Subgroups — C₃×C₄×#4034 #14322301

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4034	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×Dic₁₀	C₂	1	2	yes	maximal
3	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×#65274	C₂	1	1	yes	maximal, characteristic
5	C₃×#65265	C₂	1	1	yes	maximal, characteristic
6	C₃×#65262	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×#683	C₂	1	2	yes	maximal
9	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
10	C₃×#64936	C₂	1	2	yes	maximal
11	C₃×#64935	C₂	1	2	yes	maximal
12	C₄×#4034	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×#683	C₂²	1	2	yes	—
22	C₂×C₃×#683	C₂²	1	2	yes	—
23	C₂×C₃×#683	C₂²	1	2	yes	—
24	C₂×C₃×#683	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
29	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
32	C₃×#4034	C₄	1	8	yes	direct product factor
33	C₃×C₄×Dic₁₀	—	2	8	no	—
34	C₃×C₅×#95	C₂²	1	2	yes	—
35	C₃×#3963	C₂²	1	2	yes	—
36	C₃×#3963	C₂²	1	2	yes	—
37	C₃×#3963	C₂²	1	2	yes	—
38	C₃×C₄×C₄⋊Q₈	—	5	1	no	maximal, Hall
39	C₂×#4034	C₂×C₃	1	1	yes	characteristic
40	C₂×C₄×Dic₁₀	C₂×C₃	1	2	yes	—
41	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
42	#65274	C₂×C₃	1	1	yes	characteristic
43	#65265	C₂×C₃	1	1	yes	characteristic
44	#65262	C₂×C₃	1	1	yes	characteristic
45	C₄×C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic
46	C₄×#683	C₂×C₃	1	2	yes	—
47	C₄²×Dic₅	C₂×C₃	1	1	yes	characteristic
48	#64936	C₂×C₃	1	2	yes	—
49	#64935	C₂×C₃	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
56	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
57	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
59	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
60	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
61	C₂×C₃×Dic₁₀	—	2	4	no	—
62	C₂×C₃×Dic₁₀	—	2	4	no	—
63	C₂×C₃×Dic₁₀	C₂×C₄	1	8	yes	—
64	C₃×C₅×C₄⋊C₄	—	2	2	no	—
65	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
66	C₃×C₄²×C₅	—	2	4	no	—
67	C₃×C₄²×C₅	Q₈	1	4	yes	complemented
68	C₃×C₄⋊Dic₅	—	2	2	no	—
69	C₃×C₄⋊Dic₅	—	2	4	no	—
70	C₃×C₄⋊Dic₅	C₂×C₄	1	4	yes	—
71	C₃×#683	—	2	4	no	—
72	C₃×#683	—	2	4	no	—
73	C₃×#683	—	2	4	no	—
74	C₃×#683	C₂×C₄	1	8	yes	—
75	C₃×C₄×Dic₅	—	2	4	no	—
76	C₃×C₄×Dic₅	—	2	2	no	—
77	C₃×C₄×Dic₅	—	2	2	no	—
78	C₃×C₄×Dic₅	—	2	2	no	—
79	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
80	C₃×C₄×Dic₅	D₄	1	4	yes	—
81	C₃×C₄×Dic₅	Q₈	1	4	yes	complemented
82	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
83	C₂×C₃×C₄×Q₈	—	5	2	no	—
84	C₃×#391	—	5	2	no	—
85	C₃×#389	—	5	1	no	—
86	C₃×#389	—	5	1	no	—
87	C₃×#389	—	5	2	no	—
88	C₃×#384	—	5	1	no	—
89	C₃×C₄×C₄⋊C₄	—	5	2	no	—
90	C₃×C₄×C₄⋊C₄	—	5	1	no	—
91	C₃×C₄×C₄⋊C₄	D₅	1	1	yes	characteristic
92	C₃×C₄³	—	5	1	no	—
93	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
94	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
97	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
99	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
101	C₂×#683	C₂²×C₃	1	2	yes	—
102	C₂×#683	C₂²×C₃	1	2	yes	—
103	C₂×#683	C₂²×C₃	1	2	yes	—
104	C₂×#683	C₂²×C₃	1	2	yes	—
105	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
106	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
112	#4034	C₃×C₄	1	8	yes	direct product factor
113	C₄×Dic₁₀	—	2	8	no	—
114	C₅×#95	C₂²×C₃	1	2	yes	—
115	#3963	C₂²×C₃	1	2	yes	—
116	#3963	C₂²×C₃	1	2	yes	—
117	#3963	C₂²×C₃	1	2	yes	—
118	C₄×C₄⋊Q₈	—	5	1	no	Sylow
119	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	1	no	—
122	C₂×C₃×C₄×C₅	—	2	1	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
134	C₂×C₃×C₄×C₅	#41	1	2	yes	—
135	C₂×C₃×Dic₅	—	2	2	no	—
136	C₂×C₃×Dic₅	—	2	1	no	—
137	C₂×C₃×Dic₅	—	2	1	no	—
138	C₂×C₃×Dic₅	—	2	1	no	—
139	C₂×C₃×Dic₅	—	2	1	no	—
140	C₂×C₃×Dic₅	—	2	2	no	—
141	C₂×C₃×Dic₅	—	2	2	no	—
142	C₂×C₃×Dic₅	—	2	2	no	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
145	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
146	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
147	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
148	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
149	C₂×C₃×Dic₅	C₂×Q₈	1	2	yes	—
150	C₂×C₃×Dic₅	C₂×Q₈	1	2	yes	—
151	C₂×C₃×Dic₅	#41	1	2	yes	—
152	C₂×C₃×Dic₅	#41	1	2	yes	—
153	C₃×Dic₁₀	—	2	16	no	—
154	C₂²×C₃×Q₈	—	5	2	no	—
155	C₃×C₄⋊Q₈	—	5	8	no	—
156	C₃×C₄×Q₈	—	10	8	no	—
157	C₂×C₃×C₄⋊C₄	—	5	2	no	—
158	C₂×C₃×C₄⋊C₄	—	5	1	no	—
159	C₂×C₃×C₄⋊C₄	—	5	2	no	—
160	C₂×C₃×C₄⋊C₄	—	5	1	no	—
161	C₂×C₃×C₄⋊C₄	—	5	2	no	—
162	C₂×C₃×C₄⋊C₄	—	5	2	no	—
163	C₂×C₃×C₄⋊C₄	—	5	2	no	—
164	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
165	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
166	C₂×C₃×C₄²	—	5	1	no	—
167	C₂×C₃×C₄²	—	5	1	no	—
168	C₂×C₃×C₄²	—	5	1	no	—
169	C₂×C₃×C₄²	—	5	1	no	—
170	C₂×C₃×C₄²	—	5	1	no	—
171	C₂×C₃×C₄²	—	5	1	no	—
172	C₂×C₃×C₄²	—	5	2	no	—
173	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
174	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
175	C₃×#95	—	5	2	no	—
176	C₃×#95	—	5	2	no	—
177	C₃×#95	—	5	2	no	—
178	C₃×#95	C₂×D₅	1	2	yes	—
179	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
180	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
181	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
185	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
186	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
187	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
188	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
189	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
190	C₂×Dic₁₀	—	2	4	no	—
191	C₂×Dic₁₀	—	2	4	no	—
192	C₂×Dic₁₀	C₂×C₃×C₄	1	8	yes	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
195	C₄²×C₅	—	2	4	no	—
196	C₄²×C₅	C₃×Q₈	1	4	yes	complemented
197	C₄⋊Dic₅	—	2	2	no	—
198	C₄⋊Dic₅	—	2	4	no	—
199	C₄⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
200	#683	—	2	4	no	—
201	#683	—	2	4	no	—
202	#683	—	2	4	no	—
203	#683	C₂×C₃×C₄	1	8	yes	—
204	C₄×Dic₅	—	2	4	no	—
205	C₄×Dic₅	—	2	2	no	—
206	C₄×Dic₅	—	2	2	no	—
207	C₄×Dic₅	—	2	2	no	—
208	C₄×Dic₅	C₂×C₃×C₄	1	4	yes	—
209	C₄×Dic₅	C₃×D₄	1	4	yes	—
210	C₄×Dic₅	C₃×Q₈	1	4	yes	complemented
211	C₂×C₄⋊Q₈	—	5	1	no	—
212	C₂×C₄×Q₈	—	5	2	no	—
213	#391	—	5	2	no	—
214	#389	—	5	1	no	—
215	#389	—	5	1	no	—
216	#389	—	5	2	no	—
217	#384	—	5	1	no	—
218	C₄×C₄⋊C₄	—	5	2	no	—
219	C₄×C₄⋊C₄	—	5	1	no	—
220	C₄×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic
221	C₄³	—	5	1	no	—
222	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
223	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
225	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
226	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
227	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
228	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
229	C₃×C₄×C₅	—	2	4	no	—
230	C₃×C₄×C₅	—	2	2	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	C₄×Q₈	1	4	yes	complemented
233	C₃×C₄×C₅	C₄⋊Q₈	1	4	yes	complemented
234	C₃×Dic₅	—	2	4	no	—
235	C₃×Dic₅	—	2	2	no	—
236	C₃×Dic₅	—	2	2	no	—
237	C₃×Dic₅	—	4	2	no	—
238	C₃×Dic₅	C₄×D₄	1	4	yes	—
239	C₃×Dic₅	C₄×Q₈	1	4	yes	complemented
240	C₂×C₃×Q₈	—	5	8	no	—
241	C₂×C₃×Q₈	—	10	4	no	—
242	C₂×C₃×Q₈	—	10	4	no	—
243	C₂²×C₃×C₄	—	5	1	no	—
244	C₂²×C₃×C₄	—	5	1	no	—
245	C₂²×C₃×C₄	—	5	1	no	—
246	C₂²×C₃×C₄	—	5	2	no	—
247	C₂²×C₃×C₄	—	5	1	no	—
248	C₂²×C₃×C₄	—	5	2	no	—
249	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
250	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
252	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	—	2	2	no	—
255	C₃×C₄⋊C₄	—	5	8	no	—
256	C₃×C₄⋊C₄	—	5	4	no	—
257	C₃×C₄⋊C₄	—	10	4	no	—
258	C₃×C₄⋊C₄	—	10	4	no	—
259	C₃×C₄⋊C₄	—	10	4	no	—
260	C₃×C₄⋊C₄	—	10	4	no	—
261	C₃×C₄⋊C₄	—	10	2	no	—
262	C₃×C₄⋊C₄	C₄×D₅	1	4	yes	—
263	C₃×C₄²	—	2	4	no	—
264	C₃×C₄²	—	5	4	no	—
265	C₃×C₄²	—	5	4	no	—
266	C₃×C₄²	—	5	4	no	—
267	C₃×C₄²	—	10	2	no	—
268	C₃×C₄²	—	10	2	no	—
269	C₃×C₄²	—	10	2	no	—
270	C₃×C₄²	—	10	4	no	—
271	C₃×C₄²	Dic₁₀	1	4	yes	complemented
272	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
281	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
282	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
283	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
284	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
285	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
286	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
287	C₂×C₄×C₅	C₃×#41	1	2	yes	—
288	C₂×Dic₅	—	2	2	no	—
289	C₂×Dic₅	—	2	1	no	—
290	C₂×Dic₅	—	2	1	no	—
291	C₂×Dic₅	—	2	1	no	—
292	C₂×Dic₅	—	2	1	no	—
293	C₂×Dic₅	—	2	2	no	—
294	C₂×Dic₅	—	2	2	no	—
295	C₂×Dic₅	—	2	2	no	—
296	C₂×Dic₅	—	2	2	no	—
297	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
298	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
299	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
300	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
301	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
302	C₂×Dic₅	C₂×C₃×Q₈	1	2	yes	—
303	C₂×Dic₅	C₂×C₃×Q₈	1	2	yes	—
304	C₂×Dic₅	C₃×#41	1	2	yes	—
305	C₂×Dic₅	C₃×#41	1	2	yes	—
306	Dic₁₀	—	2	16	no	—
307	C₂²×Q₈	—	5	2	no	—
308	C₄⋊Q₈	—	5	8	no	—
309	C₄×Q₈	—	10	8	no	—
310	C₂×C₄⋊C₄	—	5	2	no	—
311	C₂×C₄⋊C₄	—	5	1	no	—
312	C₂×C₄⋊C₄	—	5	2	no	—
313	C₂×C₄⋊C₄	—	5	2	no	—
314	C₂×C₄⋊C₄	—	5	2	no	—
315	C₂×C₄⋊C₄	—	5	2	no	—
316	C₂×C₄⋊C₄	—	5	1	no	—
317	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
319	C₂×C₄²	—	5	1	no	—
320	C₂×C₄²	—	5	1	no	—
321	C₂×C₄²	—	5	1	no	—
322	C₂×C₄²	—	5	2	no	—
323	C₂×C₄²	—	5	1	no	—
324	C₂×C₄²	—	5	1	no	—
325	C₂×C₄²	—	5	1	no	—
326	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
327	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
328	#95	—	5	2	no	—
329	#95	—	5	2	no	—
330	#95	—	5	2	no	—
331	#95	C₂×C₃×D₅	1	2	yes	—
332	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
333	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
336	C₂×C₃×C₅	#532	1	1	yes	characteristic
337	C₂×C₃×C₅	#533	1	1	yes	characteristic
338	C₂×C₃×C₅	#533	1	1	yes	characteristic
339	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
340	C₃×Q₈	—	10	16	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	5	2	no	—
349	C₂×C₃×C₄	—	5	2	no	—
350	C₂×C₃×C₄	—	5	2	no	—
351	C₂×C₃×C₄	—	5	2	no	—
352	C₂×C₃×C₄	—	5	2	no	—
353	C₂×C₃×C₄	—	5	2	no	—
354	C₂×C₃×C₄	—	5	4	no	—
355	C₂×C₃×C₄	—	5	2	no	—
356	C₂×C₃×C₄	—	5	2	no	—
357	C₂×C₃×C₄	—	10	1	no	—
358	C₂×C₃×C₄	—	10	1	no	—
359	C₂×C₃×C₄	—	10	2	no	—
360	C₂×C₃×C₄	—	10	1	no	—
361	C₂×C₃×C₄	—	10	1	no	—
362	C₂×C₃×C₄	—	10	2	no	—
363	C₂×C₃×C₄	—	10	2	no	—
364	C₂×C₃×C₄	—	10	2	no	—
365	C₂×C₃×C₄	—	10	2	no	—
366	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
367	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
368	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
369	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
370	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
371	C₂×C₃×C₄	#709	1	2	yes	—
372	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
373	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
374	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
375	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
376	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
377	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
378	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
379	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
380	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
381	C₄×C₅	—	2	4	no	—
382	C₄×C₅	—	2	2	no	—
383	C₄×C₅	—	4	2	no	—
384	C₄×C₅	C₃×C₄×Q₈	1	4	yes	complemented
385	C₄×C₅	C₃×C₄⋊Q₈	1	4	yes	complemented
386	Dic₅	—	2	4	no	—
387	Dic₅	—	2	2	no	—
388	Dic₅	—	2	2	no	—
389	Dic₅	—	4	2	no	—
390	Dic₅	C₃×C₄×D₄	1	4	yes	—
391	Dic₅	C₃×C₄×Q₈	1	4	yes	complemented
392	C₂×Q₈	—	5	8	no	—
393	C₂×Q₈	—	10	4	no	—
394	C₂×Q₈	—	10	4	no	—
395	C₂²×C₄	—	5	1	no	—
396	C₂²×C₄	—	5	1	no	—
397	C₂²×C₄	—	5	1	no	—
398	C₂²×C₄	—	5	2	no	—
399	C₂²×C₄	—	5	1	no	—
400	C₂²×C₄	—	5	2	no	—
401	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
402	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
404	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
405	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	5	8	no	—
408	C₄⋊C₄	—	5	4	no	—
409	C₄⋊C₄	—	10	4	no	—
410	C₄⋊C₄	—	10	4	no	—
411	C₄⋊C₄	—	10	4	no	—
412	C₄⋊C₄	—	10	4	no	—
413	C₄⋊C₄	—	10	2	no	—
414	C₄⋊C₄	C₃×C₄×D₅	1	4	yes	—
415	C₄²	—	2	4	no	—
416	C₄²	—	5	4	no	—
417	C₄²	—	5	4	no	—
418	C₄²	—	5	4	no	—
419	C₄²	—	10	2	no	—
420	C₄²	—	10	2	no	—
421	C₄²	—	10	2	no	—
422	C₄²	—	10	4	no	—
423	C₄²	C₃×Dic₁₀	1	4	yes	complemented
424	C₃×C₅	C₄×C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
425	C₂²×C₃	C₂²×Dic₁₀	1	1	yes	characteristic
426	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
427	C₂²×C₃	C₂×#709	1	1	yes	characteristic
428	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
429	C₂²×C₃	C₂×Q₈×D₅	1	1	yes	characteristic
430	C₂²×C₃	D₅×#41	1	1	yes	characteristic
431	C₂²×C₃	D₅×#41	1	1	yes	characteristic
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	4	no	—
434	C₃×C₄	—	4	2	no	—
435	C₃×C₄	—	5	4	no	—
436	C₃×C₄	—	5	4	no	—
437	C₃×C₄	—	10	4	no	—
438	C₃×C₄	—	10	2	no	—
439	C₃×C₄	—	10	2	no	—
440	C₃×C₄	—	20	2	no	—
441	C₃×C₄	C₄×Dic₁₀	1	4	yes	complemented
442	C₃×C₄	#4034	1	4	yes	direct product factor
443	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
444	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
445	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
446	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
447	C₂×C₅	C₃×#532	1	1	yes	characteristic
448	C₂×C₅	C₃×#533	1	1	yes	characteristic
449	C₂×C₅	C₃×#533	1	1	yes	characteristic
450	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
451	Q₈	—	10	16	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	5	2	no	—
460	C₂×C₄	—	5	2	no	—
461	C₂×C₄	—	5	2	no	—
462	C₂×C₄	—	5	2	no	—
463	C₂×C₄	—	5	2	no	—
464	C₂×C₄	—	5	2	no	—
465	C₂×C₄	—	5	4	no	—
466	C₂×C₄	—	5	2	no	—
467	C₂×C₄	—	5	2	no	—
468	C₂×C₄	—	10	1	no	—
469	C₂×C₄	—	10	1	no	—
470	C₂×C₄	—	10	2	no	—
471	C₂×C₄	—	10	1	no	—
472	C₂×C₄	—	10	1	no	—
473	C₂×C₄	—	10	2	no	—
474	C₂×C₄	—	10	2	no	—
475	C₂×C₄	—	10	2	no	—
476	C₂×C₄	—	10	2	no	—
477	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
478	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
479	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
480	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
481	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
482	C₂×C₄	C₃×#709	1	2	yes	—
483	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
484	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
485	C₂×C₃	C₂×C₄×Dic₁₀	1	1	yes	characteristic
486	C₂×C₃	C₂×#4034	1	1	yes	characteristic
487	C₂×C₃	#65851	1	1	yes	characteristic
488	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
489	C₂×C₃	#65882	1	1	yes	characteristic
490	C₂×C₃	C₄×Q₈×D₅	1	1	yes	characteristic
491	C₂×C₃	#65912	1	1	yes	characteristic
492	C₅	C₃×C₄×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
493	C₂²	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
494	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
495	C₂²	C₂×C₃×#709	1	1	yes	characteristic
496	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
497	C₂²	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
498	C₂²	C₃×D₅×#41	1	1	yes	characteristic
499	C₂²	C₃×D₅×#41	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	4	2	no	—
503	C₄	—	5	4	no	—
504	C₄	—	5	4	no	—
505	C₄	—	10	4	no	—
506	C₄	—	10	2	no	—
507	C₄	—	10	2	no	—
508	C₄	—	20	2	no	—
509	C₄	C₃×C₄×Dic₁₀	1	4	yes	complemented
510	C₄	C₃×#4034	1	4	yes	direct product factor
511	C₃	C₄×#4034	1	1	yes	characteristic, direct product factor, Sylow
512	C₂	C₂×C₃×C₄×Dic₁₀	1	1	yes	characteristic
513	C₂	C₂×C₃×#4034	1	1	yes	characteristic
514	C₂	C₃×#65851	1	1	yes	characteristic
515	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
516	C₂	C₃×#65882	1	1	yes	characteristic
517	C₂	C₃×C₄×Q₈×D₅	1	1	yes	characteristic
518	C₂	C₃×#65912	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
12. C₄×#4034	C₃	direct (N × H)
32. C₃×#4034	C₄	direct (N × H)
67. C₃×C₄²×C₅	Q₈	semidirect
81. C₃×C₄×Dic₅	Q₈	semidirect
112. #4034	C₃×C₄	direct (N × H)
196. C₄²×C₅	C₃×Q₈	semidirect
210. C₄×Dic₅	C₃×Q₈	semidirect
232. C₃×C₄×C₅	C₄×Q₈	semidirect
233. C₃×C₄×C₅	C₄⋊Q₈	semidirect
239. C₃×Dic₅	C₄×Q₈	semidirect
271. C₃×C₄²	Dic₁₀	semidirect
384. C₄×C₅	C₃×C₄×Q₈	semidirect
385. C₄×C₅	C₃×C₄⋊Q₈	semidirect
391. Dic₅	C₃×C₄×Q₈	semidirect
423. C₄²	C₃×Dic₁₀	semidirect
424. C₃×C₅	C₄×C₄⋊Q₈	semidirect
441. C₃×C₄	C₄×Dic₁₀	semidirect
442. C₃×C₄	#4034	direct (N × H)
492. C₅	C₃×C₄×C₄⋊Q₈	semidirect
509. C₄	C₃×C₄×Dic₁₀	semidirect
510. C₄	C₃×#4034	direct (N × H)
511. C₃	C₄×#4034	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×C₃×#4034	2
C₂×C₃×C₄×Dic₁₀	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×#65274	2
C₃×#65265	2
C₃×#65262	2
C₃×C₄×C₄⋊Dic₅	2
C₃×C₄×#683	2
C₃×C₄²×Dic₅	2
C₃×#64936	2
C₃×#64935	2
C₄×#4034	3
C₃×C₄×C₄⋊Q₈	5

Subgroups — C3×C4×#4034 #14322301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4034 #14322301