Subgroups — C₂×C₅×#5718 #14482972

Order 1920.

3472 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×C₅×#237	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#940	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#939	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#938	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×D₄×Dic₃	C₂	1	2	yes	maximal, complemented
7	C₅×#5718	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#550	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₅×#67	C₂²	1	4	yes	—
15	C₂²×C₅×#67	C₂²	1	4	yes	—
16	C₂³×C₅×Dic₃	C₂²	1	4	yes	—
17	C₂×C₅×#237	—	2	16	no	—
18	C₂×C₅×#237	C₂²	1	16	yes	complemented
19	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
21	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
22	C₃×C₅×#127	C₂²	1	8	yes	complemented
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂×C₅×#217	C₂²	1	4	yes	—
25	C₅×#940	C₂²	1	16	yes	complemented
26	C₅×#939	C₂²	1	32	yes	complemented
27	C₅×#938	C₂²	1	16	yes	complemented
28	C₅×D₄×Dic₃	C₂²	1	16	yes	complemented
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
34	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
35	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
36	C₂×#5718	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂²×C₅×#41	—	3	2	no	—
38	C₅×#550	—	3	16	no	—
39	C₂×C₅×#127	—	3	2	no	—
40	C₂×C₅×#127	D₃	1	1	yes	characteristic, complemented
41	C₂×C₅×#121	—	3	2	no	—
42	C₂×C₅×#121	—	3	4	no	—
43	C₂×C₄×C₅×Q₈	—	3	1	no	—
44	C₂×C₄×C₅×D₄	—	3	2	no	—
45	C₂×C₄×C₅×D₄	—	3	1	no	—
46	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
47	C₂³×C₅×D₃	C₂³	1	2	yes	—
48	C₂×C₃×C₅×D₄	—	2	8	no	—
49	C₂×C₃×C₅×D₄	—	2	8	no	—
50	C₂×C₃×C₅×D₄	—	4	4	no	—
51	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
52	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
53	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₅×#67	—	2	16	no	—
58	C₂×C₅×#67	—	4	8	no	—
59	C₂×C₅×#67	C₂³	1	16	yes	—
60	C₂×C₅×#67	C₂³	1	16	yes	—
61	C₂²×C₅×Dic₃	—	2	16	no	—
62	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
63	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
64	C₂²×C₅×Dic₃	C₂³	1	16	yes	—
65	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
66	C₅×#237	—	2	64	no	—
67	C₂×C₅×D₁₂	—	2	4	no	—
68	C₂×C₅×D₁₂	C₂³	1	4	yes	—
69	C₂×C₄×C₅×D₃	—	2	8	no	—
70	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
71	C₂×C₅×Dic₆	D₄	1	8	yes	complemented
72	C₂×C₅×Dic₆	C₂³	1	4	yes	—
73	C₃×C₄²×C₅	C₂³	1	4	yes	—
74	C₅×#217	C₂³	1	16	yes	—
75	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
76	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
77	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
78	C₅×Dic₃⋊C₄	C₂³	1	8	yes	—
79	C₄×C₅×Dic₃	C₂³	1	8	yes	—
80	C₂²×#237	C₂×C₅	1	2	yes	complemented
81	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×#940	C₂×C₅	1	2	yes	complemented
83	C₂×#939	C₂×C₅	1	4	yes	complemented
84	C₂×#938	C₂×C₅	1	2	yes	complemented
85	C₂×D₄×Dic₃	C₂×C₅	1	2	yes	complemented
86	#5718	C₂×C₅	1	16	yes	direct product factor
87	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×C₅×#41	—	3	16	no	—
90	C₂×C₅×#41	—	6	16	no	—
91	C₂²×C₅×Q₈	—	3	1	no	—
92	C₂²×C₅×D₄	—	3	4	no	—
93	C₂²×C₅×D₄	—	3	4	no	—
94	C₂²×C₅×D₄	—	3	1	no	—
95	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
96	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
97	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
98	C₂³×C₄×C₅	—	3	4	no	—
99	C₂³×C₄×C₅	—	3	2	no	—
100	C₅×#127	—	3	16	no	—
101	C₅×#127	C₂×D₃	1	8	yes	complemented
102	C₅×#121	—	3	16	no	—
103	C₅×#121	—	3	32	no	—
104	C₄×C₅×Q₈	—	3	8	no	—
105	C₄×C₅×D₄	—	3	16	no	—
106	C₄×C₅×D₄	—	3	8	no	—
107	C₂×C₅×C₄⋊C₄	—	3	2	no	—
108	C₂×C₅×C₄⋊C₄	—	3	1	no	—
109	C₂×C₅×C₄⋊C₄	—	3	1	no	—
110	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
111	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
112	C₂×C₄²×C₅	—	3	2	no	—
113	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
114	C₂×#550	—	3	1	no	Sylow
115	C₂³×C₃×C₅	—	2	8	no	—
116	C₂³×C₃×C₅	—	2	8	no	—
117	C₂³×C₃×C₅	—	2	8	no	—
118	C₂³×C₃×C₅	C₂⁴	1	8	yes	—
119	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
120	C₂²×C₅×D₃	—	2	4	no	—
121	C₂²×C₅×D₃	—	2	4	no	—
122	C₂²×C₅×D₃	—	2	4	no	—
123	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
124	C₃×C₅×D₄	—	2	16	no	—
125	C₃×C₅×D₄	—	2	16	no	—
126	C₃×C₅×D₄	—	4	8	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
129	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
130	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
133	C₅×#67	—	2	32	no	—
134	C₅×#67	—	4	16	no	—
135	C₂×C₅×Dic₃	—	2	4	no	—
136	C₂×C₅×Dic₃	—	2	4	no	—
137	C₂×C₅×Dic₃	—	2	32	no	—
138	C₂×C₅×Dic₃	C₂×D₄	1	8	yes	—
139	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
140	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
141	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
142	C₅×D₁₂	—	2	8	no	—
143	C₄×C₅×D₃	—	2	16	no	—
144	C₅×Dic₆	C₂×D₄	1	16	yes	complemented
145	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
146	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
147	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
148	C₂²×#67	C₂²×C₅	1	4	yes	—
149	C₂²×#67	C₂²×C₅	1	4	yes	—
150	C₂³×Dic₃	C₂²×C₅	1	4	yes	—
151	C₂×#237	—	2	16	no	—
152	C₂×#237	C₂²×C₅	1	16	yes	complemented
153	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
154	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
155	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
156	C₃×#127	C₂²×C₅	1	8	yes	complemented
157	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
158	C₂×#217	C₂²×C₅	1	4	yes	—
159	#940	C₂²×C₅	1	16	yes	complemented
160	#939	C₂²×C₅	1	32	yes	complemented
161	#938	C₂²×C₅	1	16	yes	complemented
162	D₄×Dic₃	C₂²×C₅	1	16	yes	complemented
163	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
164	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
166	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
167	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
168	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
169	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
170	C₂⁴×C₅	—	3	2	no	—
171	C₂⁴×C₅	C₂²×D₃	1	4	yes	—
172	C₅×#41	—	6	64	no	—
173	C₂×C₅×Q₈	—	3	8	no	—
174	C₂×C₅×Q₈	—	3	4	no	—
175	C₂×C₅×D₄	—	2	8	no	—
176	C₂×C₅×D₄	—	2	8	no	—
177	C₂×C₅×D₄	—	3	16	no	—
178	C₂×C₅×D₄	—	3	16	no	—
179	C₂×C₅×D₄	—	3	4	no	—
180	C₂×C₅×D₄	—	4	4	no	—
181	C₂×C₅×D₄	—	6	16	no	—
182	C₂×C₅×D₄	—	6	4	no	—
183	C₂×C₅×D₄	—	12	8	no	—
184	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
185	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
186	C₂×C₅×D₄	C₂²×D₃	1	8	yes	—
187	C₂²×C₄×C₅	—	3	2	no	—
188	C₂²×C₄×C₅	—	3	16	no	—
189	C₂²×C₄×C₅	—	3	2	no	—
190	C₂²×C₄×C₅	—	3	2	no	—
191	C₂²×C₄×C₅	—	3	8	no	—
192	C₂²×C₄×C₅	—	6	16	no	—
193	C₂²×C₄×C₅	—	6	8	no	—
194	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
197	C₅×C₄⋊C₄	—	3	4	no	—
198	C₅×C₄⋊C₄	—	3	8	no	—
199	C₅×C₄⋊C₄	—	3	4	no	—
200	C₅×C₂²⋊C₄	—	3	16	no	—
201	C₅×C₂²⋊C₄	—	3	8	no	—
202	C₄²×C₅	—	3	8	no	—
203	C₄²×C₅	C₂²×D₃	1	4	yes	—
204	C₂²×#41	—	3	2	no	—
205	#550	—	3	16	no	—
206	C₂×#127	—	3	2	no	—
207	C₂×#127	C₅×D₃	1	1	yes	characteristic, complemented
208	C₂×#121	—	3	2	no	—
209	C₂×#121	—	3	4	no	—
210	C₂×C₄×Q₈	—	3	1	no	—
211	C₂×C₄×D₄	—	3	2	no	—
212	C₂×C₄×D₄	—	3	1	no	—
213	C₂²×C₃×C₅	—	2	8	no	—
214	C₂²×C₃×C₅	—	2	8	no	—
215	C₂²×C₃×C₅	—	2	8	no	—
216	C₂²×C₃×C₅	—	4	16	no	—
217	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
218	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
219	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
220	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
221	C₂×C₅×D₃	—	2	4	no	—
222	C₂×C₅×D₃	—	2	4	no	—
223	C₂×C₅×D₃	—	2	4	no	—
224	C₂×C₅×D₃	—	4	8	no	—
225	C₃×C₄×C₅	—	2	2	no	—
226	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
227	C₃×C₄×C₅	C₂×#41	1	4	yes	complemented
228	C₅×Dic₃	—	2	4	no	—
229	C₅×Dic₃	—	2	4	no	—
230	C₅×Dic₃	C₂²×D₄	1	8	yes	—
231	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
232	C₂³×D₃	C₂³×C₅	1	2	yes	—
233	C₂×C₃×D₄	—	2	8	no	—
234	C₂×C₃×D₄	—	2	8	no	—
235	C₂×C₃×D₄	—	4	4	no	—
236	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
237	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
238	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
239	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
240	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
241	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
242	C₂×#67	—	2	16	no	—
243	C₂×#67	—	4	8	no	—
244	C₂×#67	C₂³×C₅	1	16	yes	—
245	C₂×#67	C₂³×C₅	1	16	yes	—
246	C₂²×Dic₃	—	2	16	no	—
247	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
248	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
249	C₂²×Dic₃	C₂³×C₅	1	16	yes	—
250	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
251	#237	—	2	64	no	—
252	C₂×D₁₂	—	2	4	no	—
253	C₂×D₁₂	C₂³×C₅	1	4	yes	—
254	C₂×C₄×D₃	—	2	8	no	—
255	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
256	C₂×Dic₆	C₅×D₄	1	8	yes	complemented
257	C₂×Dic₆	C₂³×C₅	1	4	yes	—
258	C₃×C₄²	C₂³×C₅	1	4	yes	—
259	#217	C₂³×C₅	1	16	yes	—
260	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
261	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
262	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
263	Dic₃⋊C₄	C₂³×C₅	1	8	yes	—
264	C₄×Dic₃	C₂³×C₅	1	8	yes	—
265	C₂³×C₅	—	2	8	no	—
266	C₂³×C₅	—	2	8	no	—
267	C₂³×C₅	—	2	8	no	—
268	C₂³×C₅	—	3	4	no	—
269	C₂³×C₅	—	6	4	no	—
270	C₂³×C₅	—	6	4	no	—
271	C₂³×C₅	—	6	4	no	—
272	C₂³×C₅	C₂³×D₃	1	8	yes	—
273	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
274	C₅×Q₈	—	3	16	no	—
275	C₅×D₄	—	2	16	no	—
276	C₅×D₄	—	2	16	no	—
277	C₅×D₄	—	4	8	no	—
278	C₅×D₄	—	6	32	no	—
279	C₅×D₄	—	6	8	no	—
280	C₅×D₄	—	12	16	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	3	8	no	—
283	C₂×C₄×C₅	—	3	4	no	—
284	C₂×C₄×C₅	—	3	4	no	—
285	C₂×C₄×C₅	—	3	4	no	—
286	C₂×C₄×C₅	—	6	32	no	—
287	C₂×C₄×C₅	—	6	4	no	—
288	C₂×C₄×C₅	—	6	4	no	—
289	C₂×C₄×C₅	—	6	16	no	—
290	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
291	C₂×C₄×C₅	#237	1	4	yes	complemented
292	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
293	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
294	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
295	C₂×#41	—	3	16	no	—
296	C₂×#41	—	6	16	no	—
297	C₂²×Q₈	—	3	1	no	—
298	C₂²×D₄	—	3	4	no	—
299	C₂²×D₄	—	3	4	no	—
300	C₂²×D₄	—	3	1	no	—
301	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
302	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
303	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
304	C₂³×C₄	—	3	4	no	—
305	C₂³×C₄	—	3	2	no	—
306	#127	—	3	16	no	—
307	#127	C₂×C₅×D₃	1	8	yes	complemented
308	#121	—	3	16	no	—
309	#121	—	3	32	no	—
310	C₄×Q₈	—	3	8	no	—
311	C₄×D₄	—	3	16	no	—
312	C₄×D₄	—	3	8	no	—
313	C₂×C₄⋊C₄	—	3	1	no	—
314	C₂×C₄⋊C₄	—	3	2	no	—
315	C₂×C₄⋊C₄	—	3	1	no	—
316	C₂×C₂²⋊C₄	—	3	4	no	—
317	C₂×C₂²⋊C₄	—	3	2	no	—
318	C₂×C₄²	—	3	2	no	—
319	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
320	C₂×C₃×C₅	—	4	8	no	—
321	C₂×C₃×C₅	#550	1	4	yes	complemented
322	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
324	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₅×D₃	—	4	4	no	—
326	C₂³×C₃	—	2	8	no	—
327	C₂³×C₃	—	2	8	no	—
328	C₂³×C₃	—	2	8	no	—
329	C₂³×C₃	C₂⁴×C₅	1	8	yes	—
330	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
331	C₂²×D₃	—	2	4	no	—
332	C₂²×D₃	—	2	4	no	—
333	C₂²×D₃	—	2	4	no	—
334	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
335	C₃×D₄	—	2	16	no	—
336	C₃×D₄	—	2	16	no	—
337	C₃×D₄	—	4	8	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
340	C₂×C₃×C₄	C₅×#41	1	4	yes	complemented
341	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
342	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
343	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
344	#67	—	2	32	no	—
345	#67	—	4	16	no	—
346	C₂×Dic₃	—	2	4	no	—
347	C₂×Dic₃	—	2	4	no	—
348	C₂×Dic₃	—	2	32	no	—
349	C₂×Dic₃	C₂×C₅×D₄	1	8	yes	—
350	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
351	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
352	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
353	D₁₂	—	2	8	no	—
354	C₄×D₃	—	2	16	no	—
355	Dic₆	C₂×C₅×D₄	1	16	yes	complemented
356	C₂²×C₅	—	2	8	no	—
357	C₂²×C₅	—	2	8	no	—
358	C₂²×C₅	—	2	8	no	—
359	C₂²×C₅	—	4	16	no	—
360	C₂²×C₅	—	6	4	no	—
361	C₂²×C₅	—	6	4	no	—
362	C₂²×C₅	—	6	4	no	—
363	C₂²×C₅	—	12	8	no	—
364	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
365	C₂²×C₅	C₂×#237	1	2	yes	—
366	C₂²×C₅	#1004	1	2	yes	—
367	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
368	C₄×C₅	—	2	2	no	—
369	C₄×C₅	—	3	8	no	—
370	C₄×C₅	—	6	4	no	—
371	C₄×C₅	—	6	4	no	—
372	C₄×C₅	C₂×D₃×D₄	1	4	yes	—
373	C₄×C₅	C₂×#237	1	4	yes	complemented
374	C₂⁴	—	3	2	no	—
375	C₂⁴	C₂²×C₅×D₃	1	4	yes	—
376	#41	—	6	64	no	—
377	C₂×Q₈	—	3	8	no	—
378	C₂×Q₈	—	3	4	no	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	2	8	no	—
381	C₂×D₄	—	3	16	no	—
382	C₂×D₄	—	3	16	no	—
383	C₂×D₄	—	3	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	6	16	no	—
386	C₂×D₄	—	6	4	no	—
387	C₂×D₄	—	12	8	no	—
388	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
389	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
390	C₂×D₄	C₂²×C₅×D₃	1	8	yes	—
391	C₂²×C₄	—	3	2	no	—
392	C₂²×C₄	—	3	2	no	—
393	C₂²×C₄	—	3	2	no	—
394	C₂²×C₄	—	3	16	no	—
395	C₂²×C₄	—	3	8	no	—
396	C₂²×C₄	—	6	16	no	—
397	C₂²×C₄	—	6	8	no	—
398	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
401	C₄⋊C₄	—	3	4	no	—
402	C₄⋊C₄	—	3	8	no	—
403	C₄⋊C₄	—	3	4	no	—
404	C₂²⋊C₄	—	3	16	no	—
405	C₂²⋊C₄	—	3	8	no	—
406	C₄²	—	3	8	no	—
407	C₄²	C₂²×C₅×D₃	1	4	yes	—
408	C₃×C₅	C₂×#550	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	—	2	8	no	—
410	C₂²×C₃	—	2	8	no	—
411	C₂²×C₃	—	2	8	no	—
412	C₂²×C₃	—	4	16	no	—
413	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
414	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
415	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
416	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
417	C₂×D₃	—	2	4	no	—
418	C₂×D₃	—	2	4	no	—
419	C₂×D₃	—	2	4	no	—
420	C₂×D₃	—	4	8	no	—
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
423	C₃×C₄	C₂×C₅×#41	1	4	yes	complemented
424	Dic₃	—	2	4	no	—
425	Dic₃	—	2	4	no	—
426	Dic₃	C₂²×C₅×D₄	1	8	yes	—
427	C₂×C₅	—	4	8	no	—
428	C₂×C₅	—	12	4	no	—
429	C₂×C₅	#5718	1	4	yes	direct product factor
430	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
431	C₂×C₅	C₂²×#237	1	1	yes	characteristic
432	C₂×C₅	C₂×#1004	1	1	yes	characteristic
433	C₂³	—	2	8	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	3	4	no	—
437	C₂³	—	6	4	no	—
438	C₂³	—	6	4	no	—
439	C₂³	—	6	4	no	—
440	C₂³	C₂³×C₅×D₃	1	8	yes	—
441	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
442	Q₈	—	3	16	no	—
443	D₄	—	2	16	no	—
444	D₄	—	2	16	no	—
445	D₄	—	4	8	no	—
446	D₄	—	6	32	no	—
447	D₄	—	6	8	no	—
448	D₄	—	12	16	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	3	8	no	—
451	C₂×C₄	—	3	4	no	—
452	C₂×C₄	—	3	4	no	—
453	C₂×C₄	—	3	4	no	—
454	C₂×C₄	—	6	32	no	—
455	C₂×C₄	—	6	4	no	—
456	C₂×C₄	—	6	4	no	—
457	C₂×C₄	—	6	16	no	—
458	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
459	C₂×C₄	C₅×#237	1	4	yes	complemented
460	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
461	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
462	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
463	C₂×C₃	—	4	8	no	—
464	C₂×C₃	C₅×#550	1	4	yes	complemented
465	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
466	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
467	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
468	D₃	—	4	4	no	—
469	C₅	C₂×#5718	1	1	yes	characteristic, direct product factor, Sylow
470	C₂²	—	2	8	no	—
471	C₂²	—	2	8	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	4	16	no	—
474	C₂²	—	6	4	no	—
475	C₂²	—	6	4	no	—
476	C₂²	—	6	4	no	—
477	C₂²	—	12	8	no	—
478	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
479	C₂²	C₂×C₅×#237	1	2	yes	—
480	C₂²	C₅×#1004	1	2	yes	—
481	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	3	8	no	—
484	C₄	—	6	4	no	—
485	C₄	—	6	4	no	—
486	C₄	C₂×C₅×D₃×D₄	1	4	yes	—
487	C₄	C₂×C₅×#237	1	4	yes	complemented
488	C₃	C₂×C₅×#550	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	4	8	no	—
490	C₂	—	12	4	no	—
491	C₂	C₅×#5718	1	4	yes	direct product factor
492	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
493	C₂	C₂²×C₅×#237	1	1	yes	characteristic
494	C₂	C₂×C₅×#1004	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#127	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#127	D₃
hypocenter	C₃	C₂×C₅×#550
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#127

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#237	C₂	semidirect
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₂×C₅×#940	C₂	semidirect
4. C₂×C₅×#939	C₂	semidirect
5. C₂×C₅×#938	C₂	semidirect
6. C₂×C₅×D₄×Dic₃	C₂	semidirect
7. C₅×#5718	C₂	direct (N × H)
8. C₂×C₄×C₅×D₁₂	C₂	semidirect
9. C₂×C₄×C₅×Dic₆	C₂	semidirect
18. C₂×C₅×#237	C₂²	semidirect
22. C₃×C₅×#127	C₂²	semidirect
25. C₅×#940	C₂²	semidirect
26. C₅×#939	C₂²	semidirect
27. C₅×#938	C₂²	semidirect
28. C₅×D₄×Dic₃	C₂²	semidirect
34. C₄×C₅×D₁₂	C₂²	semidirect
35. C₄×C₅×Dic₆	C₂²	semidirect
36. C₂×#5718	C₅	direct (N × H)
40. C₂×C₅×#127	D₃	semidirect
71. C₂×C₅×Dic₆	D₄	semidirect
80. C₂²×#237	C₂×C₅	semidirect
81. C₂×C₃×#127	C₂×C₅	semidirect
82. C₂×#940	C₂×C₅	semidirect
83. C₂×#939	C₂×C₅	semidirect
84. C₂×#938	C₂×C₅	semidirect
85. C₂×D₄×Dic₃	C₂×C₅	semidirect
86. #5718	C₂×C₅	direct (N × H)
87. C₂×C₄×D₁₂	C₂×C₅	semidirect
88. C₂×C₄×Dic₆	C₂×C₅	semidirect
101. C₅×#127	C₂×D₃	semidirect
129. C₂×C₃×C₄×C₅	#41	semidirect
144. C₅×Dic₆	C₂×D₄	semidirect
152. C₂×#237	C₂²×C₅	semidirect
156. C₃×#127	C₂²×C₅	semidirect
159. #940	C₂²×C₅	semidirect
160. #939	C₂²×C₅	semidirect
161. #938	C₂²×C₅	semidirect
162. D₄×Dic₃	C₂²×C₅	semidirect
168. C₄×D₁₂	C₂²×C₅	semidirect
169. C₄×Dic₆	C₂²×C₅	semidirect
207. C₂×#127	C₅×D₃	semidirect
227. C₃×C₄×C₅	C₂×#41	semidirect
256. C₂×Dic₆	C₅×D₄	semidirect
291. C₂×C₄×C₅	#237	semidirect
307. #127	C₂×C₅×D₃	semidirect
321. C₂×C₃×C₅	#550	semidirect
340. C₂×C₃×C₄	C₅×#41	semidirect
355. Dic₆	C₂×C₅×D₄	semidirect
373. C₄×C₅	C₂×#237	semidirect
408. C₃×C₅	C₂×#550	semidirect
423. C₃×C₄	C₂×C₅×#41	semidirect
429. C₂×C₅	#5718	direct (N × H)
459. C₂×C₄	C₅×#237	semidirect
464. C₂×C₃	C₅×#550	semidirect
469. C₅	C₂×#5718	direct (N × H)
487. C₄	C₂×C₅×#237	semidirect
488. C₃	C₂×C₅×#550	semidirect
491. C₂	C₅×#5718	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×C₅×#237	2
C₂×C₃×C₅×#127	2
C₂×C₅×#940	2
C₂×C₅×#939	2
C₂×C₅×#938	2
C₂×C₅×D₄×Dic₃	2
C₅×#5718	2
C₂×C₄×C₅×D₁₂	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#550	3
C₂×#5718	5

Subgroups — C2×C5×#5718 #14482972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5718 #14482972