Subgroups — C₂×C₅×#5514 #14483607

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#930	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₅×#67	C₂	1	2	yes	maximal, complemented
6	C₅×#5514	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#898	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#894	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#890	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#553	—	3	1	no	maximal, Hall
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
17	C₂²×C₅×#67	C₂²	1	2	yes	—
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
20	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	complemented
26	C₂×C₅×#217	C₂²	1	1	yes	characteristic
27	C₅×#930	C₂²	1	8	yes	complemented
28	C₅×#930	C₂²	1	16	yes	complemented
29	C₄×C₅×#67	C₂²	1	8	yes	complemented
30	C₄×C₅×#67	C₂²	1	16	yes	complemented
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
36	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
38	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
42	C₅×#898	C₂²	1	16	yes	complemented
43	C₅×#895	C₂²	1	8	yes	complemented
44	C₅×#894	C₂²	1	16	yes	complemented
45	C₅×#893	C₂²	1	8	yes	complemented
46	C₅×#892	C₂²	1	8	yes	complemented
47	C₅×#890	C₂²	1	8	yes	complemented
48	C₂×#5514	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
49	C₅×#553	—	3	16	no	—
50	C₂×C₅×#126	—	3	2	no	—
51	C₂×C₅×#125	—	3	1	no	—
52	C₂×C₅×#123	—	3	2	no	—
53	C₂×C₅×#121	—	3	2	no	—
54	C₂×C₅×#121	—	3	1	no	—
55	C₂×C₅×#121	—	3	1	no	—
56	C₂×C₄×C₅×D₄	—	3	2	no	—
57	C₂×C₄×C₅×D₄	—	3	1	no	—
58	C₂×C₄×C₅×D₄	—	3	1	no	—
59	C₂×C₅×#117	—	3	1	no	—
60	C₂²×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
61	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
62	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₂³×C₅×D₃	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	—	2	4	no	—
65	C₂²×C₃×C₄×C₅	—	4	4	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₅×#67	—	2	4	no	—
73	C₂×C₅×#67	—	2	8	no	—
74	C₂×C₅×#67	C₂³	1	4	yes	—
75	C₂×C₅×#67	C₂³	1	8	yes	—
76	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
77	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
78	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
80	C₂×C₅×D₁₂	—	2	4	no	—
81	C₂×C₅×D₁₂	—	4	4	no	—
82	C₂×C₅×D₁₂	C₂³	1	4	yes	—
83	C₂×C₅×D₁₂	C₂³	1	8	yes	—
84	C₂×C₄×C₅×D₃	—	2	4	no	—
85	C₂×C₄×C₅×D₃	—	4	4	no	—
86	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
87	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
89	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
90	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
91	C₅×#217	C₂³	1	4	yes	—
92	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
93	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
94	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
95	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
96	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
97	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
98	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
99	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
100	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
101	C₄×C₅×Dic₃	C₂³	1	4	yes	—
102	C₄×C₅×Dic₃	C₂³	1	8	yes	—
103	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×#930	C₂×C₅	1	2	yes	complemented
106	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂×C₄×#67	C₂×C₅	1	2	yes	complemented
108	#5514	C₂×C₅	1	16	yes	direct product factor
109	C₂×#898	C₂×C₅	1	2	yes	complemented
110	C₂×#895	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂×#894	C₂×C₅	1	2	yes	complemented
112	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂×#890	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂²×C₅×D₄	—	3	2	no	—
116	C₂²×C₅×D₄	—	3	1	no	—
117	C₂²×C₅×D₄	—	3	1	no	—
118	C₂²×C₅×D₄	—	3	2	no	—
119	C₂³×C₄×C₅	—	3	1	no	—
120	C₂³×C₄×C₅	—	3	2	no	—
121	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
122	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
123	C₅×#126	—	3	16	no	—
124	C₅×#125	—	3	8	no	—
125	C₅×#123	—	3	16	no	—
126	C₅×#121	—	3	16	no	—
127	C₅×#121	—	3	8	no	—
128	C₅×#121	—	3	8	no	—
129	C₄×C₅×D₄	—	3	16	no	—
130	C₄×C₅×D₄	—	3	8	no	—
131	C₄×C₅×D₄	—	3	8	no	—
132	C₅×#117	—	3	8	no	—
133	C₂×C₅×C₄⋊C₄	—	3	2	no	—
134	C₂×C₅×C₄⋊C₄	—	3	1	no	—
135	C₂×C₅×C₄⋊C₄	—	3	1	no	—
136	C₂×C₅×C₄⋊C₄	—	3	2	no	—
137	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
138	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
139	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
140	C₂×C₅×C₄⋊C₄	C₂×D₃	1	8	yes	complemented
141	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
142	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
143	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
144	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
145	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
146	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
147	C₂×C₄²×C₅	—	3	2	no	—
148	C₂×C₄²×C₅	—	3	1	no	—
149	C₂×#553	—	3	1	no	Sylow
150	C₂³×C₃×C₅	—	2	2	no	—
151	C₂³×C₃×C₅	—	2	2	no	—
152	C₂³×C₃×C₅	#41	1	4	yes	—
153	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
154	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
155	C₂²×C₅×D₃	—	2	2	no	—
156	C₂²×C₅×D₃	—	2	4	no	—
157	C₂²×C₅×D₃	—	2	2	no	—
158	C₂²×C₅×D₃	—	2	4	no	—
159	C₂²×C₅×D₃	—	2	4	no	—
160	C₂²×C₅×D₃	—	2	2	no	—
161	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
162	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
163	C₂×C₃×C₄×C₅	—	2	2	no	—
164	C₂×C₃×C₄×C₅	—	2	4	no	—
165	C₂×C₃×C₄×C₅	—	2	4	no	—
166	C₂×C₃×C₄×C₅	—	2	8	no	—
167	C₂×C₃×C₄×C₅	—	4	8	no	—
168	C₂×C₃×C₄×C₅	#41	1	4	yes	—
169	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
170	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
171	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
172	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
173	C₅×#67	—	2	8	no	—
174	C₅×#67	—	2	16	no	—
175	C₂×C₅×Dic₃	—	2	2	no	—
176	C₂×C₅×Dic₃	—	2	2	no	—
177	C₂×C₅×Dic₃	—	2	4	no	—
178	C₂×C₅×Dic₃	—	2	2	no	—
179	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
180	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
181	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
182	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
183	C₅×D₁₂	—	2	8	no	—
184	C₅×D₁₂	—	4	8	no	—
185	C₄×C₅×D₃	—	2	8	no	—
186	C₄×C₅×D₃	—	4	8	no	—
187	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
188	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
189	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
190	C₂²×#67	C₂²×C₅	1	2	yes	—
191	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
192	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
193	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
194	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
195	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
197	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
198	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
199	C₂×#217	C₂²×C₅	1	1	yes	characteristic
200	#930	C₂²×C₅	1	8	yes	complemented
201	#930	C₂²×C₅	1	16	yes	complemented
202	C₄×#67	C₂²×C₅	1	8	yes	complemented
203	C₄×#67	C₂²×C₅	1	16	yes	complemented
204	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
205	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
206	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
207	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
208	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
209	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
210	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
211	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
212	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
215	#898	C₂²×C₅	1	16	yes	complemented
216	#895	C₂²×C₅	1	8	yes	complemented
217	#894	C₂²×C₅	1	16	yes	complemented
218	#893	C₂²×C₅	1	8	yes	complemented
219	#892	C₂²×C₅	1	8	yes	complemented
220	#890	C₂²×C₅	1	8	yes	complemented
221	C₂⁴×C₅	—	3	1	no	—
222	C₂⁴×C₅	—	3	2	no	—
223	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
224	C₂×C₅×D₄	—	3	8	no	—
225	C₂×C₅×D₄	—	3	4	no	—
226	C₂×C₅×D₄	—	3	4	no	—
227	C₂×C₅×D₄	—	3	8	no	—
228	C₂×C₅×D₄	—	6	8	no	—
229	C₂×C₅×D₄	—	6	4	no	—
230	C₂×C₅×D₄	—	6	4	no	—
231	C₂×C₅×D₄	—	12	4	no	—
232	C₂²×C₄×C₅	—	2	4	no	—
233	C₂²×C₄×C₅	—	3	1	no	—
234	C₂²×C₄×C₅	—	3	2	no	—
235	C₂²×C₄×C₅	—	3	1	no	—
236	C₂²×C₄×C₅	—	3	1	no	—
237	C₂²×C₄×C₅	—	3	4	no	—
238	C₂²×C₄×C₅	—	3	8	no	—
239	C₂²×C₄×C₅	—	4	4	no	—
240	C₂²×C₄×C₅	—	6	4	no	—
241	C₂²×C₄×C₅	—	12	4	no	—
242	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
243	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
244	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
245	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
246	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
247	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
248	C₅×C₄⋊C₄	—	3	4	no	—
249	C₅×C₄⋊C₄	—	3	8	no	—
250	C₅×C₄⋊C₄	—	3	4	no	—
251	C₅×C₄⋊C₄	—	3	8	no	—
252	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
253	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
254	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
255	C₅×C₂²⋊C₄	—	3	4	no	—
256	C₅×C₂²⋊C₄	—	3	8	no	—
257	C₅×C₂²⋊C₄	—	3	8	no	—
258	C₅×C₂²⋊C₄	—	3	8	no	—
259	C₅×C₂²⋊C₄	—	3	4	no	—
260	C₅×C₂²⋊C₄	—	3	8	no	—
261	C₄²×C₅	—	3	8	no	—
262	C₄²×C₅	—	3	4	no	—
263	#553	—	3	16	no	—
264	C₂×#126	—	3	2	no	—
265	C₂×#125	—	3	1	no	—
266	C₂×#123	—	3	2	no	—
267	C₂×#121	—	3	2	no	—
268	C₂×#121	—	3	1	no	—
269	C₂×#121	—	3	1	no	—
270	C₂×C₄×D₄	—	3	2	no	—
271	C₂×C₄×D₄	—	3	1	no	—
272	C₂×C₄×D₄	—	3	1	no	—
273	C₂×#117	—	3	1	no	—
274	C₂²×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
275	C₂²×C₃×C₅	—	2	8	no	—
276	C₂²×C₃×C₅	—	2	2	no	—
277	C₂²×C₃×C₅	—	2	2	no	—
278	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
279	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
280	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
281	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
282	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
283	C₂×C₅×D₃	—	2	2	no	—
284	C₂×C₅×D₃	—	2	4	no	—
285	C₂×C₅×D₃	—	2	2	no	—
286	C₂×C₅×D₃	—	2	4	no	—
287	C₂×C₅×D₃	—	2	4	no	—
288	C₂×C₅×D₃	—	2	2	no	—
289	C₂×C₅×D₃	—	4	4	no	—
290	C₂×C₅×D₃	—	4	8	no	—
291	C₃×C₄×C₅	—	2	2	no	—
292	C₃×C₄×C₅	—	2	4	no	—
293	C₃×C₄×C₅	—	2	4	no	—
294	C₃×C₄×C₅	C₂×#41	1	4	yes	—
295	C₅×Dic₃	—	2	2	no	—
296	C₅×Dic₃	—	2	2	no	—
297	C₅×Dic₃	—	2	4	no	—
298	C₅×Dic₃	—	2	2	no	—
299	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
300	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
301	C₂³×D₃	C₂³×C₅	1	2	yes	—
302	C₂²×C₃×C₄	—	2	4	no	—
303	C₂²×C₃×C₄	—	4	4	no	—
304	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
305	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
306	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
307	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
308	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
309	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
310	C₂×#67	—	2	4	no	—
311	C₂×#67	—	2	8	no	—
312	C₂×#67	C₂³×C₅	1	4	yes	—
313	C₂×#67	C₂³×C₅	1	8	yes	—
314	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
315	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
316	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
317	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
318	C₂×D₁₂	—	2	4	no	—
319	C₂×D₁₂	—	4	4	no	—
320	C₂×D₁₂	C₂³×C₅	1	4	yes	—
321	C₂×D₁₂	C₂³×C₅	1	8	yes	—
322	C₂×C₄×D₃	—	2	4	no	—
323	C₂×C₄×D₃	—	4	4	no	—
324	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
325	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
326	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
327	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
328	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
329	#217	C₂³×C₅	1	4	yes	—
330	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
331	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
332	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
333	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
334	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
335	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
336	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
337	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
338	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
339	C₄×Dic₃	C₂³×C₅	1	4	yes	—
340	C₄×Dic₃	C₂³×C₅	1	8	yes	—
341	C₂³×C₅	—	2	2	no	—
342	C₂³×C₅	—	2	2	no	—
343	C₂³×C₅	—	3	2	no	—
344	C₂³×C₅	—	3	4	no	—
345	C₂³×C₅	—	6	2	no	—
346	C₂³×C₅	—	6	4	no	—
347	C₂³×C₅	—	6	4	no	—
348	C₂³×C₅	—	6	2	no	—
349	C₂³×C₅	—	6	2	no	—
350	C₂³×C₅	—	6	4	no	—
351	C₂³×C₅	#239	1	4	yes	—
352	C₂³×C₅	C₂³×D₃	1	2	yes	—
353	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
354	C₅×D₄	—	6	16	no	—
355	C₅×D₄	—	6	8	no	—
356	C₅×D₄	—	6	8	no	—
357	C₅×D₄	—	12	8	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	4	no	—
360	C₂×C₄×C₅	—	2	4	no	—
361	C₂×C₄×C₅	—	2	8	no	—
362	C₂×C₄×C₅	—	3	2	no	—
363	C₂×C₄×C₅	—	3	4	no	—
364	C₂×C₄×C₅	—	3	2	no	—
365	C₂×C₄×C₅	—	3	2	no	—
366	C₂×C₄×C₅	—	4	8	no	—
367	C₂×C₄×C₅	—	6	2	no	—
368	C₂×C₄×C₅	—	6	2	no	—
369	C₂×C₄×C₅	—	6	4	no	—
370	C₂×C₄×C₅	—	6	2	no	—
371	C₂×C₄×C₅	—	6	8	no	—
372	C₂×C₄×C₅	—	12	8	no	—
373	C₂×C₄×C₅	#235	1	4	yes	—
374	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
375	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
376	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
377	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
378	C₂²×D₄	—	3	2	no	—
379	C₂²×D₄	—	3	1	no	—
380	C₂²×D₄	—	3	1	no	—
381	C₂²×D₄	—	3	2	no	—
382	C₂³×C₄	—	3	1	no	—
383	C₂³×C₄	—	3	2	no	—
384	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
385	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
386	#126	—	3	16	no	—
387	#125	—	3	8	no	—
388	#123	—	3	16	no	—
389	#121	—	3	16	no	—
390	#121	—	3	8	no	—
391	#121	—	3	8	no	—
392	C₄×D₄	—	3	16	no	—
393	C₄×D₄	—	3	8	no	—
394	C₄×D₄	—	3	8	no	—
395	#117	—	3	8	no	—
396	C₂×C₄⋊C₄	—	3	1	no	—
397	C₂×C₄⋊C₄	—	3	2	no	—
398	C₂×C₄⋊C₄	—	3	1	no	—
399	C₂×C₄⋊C₄	—	3	2	no	—
400	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂×C₅×D₃	1	8	yes	complemented
404	C₂×C₂²⋊C₄	—	3	1	no	—
405	C₂×C₂²⋊C₄	—	3	2	no	—
406	C₂×C₂²⋊C₄	—	3	2	no	—
407	C₂×C₂²⋊C₄	—	3	2	no	—
408	C₂×C₂²⋊C₄	—	3	1	no	—
409	C₂×C₂²⋊C₄	—	3	2	no	—
410	C₂×C₄²	—	3	2	no	—
411	C₂×C₄²	—	3	1	no	—
412	C₂×C₃×C₅	—	2	4	no	—
413	C₂×C₃×C₅	#553	1	4	yes	complemented
414	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
415	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
416	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₅×D₃	—	4	2	no	—
418	C₅×D₃	—	4	4	no	—
419	C₂³×C₃	—	2	2	no	—
420	C₂³×C₃	—	2	2	no	—
421	C₂³×C₃	C₅×#41	1	4	yes	—
422	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
423	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
424	C₂²×D₃	—	2	2	no	—
425	C₂²×D₃	—	2	4	no	—
426	C₂²×D₃	—	2	2	no	—
427	C₂²×D₃	—	2	4	no	—
428	C₂²×D₃	—	2	4	no	—
429	C₂²×D₃	—	2	2	no	—
430	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
431	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
432	C₂×C₃×C₄	—	2	2	no	—
433	C₂×C₃×C₄	—	2	4	no	—
434	C₂×C₃×C₄	—	2	4	no	—
435	C₂×C₃×C₄	—	2	8	no	—
436	C₂×C₃×C₄	—	4	8	no	—
437	C₂×C₃×C₄	C₅×#41	1	4	yes	—
438	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
439	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
440	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
441	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
442	#67	—	2	8	no	—
443	#67	—	2	16	no	—
444	C₂×Dic₃	—	2	2	no	—
445	C₂×Dic₃	—	2	2	no	—
446	C₂×Dic₃	—	2	4	no	—
447	C₂×Dic₃	—	2	2	no	—
448	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
449	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
450	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
451	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
452	D₁₂	—	2	8	no	—
453	D₁₂	—	4	8	no	—
454	C₄×D₃	—	2	8	no	—
455	C₄×D₃	—	4	8	no	—
456	C₂²×C₅	—	2	2	no	—
457	C₂²×C₅	—	2	2	no	—
458	C₂²×C₅	—	2	8	no	—
459	C₂²×C₅	—	6	2	no	—
460	C₂²×C₅	—	6	4	no	—
461	C₂²×C₅	—	6	4	no	—
462	C₂²×C₅	—	6	2	no	—
463	C₂²×C₅	—	6	2	no	—
464	C₂²×C₅	—	6	4	no	—
465	C₂²×C₅	—	12	4	no	—
466	C₂²×C₅	—	12	8	no	—
467	C₂²×C₅	C₂×#235	1	2	yes	—
468	C₂²×C₅	#1004	1	2	yes	—
469	C₂²×C₅	C₂×#239	1	4	yes	—
470	C₂²×C₅	C₂×#239	1	2	yes	—
471	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
472	C₄×C₅	—	2	2	no	—
473	C₄×C₅	—	2	4	no	—
474	C₄×C₅	—	2	4	no	—
475	C₄×C₅	—	6	2	no	—
476	C₄×C₅	—	6	2	no	—
477	C₄×C₅	—	6	4	no	—
478	C₄×C₅	—	6	2	no	—
479	C₄×C₅	C₂×#235	1	4	yes	—
480	C₂⁴	—	3	1	no	—
481	C₂⁴	—	3	2	no	—
482	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
483	C₂×D₄	—	3	8	no	—
484	C₂×D₄	—	3	4	no	—
485	C₂×D₄	—	3	4	no	—
486	C₂×D₄	—	3	8	no	—
487	C₂×D₄	—	6	8	no	—
488	C₂×D₄	—	6	4	no	—
489	C₂×D₄	—	6	4	no	—
490	C₂×D₄	—	12	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	3	1	no	—
493	C₂²×C₄	—	3	2	no	—
494	C₂²×C₄	—	3	1	no	—
495	C₂²×C₄	—	3	1	no	—
496	C₂²×C₄	—	3	4	no	—
497	C₂²×C₄	—	3	8	no	—
498	C₂²×C₄	—	4	4	no	—
499	C₂²×C₄	—	6	4	no	—
500	C₂²×C₄	—	12	4	no	—
501	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
502	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
503	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
504	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
505	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
506	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
507	C₄⋊C₄	—	3	4	no	—
508	C₄⋊C₄	—	3	8	no	—
509	C₄⋊C₄	—	3	4	no	—
510	C₄⋊C₄	—	3	8	no	—
511	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
512	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
513	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
514	C₂²⋊C₄	—	3	4	no	—
515	C₂²⋊C₄	—	3	8	no	—
516	C₂²⋊C₄	—	3	8	no	—
517	C₂²⋊C₄	—	3	8	no	—
518	C₂²⋊C₄	—	3	4	no	—
519	C₂²⋊C₄	—	3	8	no	—
520	C₄²	—	3	8	no	—
521	C₄²	—	3	4	no	—
522	C₃×C₅	C₂×#553	1	1	yes	characteristic, complemented, Hall
523	C₂²×C₃	—	2	8	no	—
524	C₂²×C₃	—	2	2	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
527	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
528	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
529	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
530	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
531	C₂×D₃	—	2	2	no	—
532	C₂×D₃	—	2	4	no	—
533	C₂×D₃	—	2	2	no	—
534	C₂×D₃	—	2	4	no	—
535	C₂×D₃	—	2	4	no	—
536	C₂×D₃	—	2	2	no	—
537	C₂×D₃	—	4	4	no	—
538	C₂×D₃	—	4	8	no	—
539	C₃×C₄	—	2	2	no	—
540	C₃×C₄	—	2	4	no	—
541	C₃×C₄	—	2	4	no	—
542	C₃×C₄	C₂×C₅×#41	1	4	yes	—
543	Dic₃	—	2	2	no	—
544	Dic₃	—	2	2	no	—
545	Dic₃	—	2	4	no	—
546	Dic₃	—	2	2	no	—
547	C₂×C₅	—	2	4	no	—
548	C₂×C₅	—	12	2	no	—
549	C₂×C₅	—	12	4	no	—
550	C₂×C₅	#5514	1	4	yes	direct product factor
551	C₂×C₅	C₂²×#235	1	1	yes	characteristic
552	C₂×C₅	C₂×#1004	1	1	yes	characteristic
553	C₂×C₅	C₂²×#239	1	1	yes	characteristic
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	3	2	no	—
557	C₂³	—	3	4	no	—
558	C₂³	—	6	2	no	—
559	C₂³	—	6	4	no	—
560	C₂³	—	6	4	no	—
561	C₂³	—	6	2	no	—
562	C₂³	—	6	2	no	—
563	C₂³	—	6	4	no	—
564	C₂³	C₅×#239	1	4	yes	—
565	C₂³	C₂³×C₅×D₃	1	2	yes	—
566	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
567	D₄	—	6	16	no	—
568	D₄	—	6	8	no	—
569	D₄	—	6	8	no	—
570	D₄	—	12	8	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	8	no	—
575	C₂×C₄	—	3	2	no	—
576	C₂×C₄	—	3	4	no	—
577	C₂×C₄	—	3	2	no	—
578	C₂×C₄	—	3	2	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	—	6	2	no	—
581	C₂×C₄	—	6	2	no	—
582	C₂×C₄	—	6	4	no	—
583	C₂×C₄	—	6	2	no	—
584	C₂×C₄	—	6	8	no	—
585	C₂×C₄	—	12	8	no	—
586	C₂×C₄	C₅×#235	1	4	yes	—
587	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
588	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
589	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
590	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
591	C₂×C₃	—	2	4	no	—
592	C₂×C₃	C₅×#553	1	4	yes	complemented
593	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
594	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
595	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
596	D₃	—	4	2	no	—
597	D₃	—	4	4	no	—
598	C₅	C₂×#5514	1	1	yes	characteristic, direct product factor, Sylow
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	8	no	—
602	C₂²	—	6	2	no	—
603	C₂²	—	6	4	no	—
604	C₂²	—	6	4	no	—
605	C₂²	—	6	2	no	—
606	C₂²	—	6	2	no	—
607	C₂²	—	6	4	no	—
608	C₂²	—	12	4	no	—
609	C₂²	—	12	8	no	—
610	C₂²	C₂×C₅×#235	1	2	yes	—
611	C₂²	C₅×#1004	1	2	yes	—
612	C₂²	C₂×C₅×#239	1	4	yes	—
613	C₂²	C₂×C₅×#239	1	2	yes	—
614	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
615	C₄	—	2	2	no	—
616	C₄	—	2	4	no	—
617	C₄	—	2	4	no	—
618	C₄	—	6	2	no	—
619	C₄	—	6	2	no	—
620	C₄	—	6	4	no	—
621	C₄	—	6	2	no	—
622	C₄	C₂×C₅×#235	1	4	yes	—
623	C₃	C₂×C₅×#553	1	1	yes	characteristic, complemented, Sylow
624	C₂	—	2	4	no	—
625	C₂	—	12	2	no	—
626	C₂	—	12	4	no	—
627	C₂	C₅×#5514	1	4	yes	direct product factor
628	C₂	C₂²×C₅×#235	1	1	yes	characteristic
629	C₂	C₂×C₅×#1004	1	1	yes	characteristic
630	C₂	C₂²×C₅×#239	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₅×#553
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
2. C₂×C₅×#930	C₂	semidirect
3. C₂×C₅×#930	C₂	semidirect
4. C₂×C₄×C₅×#67	C₂	semidirect
5. C₂×C₄×C₅×#67	C₂	semidirect
6. C₅×#5514	C₂	direct (N × H)
7. C₂×C₅×#898	C₂	semidirect
8. C₂×C₅×#895	C₂	semidirect
9. C₂×C₅×#894	C₂	semidirect
10. C₂×C₅×#893	C₂	semidirect
11. C₂×C₅×#892	C₂	semidirect
12. C₂×C₅×#890	C₂	semidirect
25. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
27. C₅×#930	C₂²	semidirect
28. C₅×#930	C₂²	semidirect
29. C₄×C₅×#67	C₂²	semidirect
30. C₄×C₅×#67	C₂²	semidirect
42. C₅×#898	C₂²	semidirect
43. C₅×#895	C₂²	semidirect
44. C₅×#894	C₂²	semidirect
45. C₅×#893	C₂²	semidirect
46. C₅×#892	C₂²	semidirect
47. C₅×#890	C₂²	semidirect
48. C₂×#5514	C₅	direct (N × H)
60. C₂²×C₅×C₄⋊C₄	D₃	semidirect
103. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
104. C₂×#930	C₂×C₅	semidirect
105. C₂×#930	C₂×C₅	semidirect
106. C₂×C₄×#67	C₂×C₅	semidirect
107. C₂×C₄×#67	C₂×C₅	semidirect
108. #5514	C₂×C₅	direct (N × H)
109. C₂×#898	C₂×C₅	semidirect
110. C₂×#895	C₂×C₅	semidirect
111. C₂×#894	C₂×C₅	semidirect
112. C₂×#893	C₂×C₅	semidirect
113. C₂×#892	C₂×C₅	semidirect
114. C₂×#890	C₂×C₅	semidirect
140. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
198. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
200. #930	C₂²×C₅	semidirect
201. #930	C₂²×C₅	semidirect
202. C₄×#67	C₂²×C₅	semidirect
203. C₄×#67	C₂²×C₅	semidirect
215. #898	C₂²×C₅	semidirect
216. #895	C₂²×C₅	semidirect
217. #894	C₂²×C₅	semidirect
218. #893	C₂²×C₅	semidirect
219. #892	C₂²×C₅	semidirect
220. #890	C₂²×C₅	semidirect
274. C₂²×C₄⋊C₄	C₅×D₃	semidirect
403. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
413. C₂×C₃×C₅	#553	semidirect
522. C₃×C₅	C₂×#553	semidirect
550. C₂×C₅	#5514	direct (N × H)
592. C₂×C₃	C₅×#553	semidirect
598. C₅	C₂×#5514	direct (N × H)
623. C₃	C₂×C₅×#553	semidirect
627. C₂	C₅×#5514	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×C₅×C₄⋊C₄	2
C₂×C₅×#930	2
C₂×C₄×C₅×#67	2
C₅×#5514	2
C₂×C₅×#898	2
C₂×C₅×#895	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×#892	2
C₂×C₅×#890	2
C₂×C₅×#553	3
C₂×#5514	5

Subgroups — C2×C5×#5514 #14483607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5514 #14483607