Subgroups — C₃×D₄×#704 #14415692

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#704	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₃×#65798	C₂	1	2	yes	maximal, complemented
4	C₃×#65774	C₂	1	2	yes	maximal, complemented
5	C₃×#65773	C₂	1	4	yes	maximal, complemented
6	C₃×D₄×#170	C₂	1	2	yes	maximal, complemented
7	C₃×#65758	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#704	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×#704	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic
11	C₂³×C₃×Dic₅	C₂²	1	2	yes	—
12	C₂×C₃×#704	—	2	8	no	—
13	C₂×C₃×#704	C₂²	1	1	yes	characteristic
14	C₂×C₃×#704	C₂²	1	2	yes	—
15	C₂×C₃×#704	C₂²	1	1	yes	characteristic
16	C₂×C₃×#704	C₂²	1	4	yes	complemented
17	C₂²×C₃×#170	C₂²	1	4	yes	complemented
18	C₂×C₃×C₂²⋊Dic₅	C₄	1	2	yes	—
19	C₃×D₄×Dic₅	C₄	1	2	yes	—
20	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic
21	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic
22	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
23	C₃×D₄×Dic₅	C₂²	1	2	yes	—
24	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄⋊Dic₅	C₄	1	1	yes	characteristic
26	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
27	C₃×C₂²⋊#170	C₂²	1	4	yes	complemented
28	C₃×C₂²⋊#170	C₂²	1	4	yes	complemented
29	C₃×#4004	C₂²	1	2	yes	complemented
30	C₃×#4002	C₂²	1	2	yes	complemented
31	C₃×C₄⋊#170	C₂²	1	2	yes	complemented
32	C₃×C₄×#170	C₂²	1	2	yes	complemented
33	C₃×D₄×M₁₆	—	5	1	no	maximal, Hall
34	C₂²×#704	C₂×C₃	1	2	yes	complemented
35	C₂×D₄×Dic₅	C₂×C₃	1	1	yes	characteristic
36	#65798	C₂×C₃	1	2	yes	complemented
37	#65774	C₂×C₃	1	2	yes	complemented
38	#65773	C₂×C₃	1	4	yes	complemented
39	D₄×#170	C₂×C₃	1	2	yes	complemented
40	#65758	C₂×C₃	1	1	yes	characteristic, complemented
41	C₄×#704	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₅×D₄	—	2	4	no	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃×Dic₅	—	2	4	no	—
49	C₂²×C₃×Dic₅	—	2	4	no	—
50	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
51	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
52	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
53	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
55	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
56	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
57	C₃×#704	—	2	4	no	—
58	C₃×#704	—	2	2	no	—
59	C₃×#704	—	2	8	no	—
60	C₃×#704	D₄	1	4	yes	direct product factor
61	C₂×C₃×#170	—	2	8	no	—
62	C₂×C₃×#170	C₂³	1	2	yes	—
63	C₂×C₃×#170	C₂³	1	4	yes	—
64	C₂×C₃×#170	C₂³	1	2	yes	—
65	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
66	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
67	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
68	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
69	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
70	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
72	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
75	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×M₁₆	—	5	2	no	—
77	C₂×C₃×C₄×D₄	—	5	1	no	—
78	C₃×#436	—	5	2	no	—
79	C₃×#435	—	5	4	no	—
80	C₃×C₈×D₄	—	5	2	no	—
81	C₃×#423	—	5	1	no	—
82	C₃×#407	—	5	2	no	—
83	C₃×C₄×M₁₆	—	5	1	no	—
84	C₂²×C₅×D₄	C₃×C₄	1	1	yes	characteristic
85	C₂³×Dic₅	C₂²×C₃	1	2	yes	—
86	C₂×#704	—	2	8	no	—
87	C₂×#704	C₂²×C₃	1	1	yes	characteristic
88	C₂×#704	C₂²×C₃	1	2	yes	—
89	C₂×#704	C₂²×C₃	1	1	yes	characteristic
90	C₂×#704	C₂²×C₃	1	4	yes	complemented
91	C₂²×#170	C₂²×C₃	1	4	yes	complemented
92	C₂×C₂²⋊Dic₅	C₃×C₄	1	2	yes	—
93	D₄×Dic₅	C₃×C₄	1	2	yes	—
94	D₄×Dic₅	C₃×C₄	1	1	yes	characteristic
95	D₄×Dic₅	C₃×C₄	1	1	yes	characteristic
96	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
97	D₄×Dic₅	C₂²×C₃	1	2	yes	—
98	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₄⋊Dic₅	C₃×C₄	1	1	yes	characteristic
100	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
101	C₂²⋊#170	C₂²×C₃	1	4	yes	complemented
102	C₂²⋊#170	C₂²×C₃	1	4	yes	complemented
103	#4004	C₂²×C₃	1	2	yes	complemented
104	#4002	C₂²×C₃	1	2	yes	complemented
105	C₄⋊#170	C₂²×C₃	1	2	yes	complemented
106	C₄×#170	C₂²×C₃	1	2	yes	complemented
107	D₄×M₁₆	—	5	1	no	Sylow
108	C₂³×C₃×C₅	—	2	4	no	—
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	—	4	2	no	—
111	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
112	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
114	C₃×C₅×D₄	—	2	4	no	—
115	C₃×C₅×D₄	—	2	2	no	—
116	C₃×C₅×D₄	M₁₆	1	4	yes	complemented
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×Dic₅	—	2	4	no	—
121	C₂×C₃×Dic₅	—	2	4	no	—
122	C₂×C₃×Dic₅	—	2	4	no	—
123	C₂×C₃×Dic₅	—	2	2	no	—
124	C₂×C₃×Dic₅	—	2	2	no	—
125	C₂×C₃×Dic₅	—	2	2	no	—
126	C₂×C₃×Dic₅	—	2	2	no	—
127	C₂×C₃×Dic₅	—	4	1	no	—
128	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
134	C₂×C₃×Dic₅	#41	1	2	yes	—
135	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
136	C₃×#170	—	2	4	no	—
137	C₃×#170	—	2	2	no	—
138	C₃×#170	C₂×D₄	1	4	yes	complemented
139	C₂²×C₃×D₄	AGL(1,𝔽₅)	1	1	yes	characteristic
140	C₂³×C₃×C₄	—	5	2	no	—
141	C₂×C₃×M₁₆	—	5	1	no	—
142	C₂×C₃×M₁₆	—	5	2	no	—
143	C₂×C₃×M₁₆	—	5	4	no	—
144	C₂×C₃×M₁₆	—	5	1	no	—
145	C₂×C₃×M₁₆	—	10	8	no	—
146	C₂²×C₃×C₈	—	5	4	no	—
147	C₃×C₄×D₄	—	5	2	no	—
148	C₃×C₄×D₄	—	5	1	no	—
149	C₃×C₄×D₄	—	5	1	no	—
150	C₃×C₄×D₄	—	5	1	no	—
151	C₃×C₄×D₄	—	5	2	no	—
152	C₃×C₄×D₄	—	5	1	no	—
153	C₂×C₃×C₄⋊C₄	—	5	1	no	—
154	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
155	C₂×C₃×C₄²	—	5	1	no	—
156	C₃×C₄⋊C₈	—	5	2	no	—
157	C₃×C₄⋊C₈	—	5	2	no	—
158	C₃×C₂²⋊C₈	—	5	4	no	—
159	C₃×C₂²⋊C₈	—	5	4	no	—
160	C₃×#97	—	5	2	no	—
161	C₃×C₄×C₈	—	5	2	no	—
162	C₂⁴×C₅	C₂×C₃×C₄	1	2	yes	—
163	C₂×C₅×D₄	—	2	4	no	—
164	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
165	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂²×Dic₅	—	2	4	no	—
169	C₂²×Dic₅	—	2	4	no	—
170	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
171	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
172	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
173	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
174	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
175	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
176	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
177	#704	—	2	4	no	—
178	#704	—	2	2	no	—
179	#704	—	2	8	no	—
180	#704	C₃×D₄	1	4	yes	direct product factor
181	C₂×#170	—	2	8	no	—
182	C₂×#170	C₂³×C₃	1	4	yes	—
183	C₂×#170	C₂³×C₃	1	2	yes	—
184	C₂×#170	C₂³×C₃	1	2	yes	—
185	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
186	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
187	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
188	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
189	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
190	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
191	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
192	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
193	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
194	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
195	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
196	C₂²×M₁₆	—	5	2	no	—
197	C₂×C₄×D₄	—	5	1	no	—
198	#436	—	5	2	no	—
199	#435	—	5	4	no	—
200	C₈×D₄	—	5	2	no	—
201	#423	—	5	1	no	—
202	#407	—	5	2	no	—
203	C₄×M₁₆	—	5	1	no	—
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	—	2	1	no	—
207	C₂²×C₃×C₅	—	2	2	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	—	2	2	no	—
210	C₂²×C₃×C₅	—	2	2	no	—
211	C₂²×C₃×C₅	—	4	8	no	—
212	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
213	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	complemented
214	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
217	C₃×Dic₅	—	2	2	no	—
218	C₃×Dic₅	—	2	2	no	—
219	C₃×Dic₅	—	2	1	no	—
220	C₃×Dic₅	—	2	1	no	—
221	C₃×Dic₅	C₄×D₄	1	2	yes	—
222	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
223	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
224	C₂⁴×C₃	C₂×AGL(1,𝔽₅)	1	2	yes	—
225	C₂×C₃×D₄	—	2	4	no	—
226	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
227	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
228	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
229	C₂²×C₃×C₄	—	5	1	no	—
230	C₂²×C₃×C₄	—	5	2	no	—
231	C₂²×C₃×C₄	—	5	2	no	—
232	C₂²×C₃×C₄	—	5	2	no	—
233	C₂²×C₃×C₄	—	5	2	no	—
234	C₂²×C₃×C₄	—	5	2	no	—
235	C₂²×C₃×C₄	—	5	1	no	—
236	C₂²×C₃×C₄	—	10	4	no	—
237	C₂²×C₃×C₄	—	10	4	no	—
238	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
239	C₃×M₁₆	—	5	4	no	—
240	C₃×M₁₆	—	10	8	no	—
241	C₃×M₁₆	—	10	2	no	—
242	C₃×M₁₆	—	10	4	no	—
243	C₂×C₃×C₈	—	5	2	no	—
244	C₂×C₃×C₈	—	5	2	no	—
245	C₂×C₃×C₈	—	5	4	no	—
246	C₂×C₃×C₈	—	10	8	no	—
247	C₃×C₄⋊C₄	—	5	2	no	—
248	C₃×C₄⋊C₄	—	5	1	no	—
249	C₃×C₄⋊C₄	—	5	1	no	—
250	C₃×C₂²⋊C₄	—	5	2	no	—
251	C₃×C₂²⋊C₄	—	5	2	no	—
252	C₃×C₂²⋊C₄	—	5	2	no	—
253	C₃×C₂²⋊C₄	—	5	2	no	—
254	C₃×C₄²	—	5	1	no	—
255	C₃×C₄²	—	5	1	no	—
256	C₃×C₄²	—	5	1	no	—
257	C₃×C₄²	—	5	1	no	—
258	C₂³×C₅	—	2	4	no	—
259	C₂³×C₅	—	2	4	no	—
260	C₂³×C₅	—	4	2	no	—
261	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
262	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
263	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
264	C₅×D₄	—	2	4	no	—
265	C₅×D₄	—	2	2	no	—
266	C₅×D₄	C₃×M₁₆	1	4	yes	complemented
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
270	C₂×Dic₅	—	2	4	no	—
271	C₂×Dic₅	—	2	4	no	—
272	C₂×Dic₅	—	2	4	no	—
273	C₂×Dic₅	—	2	2	no	—
274	C₂×Dic₅	—	2	2	no	—
275	C₂×Dic₅	—	2	2	no	—
276	C₂×Dic₅	—	2	2	no	—
277	C₂×Dic₅	—	4	1	no	—
278	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
279	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
280	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
281	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
282	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
283	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
284	C₂×Dic₅	C₃×#41	1	2	yes	—
285	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
286	#170	—	2	4	no	—
287	#170	—	2	2	no	—
288	#170	C₂×C₃×D₄	1	4	yes	complemented
289	C₂²×D₄	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
290	C₂³×C₄	—	5	2	no	—
291	C₂×M₁₆	—	5	1	no	—
292	C₂×M₁₆	—	5	2	no	—
293	C₂×M₁₆	—	5	1	no	—
294	C₂×M₁₆	—	5	4	no	—
295	C₂×M₁₆	—	10	8	no	—
296	C₂²×C₈	—	5	4	no	—
297	C₄×D₄	—	5	1	no	—
298	C₄×D₄	—	5	2	no	—
299	C₄×D₄	—	5	1	no	—
300	C₄×D₄	—	5	2	no	—
301	C₄×D₄	—	5	1	no	—
302	C₄×D₄	—	5	1	no	—
303	C₂×C₄⋊C₄	—	5	1	no	—
304	C₂×C₂²⋊C₄	—	5	2	no	—
305	C₂×C₄²	—	5	1	no	—
306	C₄⋊C₈	—	5	2	no	—
307	C₄⋊C₈	—	5	2	no	—
308	C₂²⋊C₈	—	5	4	no	—
309	C₂²⋊C₈	—	5	4	no	—
310	#97	—	5	2	no	—
311	C₄×C₈	—	5	2	no	—
312	C₂×C₃×C₅	—	2	2	no	—
313	C₂×C₃×C₅	—	2	4	no	—
314	C₂×C₃×C₅	—	4	2	no	—
315	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
316	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
317	C₂×C₃×C₅	#568	1	1	yes	characteristic
318	C₂³×C₃	—	2	4	no	—
319	C₂³×C₃	—	2	4	no	—
320	C₂³×C₃	—	4	2	no	—
321	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
322	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
323	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
324	C₃×D₄	—	2	4	no	—
325	C₃×D₄	—	2	2	no	—
326	C₃×D₄	#704	1	4	yes	direct product factor
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	5	2	no	—
329	C₂×C₃×C₄	—	5	2	no	—
330	C₂×C₃×C₄	—	5	1	no	—
331	C₂×C₃×C₄	—	5	1	no	—
332	C₂×C₃×C₄	—	5	1	no	—
333	C₂×C₃×C₄	—	5	1	no	—
334	C₂×C₃×C₄	—	5	2	no	—
335	C₂×C₃×C₄	—	5	2	no	—
336	C₂×C₃×C₄	—	10	2	no	—
337	C₂×C₃×C₄	—	10	2	no	—
338	C₂×C₃×C₄	—	10	4	no	—
339	C₂×C₃×C₄	—	10	4	no	—
340	C₂×C₃×C₄	—	10	2	no	—
341	C₂×C₃×C₄	—	10	2	no	—
342	C₂×C₃×C₄	—	10	4	no	—
343	C₂×C₃×C₄	—	20	1	no	—
344	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
346	C₃×C₈	—	5	4	no	—
347	C₃×C₈	—	10	4	no	—
348	C₃×C₈	—	10	2	no	—
349	C₂²×C₅	—	2	1	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	2	2	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	—	2	2	no	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	2	2	no	—
356	C₂²×C₅	—	4	8	no	—
357	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
358	C₂²×C₅	C₂×C₃×M₁₆	1	4	yes	complemented
359	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	complemented
362	Dic₅	—	2	1	no	—
363	Dic₅	—	2	1	no	—
364	Dic₅	—	2	2	no	—
365	Dic₅	—	2	2	no	—
366	Dic₅	C₃×C₄×D₄	1	2	yes	—
367	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
368	Dic₅	C₂×C₃×#41	1	1	yes	characteristic
369	C₂⁴	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
372	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
373	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₂²×C₄	—	5	1	no	—
375	C₂²×C₄	—	5	2	no	—
376	C₂²×C₄	—	5	2	no	—
377	C₂²×C₄	—	5	2	no	—
378	C₂²×C₄	—	5	2	no	—
379	C₂²×C₄	—	5	2	no	—
380	C₂²×C₄	—	5	1	no	—
381	C₂²×C₄	—	10	4	no	—
382	C₂²×C₄	—	10	4	no	—
383	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
384	M₁₆	—	5	4	no	—
385	M₁₆	—	10	8	no	—
386	M₁₆	—	10	4	no	—
387	M₁₆	—	10	2	no	—
388	C₂×C₈	—	5	2	no	—
389	C₂×C₈	—	5	2	no	—
390	C₂×C₈	—	5	4	no	—
391	C₂×C₈	—	10	8	no	—
392	C₄⋊C₄	—	5	2	no	—
393	C₄⋊C₄	—	5	1	no	—
394	C₄⋊C₄	—	5	1	no	—
395	C₂²⋊C₄	—	5	2	no	—
396	C₂²⋊C₄	—	5	2	no	—
397	C₂²⋊C₄	—	5	2	no	—
398	C₂²⋊C₄	—	5	2	no	—
399	C₄²	—	5	1	no	—
400	C₄²	—	5	1	no	—
401	C₄²	—	5	1	no	—
402	C₄²	—	5	1	no	—
403	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	2	no	—
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	4	8	no	—
412	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	2	yes	—
413	C₂²×C₃	C₂×#704	1	4	yes	complemented
414	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	5	2	no	—
417	C₃×C₄	—	5	1	no	—
418	C₃×C₄	—	5	1	no	—
419	C₃×C₄	—	10	1	no	—
420	C₃×C₄	—	10	1	no	—
421	C₃×C₄	—	10	2	no	—
422	C₃×C₄	—	10	2	no	—
423	C₃×C₄	C₂×#704	1	2	yes	complemented
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	—	2	4	no	—
426	C₂×C₅	—	4	2	no	—
427	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
428	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
429	C₂×C₅	C₃×#568	1	1	yes	characteristic
430	C₂³	—	2	4	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	4	2	no	—
433	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
434	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
435	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
436	D₄	—	2	4	no	—
437	D₄	—	2	2	no	—
438	D₄	C₃×#704	1	4	yes	direct product factor
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	5	2	no	—
441	C₂×C₄	—	5	2	no	—
442	C₂×C₄	—	5	1	no	—
443	C₂×C₄	—	5	1	no	—
444	C₂×C₄	—	5	1	no	—
445	C₂×C₄	—	5	1	no	—
446	C₂×C₄	—	5	2	no	—
447	C₂×C₄	—	5	2	no	—
448	C₂×C₄	—	10	2	no	—
449	C₂×C₄	—	10	2	no	—
450	C₂×C₄	—	10	2	no	—
451	C₂×C₄	—	10	2	no	—
452	C₂×C₄	—	10	4	no	—
453	C₂×C₄	—	10	4	no	—
454	C₂×C₄	—	10	4	no	—
455	C₂×C₄	—	20	1	no	—
456	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
457	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
458	C₈	—	5	4	no	—
459	C₈	—	10	4	no	—
460	C₈	—	10	2	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	2	4	no	—
463	C₂×C₃	—	4	2	no	—
464	C₂×C₃	#66256	1	1	yes	characteristic
465	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
466	C₂×C₃	C₂²×#704	1	1	yes	characteristic
467	C₅	C₃×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	8	no	—
476	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	2	yes	—
477	C₂²	C₂×C₃×#704	1	4	yes	complemented
478	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	5	1	no	—
481	C₄	—	5	1	no	—
482	C₄	—	5	2	no	—
483	C₄	—	10	1	no	—
484	C₄	—	10	1	no	—
485	C₄	—	10	2	no	—
486	C₄	—	10	2	no	—
487	C₄	C₂×C₃×#704	1	2	yes	complemented
488	C₃	D₄×#704	1	1	yes	characteristic, direct product factor, Sylow
489	C₂	—	2	2	no	—
490	C₂	—	2	4	no	—
491	C₂	—	4	2	no	—
492	C₂	C₃×#66256	1	1	yes	characteristic
493	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
494	C₂	C₂²×C₃×#704	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting, prime radical	C₂²×C₃×C₅×D₄	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₂²×C₃×D₄	AGL(1,𝔽₅)
hypocenter	C₅	C₃×D₄×M₁₆
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#704	C₂	semidirect
3. C₃×#65798	C₂	semidirect
4. C₃×#65774	C₂	semidirect
5. C₃×#65773	C₂	semidirect
6. C₃×D₄×#170	C₂	semidirect
7. C₃×#65758	C₂	semidirect
8. C₃×C₄×#704	C₂	semidirect
9. D₄×#704	C₃	direct (N × H)
16. C₂×C₃×#704	C₂²	semidirect
17. C₂²×C₃×#170	C₂²	semidirect
27. C₃×C₂²⋊#170	C₂²	semidirect
28. C₃×C₂²⋊#170	C₂²	semidirect
29. C₃×#4004	C₂²	semidirect
30. C₃×#4002	C₂²	semidirect
31. C₃×C₄⋊#170	C₂²	semidirect
32. C₃×C₄×#170	C₂²	semidirect
34. C₂²×#704	C₂×C₃	semidirect
36. #65798	C₂×C₃	semidirect
37. #65774	C₂×C₃	semidirect
38. #65773	C₂×C₃	semidirect
39. D₄×#170	C₂×C₃	semidirect
40. #65758	C₂×C₃	semidirect
41. C₄×#704	C₂×C₃	semidirect
60. C₃×#704	D₄	direct (N × H)
90. C₂×#704	C₂²×C₃	semidirect
91. C₂²×#170	C₂²×C₃	semidirect
101. C₂²⋊#170	C₂²×C₃	semidirect
102. C₂²⋊#170	C₂²×C₃	semidirect
103. #4004	C₂²×C₃	semidirect
104. #4002	C₂²×C₃	semidirect
105. C₄⋊#170	C₂²×C₃	semidirect
106. C₄×#170	C₂²×C₃	semidirect
116. C₃×C₅×D₄	M₁₆	semidirect
138. C₃×#170	C₂×D₄	semidirect
180. #704	C₃×D₄	direct (N × H)
213. C₂²×C₃×C₅	C₂×M₁₆	semidirect
216. C₃×C₄×C₅	C₂×M₁₆	semidirect
266. C₅×D₄	C₃×M₁₆	semidirect
288. #170	C₂×C₃×D₄	semidirect
326. C₃×D₄	#704	direct (N × H)
358. C₂²×C₅	C₂×C₃×M₁₆	semidirect
361. C₄×C₅	C₂×C₃×M₁₆	semidirect
403. C₃×C₅	D₄×M₁₆	semidirect
413. C₂²×C₃	C₂×#704	semidirect
423. C₃×C₄	C₂×#704	semidirect
438. D₄	C₃×#704	direct (N × H)
467. C₅	C₃×D₄×M₁₆	semidirect
477. C₂²	C₂×C₃×#704	semidirect
487. C₄	C₂×C₃×#704	semidirect
488. C₃	D₄×#704	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×#704	2
C₂×C₃×D₄×Dic₅	2
C₃×#65798	2
C₃×#65774	2
C₃×#65773	2
C₃×D₄×#170	2
C₃×#65758	2
C₃×C₄×#704	2
D₄×#704	3
C₃×D₄×M₁₆	5

Subgroups — C3×D4×#704 #14415692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×#704 #14415692