6. C₂×C₃×#3941	C₂	semidirect
7. C₂×#65335	C₃	direct (N × H)
9. C₂²×C₃×C₅×Q₈	C₂²	semidirect
17. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
19. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
22. C₂×C₃×#688	C₂²	semidirect
23. C₂²×C₃×#168	C₂²	semidirect
24. C₃×C₂²⋊#168	C₂²	semidirect
25. C₃×#3941	C₂²	semidirect
28. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
29. C₂²×#688	C₂×C₃	semidirect
30. C₂×C₂²⋊#168	C₂×C₃	semidirect
31. #65335	C₂×C₃	direct (N × H)
32. C₂×#3941	C₂×C₃	semidirect
41. C₂×C₃×C₅×Q₈	C₂³	semidirect
59. C₃×C₅×C₄⋊C₄	C₂³	semidirect
63. C₂×C₃×#168	C₂³	semidirect
66. C₂×C₃×C₂²⋊Q₈	D₅	semidirect
71. C₂²×C₅×Q₈	C₂²×C₃	semidirect
79. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
81. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
84. C₂×#688	C₂²×C₃	semidirect
85. C₂²×#168	C₂²×C₃	semidirect
86. C₂²⋊#168	C₂²×C₃	semidirect
87. #3941	C₂²×C₃	semidirect
91. C₂³×C₃×C₅	SD₁₆	semidirect
121. C₂²×C₃×Q₈	C₂×D₅	semidirect
132. C₃×C₂²⋊Q₈	C₂×D₅	semidirect
134. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
146. C₂×C₅×Q₈	C₂³×C₃	semidirect
164. C₅×C₄⋊C₄	C₂³×C₃	semidirect
168. C₂×#168	C₂³×C₃	semidirect
171. C₂×C₂²⋊Q₈	C₃×D₅	semidirect
180. C₂²×C₃×C₅	C₂×SD₁₆	semidirect
201. C₂×C₃×Q₈	C₂²×D₅	semidirect
222. C₃×C₄⋊C₄	C₂²×D₅	semidirect
226. C₂³×C₅	C₃×SD₁₆	semidirect
256. C₂²×Q₈	C₂×C₃×D₅	semidirect
267. C₂²⋊Q₈	C₂×C₃×D₅	semidirect
269. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
274. C₂×C₃×C₅	#450	semidirect
289. C₂³×C₃	#688	semidirect
315. C₂²×C₅	C₂×C₃×SD₁₆	semidirect
336. C₂×Q₈	C₂²×C₃×D₅	semidirect
357. C₄⋊C₄	C₂²×C₃×D₅	semidirect
359. C₃×C₅	C₂×#450	semidirect
370. C₂²×C₃	C₂×#688	semidirect
379. C₂×C₅	C₃×#450	semidirect
394. C₂³	C₃×#688	semidirect
417. C₂×C₃	#65335	direct (N × H)
421. C₅	C₂×C₃×#450	semidirect
432. C₂²	C₂×C₃×#688	semidirect
440. C₃	C₂×#65335	direct (N × H)
443. C₂	C₃×#65335	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×D₂₀	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂²×C₃×#688	2
C₂×C₃×C₂²⋊#168	2
C₃×#65335	2
C₂×C₃×#3941	2
C₂×#65335	3
C₂×C₃×#450	5

Subgroups — C2×C3×#65335 #14423236

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65335 #14423236