Subgroups — C₂×C₅×#5579 #14483805

Order 1920.

2400 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#946	C₂	1	2	yes	maximal, complemented
3	C₅×#5579	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#896	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×D₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₅×D₁₂	C₂	1	2	yes	maximal
7	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅×#870	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#869	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#554	—	3	1	no	maximal, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
14	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
15	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
16	C₃×C₄×C₅×Q₈	C₂²	1	8	yes	complemented
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
21	C₅×#946	C₂²	1	16	yes	complemented
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
25	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
26	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
28	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
29	C₅×#896	C₂²	1	32	yes	complemented
30	C₅×D₃×C₄⋊C₄	C₂²	1	16	yes	complemented
31	C₄×C₅×D₁₂	C₂²	1	16	yes	—
32	C₄×C₅×D₁₂	C₂²	1	8	yes	—
33	C₅×#870	C₂²	1	16	yes	complemented
34	C₅×#869	C₂²	1	8	yes	complemented
35	C₂×#5579	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₅×#554	—	3	16	no	—
37	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
38	C₂×C₅×#125	—	3	2	no	—
39	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
40	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
41	C₂×C₄×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
42	C₂×C₄×C₅×D₄	—	3	2	no	—
43	C₂×C₄×C₅×D₄	—	3	1	no	—
44	C₂²×C₅×C₄⋊C₄	—	3	2	no	—
45	C₂³×C₅×D₃	C₂³	1	2	yes	—
46	C₂×C₃×C₅×Q₈	—	2	4	no	—
47	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
54	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
55	C₂×C₅×D₁₂	Q₈	1	8	yes	complemented
56	C₂×C₅×D₁₂	C₂³	1	4	yes	—
57	C₂×C₄×C₅×D₃	—	2	8	no	—
58	C₂×C₄×C₅×D₃	—	4	8	no	—
59	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
60	C₂×C₄×C₅×D₃	C₂³	1	16	yes	—
61	C₂×C₅×Dic₆	—	4	4	no	—
62	C₂×C₅×Dic₆	C₂³	1	8	yes	—
63	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
65	C₃×C₄²×C₅	C₂³	1	4	yes	—
66	C₃×C₄²×C₅	C₂³	1	8	yes	—
67	C₅×(C₂×D₃)⋊C₄	C₂³	1	8	yes	—
68	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	—
69	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
70	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
71	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
72	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
73	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
74	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×#946	C₂×C₅	1	2	yes	complemented
76	#5579	C₂×C₅	1	16	yes	direct product factor
77	C₂×#896	C₂×C₅	1	4	yes	complemented
78	C₂×D₃×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
79	C₂×C₄×D₁₂	C₂×C₅	1	2	yes	—
80	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic
81	C₂×#870	C₂×C₅	1	2	yes	complemented
82	C₂×#869	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×Q₈	—	3	2	no	—
84	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
85	C₂²×C₅×D₄	—	3	1	no	—
86	C₂³×C₄×C₅	—	3	2	no	—
87	C₂³×C₄×C₅	—	3	4	no	—
88	C₅×C₄⋊Q₈	—	3	8	no	—
89	C₅×#125	—	3	16	no	—
90	C₅×C₂²⋊Q₈	—	3	16	no	—
91	C₅×C₂²⋊Q₈	—	3	32	no	—
92	C₄×C₅×Q₈	C₂×D₃	1	8	yes	complemented
93	C₄×C₅×D₄	—	3	16	no	—
94	C₄×C₅×D₄	—	3	8	no	—
95	C₂×C₅×C₄⋊C₄	—	3	4	no	—
96	C₂×C₅×C₄⋊C₄	—	3	4	no	—
97	C₂×C₅×C₄⋊C₄	—	3	2	no	—
98	C₂×C₅×C₄⋊C₄	—	3	1	no	—
99	C₂×C₅×C₄⋊C₄	—	3	2	no	—
100	C₂×C₅×C₄⋊C₄	—	3	16	no	—
101	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
103	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
104	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
105	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
106	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
107	C₂×#554	—	3	1	no	Sylow
108	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
109	C₂²×C₅×D₃	—	2	4	no	—
110	C₂²×C₅×D₃	—	2	4	no	—
111	C₂²×C₅×D₃	C₂×Q₈	1	8	yes	—
112	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
113	C₃×C₅×Q₈	—	2	8	no	—
114	C₂×C₃×C₄×C₅	—	2	4	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	4	no	—
117	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
118	C₂×C₃×C₄×C₅	#41	1	4	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
120	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
121	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
124	C₂×C₅×Dic₃	—	2	4	no	—
125	C₂×C₅×Dic₃	—	2	8	no	—
126	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
127	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
128	C₅×D₁₂	C₂×Q₈	1	16	yes	complemented
129	C₄×C₅×D₃	—	2	16	no	—
130	C₄×C₅×D₃	—	4	16	no	—
131	C₅×Dic₆	—	4	8	no	—
132	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
133	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
134	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
135	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
136	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
137	C₃×C₄×Q₈	C₂²×C₅	1	8	yes	complemented
138	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
142	#946	C₂²×C₅	1	16	yes	complemented
143	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
144	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
145	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
146	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
147	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
148	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
149	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
150	#896	C₂²×C₅	1	32	yes	complemented
151	D₃×C₄⋊C₄	C₂²×C₅	1	16	yes	complemented
152	C₄×D₁₂	C₂²×C₅	1	16	yes	—
153	C₄×D₁₂	C₂²×C₅	1	8	yes	—
154	#870	C₂²×C₅	1	16	yes	complemented
155	#869	C₂²×C₅	1	8	yes	complemented
156	C₂⁴×C₅	—	3	2	no	—
157	C₂×C₅×Q₈	—	2	4	no	—
158	C₂×C₅×Q₈	—	3	8	no	—
159	C₂×C₅×Q₈	—	12	4	no	—
160	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
161	C₂×C₅×D₄	—	3	8	no	—
162	C₂×C₅×D₄	—	3	4	no	—
163	C₂²×C₄×C₅	—	3	2	no	—
164	C₂²×C₄×C₅	—	3	4	no	—
165	C₂²×C₄×C₅	—	3	8	no	—
166	C₂²×C₄×C₅	—	3	16	no	—
167	C₂²×C₄×C₅	—	6	8	no	—
168	C₂²×C₄×C₅	—	12	8	no	—
169	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
170	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
172	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₅×C₄⋊C₄	—	3	16	no	—
175	C₅×C₄⋊C₄	—	3	8	no	—
176	C₅×C₄⋊C₄	—	3	4	no	—
177	C₅×C₄⋊C₄	—	3	8	no	—
178	C₅×C₄⋊C₄	—	3	16	no	—
179	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
180	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
181	C₅×C₂²⋊C₄	—	3	8	no	—
182	C₅×C₂²⋊C₄	—	3	16	no	—
183	C₄²×C₅	C₂²×D₃	1	8	yes	—
184	C₄²×C₅	C₂²×D₃	1	4	yes	—
185	#554	—	3	16	no	—
186	C₂×C₄⋊Q₈	—	3	1	no	—
187	C₂×#125	—	3	2	no	—
188	C₂×C₂²⋊Q₈	—	3	2	no	—
189	C₂×C₂²⋊Q₈	—	3	4	no	—
190	C₂×C₄×Q₈	C₅×D₃	1	1	yes	characteristic, complemented
191	C₂×C₄×D₄	—	3	2	no	—
192	C₂×C₄×D₄	—	3	1	no	—
193	C₂²×C₄⋊C₄	—	3	2	no	—
194	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
195	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
196	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
197	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
198	C₂×C₅×D₃	—	2	16	no	—
199	C₂×C₅×D₃	—	2	4	no	—
200	C₂×C₅×D₃	—	2	4	no	—
201	C₂×C₅×D₃	C₂²×Q₈	1	8	yes	—
202	C₃×C₄×C₅	—	2	4	no	—
203	C₃×C₄×C₅	—	2	2	no	—
204	C₃×C₄×C₅	—	2	4	no	—
205	C₃×C₄×C₅	C₂²×Q₈	1	4	yes	—
206	C₃×C₄×C₅	C₂×#41	1	4	yes	—
207	C₅×Dic₃	—	2	4	no	—
208	C₅×Dic₃	—	2	8	no	—
209	C₂³×D₃	C₂³×C₅	1	2	yes	—
210	C₂×C₃×Q₈	—	2	4	no	—
211	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
212	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
213	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
214	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
217	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
218	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
219	C₂×D₁₂	C₅×Q₈	1	8	yes	complemented
220	C₂×D₁₂	C₂³×C₅	1	4	yes	—
221	C₂×C₄×D₃	—	2	8	no	—
222	C₂×C₄×D₃	—	4	8	no	—
223	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
224	C₂×C₄×D₃	C₂³×C₅	1	16	yes	—
225	C₂×Dic₆	—	4	4	no	—
226	C₂×Dic₆	C₂³×C₅	1	8	yes	—
227	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
228	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
229	C₃×C₄²	C₂³×C₅	1	4	yes	—
230	C₃×C₄²	C₂³×C₅	1	8	yes	—
231	(C₂×D₃)⋊C₄	C₂³×C₅	1	8	yes	—
232	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	—
233	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
234	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
235	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
236	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
237	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
238	C₂³×C₅	—	3	8	no	—
239	C₂³×C₅	—	3	4	no	—
240	C₂³×C₅	—	6	4	no	—
241	C₂³×C₅	—	6	4	no	—
242	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
243	C₅×Q₈	—	2	8	no	—
244	C₅×Q₈	—	12	8	no	—
245	C₅×D₄	—	3	16	no	—
246	C₂×C₄×C₅	—	2	4	no	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	3	4	no	—
250	C₂×C₄×C₅	—	3	8	no	—
251	C₂×C₄×C₅	—	6	4	no	—
252	C₂×C₄×C₅	—	6	8	no	—
253	C₂×C₄×C₅	—	6	16	no	—
254	C₂×C₄×C₅	—	12	16	no	—
255	C₂×C₄×C₅	#235	1	4	yes	—
256	C₂×C₄×C₅	D₃×Q₈	1	4	yes	—
257	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
258	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
259	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
260	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
261	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
262	C₂²×Q₈	—	3	2	no	—
263	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
264	C₂²×D₄	—	3	1	no	—
265	C₂³×C₄	—	3	2	no	—
266	C₂³×C₄	—	3	4	no	—
267	C₄⋊Q₈	—	3	8	no	—
268	#125	—	3	16	no	—
269	C₂²⋊Q₈	—	3	16	no	—
270	C₂²⋊Q₈	—	3	32	no	—
271	C₄×Q₈	C₂×C₅×D₃	1	8	yes	complemented
272	C₄×D₄	—	3	16	no	—
273	C₄×D₄	—	3	8	no	—
274	C₂×C₄⋊C₄	—	3	4	no	—
275	C₂×C₄⋊C₄	—	3	2	no	—
276	C₂×C₄⋊C₄	—	3	1	no	—
277	C₂×C₄⋊C₄	—	3	2	no	—
278	C₂×C₄⋊C₄	—	3	4	no	—
279	C₂×C₄⋊C₄	—	3	16	no	—
280	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
282	C₂×C₂²⋊C₄	—	3	2	no	—
283	C₂×C₂²⋊C₄	—	3	4	no	—
284	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
285	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
286	C₂×C₃×C₅	#554	1	4	yes	complemented
287	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
289	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	C₅×D₃	—	2	8	no	—
291	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
292	C₂²×D₃	—	2	4	no	—
293	C₂²×D₃	—	2	4	no	—
294	C₂²×D₃	C₂×C₅×Q₈	1	8	yes	—
295	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
296	C₃×Q₈	—	2	8	no	—
297	C₂×C₃×C₄	—	2	4	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	4	no	—
300	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
301	C₂×C₃×C₄	C₅×#41	1	4	yes	—
302	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
303	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
304	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
305	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
306	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
307	C₂×Dic₃	—	2	4	no	—
308	C₂×Dic₃	—	2	8	no	—
309	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
310	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
311	D₁₂	C₂×C₅×Q₈	1	16	yes	complemented
312	C₄×D₃	—	2	16	no	—
313	C₄×D₃	—	4	16	no	—
314	Dic₆	—	4	8	no	—
315	C₂²×C₅	—	3	8	no	—
316	C₂²×C₅	—	6	4	no	—
317	C₂²×C₅	—	6	4	no	—
318	C₂²×C₅	—	6	16	no	—
319	C₂²×C₅	C₂×#235	1	2	yes	—
320	C₂²×C₅	C₂×D₃×Q₈	1	2	yes	—
321	C₂²×C₅	#1009	1	2	yes	—
322	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
323	C₄×C₅	—	2	4	no	—
324	C₄×C₅	—	2	4	no	—
325	C₄×C₅	—	2	2	no	—
326	C₄×C₅	—	6	4	no	—
327	C₄×C₅	—	6	8	no	—
328	C₄×C₅	C₂×#235	1	4	yes	—
329	C₄×C₅	C₂×D₃×Q₈	1	4	yes	—
330	C₂⁴	—	3	2	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	3	8	no	—
333	C₂×Q₈	—	12	4	no	—
334	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
335	C₂×D₄	—	3	8	no	—
336	C₂×D₄	—	3	4	no	—
337	C₂²×C₄	—	3	2	no	—
338	C₂²×C₄	—	3	4	no	—
339	C₂²×C₄	—	3	8	no	—
340	C₂²×C₄	—	3	16	no	—
341	C₂²×C₄	—	6	8	no	—
342	C₂²×C₄	—	12	8	no	—
343	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
344	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
346	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
347	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
348	C₄⋊C₄	—	3	16	no	—
349	C₄⋊C₄	—	3	8	no	—
350	C₄⋊C₄	—	3	4	no	—
351	C₄⋊C₄	—	3	8	no	—
352	C₄⋊C₄	—	3	16	no	—
353	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
354	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
355	C₂²⋊C₄	—	3	8	no	—
356	C₂²⋊C₄	—	3	16	no	—
357	C₄²	C₂²×C₅×D₃	1	8	yes	—
358	C₄²	C₂²×C₅×D₃	1	4	yes	—
359	C₃×C₅	C₂×#554	1	1	yes	characteristic, complemented, Hall
360	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
361	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
362	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
363	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
364	C₂×D₃	—	2	16	no	—
365	C₂×D₃	—	2	4	no	—
366	C₂×D₃	—	2	4	no	—
367	C₂×D₃	C₂²×C₅×Q₈	1	8	yes	—
368	C₃×C₄	—	2	4	no	—
369	C₃×C₄	—	2	2	no	—
370	C₃×C₄	—	2	4	no	—
371	C₃×C₄	C₂²×C₅×Q₈	1	4	yes	—
372	C₃×C₄	C₂×C₅×#41	1	4	yes	—
373	Dic₃	—	2	4	no	—
374	Dic₃	—	2	8	no	—
375	C₂×C₅	—	6	8	no	—
376	C₂×C₅	#5579	1	4	yes	direct product factor
377	C₂×C₅	C₂²×#235	1	1	yes	characteristic
378	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
379	C₂×C₅	C₂×#1009	1	1	yes	characteristic
380	C₂³	—	3	8	no	—
381	C₂³	—	3	4	no	—
382	C₂³	—	6	4	no	—
383	C₂³	—	6	4	no	—
384	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
385	Q₈	—	2	8	no	—
386	Q₈	—	12	8	no	—
387	D₄	—	3	16	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	3	4	no	—
392	C₂×C₄	—	3	8	no	—
393	C₂×C₄	—	6	4	no	—
394	C₂×C₄	—	6	8	no	—
395	C₂×C₄	—	6	16	no	—
396	C₂×C₄	—	12	16	no	—
397	C₂×C₄	C₅×#235	1	4	yes	—
398	C₂×C₄	C₅×D₃×Q₈	1	4	yes	—
399	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
400	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
401	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
402	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
403	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
404	C₂×C₃	C₅×#554	1	4	yes	complemented
405	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
406	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
407	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
408	D₃	—	2	8	no	—
409	C₅	C₂×#5579	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	3	8	no	—
411	C₂²	—	6	4	no	—
412	C₂²	—	6	4	no	—
413	C₂²	—	6	16	no	—
414	C₂²	C₂×C₅×#235	1	2	yes	—
415	C₂²	C₂×C₅×D₃×Q₈	1	2	yes	—
416	C₂²	C₅×#1009	1	2	yes	—
417	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
418	C₄	—	2	4	no	—
419	C₄	—	2	4	no	—
420	C₄	—	2	2	no	—
421	C₄	—	6	4	no	—
422	C₄	—	6	8	no	—
423	C₄	C₂×C₅×#235	1	4	yes	—
424	C₄	C₂×C₅×D₃×Q₈	1	4	yes	—
425	C₃	C₂×C₅×#554	1	1	yes	characteristic, complemented, Sylow
426	C₂	—	6	8	no	—
427	C₂	C₅×#5579	1	4	yes	direct product factor
428	C₂	C₂²×C₅×#235	1	1	yes	characteristic
429	C₂	C₂²×C₅×D₃×Q₈	1	1	yes	characteristic
430	C₂	C₂×C₅×#1009	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×C₄×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
hypercenter	C₂×C₄×C₅×Q₈	D₃
hypocenter	C₃	C₂×C₅×#554
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
2. C₂×C₅×#946	C₂	semidirect
3. C₅×#5579	C₂	direct (N × H)
4. C₂×C₅×#896	C₂	semidirect
5. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
8. C₂×C₅×#870	C₂	semidirect
9. C₂×C₅×#869	C₂	semidirect
16. C₃×C₄×C₅×Q₈	C₂²	semidirect
21. C₅×#946	C₂²	semidirect
29. C₅×#896	C₂²	semidirect
30. C₅×D₃×C₄⋊C₄	C₂²	semidirect
33. C₅×#870	C₂²	semidirect
34. C₅×#869	C₂²	semidirect
35. C₂×#5579	C₅	direct (N × H)
41. C₂×C₄×C₅×Q₈	D₃	semidirect
55. C₂×C₅×D₁₂	Q₈	semidirect
74. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
75. C₂×#946	C₂×C₅	semidirect
76. #5579	C₂×C₅	direct (N × H)
77. C₂×#896	C₂×C₅	semidirect
78. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
81. C₂×#870	C₂×C₅	semidirect
82. C₂×#869	C₂×C₅	semidirect
92. C₄×C₅×Q₈	C₂×D₃	semidirect
128. C₅×D₁₂	C₂×Q₈	semidirect
137. C₃×C₄×Q₈	C₂²×C₅	semidirect
142. #946	C₂²×C₅	semidirect
150. #896	C₂²×C₅	semidirect
151. D₃×C₄⋊C₄	C₂²×C₅	semidirect
154. #870	C₂²×C₅	semidirect
155. #869	C₂²×C₅	semidirect
190. C₂×C₄×Q₈	C₅×D₃	semidirect
219. C₂×D₁₂	C₅×Q₈	semidirect
271. C₄×Q₈	C₂×C₅×D₃	semidirect
286. C₂×C₃×C₅	#554	semidirect
311. D₁₂	C₂×C₅×Q₈	semidirect
359. C₃×C₅	C₂×#554	semidirect
376. C₂×C₅	#5579	direct (N × H)
404. C₂×C₃	C₅×#554	semidirect
409. C₅	C₂×#5579	direct (N × H)
425. C₃	C₂×C₅×#554	semidirect
427. C₂	C₅×#5579	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×C₄×C₅×Q₈	2
C₂×C₅×#946	2
C₅×#5579	2
C₂×C₅×#896	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#870	2
C₂×C₅×#869	2
C₂×C₅×#554	3
C₂×#5579	5

Subgroups — C2×C5×#5579 #14483805

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5579 #14483805