Subgroups — C₂×D₃×#3994 #14413284

Order 1920.

1200 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₂×D₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×#91223	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3994	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#91160	C₂	1	2	yes	maximal, complemented
6	D₃×#3994	C₂	1	8	yes	maximal, direct product factor
7	C₂²×#3994	—	3	1	no	maximal, Hall
8	C₂²×D₃×AGL(1,𝔽₅)	—	2	2	no	—
9	C₂×C₄×D₃×D₅	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
11	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
12	C₂×Dic₃⋊AGL(1,𝔽₅)	—	2	2	no	—
13	D₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
14	D₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	8	yes	—
15	C₂×C₈×D₁₅	C₄	1	1	yes	characteristic, complemented
16	C₂×C₅×D₃×C₈	C₄	1	1	yes	characteristic, complemented
17	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
18	C₂×#6648	C₄	1	1	yes	characteristic, complemented
19	C₂×D₃×#168	C₄	1	1	yes	characteristic, complemented
20	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	D₃×C₈×D₅	C₄	1	4	yes	complemented
22	D₃×C₈×D₅	C₂²	1	4	yes	—
23	#91223	C₂²	1	4	yes	complemented
24	C₃×#3994	C₂²	1	4	yes	complemented
25	#91160	C₂²	1	8	yes	complemented
26	C₂×D₃×#107	—	5	1	no	maximal, Hall
27	C₂²×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
28	C₂²×C₈×D₅	—	3	1	no	—
29	C₂×#3994	—	3	1	no	—
30	C₂×#3994	—	3	8	no	—
31	C₂×#3994	—	3	2	no	—
32	C₂×#3994	D₃	1	1	yes	characteristic, direct product factor
33	C₂²×D₃×D₅	D₄	1	1	yes	characteristic
34	C₂²×ΓL(1,𝔽₁₆)	—	2	2	no	—
35	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
36	C₂×D₃×AGL(1,𝔽₅)	—	2	8	no	—
37	C₂×D₃×AGL(1,𝔽₅)	—	4	8	no	—
38	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
41	C₂×#1200	Q₈	1	1	yes	characteristic
42	C₂×D₃×Dic₅	Q₈	1	1	yes	characteristic
43	C₂×D₅×Dic₃	D₄	1	1	yes	characteristic
44	C₄×D₃×D₅	C₂×C₄	1	2	yes	—
45	C₄×D₃×D₅	D₄	1	2	yes	—
46	C₄×D₃×D₅	Q₈	1	2	yes	—
47	C₄×D₃×D₅	C₂³	1	2	yes	—
48	C₄⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
49	C₄⋊ΓL(1,𝔽₁₆)	C₂³	1	4	yes	—
50	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
51	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	4	yes	—
52	Dic₃⋊AGL(1,𝔽₅)	—	2	8	no	—
53	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic, complemented
54	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic, complemented
55	C₈×D₁₅	C₂×C₄	1	4	yes	complemented
56	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic, complemented
57	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
58	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic, complemented
59	C₃×C₈×D₅	C₂×C₄	1	2	yes	complemented
60	C₃×C₈×D₅	C₂³	1	2	yes	—
61	#6648	C₂×C₄	1	4	yes	complemented
62	D₃×#168	C₂×C₄	1	4	yes	complemented
63	D₅×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
64	D₅×C₃⋊C₈	C₂³	1	2	yes	—
65	C₂²×D₃×C₈	—	5	1	no	—
66	C₂×D₃×C₄⋊C₄	—	5	2	no	—
67	C₂×C₃×#107	—	5	1	no	—
68	C₂×#818	—	5	1	no	—
69	C₂×#807	—	5	2	no	—
70	D₃×#107	—	5	8	no	—
71	C₂³×AGL(1,𝔽₅)	—	6	2	no	—
72	C₂²×C₄×D₅	—	3	1	no	—
73	C₂×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
74	C₂×C₄⋊AGL(1,𝔽₅)	—	3	8	no	—
75	C₂×C₄⋊AGL(1,𝔽₅)	—	6	4	no	—
76	C₂×C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
77	C₂×C₄⋊AGL(1,𝔽₅)	C₂×D₃	1	2	yes	—
78	C₂²×C₅×C₈	—	3	1	no	—
79	C₂²×#168	—	3	1	no	—
80	C₂×C₈×D₅	—	3	1	no	—
81	C₂×C₈×D₅	—	3	1	no	—
82	C₂×C₈×D₅	—	3	1	no	—
83	C₂×C₈×D₅	—	3	4	no	—
84	C₂×C₈×D₅	—	3	4	no	—
85	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
86	#3994	—	3	8	no	—
87	#3994	—	3	4	no	—
88	#3994	C₂×D₃	1	4	yes	direct product factor
89	C₂²×#107	—	15	1	no	Sylow
90	C₂²×D₁₅	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₅×D₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
93	C₂×D₃×D₅	C₄⋊C₄	1	2	yes	—
94	C₂×D₃×D₅	D₈	1	4	yes	—
95	C₂×D₃×D₅	Q₁₆	1	4	yes	—
96	C₂×D₃×D₅	C₂×D₄	1	2	yes	—
97	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
98	C₂×ΓL(1,𝔽₁₆)	—	4	4	no	—
99	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
100	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
101	D₃×AGL(1,𝔽₅)	—	4	16	no	—
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×Dic₁₅	C₄⋊C₄	1	1	yes	characteristic
104	C₄×D₁₅	C₄⋊C₄	1	2	yes	—
105	C₄×D₁₅	C₂²×C₄	1	2	yes	—
106	C₂×C₅×Dic₃	C₄⋊C₄	1	1	yes	characteristic
107	C₄×C₅×D₃	C₄⋊C₄	1	2	yes	—
108	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
109	C₂×C₃×Dic₅	C₂×Q₈	1	1	yes	characteristic
110	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
111	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
112	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
113	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
114	#1200	C₄⋊C₄	1	2	yes	—
115	#1200	C₂×Q₈	1	2	yes	—
116	D₃×Dic₅	C₄⋊C₄	1	2	yes	—
117	D₃×Dic₅	C₂×Q₈	1	2	yes	—
118	D₅×Dic₃	C₄⋊C₄	1	2	yes	—
119	D₅×Dic₃	C₂×D₄	1	2	yes	—
120	C₃×C₅×C₈	C₂²×C₄	1	2	yes	complemented
121	C₃⋊#168	C₂²×C₄	1	2	yes	complemented
122	C₃×#168	C₂²×C₄	1	2	yes	complemented
123	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	complemented
124	C₂²×C₄×D₃	—	5	1	no	—
125	C₂²×C₄×D₃	—	10	2	no	—
126	C₂²×C₃×C₈	—	5	1	no	—
127	C₂×C₃×C₄⋊C₄	—	5	2	no	—
128	C₂×C₄⋊Dic₃	—	5	2	no	—
129	C₂×Dic₃⋊C₄	—	10	2	no	—
130	C₂²×C₃⋊C₈	—	5	1	no	—
131	C₂×D₃×C₈	—	5	1	no	—
132	C₂×D₃×C₈	—	5	1	no	—
133	C₂×D₃×C₈	—	5	1	no	—
134	C₂×D₃×C₈	—	5	4	no	—
135	C₂×D₃×C₈	—	5	4	no	—
136	C₂×D₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
137	D₃×C₄⋊C₄	—	5	8	no	—
138	D₃×C₄⋊C₄	—	10	4	no	—
139	C₃×#107	—	5	4	no	—
140	#818	—	5	4	no	—
141	#807	—	5	8	no	—
142	C₂³×D₅	—	3	1	no	—
143	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
144	C₂²×AGL(1,𝔽₅)	—	6	8	no	—
145	C₂²×AGL(1,𝔽₅)	—	6	2	no	—
146	C₂²×AGL(1,𝔽₅)	—	12	8	no	—
147	C₂²×C₄×C₅	—	3	1	no	—
148	C₂²×Dic₅	—	3	1	no	—
149	C₂×C₄×D₅	—	3	1	no	—
150	C₂×C₄×D₅	—	3	1	no	—
151	C₂×C₄×D₅	—	3	1	no	—
152	C₂×C₄×D₅	—	3	2	no	—
153	C₂×C₄×D₅	—	3	2	no	—
154	C₂×C₄×D₅	—	3	2	no	—
155	C₂×C₄×D₅	—	3	2	no	—
156	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
157	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
158	C₄⋊AGL(1,𝔽₅)	—	3	4	no	—
159	C₄⋊AGL(1,𝔽₅)	—	6	8	no	—
160	C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
161	C₄⋊AGL(1,𝔽₅)	C₂²×D₃	1	4	yes	—
162	C₂×C₅×C₈	—	3	1	no	—
163	C₂×C₅×C₈	—	3	4	no	—
164	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic, complemented
165	C₂×#168	—	3	1	no	—
166	C₂×#168	—	3	4	no	—
167	C₂×#168	C₄×D₃	1	1	yes	characteristic, complemented
168	C₈×D₅	—	3	2	no	—
169	C₈×D₅	—	3	2	no	—
170	C₈×D₅	—	3	4	no	—
171	C₈×D₅	—	3	4	no	—
172	C₈×D₅	C₄×D₃	1	2	yes	complemented
173	C₈×D₅	C₂²×D₃	1	2	yes	—
174	C₂³×C₈	—	15	1	no	—
175	C₂²×C₄⋊C₄	—	15	2	no	—
176	C₂×#107	—	5	1	no	—
177	C₂×#107	—	15	8	no	—
178	C₂×#107	—	15	2	no	—
179	C₂×#107	—	15	1	no	—
180	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×D₁₅	#107	1	4	yes	complemented
182	C₂×D₁₅	C₂×C₄⋊C₄	1	2	yes	—
183	C₂×C₅×D₃	#107	1	4	yes	complemented
184	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
185	C₂×C₃×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₃×D₅	C₂×D₈	1	2	yes	—
187	C₂×C₃×D₅	C₂×Q₁₆	1	2	yes	—
188	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
189	D₃×D₅	#107	1	8	yes	complemented
190	D₃×D₅	C₂×D₈	1	4	yes	—
191	D₃×D₅	C₂×Q₁₆	1	4	yes	—
192	ΓL(1,𝔽₁₆)	—	4	4	no	—
193	C₃×AGL(1,𝔽₅)	—	4	4	no	—
194	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
196	Dic₁₅	C₂×C₄⋊C₄	1	2	yes	—
197	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₃×Dic₅	C₂²×Q₈	1	1	yes	characteristic
199	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
200	C₂³×D₃	—	5	1	no	—
201	C₂²×C₃×C₄	—	5	1	no	—
202	C₂²×C₃×C₄	—	10	2	no	—
203	C₂²×Dic₃	—	5	1	no	—
204	C₂²×Dic₃	—	10	2	no	—
205	C₂×C₄×D₃	—	5	1	no	—
206	C₂×C₄×D₃	—	5	1	no	—
207	C₂×C₄×D₃	—	5	1	no	—
208	C₂×C₄×D₃	—	5	2	no	—
209	C₂×C₄×D₃	—	5	2	no	—
210	C₂×C₄×D₃	—	5	2	no	—
211	C₂×C₄×D₃	—	5	2	no	—
212	C₂×C₄×D₃	—	10	8	no	—
213	C₂×C₄×D₃	—	20	8	no	—
214	C₂×C₄×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
215	C₂×C₃×C₈	—	5	1	no	—
216	C₂×C₃×C₈	—	5	2	no	—
217	C₂×C₃×C₈	—	5	2	no	—
218	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
219	C₃×C₄⋊C₄	—	5	4	no	—
220	C₃×C₄⋊C₄	—	10	2	no	—
221	C₄⋊Dic₃	—	5	4	no	—
222	C₄⋊Dic₃	—	10	2	no	—
223	Dic₃⋊C₄	—	10	8	no	—
224	C₂×C₃⋊C₈	—	5	1	no	—
225	C₂×C₃⋊C₈	—	5	2	no	—
226	C₂×C₃⋊C₈	—	5	2	no	—
227	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
228	D₃×C₈	—	5	4	no	—
229	D₃×C₈	—	5	4	no	—
230	D₃×C₈	—	5	4	no	—
231	D₃×C₈	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
232	C₂³×C₅	—	3	1	no	—
233	C₂²×D₅	—	3	1	no	—
234	C₂²×D₅	—	3	2	no	—
235	C₂²×D₅	—	3	4	no	—
236	C₂²×D₅	—	3	4	no	—
237	C₂²×D₅	—	3	2	no	—
238	C₂²×D₅	D₃×D₄	1	1	yes	characteristic
239	C₂×AGL(1,𝔽₅)	—	2	4	no	—
240	C₂×AGL(1,𝔽₅)	—	4	4	no	—
241	C₂×AGL(1,𝔽₅)	—	6	4	no	—
242	C₂×AGL(1,𝔽₅)	—	12	16	no	—
243	C₂×AGL(1,𝔽₅)	—	12	4	no	—
244	C₂×C₄×C₅	—	3	1	no	—
245	C₂×C₄×C₅	—	3	2	no	—
246	C₂×C₄×C₅	—	3	2	no	—
247	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
248	C₂×Dic₅	—	3	1	no	—
249	C₂×Dic₅	—	3	2	no	—
250	C₂×Dic₅	—	3	2	no	—
251	C₂×Dic₅	D₃×Q₈	1	1	yes	characteristic
252	C₄×D₅	—	3	2	no	—
253	C₄×D₅	—	3	2	no	—
254	C₄×D₅	—	3	2	no	—
255	C₄×D₅	—	3	2	no	—
256	C₄×D₅	—	3	2	no	—
257	C₄×D₅	—	3	2	no	—
258	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
259	C₄×D₅	D₃×D₄	1	1	yes	characteristic
260	C₄×D₅	D₃×Q₈	1	1	yes	characteristic
261	C₄×D₅	C₂³×D₃	1	1	yes	characteristic
262	C₅×C₈	—	3	2	no	—
263	C₅×C₈	C₂×C₄×D₃	1	2	yes	complemented
264	#168	—	3	2	no	—
265	#168	C₂×C₄×D₃	1	2	yes	complemented
266	C₂³×C₄	—	15	1	no	—
267	C₂³×C₄	—	30	2	no	—
268	C₂²×C₈	—	3	1	no	—
269	C₂²×C₈	—	5	1	no	—
270	C₂²×C₈	—	15	4	no	—
271	C₂²×C₈	—	15	1	no	—
272	C₂²×C₈	—	15	4	no	—
273	C₂²×C₈	—	15	1	no	—
274	C₂²×C₈	—	15	1	no	—
275	C₂²×C₈	—	15	1	no	—
276	C₂×C₄⋊C₄	—	5	2	no	—
277	C₂×C₄⋊C₄	—	15	8	no	—
278	C₂×C₄⋊C₄	—	15	2	no	—
279	C₂×C₄⋊C₄	—	30	4	no	—
280	C₂×C₄⋊C₄	—	30	2	no	—
281	#107	—	5	4	no	—
282	#107	—	15	8	no	—
283	#107	—	15	4	no	—
284	C₂×C₃×C₅	C₂×#107	1	2	yes	complemented
285	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
286	D₁₅	C₂×#107	1	4	yes	complemented
287	C₃×D₅	C₂×#107	1	2	yes	complemented
288	C₃×D₅	C₂²×D₈	1	1	yes	characteristic
289	C₃×D₅	C₂²×Q₁₆	1	1	yes	characteristic
290	C₅×D₃	C₂×#107	1	4	yes	complemented
291	C₂³×C₃	—	5	1	no	—
292	C₂²×D₃	—	5	1	no	—
293	C₂²×D₃	—	5	2	no	—
294	C₂²×D₃	—	5	2	no	—
295	C₂²×D₃	—	5	4	no	—
296	C₂²×D₃	—	5	4	no	—
297	C₂²×D₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
298	C₂×C₃×C₄	—	5	1	no	—
299	C₂×C₃×C₄	—	5	1	no	—
300	C₂×C₃×C₄	—	5	1	no	—
301	C₂×C₃×C₄	—	5	1	no	—
302	C₂×C₃×C₄	—	5	1	no	—
303	C₂×C₃×C₄	—	10	4	no	—
304	C₂×C₃×C₄	—	20	4	no	—
305	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
306	C₂×Dic₃	—	5	1	no	—
307	C₂×Dic₃	—	5	2	no	—
308	C₂×Dic₃	—	5	2	no	—
309	C₂×Dic₃	—	10	4	no	—
310	C₂×Dic₃	—	20	4	no	—
311	C₂×Dic₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
312	C₄×D₃	—	5	2	no	—
313	C₄×D₃	—	5	2	no	—
314	C₄×D₃	—	5	2	no	—
315	C₄×D₃	—	5	2	no	—
316	C₄×D₃	—	5	2	no	—
317	C₄×D₃	—	5	2	no	—
318	C₄×D₃	—	20	16	no	—
319	C₄×D₃	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
320	C₄×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
321	C₃×C₈	—	5	2	no	—
322	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
323	C₃⋊C₈	—	5	2	no	—
324	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
325	C₂²×C₅	—	3	4	no	—
326	C₂²×C₅	—	3	2	no	—
327	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
328	C₂×D₅	—	3	4	no	—
329	C₂×D₅	—	3	2	no	—
330	C₂×D₅	—	3	8	no	—
331	C₂×D₅	—	3	4	no	—
332	C₂×D₅	—	3	4	no	—
333	C₂×D₅	D₃×C₄⋊C₄	1	1	yes	characteristic
334	C₂×D₅	D₃×D₈	1	2	yes	—
335	C₂×D₅	D₃×Q₁₆	1	2	yes	—
336	C₂×D₅	C₂×D₃×D₄	1	1	yes	characteristic
337	AGL(1,𝔽₅)	—	4	4	no	—
338	AGL(1,𝔽₅)	—	12	4	no	—
339	C₄×C₅	—	3	2	no	—
340	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
341	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
342	Dic₅	—	3	2	no	—
343	Dic₅	D₃×C₄⋊C₄	1	1	yes	characteristic
344	Dic₅	C₂×D₃×Q₈	1	1	yes	characteristic
345	C₂⁴	—	15	1	no	—
346	C₂²×C₄	—	3	1	no	—
347	C₂²×C₄	—	5	1	no	—
348	C₂²×C₄	—	10	2	no	—
349	C₂²×C₄	—	15	2	no	—
350	C₂²×C₄	—	15	2	no	—
351	C₂²×C₄	—	15	2	no	—
352	C₂²×C₄	—	15	1	no	—
353	C₂²×C₄	—	15	2	no	—
354	C₂²×C₄	—	15	1	no	—
355	C₂²×C₄	—	15	1	no	—
356	C₂²×C₄	—	15	1	no	—
357	C₂²×C₄	—	30	8	no	—
358	C₂²×C₄	—	30	2	no	—
359	C₂²×C₄	—	60	8	no	—
360	C₂×C₈	—	3	1	no	—
361	C₂×C₈	—	3	4	no	—
362	C₂×C₈	—	5	1	no	—
363	C₂×C₈	—	5	2	no	—
364	C₂×C₈	—	5	2	no	—
365	C₂×C₈	—	15	4	no	—
366	C₂×C₈	—	15	2	no	—
367	C₂×C₈	—	15	2	no	—
368	C₂×C₈	—	15	4	no	—
369	C₂×C₈	—	15	1	no	—
370	C₂×C₈	—	15	4	no	—
371	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
372	C₄⋊C₄	—	5	4	no	—
373	C₄⋊C₄	—	10	2	no	—
374	C₄⋊C₄	—	15	4	no	—
375	C₄⋊C₄	—	30	2	no	—
376	C₄⋊C₄	—	30	8	no	—
377	C₃×C₅	C₂²×#107	1	1	yes	characteristic, complemented, Hall
378	C₂²×C₃	—	5	2	no	—
379	C₂²×C₃	—	5	2	no	—
380	C₂²×C₃	—	5	1	no	—
381	C₂²×C₃	—	5	1	no	—
382	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₂×D₃	—	5	4	no	—
384	C₂×D₃	—	5	2	no	—
385	C₂×D₃	—	5	8	no	—
386	C₂×D₃	—	5	4	no	—
387	C₂×D₃	—	5	4	no	—
388	C₂×D₃	#3994	1	4	yes	direct product factor
389	C₂×D₃	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
390	C₃×C₄	—	5	1	no	—
391	C₃×C₄	—	5	1	no	—
392	C₃×C₄	—	20	4	no	—
393	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
394	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
395	Dic₃	—	5	2	no	—
396	Dic₃	—	20	4	no	—
397	Dic₃	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
398	C₂×C₅	—	3	4	no	—
399	C₂×C₅	D₃×#107	1	2	yes	complemented
400	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
401	D₅	—	3	4	no	—
402	D₅	D₃×#107	1	2	yes	complemented
403	D₅	C₂×D₃×D₈	1	1	yes	characteristic
404	D₅	C₂×D₃×Q₁₆	1	1	yes	characteristic
405	C₂³	—	3	1	no	—
406	C₂³	—	5	1	no	—
407	C₂³	—	15	2	no	—
408	C₂³	—	15	2	no	—
409	C₂³	—	15	4	no	—
410	C₂³	—	15	4	no	—
411	C₂³	—	15	1	no	—
412	C₂×C₄	—	3	1	no	—
413	C₂×C₄	—	3	2	no	—
414	C₂×C₄	—	3	2	no	—
415	C₂×C₄	—	5	1	no	—
416	C₂×C₄	—	5	1	no	—
417	C₂×C₄	—	5	1	no	—
418	C₂×C₄	—	5	1	no	—
419	C₂×C₄	—	5	1	no	—
420	C₂×C₄	—	10	4	no	—
421	C₂×C₄	—	15	2	no	—
422	C₂×C₄	—	15	2	no	—
423	C₂×C₄	—	15	2	no	—
424	C₂×C₄	—	15	2	no	—
425	C₂×C₄	—	15	2	no	—
426	C₂×C₄	—	15	2	no	—
427	C₂×C₄	—	15	1	no	—
428	C₂×C₄	—	15	2	no	—
429	C₂×C₄	—	15	2	no	—
430	C₂×C₄	—	20	4	no	—
431	C₂×C₄	—	30	4	no	—
432	C₂×C₄	—	60	16	no	—
433	C₂×C₄	—	60	4	no	—
434	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
435	C₈	—	3	2	no	—
436	C₈	—	5	2	no	—
437	C₈	—	15	2	no	—
438	C₈	C₂×D₃×AGL(1,𝔽₅)	1	2	yes	complemented
439	C₂×C₃	—	5	1	no	—
440	C₂×C₃	—	5	1	no	—
441	C₂×C₃	—	5	2	no	—
442	C₂×C₃	C₂×#3994	1	2	yes	complemented
443	C₂×C₃	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
444	D₃	—	5	4	no	—
445	D₃	C₂×#3994	1	4	yes	direct product factor
446	C₅	C₂×D₃×#107	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	3	2	no	—
448	C₂²	—	3	4	no	—
449	C₂²	—	5	1	no	—
450	C₂²	—	5	1	no	—
451	C₂²	—	5	2	no	—
452	C₂²	—	5	2	no	—
453	C₂²	—	15	4	no	—
454	C₂²	—	15	8	no	—
455	C₂²	—	15	4	no	—
456	C₂²	—	15	2	no	—
457	C₂²	—	15	4	no	—
458	C₂²	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
459	C₄	—	3	2	no	—
460	C₄	—	5	1	no	—
461	C₄	—	5	1	no	—
462	C₄	—	15	2	no	—
463	C₄	—	20	4	no	—
464	C₄	—	60	4	no	—
465	C₄	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
466	C₄	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
467	C₃	C₂²×#3994	1	1	yes	characteristic, complemented, Sylow
468	C₂	—	3	4	no	—
469	C₂	—	5	1	no	—
470	C₂	—	5	2	no	—
471	C₂	—	5	1	no	—
472	C₂	—	15	4	no	—
473	C₂	D₃×#3994	1	2	yes	direct product factor
474	C₂	C₂×D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃×C₄⋊AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂²×D₃×D₅	D₄
cosocle	C₃×C₄×D₅	C₂⁴
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂²×#107
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#91223	C₂	semidirect
4. C₂×C₃×#3994	C₂	semidirect
5. C₂×#91160	C₂	semidirect
6. D₃×#3994	C₂	direct (N × H)
15. C₂×C₈×D₁₅	C₄	semidirect
16. C₂×C₅×D₃×C₈	C₄	semidirect
18. C₂×#6648	C₄	semidirect
19. C₂×D₃×#168	C₄	semidirect
21. D₃×C₈×D₅	C₄	semidirect
23. #91223	C₂²	semidirect
24. C₃×#3994	C₂²	semidirect
25. #91160	C₂²	semidirect
32. C₂×#3994	D₃	direct (N × H)
53. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
54. C₂×C₃⋊#168	C₂×C₄	semidirect
55. C₈×D₁₅	C₂×C₄	semidirect
56. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
57. C₅×D₃×C₈	C₂×C₄	semidirect
58. C₂×C₃×#168	C₂×C₄	semidirect
59. C₃×C₈×D₅	C₂×C₄	semidirect
61. #6648	C₂×C₄	semidirect
62. D₃×#168	C₂×C₄	semidirect
63. D₅×C₃⋊C₈	C₂×C₄	semidirect
88. #3994	C₂×D₃	direct (N × H)
120. C₃×C₅×C₈	C₂²×C₄	semidirect
121. C₃⋊#168	C₂²×C₄	semidirect
122. C₃×#168	C₂²×C₄	semidirect
123. C₅×C₃⋊C₈	C₂²×C₄	semidirect
136. C₂×D₃×C₈	AGL(1,𝔽₅)	semidirect
164. C₂×C₅×C₈	C₄×D₃	semidirect
167. C₂×#168	C₄×D₃	semidirect
172. C₈×D₅	C₄×D₃	semidirect
181. C₂×D₁₅	#107	semidirect
183. C₂×C₅×D₃	#107	semidirect
189. D₃×D₅	#107	semidirect
218. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
227. C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	semidirect
231. D₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
263. C₅×C₈	C₂×C₄×D₃	semidirect
265. #168	C₂×C₄×D₃	semidirect
284. C₂×C₃×C₅	C₂×#107	semidirect
286. D₁₅	C₂×#107	semidirect
287. C₃×D₅	C₂×#107	semidirect
290. C₅×D₃	C₂×#107	semidirect
322. C₃×C₈	C₂²×AGL(1,𝔽₅)	semidirect
324. C₃⋊C₈	C₂²×AGL(1,𝔽₅)	semidirect
371. C₂×C₈	D₃×AGL(1,𝔽₅)	semidirect
377. C₃×C₅	C₂²×#107	semidirect
388. C₂×D₃	#3994	direct (N × H)
399. C₂×C₅	D₃×#107	semidirect
402. D₅	D₃×#107	semidirect
438. C₈	C₂×D₃×AGL(1,𝔽₅)	semidirect
442. C₂×C₃	C₂×#3994	semidirect
445. D₃	C₂×#3994	direct (N × H)
446. C₅	C₂×D₃×#107	semidirect
467. C₃	C₂²×#3994	semidirect
473. C₂	D₃×#3994	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×D₃×C₄⋊AGL(1,𝔽₅)	2
C₂×D₃×C₈×D₅	2
C₂×#91223	2
C₂×C₃×#3994	2
C₂×#91160	2
D₃×#3994	2
C₂²×#3994	3
C₂×D₃×#107	5

Subgroups — C2×D3×#3994 #14413284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×#3994 #14413284