Subgroups — C₃×#10617422 #14417345

Order 1920.

1056 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66258	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#65767	C₂	1	2	yes	maximal, complemented
4	C₃×#65731	C₂	1	4	yes	maximal, complemented
5	C₃×D₈×AGL(1,𝔽₅)	C₂	1	4	yes	maximal, complemented
6	C₃×#65721	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65718	C₂	1	1	yes	maximal, characteristic, complemented
8	#10617422	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
10	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
11	C₃×D₄×AGL(1,𝔽₅)	—	2	4	no	—
12	C₃×D₄×AGL(1,𝔽₅)	C₂²	1	8	yes	complemented
13	C₃×#4130	C₂²	1	2	yes	—
14	C₃×#4130	C₂²	1	1	yes	characteristic
15	C₃×D₅⋊M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₈	C₄	1	1	yes	characteristic, complemented
17	C₂×C₃×#686	C₄	1	2	yes	complemented
18	C₃×D₅×D₈	C₄	1	2	yes	complemented
19	C₃×D₅×D₈	C₄	1	2	yes	complemented
20	C₃×D₅×D₈	C₂²	1	2	yes	—
21	C₃×D₅×D₈	C₂²	1	2	yes	—
22	C₂×C₃×D₄₀	C₄	1	1	yes	characteristic, complemented
23	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
24	C₃×#4007	C₂²	1	8	yes	complemented
25	C₃×#3994	C₂²	1	2	yes	complemented
26	C₃×#3993	C₂²	1	2	yes	complemented
27	C₃×#3992	C₂²	1	2	yes	complemented
28	C₃×C₈×AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
29	C₃×#2948	—	5	1	no	maximal, Hall
30	#66258	C₂×C₃	1	2	yes	complemented
31	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic
32	#65767	C₂×C₃	1	2	yes	complemented
33	#65731	C₂×C₃	1	4	yes	complemented
34	D₈×AGL(1,𝔽₅)	C₂×C₃	1	4	yes	complemented
35	#65721	C₂×C₃	1	1	yes	characteristic, complemented
36	#65718	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂³×C₃×D₅	—	2	2	no	—
38	C₂²×C₃×AGL(1,𝔽₅)	—	2	8	no	—
39	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	complemented
40	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
41	C₃×D₄×D₅	—	2	2	no	—
42	C₃×D₄×D₅	—	2	2	no	—
43	C₃×D₄×D₅	C₂×C₄	1	4	yes	complemented
44	C₃×D₄×D₅	C₂³	1	4	yes	—
45	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	complemented
46	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
47	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
48	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	8	no	—
49	C₃×C₂²⋊AGL(1,𝔽₅)	D₄	1	2	yes	—
50	C₃×#704	—	2	1	no	—
51	C₃×C₄⋊AGL(1,𝔽₅)	D₄	1	2	yes	—
52	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	4	yes	—
53	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
54	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	2	yes	—
55	C₃×#700	—	2	1	no	—
56	C₃×D₅⋊C₈	C₂³	1	2	yes	—
57	C₃×C₅×D₈	C₂×C₄	1	2	yes	complemented
58	C₃×C₅×D₈	C₂×C₄	1	2	yes	complemented
59	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic, complemented
60	C₃×#686	C₂×C₄	1	4	yes	complemented
61	C₃×#686	C₂×C₄	1	4	yes	complemented
62	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic, complemented
63	C₃×D₄₀	C₂×C₄	1	2	yes	complemented
64	C₃×D₄₀	C₂×C₄	1	2	yes	complemented
65	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic, complemented
66	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic, complemented
67	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
68	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×D₈	—	5	1	no	—
70	C₃×#518	—	5	2	no	—
71	C₃×#442	—	5	4	no	—
72	C₃×C₄×D₈	—	5	4	no	—
73	C₃×#427	—	5	1	no	—
74	C₃×#418	—	5	2	no	—
75	C₃×#405	—	5	1	no	—
76	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
77	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
78	D₄×AGL(1,𝔽₅)	—	2	4	no	—
79	D₄×AGL(1,𝔽₅)	C₂²×C₃	1	8	yes	complemented
80	#4130	C₂²×C₃	1	2	yes	—
81	#4130	C₂²×C₃	1	1	yes	characteristic
82	D₅⋊M₁₆	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×D₈	C₃×C₄	1	1	yes	characteristic, complemented
84	C₂×#686	C₃×C₄	1	2	yes	complemented
85	D₅×D₈	C₃×C₄	1	2	yes	complemented
86	D₅×D₈	C₃×C₄	1	2	yes	complemented
87	D₅×D₈	C₂²×C₃	1	2	yes	—
88	D₅×D₈	C₂²×C₃	1	2	yes	—
89	C₂×D₄₀	C₃×C₄	1	1	yes	characteristic, complemented
90	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
91	#4007	C₂²×C₃	1	8	yes	complemented
92	#3994	C₂²×C₃	1	2	yes	complemented
93	#3993	C₂²×C₃	1	2	yes	complemented
94	#3992	C₂²×C₃	1	2	yes	complemented
95	C₈×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	complemented
96	#2948	—	5	1	no	Sylow
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂²×C₃×D₅	—	2	2	no	—
99	C₂²×C₃×D₅	—	2	4	no	—
100	C₂²×C₃×D₅	—	2	4	no	—
101	C₂²×C₃×D₅	—	8	4	no	—
102	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
104	C₂×C₃×AGL(1,𝔽₅)	—	8	8	no	—
105	C₂×C₃×AGL(1,𝔽₅)	C₂×D₄	1	4	yes	—
106	C₃×C₅×D₄	—	2	2	no	—
107	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₃×C₂²⋊D₅	—	2	4	no	—
110	C₃×C₂²⋊D₅	—	2	4	no	—
111	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
112	C₃×D₂₀	—	2	2	no	—
113	C₃×D₂₀	C₂²×C₄	1	4	yes	—
114	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
115	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
116	C₃×C₄×D₅	#41	1	1	yes	characteristic
117	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
118	C₃×#170	—	2	2	no	—
119	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
121	C₃×#168	C₂²×C₄	1	1	yes	characteristic
122	C₃×#168	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₃×D₄	—	5	2	no	—
124	C₂×C₃×D₈	—	5	2	no	—
125	C₂×C₃×D₈	—	5	2	no	—
126	C₂×C₃×D₈	—	5	2	no	—
127	C₂×C₃×D₈	—	5	2	no	—
128	C₂×C₃×D₈	—	5	2	no	—
129	C₂×C₃×D₈	—	5	1	no	—
130	C₂×C₃×D₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
131	C₂×C₃×M₁₆	—	5	1	no	—
132	C₂²×C₃×C₈	—	5	1	no	—
133	C₃×C₄×D₄	—	5	8	no	—
134	C₃×C₄×D₄	—	10	4	no	—
135	C₃×#117	—	5	1	no	—
136	C₃×#117	—	5	2	no	—
137	C₂×C₃×C₂²⋊C₄	—	10	4	no	—
138	C₃×#107	—	5	2	no	—
139	C₃×#106	—	5	2	no	—
140	C₃×#102	—	5	8	no	—
141	C₃×#97	—	5	2	no	—
142	C₃×C₄×C₈	—	5	2	no	—
143	C₂³×D₅	—	2	2	no	—
144	C₂²×AGL(1,𝔽₅)	—	2	8	no	—
145	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	complemented
146	C₂×C₂²⋊D₅	—	2	2	no	—
147	D₄×D₅	—	2	2	no	—
148	D₄×D₅	—	2	2	no	—
149	D₄×D₅	C₂×C₃×C₄	1	4	yes	complemented
150	D₄×D₅	C₂³×C₃	1	4	yes	—
151	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	complemented
152	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
153	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
154	C₂²⋊AGL(1,𝔽₅)	—	2	8	no	—
155	C₂²⋊AGL(1,𝔽₅)	C₃×D₄	1	2	yes	—
156	#704	—	2	1	no	—
157	C₄⋊AGL(1,𝔽₅)	C₃×D₄	1	2	yes	—
158	C₄⋊AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
159	C₄×AGL(1,𝔽₅)	—	2	2	no	—
160	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
161	#700	—	2	1	no	—
162	D₅⋊C₈	C₂³×C₃	1	2	yes	—
163	C₅×D₈	C₂×C₃×C₄	1	2	yes	complemented
164	C₅×D₈	C₂×C₃×C₄	1	2	yes	complemented
165	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic, complemented
166	#686	C₂×C₃×C₄	1	4	yes	complemented
167	#686	C₂×C₃×C₄	1	4	yes	complemented
168	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic, complemented
169	D₄₀	C₂×C₃×C₄	1	2	yes	complemented
170	D₄₀	C₂×C₃×C₄	1	2	yes	complemented
171	C₈×D₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
172	C₈×D₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
173	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
174	C₈×D₅	C₂³×C₃	1	1	yes	characteristic
175	C₂²×D₈	—	5	1	no	—
176	#518	—	5	2	no	—
177	#442	—	5	4	no	—
178	C₄×D₈	—	5	4	no	—
179	#427	—	5	1	no	—
180	#418	—	5	2	no	—
181	#405	—	5	1	no	—
182	C₂²×C₃×C₅	—	2	4	no	—
183	C₂²×C₃×C₅	—	8	2	no	—
184	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
185	C₂×C₃×D₅	—	2	2	no	—
186	C₂×C₃×D₅	—	2	4	no	—
187	C₂×C₃×D₅	—	4	8	no	—
188	C₂×C₃×D₅	—	8	4	no	—
189	C₂×C₃×D₅	—	8	2	no	—
190	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
191	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
192	C₃×AGL(1,𝔽₅)	—	2	4	no	—
193	C₃×AGL(1,𝔽₅)	—	4	4	no	—
194	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
196	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
197	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
198	C₂⁴×C₃	—	10	2	no	—
199	C₂×C₃×D₄	—	5	4	no	—
200	C₂×C₃×D₄	—	5	4	no	—
201	C₂×C₃×D₄	—	5	2	no	—
202	C₂×C₃×D₄	—	10	2	no	—
203	C₂×C₃×D₄	—	10	2	no	—
204	C₂×C₃×D₄	—	10	2	no	—
205	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
206	C₂²×C₃×C₄	—	5	1	no	—
207	C₂²×C₃×C₄	—	10	8	no	—
208	C₃×D₈	—	5	4	no	—
209	C₃×D₈	—	5	4	no	—
210	C₃×D₈	—	5	2	no	—
211	C₃×D₈	—	5	2	no	—
212	C₃×D₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
213	C₃×D₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
214	C₃×M₁₆	—	10	1	no	—
215	C₃×M₁₆	—	10	1	no	—
216	C₂×C₃×C₈	—	5	1	no	—
217	C₂×C₃×C₈	—	5	1	no	—
218	C₂×C₃×C₈	—	5	1	no	—
219	C₂×C₃×C₈	—	5	1	no	—
220	C₂×C₃×C₈	—	5	1	no	—
221	C₂×C₃×C₈	—	5	2	no	—
222	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
223	C₃×C₄⋊C₄	—	5	2	no	—
224	C₃×C₄⋊C₄	—	5	4	no	—
225	C₃×C₂²⋊C₄	—	5	2	no	—
226	C₃×C₂²⋊C₄	—	10	8	no	—
227	C₃×C₂²⋊C₄	—	10	2	no	—
228	C₃×C₄²	—	5	2	no	—
229	C₃×C₄²	—	10	2	no	—
230	C₂³×C₅	—	2	2	no	—
231	C₂²×D₅	—	2	2	no	—
232	C₂²×D₅	—	2	4	no	—
233	C₂²×D₅	—	2	4	no	—
234	C₂²×D₅	—	8	4	no	—
235	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×AGL(1,𝔽₅)	—	2	4	no	—
237	C₂×AGL(1,𝔽₅)	—	8	8	no	—
238	C₂×AGL(1,𝔽₅)	C₂×C₃×D₄	1	4	yes	—
239	C₅×D₄	—	2	2	no	—
240	C₅×D₄	C₂²×C₃×C₄	1	4	yes	—
241	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
242	C₂²⋊D₅	—	2	4	no	—
243	C₂²⋊D₅	—	2	4	no	—
244	C₂×Dic₅	C₃×#41	1	1	yes	characteristic
245	D₂₀	—	2	2	no	—
246	D₂₀	C₂²×C₃×C₄	1	4	yes	—
247	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
248	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
249	C₄×D₅	C₃×#41	1	1	yes	characteristic
250	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
251	#170	—	2	2	no	—
252	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
253	C₅×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
254	#168	C₂²×C₃×C₄	1	1	yes	characteristic
255	#168	C₂²×C₃×C₄	1	1	yes	characteristic
256	C₂²×D₄	—	5	2	no	—
257	C₂×D₈	—	5	2	no	—
258	C₂×D₈	—	5	2	no	—
259	C₂×D₈	—	5	2	no	—
260	C₂×D₈	—	5	2	no	—
261	C₂×D₈	—	5	2	no	—
262	C₂×D₈	—	5	1	no	—
263	C₂×D₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
264	C₂×M₁₆	—	5	1	no	—
265	C₂²×C₈	—	5	1	no	—
266	C₄×D₄	—	5	8	no	—
267	C₄×D₄	—	10	4	no	—
268	#117	—	5	1	no	—
269	#117	—	5	2	no	—
270	C₂×C₂²⋊C₄	—	10	4	no	—
271	#107	—	5	2	no	—
272	#106	—	5	2	no	—
273	#102	—	5	8	no	—
274	#97	—	5	2	no	—
275	C₄×C₈	—	5	2	no	—
276	C₂×C₃×C₅	—	2	1	no	—
277	C₂×C₃×C₅	—	4	4	no	—
278	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
279	C₃×D₅	—	2	1	no	—
280	C₃×D₅	—	4	4	no	—
281	C₃×D₅	#576	1	2	yes	—
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	—	5	1	no	—
284	C₂³×C₃	—	10	4	no	—
285	C₂³×C₃	—	10	4	no	—
286	C₂³×C₃	—	10	2	no	—
287	C₂³×C₃	—	40	4	no	—
288	C₃×D₄	—	2	2	no	—
289	C₃×D₄	—	5	4	no	—
290	C₃×D₄	—	10	4	no	—
291	C₃×D₄	—	10	4	no	—
292	C₃×D₄	—	10	2	no	—
293	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	4	yes	—
294	C₂×C₃×C₄	—	5	1	no	—
295	C₂×C₃×C₄	—	5	1	no	—
296	C₂×C₃×C₄	—	5	1	no	—
297	C₂×C₃×C₄	—	5	1	no	—
298	C₂×C₃×C₄	—	5	1	no	—
299	C₂×C₃×C₄	—	5	4	no	—
300	C₂×C₃×C₄	—	10	4	no	—
301	C₂×C₃×C₄	—	40	8	no	—
302	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
303	C₃×C₈	—	5	1	no	—
304	C₃×C₈	—	5	1	no	—
305	C₃×C₈	—	10	2	no	—
306	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
307	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	8	2	no	—
310	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
311	C₂×D₅	—	2	2	no	—
312	C₂×D₅	—	2	4	no	—
313	C₂×D₅	—	4	8	no	—
314	C₂×D₅	—	8	4	no	—
315	C₂×D₅	—	8	2	no	—
316	C₂×D₅	C₃×C₄×D₄	1	1	yes	characteristic
317	C₂×D₅	C₂²×C₃×D₄	1	1	yes	characteristic
318	AGL(1,𝔽₅)	—	2	4	no	—
319	AGL(1,𝔽₅)	—	4	4	no	—
320	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
321	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
322	Dic₅	C₃×C₄×D₄	1	1	yes	characteristic
323	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
324	C₂⁴	—	10	2	no	—
325	C₂×D₄	—	5	4	no	—
326	C₂×D₄	—	5	4	no	—
327	C₂×D₄	—	5	2	no	—
328	C₂×D₄	—	10	2	no	—
329	C₂×D₄	—	10	2	no	—
330	C₂×D₄	—	10	2	no	—
331	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	10	8	no	—
334	D₈	—	5	4	no	—
335	D₈	—	5	4	no	—
336	D₈	—	5	2	no	—
337	D₈	—	5	2	no	—
338	D₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
339	D₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
340	M₁₆	—	10	1	no	—
341	M₁₆	—	10	1	no	—
342	C₂×C₈	—	5	1	no	—
343	C₂×C₈	—	5	1	no	—
344	C₂×C₈	—	5	1	no	—
345	C₂×C₈	—	5	1	no	—
346	C₂×C₈	—	5	1	no	—
347	C₂×C₈	—	5	2	no	—
348	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
349	C₄⋊C₄	—	5	2	no	—
350	C₄⋊C₄	—	5	4	no	—
351	C₂²⋊C₄	—	5	2	no	—
352	C₂²⋊C₄	—	10	8	no	—
353	C₂²⋊C₄	—	10	2	no	—
354	C₄²	—	5	2	no	—
355	C₄²	—	10	2	no	—
356	C₃×C₅	#2948	1	1	yes	characteristic, complemented, Hall
357	C₂²×C₃	—	2	4	no	—
358	C₂²×C₃	—	5	1	no	—
359	C₂²×C₃	—	5	1	no	—
360	C₂²×C₃	—	8	2	no	—
361	C₂²×C₃	—	10	2	no	—
362	C₂²×C₃	—	10	4	no	—
363	C₂²×C₃	—	20	8	no	—
364	C₂²×C₃	—	40	2	no	—
365	C₂²×C₃	—	40	4	no	—
366	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₃×C₄	—	5	1	no	—
368	C₃×C₄	—	5	1	no	—
369	C₃×C₄	—	10	4	no	—
370	C₃×C₄	—	20	4	no	—
371	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
372	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
373	C₂×C₅	—	2	1	no	—
374	C₂×C₅	—	4	4	no	—
375	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
376	D₅	—	2	1	no	—
377	D₅	—	4	4	no	—
378	D₅	C₃×#576	1	2	yes	—
379	C₂³	—	2	2	no	—
380	C₂³	—	5	1	no	—
381	C₂³	—	10	4	no	—
382	C₂³	—	10	4	no	—
383	C₂³	—	10	2	no	—
384	C₂³	—	40	4	no	—
385	D₄	—	2	2	no	—
386	D₄	—	5	4	no	—
387	D₄	—	10	4	no	—
388	D₄	—	10	4	no	—
389	D₄	—	10	2	no	—
390	D₄	C₂²×C₃×AGL(1,𝔽₅)	1	4	yes	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	5	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	1	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	4	no	—
397	C₂×C₄	—	10	4	no	—
398	C₂×C₄	—	40	8	no	—
399	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
400	C₈	—	5	1	no	—
401	C₈	—	5	1	no	—
402	C₈	—	10	2	no	—
403	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
404	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
405	C₂×C₃	—	2	1	no	—
406	C₂×C₃	—	4	4	no	—
407	C₂×C₃	—	5	2	no	—
408	C₂×C₃	—	10	1	no	—
409	C₂×C₃	—	20	4	no	—
410	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
411	C₅	C₃×#2948	1	1	yes	characteristic, complemented, Sylow
412	C₂²	—	2	4	no	—
413	C₂²	—	5	1	no	—
414	C₂²	—	5	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	10	2	no	—
417	C₂²	—	10	4	no	—
418	C₂²	—	20	8	no	—
419	C₂²	—	40	2	no	—
420	C₂²	—	40	4	no	—
421	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
422	C₄	—	5	1	no	—
423	C₄	—	5	1	no	—
424	C₄	—	10	4	no	—
425	C₄	—	20	4	no	—
426	C₄	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
427	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
428	C₃	#10617422	1	1	yes	characteristic, direct product factor, Sylow
429	C₂	—	2	1	no	—
430	C₂	—	4	4	no	—
431	C₂	—	5	2	no	—
432	C₂	—	10	1	no	—
433	C₂	—	20	4	no	—
434	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₄	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×D₈	C₄
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₂×C₃×D₅×D₈	C₂
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₂×C₃×D₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2948
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₃×#66258	C₂	semidirect
3. C₃×#65767	C₂	semidirect
4. C₃×#65731	C₂	semidirect
5. C₃×D₈×AGL(1,𝔽₅)	C₂	semidirect
6. C₃×#65721	C₂	semidirect
7. C₃×#65718	C₂	semidirect
8. #10617422	C₃	direct (N × H)
12. C₃×D₄×AGL(1,𝔽₅)	C₂²	semidirect
16. C₂×C₃×C₅×D₈	C₄	semidirect
17. C₂×C₃×#686	C₄	semidirect
18. C₃×D₅×D₈	C₄	semidirect
19. C₃×D₅×D₈	C₄	semidirect
22. C₂×C₃×D₄₀	C₄	semidirect
24. C₃×#4007	C₂²	semidirect
25. C₃×#3994	C₂²	semidirect
26. C₃×#3993	C₂²	semidirect
27. C₃×#3992	C₂²	semidirect
28. C₃×C₈×AGL(1,𝔽₅)	C₂²	semidirect
30. #66258	C₂×C₃	semidirect
32. #65767	C₂×C₃	semidirect
33. #65731	C₂×C₃	semidirect
34. D₈×AGL(1,𝔽₅)	C₂×C₃	semidirect
35. #65721	C₂×C₃	semidirect
36. #65718	C₂×C₃	semidirect
39. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
43. C₃×D₄×D₅	C₂×C₄	semidirect
45. C₂×C₃×D₂₀	C₂×C₄	semidirect
57. C₃×C₅×D₈	C₂×C₄	semidirect
58. C₃×C₅×D₈	C₂×C₄	semidirect
59. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
60. C₃×#686	C₂×C₄	semidirect
61. C₃×#686	C₂×C₄	semidirect
62. C₂×C₃×#168	C₂×C₄	semidirect
63. C₃×D₄₀	C₂×C₄	semidirect
64. C₃×D₄₀	C₂×C₄	semidirect
65. C₃×C₈×D₅	C₂×C₄	semidirect
66. C₃×C₈×D₅	C₂×C₄	semidirect
79. D₄×AGL(1,𝔽₅)	C₂²×C₃	semidirect
83. C₂×C₅×D₈	C₃×C₄	semidirect
84. C₂×#686	C₃×C₄	semidirect
85. D₅×D₈	C₃×C₄	semidirect
86. D₅×D₈	C₃×C₄	semidirect
89. C₂×D₄₀	C₃×C₄	semidirect
91. #4007	C₂²×C₃	semidirect
92. #3994	C₂²×C₃	semidirect
93. #3993	C₂²×C₃	semidirect
94. #3992	C₂²×C₃	semidirect
95. C₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
130. C₂×C₃×D₈	AGL(1,𝔽₅)	semidirect
145. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
149. D₄×D₅	C₂×C₃×C₄	semidirect
151. C₂×D₂₀	C₂×C₃×C₄	semidirect
163. C₅×D₈	C₂×C₃×C₄	semidirect
164. C₅×D₈	C₂×C₃×C₄	semidirect
165. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
166. #686	C₂×C₃×C₄	semidirect
167. #686	C₂×C₃×C₄	semidirect
168. C₂×#168	C₂×C₃×C₄	semidirect
169. D₄₀	C₂×C₃×C₄	semidirect
170. D₄₀	C₂×C₃×C₄	semidirect
171. C₈×D₅	C₂×C₃×C₄	semidirect
172. C₈×D₅	C₂×C₃×C₄	semidirect
205. C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	semidirect
212. C₃×D₈	C₂×AGL(1,𝔽₅)	semidirect
213. C₃×D₈	C₂×AGL(1,𝔽₅)	semidirect
222. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
263. C₂×D₈	C₃×AGL(1,𝔽₅)	semidirect
331. C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
338. D₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
339. D₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
348. C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	semidirect
356. C₃×C₅	#2948	semidirect
411. C₅	C₃×#2948	semidirect
428. C₃	#10617422	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#66258	2
C₂×C₃×D₅×D₈	2
C₃×#65767	2
C₃×#65731	2
C₃×D₈×AGL(1,𝔽₅)	2
C₃×#65721	2
C₃×#65718	2
#10617422	3
C₃×#2948	5

Subgroups — C3×#10617422 #14417345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617422 #14417345