Subgroups — C₃×D₄×#676 #14415667

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#676	C₂	1	2	yes	maximal, complemented
2	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65400	C₂	1	2	yes	maximal, complemented
5	C₃×D₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65127	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65126	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65019	C₂	1	2	yes	maximal, complemented
9	C₃×#65015	C₂	1	2	yes	maximal, complemented
10	C₃×#64977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#676	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×#676	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×D₄×D₅	C₄	1	1	yes	characteristic
14	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₃×D₄×Dic₅	C₄	1	1	yes	characteristic
18	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
19	C₂²×C₃×#168	C₂²	1	2	yes	complemented
20	C₂×C₃×#676	—	2	8	no	—
21	C₂×C₃×#676	C₂²	1	2	yes	—
22	C₂×C₃×#676	C₂²	1	1	yes	characteristic
23	C₂×C₃×#676	C₂²	1	1	yes	characteristic
24	C₂×C₃×#676	C₂²	1	2	yes	complemented
25	C₂×C₃×#676	C₂²	1	2	yes	complemented
26	C₃×#4039	C₄	1	1	yes	characteristic
27	C₃×D₅×C₄⋊C₄	C₄	1	1	yes	characteristic
28	C₃×#4027	C₄	1	2	yes	—
29	C₃×D₅×C₂²⋊C₄	C₄	1	2	yes	—
30	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
31	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
34	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₂²⋊#168	C₂²	1	2	yes	complemented
36	C₃×#3952	C₂²	1	2	yes	complemented
37	C₃×#3952	C₂²	1	2	yes	complemented
38	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3946	C₂²	1	2	yes	complemented
41	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
42	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
43	C₃×D₄×M₁₆	—	5	1	no	maximal, Hall
44	C₂²×#676	C₂×C₃	1	2	yes	complemented
45	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic
46	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
47	#65400	C₂×C₃	1	2	yes	complemented
48	D₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
49	#65127	C₂×C₃	1	1	yes	characteristic, complemented
50	#65126	C₂×C₃	1	1	yes	characteristic, complemented
51	#65019	C₂×C₃	1	2	yes	complemented
52	#65015	C₂×C₃	1	2	yes	complemented
53	#64977	C₂×C₃	1	1	yes	characteristic, complemented
54	C₄×#676	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
59	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
60	C₃×D₄×D₅	—	2	4	no	—
61	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	—	2	4	no	—
63	C₂×C₃×C₄×D₅	—	2	4	no	—
64	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
65	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
66	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
69	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	—	2	4	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
78	C₃×#685	C₂×C₄	1	2	yes	—
79	C₃×#685	C₂×C₄	1	2	yes	—
80	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₃×#683	C₂×C₄	1	2	yes	—
82	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
85	C₂×C₃×#168	—	2	4	no	—
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₂×C₃×#168	C₂³	1	2	yes	—
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₃×#676	—	2	4	no	—
90	C₃×#676	—	2	2	no	—
91	C₃×#676	—	2	4	no	—
92	C₃×#676	—	2	4	no	—
93	C₃×#676	D₄	1	4	yes	direct product factor
94	C₂²×C₃×M₁₆	—	5	2	no	—
95	C₂×C₃×C₄×D₄	—	5	1	no	—
96	C₃×#436	—	5	1	no	—
97	C₃×#436	—	5	1	no	—
98	C₃×#435	—	5	2	no	—
99	C₃×#435	—	5	2	no	—
100	C₃×C₈×D₄	—	5	1	no	—
101	C₃×C₈×D₄	D₅	1	1	yes	characteristic, complemented
102	C₃×#423	—	5	1	no	—
103	C₃×#407	—	5	2	no	—
104	C₃×C₄×M₁₆	—	5	1	no	—
105	C₂×D₄×D₅	C₃×C₄	1	1	yes	characteristic
106	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
107	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
108	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
109	D₄×Dic₅	C₃×C₄	1	1	yes	characteristic
110	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
111	C₂²×#168	C₂²×C₃	1	2	yes	complemented
112	C₂×#676	—	2	8	no	—
113	C₂×#676	C₂²×C₃	1	2	yes	—
114	C₂×#676	C₂²×C₃	1	1	yes	characteristic
115	C₂×#676	C₂²×C₃	1	1	yes	characteristic
116	C₂×#676	C₂²×C₃	1	2	yes	complemented
117	C₂×#676	C₂²×C₃	1	2	yes	complemented
118	#4039	C₃×C₄	1	1	yes	characteristic
119	D₅×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
120	#4027	C₃×C₄	1	2	yes	—
121	D₅×C₂²⋊C₄	C₃×C₄	1	2	yes	—
122	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
123	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
124	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
126	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂²⋊#168	C₂²×C₃	1	2	yes	complemented
128	#3952	C₂²×C₃	1	2	yes	complemented
129	#3952	C₂²×C₃	1	2	yes	complemented
130	#3947	C₂²×C₃	1	1	yes	characteristic, complemented
131	#3947	C₂²×C₃	1	1	yes	characteristic, complemented
132	#3946	C₂²×C₃	1	2	yes	complemented
133	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
134	C₄×#168	C₂²×C₃	1	1	yes	characteristic, complemented
135	D₄×M₁₆	—	5	1	no	Sylow
136	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
137	C₂²×C₃×D₅	—	2	4	no	—
138	C₂²×C₃×D₅	—	2	4	no	—
139	C₂²×C₃×D₅	—	4	2	no	—
140	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
141	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
142	C₃×C₅×D₄	M₁₆	1	4	yes	complemented
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₃×C₂²⋊D₅	—	2	4	no	—
150	C₂×C₃×Dic₅	—	2	4	no	—
151	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
154	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
155	C₃×D₂₀	—	2	2	no	—
156	C₃×C₄×D₅	—	2	4	no	—
157	C₃×C₄×D₅	—	2	2	no	—
158	C₃×C₄×D₅	—	2	2	no	—
159	C₃×C₄×D₅	—	2	2	no	—
160	C₃×C₄×D₅	—	2	4	no	—
161	C₃×C₄×D₅	—	4	1	no	—
162	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
163	C₃×C₄×D₅	#41	1	2	yes	—
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×C₅×C₈	—	2	1	no	—
166	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
167	C₃×#168	—	2	2	no	—
168	C₃×#168	—	2	1	no	—
169	C₃×#168	C₂×D₄	1	2	yes	complemented
170	C₂²×C₃×D₄	—	5	1	no	—
171	C₂³×C₃×C₄	—	5	2	no	—
172	C₂×C₃×M₁₆	—	5	1	no	—
173	C₂×C₃×M₁₆	—	5	2	no	—
174	C₂×C₃×M₁₆	—	5	2	no	—
175	C₂×C₃×M₁₆	—	5	2	no	—
176	C₂×C₃×M₁₆	—	5	1	no	—
177	C₂×C₃×M₁₆	—	10	8	no	—
178	C₂²×C₃×C₈	—	5	2	no	—
179	C₂²×C₃×C₈	C₂×D₅	1	2	yes	complemented
180	C₃×C₄×D₄	—	5	1	no	—
181	C₃×C₄×D₄	—	5	2	no	—
182	C₃×C₄×D₄	—	5	1	no	—
183	C₃×C₄×D₄	—	5	2	no	—
184	C₃×C₄×D₄	—	5	1	no	—
185	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
186	C₂×C₃×C₄⋊C₄	—	5	1	no	—
187	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
188	C₂×C₃×C₄²	—	5	1	no	—
189	C₃×C₄⋊C₈	—	5	2	no	—
190	C₃×C₄⋊C₈	—	5	1	no	—
191	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
192	C₃×C₂²⋊C₈	—	5	2	no	—
193	C₃×C₂²⋊C₈	—	5	2	no	—
194	C₃×C₂²⋊C₈	—	5	2	no	—
195	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	complemented
196	C₃×#97	—	5	1	no	—
197	C₃×#97	—	5	1	no	—
198	C₃×C₄×C₈	—	5	1	no	—
199	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
200	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
201	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
203	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
204	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
205	D₄×D₅	—	2	4	no	—
206	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂×C₄×D₅	—	2	4	no	—
208	C₂×C₄×D₅	—	2	4	no	—
209	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
210	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
211	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
212	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
213	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
214	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
215	C₂×C₅×C₈	—	2	4	no	—
216	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
217	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
219	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
220	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
221	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
222	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
223	#685	C₂×C₃×C₄	1	2	yes	—
224	#685	C₂×C₃×C₄	1	2	yes	—
225	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
226	#683	C₂×C₃×C₄	1	2	yes	—
227	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
228	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
229	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
230	C₂×#168	—	2	4	no	—
231	C₂×#168	C₂³×C₃	1	1	yes	characteristic
232	C₂×#168	C₂³×C₃	1	2	yes	—
233	C₂×#168	C₂³×C₃	1	1	yes	characteristic
234	#676	—	2	4	no	—
235	#676	—	2	2	no	—
236	#676	—	2	4	no	—
237	#676	—	2	4	no	—
238	#676	C₃×D₄	1	4	yes	direct product factor
239	C₂²×M₁₆	—	5	2	no	—
240	C₂×C₄×D₄	—	5	1	no	—
241	#436	—	5	1	no	—
242	#436	—	5	1	no	—
243	#435	—	5	2	no	—
244	#435	—	5	2	no	—
245	C₈×D₄	—	5	1	no	—
246	C₈×D₄	C₃×D₅	1	1	yes	characteristic, complemented
247	#423	—	5	1	no	—
248	#407	—	5	2	no	—
249	C₄×M₁₆	—	5	1	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	complemented
253	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₃×D₅	—	2	1	no	—
255	C₂×C₃×D₅	—	2	1	no	—
256	C₂×C₃×D₅	—	2	2	no	—
257	C₂×C₃×D₅	—	2	2	no	—
258	C₂×C₃×D₅	—	2	2	no	—
259	C₂×C₃×D₅	—	4	8	no	—
260	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
261	C₃×C₄×C₅	—	2	2	no	—
262	C₃×C₄×C₅	—	2	1	no	—
263	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	complemented
264	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
265	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
266	C₃×Dic₅	—	2	2	no	—
267	C₃×Dic₅	—	2	1	no	—
268	C₃×Dic₅	—	2	1	no	—
269	C₃×Dic₅	C₄×D₄	1	2	yes	—
270	C₂⁴×C₃	—	5	2	no	—
271	C₂×C₃×D₄	—	5	2	no	—
272	C₂×C₃×D₄	—	5	1	no	—
273	C₂×C₃×D₄	—	10	4	no	—
274	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
275	C₂²×C₃×C₄	—	5	1	no	—
276	C₂²×C₃×C₄	—	5	2	no	—
277	C₂²×C₃×C₄	—	5	1	no	—
278	C₂²×C₃×C₄	—	5	2	no	—
279	C₂²×C₃×C₄	—	5	2	no	—
280	C₂²×C₃×C₄	—	5	2	no	—
281	C₂²×C₃×C₄	—	5	1	no	—
282	C₂²×C₃×C₄	—	10	4	no	—
283	C₂²×C₃×C₄	—	10	4	no	—
284	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
285	C₃×M₁₆	—	5	4	no	—
286	C₃×M₁₆	—	10	4	no	—
287	C₃×M₁₆	—	10	2	no	—
288	C₃×M₁₆	—	10	4	no	—
289	C₃×M₁₆	—	10	4	no	—
290	C₂×C₃×C₈	—	2	4	no	—
291	C₂×C₃×C₈	—	5	1	no	—
292	C₂×C₃×C₈	—	5	1	no	—
293	C₂×C₃×C₈	—	5	2	no	—
294	C₂×C₃×C₈	—	10	4	no	—
295	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
296	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
297	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
298	C₃×C₄⋊C₄	—	5	2	no	—
299	C₃×C₄⋊C₄	—	5	1	no	—
300	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
301	C₃×C₂²⋊C₄	—	5	2	no	—
302	C₃×C₂²⋊C₄	—	5	2	no	—
303	C₃×C₂²⋊C₄	—	5	2	no	—
304	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
305	C₃×C₄²	—	5	1	no	—
306	C₃×C₄²	—	5	1	no	—
307	C₃×C₄²	—	5	1	no	—
308	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
309	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
310	C₂²×D₅	—	2	4	no	—
311	C₂²×D₅	—	2	4	no	—
312	C₂²×D₅	—	4	2	no	—
313	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
314	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
315	C₅×D₄	C₃×M₁₆	1	4	yes	complemented
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
320	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
322	C₂²⋊D₅	—	2	4	no	—
323	C₂×Dic₅	—	2	4	no	—
324	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
325	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
326	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
327	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
328	D₂₀	—	2	2	no	—
329	C₄×D₅	—	2	4	no	—
330	C₄×D₅	—	2	2	no	—
331	C₄×D₅	—	2	2	no	—
332	C₄×D₅	—	2	2	no	—
333	C₄×D₅	—	2	4	no	—
334	C₄×D₅	—	4	1	no	—
335	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
336	C₄×D₅	C₃×#41	1	2	yes	—
337	C₅×C₈	—	2	2	no	—
338	C₅×C₈	—	2	1	no	—
339	C₅×C₈	C₂×C₃×D₄	1	2	yes	complemented
340	#168	—	2	2	no	—
341	#168	—	2	1	no	—
342	#168	C₂×C₃×D₄	1	2	yes	complemented
343	C₂²×D₄	—	5	1	no	—
344	C₂³×C₄	—	5	2	no	—
345	C₂×M₁₆	—	5	1	no	—
346	C₂×M₁₆	—	5	2	no	—
347	C₂×M₁₆	—	5	2	no	—
348	C₂×M₁₆	—	5	2	no	—
349	C₂×M₁₆	—	5	1	no	—
350	C₂×M₁₆	—	10	8	no	—
351	C₂²×C₈	—	5	2	no	—
352	C₂²×C₈	C₂×C₃×D₅	1	2	yes	complemented
353	C₄×D₄	—	5	1	no	—
354	C₄×D₄	—	5	2	no	—
355	C₄×D₄	—	5	1	no	—
356	C₄×D₄	—	5	2	no	—
357	C₄×D₄	—	5	1	no	—
358	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
359	C₂×C₄⋊C₄	—	5	1	no	—
360	C₂×C₂²⋊C₄	—	5	2	no	—
361	C₂×C₄²	—	5	1	no	—
362	C₄⋊C₈	—	5	2	no	—
363	C₄⋊C₈	—	5	1	no	—
364	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
365	C₂²⋊C₈	—	5	2	no	—
366	C₂²⋊C₈	—	5	2	no	—
367	C₂²⋊C₈	—	5	2	no	—
368	C₂²⋊C₈	C₂×C₃×D₅	1	2	yes	complemented
369	#97	—	5	1	no	—
370	#97	—	5	1	no	—
371	C₄×C₈	—	5	1	no	—
372	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
373	C₂×C₃×C₅	—	2	4	no	—
374	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
375	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
376	C₂×C₃×C₅	#568	1	1	yes	characteristic
377	C₃×D₅	—	2	2	no	—
378	C₃×D₅	—	4	2	no	—
379	C₂³×C₃	—	5	1	no	—
380	C₂³×C₃	—	5	2	no	—
381	C₂³×C₃	—	10	4	no	—
382	C₂³×C₃	—	10	4	no	—
383	C₂³×C₃	—	20	2	no	—
384	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
385	C₃×D₄	—	10	4	no	—
386	C₃×D₄	—	10	2	no	—
387	C₃×D₄	#676	1	4	yes	direct product factor
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	5	1	no	—
391	C₂×C₃×C₄	—	5	2	no	—
392	C₂×C₃×C₄	—	5	2	no	—
393	C₂×C₃×C₄	—	5	1	no	—
394	C₂×C₃×C₄	—	5	1	no	—
395	C₂×C₃×C₄	—	5	2	no	—
396	C₂×C₃×C₄	—	10	4	no	—
397	C₂×C₃×C₄	—	10	4	no	—
398	C₂×C₃×C₄	—	10	4	no	—
399	C₂×C₃×C₄	—	10	2	no	—
400	C₂×C₃×C₄	—	10	2	no	—
401	C₂×C₃×C₄	—	10	2	no	—
402	C₂×C₃×C₄	—	20	1	no	—
403	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
405	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
407	C₃×C₈	—	2	2	no	—
408	C₃×C₈	—	2	1	no	—
409	C₃×C₈	—	5	2	no	—
410	C₃×C₈	—	10	2	no	—
411	C₃×C₈	—	10	1	no	—
412	C₃×C₈	D₄×D₅	1	2	yes	complemented
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	C₂×C₃×M₁₆	1	4	yes	complemented
416	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
417	C₂×D₅	—	2	1	no	—
418	C₂×D₅	—	2	1	no	—
419	C₂×D₅	—	2	2	no	—
420	C₂×D₅	—	2	2	no	—
421	C₂×D₅	—	2	2	no	—
422	C₂×D₅	—	4	8	no	—
423	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
424	C₄×C₅	—	2	1	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	complemented
427	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
428	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
429	Dic₅	—	2	1	no	—
430	Dic₅	—	2	1	no	—
431	Dic₅	—	2	2	no	—
432	Dic₅	C₃×C₄×D₄	1	2	yes	—
433	C₂⁴	—	5	2	no	—
434	C₂×D₄	—	5	2	no	—
435	C₂×D₄	—	5	1	no	—
436	C₂×D₄	—	10	4	no	—
437	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
438	C₂²×C₄	—	5	1	no	—
439	C₂²×C₄	—	5	2	no	—
440	C₂²×C₄	—	5	1	no	—
441	C₂²×C₄	—	5	2	no	—
442	C₂²×C₄	—	5	2	no	—
443	C₂²×C₄	—	5	2	no	—
444	C₂²×C₄	—	5	1	no	—
445	C₂²×C₄	—	10	4	no	—
446	C₂²×C₄	—	10	4	no	—
447	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
448	M₁₆	—	5	4	no	—
449	M₁₆	—	10	4	no	—
450	M₁₆	—	10	4	no	—
451	M₁₆	—	10	2	no	—
452	M₁₆	—	10	4	no	—
453	C₂×C₈	—	2	4	no	—
454	C₂×C₈	—	5	1	no	—
455	C₂×C₈	—	5	1	no	—
456	C₂×C₈	—	5	2	no	—
457	C₂×C₈	—	10	4	no	—
458	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
459	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
460	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
461	C₄⋊C₄	—	5	2	no	—
462	C₄⋊C₄	—	5	1	no	—
463	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
464	C₂²⋊C₄	—	5	2	no	—
465	C₂²⋊C₄	—	5	2	no	—
466	C₂²⋊C₄	—	5	2	no	—
467	C₂²⋊C₄	C₃×C₄×D₅	1	2	yes	—
468	C₄²	—	5	1	no	—
469	C₄²	—	5	1	no	—
470	C₄²	—	5	1	no	—
471	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
472	C₃×C₅	D₄×M₁₆	1	1	yes	characteristic, complemented, Hall
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	5	2	no	—
476	C₂²×C₃	—	10	1	no	—
477	C₂²×C₃	—	10	1	no	—
478	C₂²×C₃	—	10	2	no	—
479	C₂²×C₃	—	10	2	no	—
480	C₂²×C₃	—	10	2	no	—
481	C₂²×C₃	—	20	8	no	—
482	C₂²×C₃	C₂×#676	1	4	yes	complemented
483	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	2	2	no	—
486	C₃×C₄	—	5	2	no	—
487	C₃×C₄	—	10	1	no	—
488	C₃×C₄	—	10	1	no	—
489	C₃×C₄	—	10	2	no	—
490	C₃×C₄	C₂×#676	1	2	yes	complemented
491	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
492	C₃×C₄	D₅×#41	1	1	yes	characteristic
493	C₂×C₅	—	2	4	no	—
494	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
495	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
496	C₂×C₅	C₃×#568	1	1	yes	characteristic
497	D₅	—	2	2	no	—
498	D₅	—	4	2	no	—
499	C₂³	—	5	1	no	—
500	C₂³	—	5	2	no	—
501	C₂³	—	10	4	no	—
502	C₂³	—	10	4	no	—
503	C₂³	—	20	2	no	—
504	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
505	D₄	—	10	4	no	—
506	D₄	—	10	2	no	—
507	D₄	C₃×#676	1	4	yes	direct product factor
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	5	1	no	—
511	C₂×C₄	—	5	2	no	—
512	C₂×C₄	—	5	2	no	—
513	C₂×C₄	—	5	1	no	—
514	C₂×C₄	—	5	1	no	—
515	C₂×C₄	—	5	2	no	—
516	C₂×C₄	—	10	4	no	—
517	C₂×C₄	—	10	4	no	—
518	C₂×C₄	—	10	4	no	—
519	C₂×C₄	—	10	2	no	—
520	C₂×C₄	—	10	2	no	—
521	C₂×C₄	—	10	2	no	—
522	C₂×C₄	—	20	1	no	—
523	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
524	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
525	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
526	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
527	C₈	—	2	2	no	—
528	C₈	—	2	1	no	—
529	C₈	—	5	2	no	—
530	C₈	—	10	2	no	—
531	C₈	—	10	1	no	—
532	C₈	C₃×D₄×D₅	1	2	yes	complemented
533	C₂×C₃	—	2	4	no	—
534	C₂×C₃	—	10	2	no	—
535	C₂×C₃	—	20	2	no	—
536	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
537	C₂×C₃	C₂²×#676	1	1	yes	characteristic
538	C₂×C₃	#66084	1	1	yes	characteristic
539	C₅	C₃×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	5	2	no	—
543	C₂²	—	10	1	no	—
544	C₂²	—	10	1	no	—
545	C₂²	—	10	2	no	—
546	C₂²	—	10	2	no	—
547	C₂²	—	10	2	no	—
548	C₂²	—	20	8	no	—
549	C₂²	C₂×C₃×#676	1	4	yes	complemented
550	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
551	C₄	—	2	2	no	—
552	C₄	—	2	1	no	—
553	C₄	—	5	2	no	—
554	C₄	—	10	2	no	—
555	C₄	—	10	1	no	—
556	C₄	—	10	1	no	—
557	C₄	C₂×C₃×#676	1	2	yes	complemented
558	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
559	C₄	C₃×D₅×#41	1	1	yes	characteristic
560	C₃	D₄×#676	1	1	yes	characteristic, direct product factor, Sylow
561	C₂	—	2	4	no	—
562	C₂	—	10	2	no	—
563	C₂	—	20	2	no	—
564	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
565	C₂	C₂²×C₃×#676	1	1	yes	characteristic
566	C₂	C₃×#66084	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×C₈×D₄	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×D₄×D₅	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₈×D₄	D₅
hypocenter	C₅	C₃×D₄×M₁₆
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×#676	C₂	semidirect
3. C₃×C₅×C₈×D₄	C₂	semidirect
4. C₃×#65400	C₂	semidirect
5. C₃×D₄×#168	C₂	semidirect
6. C₃×#65127	C₂	semidirect
7. C₃×#65126	C₂	semidirect
8. C₃×#65019	C₂	semidirect
9. C₃×#65015	C₂	semidirect
10. C₃×#64977	C₂	semidirect
11. C₃×C₄×#676	C₂	semidirect
12. D₄×#676	C₃	direct (N × H)
15. C₂²×C₃×C₅×C₈	C₂²	semidirect
19. C₂²×C₃×#168	C₂²	semidirect
24. C₂×C₃×#676	C₂²	semidirect
25. C₂×C₃×#676	C₂²	semidirect
32. C₃×C₅×C₄⋊C₈	C₂²	semidirect
33. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
34. C₃×C₄×C₅×C₈	C₂²	semidirect
35. C₃×C₂²⋊#168	C₂²	semidirect
36. C₃×#3952	C₂²	semidirect
37. C₃×#3952	C₂²	semidirect
38. C₃×#3947	C₂²	semidirect
39. C₃×#3947	C₂²	semidirect
40. C₃×#3946	C₂²	semidirect
41. C₃×C₄⋊#168	C₂²	semidirect
42. C₃×C₄×#168	C₂²	semidirect
44. C₂²×#676	C₂×C₃	semidirect
46. C₅×C₈×D₄	C₂×C₃	semidirect
47. #65400	C₂×C₃	semidirect
48. D₄×#168	C₂×C₃	semidirect
49. #65127	C₂×C₃	semidirect
50. #65126	C₂×C₃	semidirect
51. #65019	C₂×C₃	semidirect
52. #65015	C₂×C₃	semidirect
53. #64977	C₂×C₃	semidirect
54. C₄×#676	C₂×C₃	semidirect
93. C₃×#676	D₄	direct (N × H)
101. C₃×C₈×D₄	D₅	semidirect
107. C₂²×C₅×C₈	C₂²×C₃	semidirect
111. C₂²×#168	C₂²×C₃	semidirect
116. C₂×#676	C₂²×C₃	semidirect
117. C₂×#676	C₂²×C₃	semidirect
124. C₅×C₄⋊C₈	C₂²×C₃	semidirect
125. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
126. C₄×C₅×C₈	C₂²×C₃	semidirect
127. C₂²⋊#168	C₂²×C₃	semidirect
128. #3952	C₂²×C₃	semidirect
129. #3952	C₂²×C₃	semidirect
130. #3947	C₂²×C₃	semidirect
131. #3947	C₂²×C₃	semidirect
132. #3946	C₂²×C₃	semidirect
133. C₄⋊#168	C₂²×C₃	semidirect
134. C₄×#168	C₂²×C₃	semidirect
142. C₃×C₅×D₄	M₁₆	semidirect
166. C₃×C₅×C₈	C₂×D₄	semidirect
169. C₃×#168	C₂×D₄	semidirect
179. C₂²×C₃×C₈	C₂×D₅	semidirect
191. C₃×C₄⋊C₈	C₂×D₅	semidirect
195. C₃×C₂²⋊C₈	C₂×D₅	semidirect
199. C₃×C₄×C₈	C₂×D₅	semidirect
238. #676	C₃×D₄	direct (N × H)
246. C₈×D₄	C₃×D₅	semidirect
252. C₂²×C₃×C₅	C₂×M₁₆	semidirect
263. C₃×C₄×C₅	C₂×M₁₆	semidirect
315. C₅×D₄	C₃×M₁₆	semidirect
339. C₅×C₈	C₂×C₃×D₄	semidirect
342. #168	C₂×C₃×D₄	semidirect
352. C₂²×C₈	C₂×C₃×D₅	semidirect
364. C₄⋊C₈	C₂×C₃×D₅	semidirect
368. C₂²⋊C₈	C₂×C₃×D₅	semidirect
372. C₄×C₈	C₂×C₃×D₅	semidirect
387. C₃×D₄	#676	direct (N × H)
412. C₃×C₈	D₄×D₅	semidirect
415. C₂²×C₅	C₂×C₃×M₁₆	semidirect
426. C₄×C₅	C₂×C₃×M₁₆	semidirect
472. C₃×C₅	D₄×M₁₆	semidirect
482. C₂²×C₃	C₂×#676	semidirect
490. C₃×C₄	C₂×#676	semidirect
507. D₄	C₃×#676	direct (N × H)
532. C₈	C₃×D₄×D₅	semidirect
539. C₅	C₃×D₄×M₁₆	semidirect
549. C₂²	C₂×C₃×#676	semidirect
557. C₄	C₂×C₃×#676	semidirect
560. C₃	D₄×#676	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×#676	2
C₃×C₄×D₄×D₅	2
C₃×C₅×C₈×D₄	2
C₃×#65400	2
C₃×D₄×#168	2
C₃×#65127	2
C₃×#65126	2
C₃×#65019	2
C₃×#65015	2
C₃×#64977	2
C₃×C₄×#676	2
D₄×#676	3
C₃×D₄×M₁₆	5

Subgroups — C3×D4×#676 #14415667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×#676 #14415667