Subgroups — C₃×C₄×#4097 #14416821

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4097	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65521	C₂	1	1	yes	maximal, characteristic
5	C₃×#65319	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#689	C₂	1	2	yes	maximal, complemented
7	C₃×#65307	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#687	C₂	1	2	yes	maximal, complemented
9	C₃×#65293	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65284	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#4097	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₅×D₄	—	2	1	no	—
18	C₃×C₄×C₅×D₄	—	2	1	no	—
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₃×C₅×#117	—	2	1	no	—
22	C₃×C₅×#117	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄²×C₅	—	2	1	no	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₃×#4097	C₄	1	8	yes	direct product factor
26	C₂×C₃×#689	C₂²	1	2	yes	—
27	C₂×C₃×#687	C₂²	1	2	yes	—
28	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×#683	—	2	1	no	—
30	C₂×C₃×C₄×Dic₅	—	2	1	no	—
31	C₂×C₃×#681	C₂²	1	1	yes	characteristic
32	C₂×C₃×#681	C₂²	1	1	yes	characteristic
33	C₃×C₄×Dic₁₀	—	2	1	no	—
34	C₃×C₄×Dic₁₀	—	2	1	no	—
35	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
36	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
37	C₃×#3967	C₂²	1	2	yes	—
38	C₃×#3964	C₂²	1	2	yes	—
39	C₃×#3942	C₂²	1	2	yes	—
40	C₃×#3942	C₂²	1	2	yes	—
41	C₃×#3940	C₂²	1	2	yes	—
42	C₃×#3939	C₂²	1	2	yes	—
43	C₃×#3935	C₂²	1	2	yes	—
44	C₃×C₄×#168	C₂²	1	2	yes	—
45	C₃×C₄×#137	—	5	1	no	maximal, Hall
46	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic
47	C₂×#4097	C₂×C₃	1	1	yes	characteristic
48	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
49	#65521	C₂×C₃	1	1	yes	characteristic
50	#65319	C₂×C₃	1	2	yes	complemented
51	C₄×#689	C₂×C₃	1	2	yes	complemented
52	#65307	C₂×C₃	1	2	yes	complemented
53	C₄×#687	C₂×C₃	1	2	yes	complemented
54	#65293	C₂×C₃	1	1	yes	characteristic, complemented
55	#65284	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×#681	C₂×C₃	1	1	yes	characteristic, complemented
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	C₂×C₄	1	4	yes	—
59	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×Dic₅	—	2	1	no	—
69	C₂²×C₃×Dic₅	—	2	1	no	—
70	C₂×C₃×Dic₁₀	—	2	1	no	—
71	C₂×C₃×Dic₁₀	—	2	2	no	—
72	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	complemented
73	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
79	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
80	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₃×C₄²×C₅	—	2	1	no	—
82	C₃×C₄²×C₅	—	2	1	no	—
83	C₃×C₄²×C₅	—	2	1	no	—
84	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
85	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
86	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
87	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₃×#689	C₂×C₄	1	8	yes	complemented
89	C₃×#687	C₂×C₄	1	8	yes	complemented
90	C₃×C₄⋊Dic₅	—	2	1	no	—
91	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
92	C₃×#683	—	2	2	no	—
93	C₃×#683	—	2	2	no	—
94	C₃×C₄×Dic₅	—	2	2	no	—
95	C₃×C₄×Dic₅	—	2	2	no	—
96	C₃×#681	—	2	2	no	—
97	C₃×#681	C₂×C₄	1	4	yes	complemented
98	C₂×C₃×#168	C₂³	1	2	yes	—
99	C₂×C₃×#168	C₂³	1	2	yes	—
100	C₂×C₃×#137	—	5	1	no	—
101	C₃×C₄×#41	D₅	1	1	yes	characteristic
102	C₂×C₃×C₄×Q₈	—	5	1	no	—
103	C₃×#441	—	5	2	no	—
104	C₃×#440	—	5	2	no	—
105	C₃×C₄×Q₁₆	—	5	2	no	—
106	C₃×C₄×SD₁₆	—	5	2	no	—
107	C₃×#428	—	5	1	no	—
108	C₃×#419	—	5	1	no	—
109	C₃×#417	—	5	1	no	—
110	C₃×C₄×M₁₆	—	5	1	no	—
111	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
112	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
113	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₅×D₄	—	2	1	no	—
116	C₄×C₅×D₄	—	2	1	no	—
117	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
118	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
119	C₅×#117	—	2	1	no	—
120	C₅×#117	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₄²×C₅	—	2	1	no	—
122	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
123	#4097	C₃×C₄	1	8	yes	direct product factor
124	C₂×#689	C₂²×C₃	1	2	yes	—
125	C₂×#687	C₂²×C₃	1	2	yes	—
126	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
127	C₂×#683	—	2	1	no	—
128	C₂×C₄×Dic₅	—	2	1	no	—
129	C₂×#681	C₂²×C₃	1	1	yes	characteristic
130	C₂×#681	C₂²×C₃	1	1	yes	characteristic
131	C₄×Dic₁₀	—	2	1	no	—
132	C₄×Dic₁₀	—	2	1	no	—
133	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
134	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
135	#3967	C₂²×C₃	1	2	yes	—
136	#3964	C₂²×C₃	1	2	yes	—
137	#3942	C₂²×C₃	1	2	yes	—
138	#3942	C₂²×C₃	1	2	yes	—
139	#3940	C₂²×C₃	1	2	yes	—
140	#3939	C₂²×C₃	1	2	yes	—
141	#3935	C₂²×C₃	1	2	yes	—
142	C₄×#168	C₂²×C₃	1	2	yes	—
143	C₄×#137	—	5	1	no	Sylow
144	C₂³×C₃×C₅	—	2	1	no	—
145	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
146	C₃×C₅×Q₈	—	2	1	no	—
147	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
148	C₃×C₅×D₄	—	2	4	no	—
149	C₃×C₅×D₄	—	2	1	no	—
150	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	4	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	1	no	—
156	C₂×C₃×C₄×C₅	—	4	1	no	—
157	C₂×C₃×C₄×C₅	—	4	2	no	—
158	C₂×C₃×C₄×C₅	—	4	2	no	—
159	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×C₄×C₅	#41	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
167	C₂×C₃×Dic₅	—	2	4	no	—
168	C₂×C₃×Dic₅	—	2	2	no	—
169	C₂×C₃×Dic₅	—	2	2	no	—
170	C₂×C₃×Dic₅	—	4	2	no	—
171	C₃×Dic₁₀	—	2	4	no	—
172	C₃×Dic₁₀	—	2	2	no	—
173	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
174	C₃×#168	—	2	2	no	—
175	C₃×#168	C₂²×C₄	1	4	yes	—
176	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
177	C₂²×C₃×Q₈	—	5	1	no	—
178	C₃×#137	—	5	8	no	—
179	C₂×C₃×Q₁₆	—	5	2	no	—
180	C₂×C₃×SD₁₆	—	5	2	no	—
181	C₂×C₃×M₁₆	—	5	1	no	—
182	C₂×C₃×M₁₆	—	5	1	no	—
183	C₃×C₄×Q₈	—	5	2	no	—
184	C₃×C₄×Q₈	—	5	2	no	—
185	C₃×C₄×Q₈	—	10	1	no	—
186	C₃×C₄×Q₈	—	10	1	no	—
187	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
188	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
189	C₃×C₄×D₄	—	2	1	no	—
190	C₃×C₄×D₄	—	2	1	no	—
191	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
192	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
193	C₃×#117	—	2	1	no	—
194	C₃×#117	C₂×D₅	1	1	yes	characteristic
195	C₂×C₃×C₄⋊C₄	—	5	1	no	—
196	C₂×C₃×C₄⋊C₄	—	10	1	no	—
197	C₂×C₃×C₄²	—	2	1	no	—
198	C₂×C₃×C₄²	—	10	1	no	—
199	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
200	C₃×#107	—	5	2	no	—
201	C₃×#106	—	5	2	no	—
202	C₃×#103	—	5	2	no	—
203	C₃×#103	—	5	2	no	—
204	C₃×#103	—	5	2	no	—
205	C₃×#102	—	5	2	no	—
206	C₃×#97	—	5	2	no	—
207	C₃×C₄×C₈	—	5	2	no	—
208	C₅×#41	—	2	2	no	—
209	C₅×#41	C₂×C₃×C₄	1	4	yes	—
210	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₅×D₄	—	2	1	no	—
212	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
213	C₂²×C₄×C₅	—	2	1	no	—
214	C₂²×C₄×C₅	—	2	1	no	—
215	C₂²×C₄×C₅	—	2	1	no	—
216	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
219	C₂²×Dic₅	—	2	1	no	—
220	C₂²×Dic₅	—	2	1	no	—
221	C₂×Dic₁₀	—	2	1	no	—
222	C₂×Dic₁₀	—	2	2	no	—
223	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	complemented
224	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	2	1	no	—
227	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
228	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
229	C₅×C₂²⋊C₄	—	2	1	no	—
230	C₅×C₂²⋊C₄	—	2	1	no	—
231	C₅×C₂²⋊C₄	—	2	1	no	—
232	C₄²×C₅	—	2	1	no	—
233	C₄²×C₅	—	2	1	no	—
234	C₄²×C₅	—	2	1	no	—
235	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
236	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
237	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
238	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
239	#689	C₂×C₃×C₄	1	8	yes	complemented
240	#687	C₂×C₃×C₄	1	8	yes	complemented
241	C₄⋊Dic₅	—	2	1	no	—
242	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
243	#683	—	2	2	no	—
244	#683	—	2	2	no	—
245	C₄×Dic₅	—	2	2	no	—
246	C₄×Dic₅	—	2	2	no	—
247	#681	—	2	2	no	—
248	#681	C₂×C₃×C₄	1	4	yes	complemented
249	C₂×#168	C₂³×C₃	1	2	yes	—
250	C₂×#168	C₂³×C₃	1	2	yes	—
251	C₂×#137	—	5	1	no	—
252	C₄×#41	C₃×D₅	1	1	yes	characteristic
253	C₂×C₄×Q₈	—	5	1	no	—
254	#441	—	5	2	no	—
255	#440	—	5	2	no	—
256	C₄×Q₁₆	—	5	2	no	—
257	C₄×SD₁₆	—	5	2	no	—
258	#428	—	5	1	no	—
259	#419	—	5	1	no	—
260	#417	—	5	1	no	—
261	C₄×M₁₆	—	5	1	no	—
262	C₂²×C₃×C₅	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	—	4	1	no	—
266	C₂²×C₃×C₅	—	4	1	no	—
267	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
268	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
269	C₃×C₄×C₅	—	2	2	no	—
270	C₃×C₄×C₅	—	2	1	no	—
271	C₃×C₄×C₅	—	2	1	no	—
272	C₃×C₄×C₅	—	2	1	no	—
273	C₃×C₄×C₅	—	4	1	no	—
274	C₃×C₄×C₅	—	4	1	no	—
275	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
276	C₃×C₄×C₅	#137	1	2	yes	complemented
277	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
278	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
279	C₃×Dic₅	—	2	4	no	—
280	C₃×Dic₅	—	4	2	no	—
281	C₃×#41	—	2	2	no	—
282	C₃×#41	C₄×D₅	1	4	yes	—
283	C₂×C₃×Q₈	—	5	4	no	—
284	C₂×C₃×Q₈	—	5	2	no	—
285	C₂×C₃×Q₈	—	10	2	no	—
286	C₂×C₃×Q₈	—	10	1	no	—
287	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
288	C₂×C₃×D₄	—	2	1	no	—
289	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
290	C₂²×C₃×C₄	—	2	1	no	—
291	C₂²×C₃×C₄	—	2	1	no	—
292	C₂²×C₃×C₄	—	2	1	no	—
293	C₂²×C₃×C₄	—	10	1	no	—
294	C₂²×C₃×C₄	—	10	1	no	—
295	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
296	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
297	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
298	C₃×Q₁₆	—	5	8	no	—
299	C₃×SD₁₆	—	5	8	no	—
300	C₃×M₁₆	—	5	4	no	—
301	C₃×M₁₆	—	10	2	no	—
302	C₂×C₃×C₈	—	5	2	no	—
303	C₂×C₃×C₈	—	5	2	no	—
304	C₃×C₄⋊C₄	—	2	1	no	—
305	C₃×C₄⋊C₄	—	2	1	no	—
306	C₃×C₄⋊C₄	—	5	2	no	—
307	C₃×C₄⋊C₄	—	10	2	no	—
308	C₃×C₄⋊C₄	—	10	2	no	—
309	C₃×C₄⋊C₄	—	10	1	no	—
310	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
311	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
312	C₃×C₂²⋊C₄	—	2	1	no	—
313	C₃×C₂²⋊C₄	—	2	1	no	—
314	C₃×C₂²⋊C₄	—	2	1	no	—
315	C₃×C₄²	—	2	1	no	—
316	C₃×C₄²	—	2	1	no	—
317	C₃×C₄²	—	2	1	no	—
318	C₃×C₄²	—	10	2	no	—
319	C₃×C₄²	—	10	2	no	—
320	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
321	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
322	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
323	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
324	C₂³×C₅	—	2	1	no	—
325	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
326	C₅×Q₈	—	2	1	no	—
327	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
328	C₅×D₄	—	2	4	no	—
329	C₅×D₄	—	2	1	no	—
330	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
331	C₂×C₄×C₅	—	2	1	no	—
332	C₂×C₄×C₅	—	2	4	no	—
333	C₂×C₄×C₅	—	2	2	no	—
334	C₂×C₄×C₅	—	2	1	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	4	1	no	—
337	C₂×C₄×C₅	—	4	2	no	—
338	C₂×C₄×C₅	—	4	2	no	—
339	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
340	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
341	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
342	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
344	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
345	C₂×C₄×C₅	C₃×#41	1	2	yes	—
346	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
347	C₂×Dic₅	—	2	4	no	—
348	C₂×Dic₅	—	2	2	no	—
349	C₂×Dic₅	—	2	2	no	—
350	C₂×Dic₅	—	4	2	no	—
351	Dic₁₀	—	2	4	no	—
352	Dic₁₀	—	2	2	no	—
353	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
354	#168	—	2	2	no	—
355	#168	C₂²×C₃×C₄	1	4	yes	—
356	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
357	C₂²×Q₈	—	5	1	no	—
358	#137	—	5	8	no	—
359	C₂×Q₁₆	—	5	2	no	—
360	C₂×SD₁₆	—	5	2	no	—
361	C₂×M₁₆	—	5	1	no	—
362	C₂×M₁₆	—	5	1	no	—
363	C₄×Q₈	—	5	2	no	—
364	C₄×Q₈	—	5	2	no	—
365	C₄×Q₈	—	10	1	no	—
366	C₄×Q₈	—	10	1	no	—
367	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
368	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
372	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
373	#117	—	2	1	no	—
374	#117	C₂×C₃×D₅	1	1	yes	characteristic
375	C₂×C₄⋊C₄	—	5	1	no	—
376	C₂×C₄⋊C₄	—	10	1	no	—
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	—	10	1	no	—
379	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
380	#107	—	5	2	no	—
381	#106	—	5	2	no	—
382	#103	—	5	2	no	—
383	#103	—	5	2	no	—
384	#103	—	5	2	no	—
385	#102	—	5	2	no	—
386	#97	—	5	2	no	—
387	C₄×C₈	—	5	2	no	—
388	C₂×C₃×C₅	—	2	2	no	—
389	C₂×C₃×C₅	—	4	2	no	—
390	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
391	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
392	C₂×C₃×C₅	#575	1	1	yes	characteristic
393	C₂³×C₃	—	2	1	no	—
394	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
395	C₃×Q₈	—	2	1	no	—
396	C₃×Q₈	—	5	4	no	—
397	C₃×Q₈	—	10	2	no	—
398	C₃×Q₈	—	10	4	no	—
399	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
400	C₃×D₄	—	2	4	no	—
401	C₃×D₄	—	2	1	no	—
402	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	4	no	—
406	C₂×C₃×C₄	—	2	1	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	4	1	no	—
409	C₂×C₃×C₄	—	4	2	no	—
410	C₂×C₃×C₄	—	4	2	no	—
411	C₂×C₃×C₄	—	10	2	no	—
412	C₂×C₃×C₄	—	10	4	no	—
413	C₂×C₃×C₄	—	10	2	no	—
414	C₂×C₃×C₄	—	20	2	no	—
415	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
416	C₂×C₃×C₄	#709	1	2	yes	—
417	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
420	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
423	C₃×C₈	—	5	4	no	—
424	C₃×C₈	—	10	2	no	—
425	C₂²×C₅	—	2	1	no	—
426	C₂²×C₅	—	2	1	no	—
427	C₂²×C₅	—	2	2	no	—
428	C₂²×C₅	—	4	1	no	—
429	C₂²×C₅	—	4	1	no	—
430	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
431	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	—	2	1	no	—
435	C₄×C₅	—	2	2	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
439	C₄×C₅	C₃×#137	1	2	yes	complemented
440	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
441	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
442	Dic₅	—	2	4	no	—
443	Dic₅	—	4	2	no	—
444	#41	—	2	2	no	—
445	#41	C₃×C₄×D₅	1	4	yes	—
446	C₂×Q₈	—	5	4	no	—
447	C₂×Q₈	—	5	2	no	—
448	C₂×Q₈	—	10	2	no	—
449	C₂×Q₈	—	10	1	no	—
450	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	10	1	no	—
457	C₂²×C₄	—	10	1	no	—
458	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
459	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
460	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
461	Q₁₆	—	5	8	no	—
462	SD₁₆	—	5	8	no	—
463	M₁₆	—	5	4	no	—
464	M₁₆	—	10	2	no	—
465	C₂×C₈	—	5	2	no	—
466	C₂×C₈	—	5	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	5	2	no	—
470	C₄⋊C₄	—	10	1	no	—
471	C₄⋊C₄	—	10	2	no	—
472	C₄⋊C₄	—	10	2	no	—
473	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
474	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	10	2	no	—
482	C₄²	—	10	2	no	—
483	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
484	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
485	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
486	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
487	C₃×C₅	C₄×#137	1	1	yes	characteristic, complemented, Hall
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	—	2	2	no	—
491	C₂²×C₃	—	4	1	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
494	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
495	C₃×C₄	—	2	2	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	2	1	no	—
499	C₃×C₄	—	4	1	no	—
500	C₃×C₄	—	4	1	no	—
501	C₃×C₄	—	10	4	no	—
502	C₃×C₄	—	20	2	no	—
503	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
504	C₃×C₄	#4097	1	2	yes	direct product factor
505	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
506	C₃×C₄	C₂×#709	1	1	yes	characteristic
507	C₂×C₅	—	2	2	no	—
508	C₂×C₅	—	4	2	no	—
509	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
510	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
511	C₂×C₅	C₃×#575	1	1	yes	characteristic
512	C₂³	—	2	1	no	—
513	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
514	Q₈	—	2	1	no	—
515	Q₈	—	5	4	no	—
516	Q₈	—	10	2	no	—
517	Q₈	—	10	4	no	—
518	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
519	D₄	—	2	4	no	—
520	D₄	—	2	1	no	—
521	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	10	2	no	—
531	C₂×C₄	—	10	4	no	—
532	C₂×C₄	—	10	2	no	—
533	C₂×C₄	—	20	2	no	—
534	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
535	C₂×C₄	C₃×#709	1	2	yes	—
536	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
537	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
538	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
539	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
540	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
541	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
542	C₈	—	5	4	no	—
543	C₈	—	10	2	no	—
544	C₂×C₃	—	2	2	no	—
545	C₂×C₃	—	4	2	no	—
546	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
547	C₂×C₃	#66156	1	1	yes	characteristic
548	C₂×C₃	C₂×#4097	1	1	yes	characteristic
549	C₅	C₃×C₄×#137	1	1	yes	characteristic, complemented, Sylow
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
556	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	10	4	no	—
564	C₄	—	20	2	no	—
565	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
566	C₄	C₃×#4097	1	2	yes	direct product factor
567	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
568	C₄	C₂×C₃×#709	1	1	yes	characteristic
569	C₃	C₄×#4097	1	1	yes	characteristic, direct product factor, Sylow
570	C₂	—	2	2	no	—
571	C₂	—	4	2	no	—
572	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
573	C₂	C₃×#66156	1	1	yes	characteristic
574	C₂	C₂×C₃×#4097	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×#41	D₅
hypocenter	C₅	C₃×C₄×#137
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
5. C₃×#65319	C₂	semidirect
6. C₃×C₄×#689	C₂	semidirect
7. C₃×#65307	C₂	semidirect
8. C₃×C₄×#687	C₂	semidirect
9. C₃×#65293	C₂	semidirect
10. C₃×#65284	C₂	semidirect
11. C₃×C₄×#681	C₂	semidirect
12. C₄×#4097	C₃	direct (N × H)
25. C₃×#4097	C₄	direct (N × H)
48. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
50. #65319	C₂×C₃	semidirect
51. C₄×#689	C₂×C₃	semidirect
52. #65307	C₂×C₃	semidirect
53. C₄×#687	C₂×C₃	semidirect
54. #65293	C₂×C₃	semidirect
55. #65284	C₂×C₃	semidirect
56. C₄×#681	C₂×C₃	semidirect
72. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
88. C₃×#689	C₂×C₄	semidirect
89. C₃×#687	C₂×C₄	semidirect
97. C₃×#681	C₂×C₄	semidirect
123. #4097	C₃×C₄	direct (N × H)
223. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
239. #689	C₂×C₃×C₄	semidirect
240. #687	C₂×C₃×C₄	semidirect
248. #681	C₂×C₃×C₄	semidirect
276. C₃×C₄×C₅	#137	semidirect
439. C₄×C₅	C₃×#137	semidirect
487. C₃×C₅	C₄×#137	semidirect
504. C₃×C₄	#4097	direct (N × H)
549. C₅	C₃×C₄×#137	semidirect
566. C₄	C₃×#4097	direct (N × H)
569. C₃	C₄×#4097	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×C₄×C₅×#41	2
C₂×C₃×#4097	2
C₂×C₃×C₄×Dic₁₀	2
C₃×#65521	2
C₃×#65319	2
C₃×C₄×#689	2
C₃×#65307	2
C₃×C₄×#687	2
C₃×#65293	2
C₃×#65284	2
C₃×C₄×#681	2
C₄×#4097	3
C₃×C₄×#137	5

Subgroups — C3×C4×#4097 #14416821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#4097 #14416821