Subgroups — C₂×C₃×D₅×C₂²⋊Q₈ #14479409

Order 1920.

3680 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4092	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4070	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×D₅×C₂²⋊Q₈	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4042	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×D₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×D₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×D₅×C₂²⋊C₄	C₂	1	2	yes	maximal
12	C₂×C₃×#4024	C₂	1	2	yes	maximal, complemented
13	C₂×D₅×C₂²⋊Q₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×Q₈×D₅	—	2	8	no	—
19	C₂×C₃×Q₈×D₅	C₂²	1	8	yes	complemented
20	C₂²×C₃×C₄×D₅	—	2	8	no	—
21	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₅	C₂²	1	8	yes	—
23	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
26	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
27	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
28	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	complemented
30	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	complemented
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
35	C₃×#4092	C₂²	1	8	yes	complemented
36	C₂×C₃×#685	C₂²	1	2	yes	—
37	C₂×C₃×#685	C₂²	1	2	yes	—
38	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
39	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
40	C₃×#4070	C₂²	1	8	yes	complemented
41	C₂×C₃×#683	C₂²	1	2	yes	complemented
42	C₂×C₃×#683	C₂²	1	2	yes	complemented
43	C₂×C₃×#683	C₂²	1	2	yes	complemented
44	C₃×#4043	C₂²	1	8	yes	complemented
45	C₃×#4042	C₂²	1	16	yes	complemented
46	C₃×D₅×C₄⋊C₄	C₂²	1	16	yes	complemented
47	C₃×D₅×C₄⋊C₄	C₂²	1	8	yes	complemented
48	C₃×D₅×C₂²⋊C₄	C₂²	1	16	yes	—
49	C₃×#4024	C₂²	1	16	yes	complemented
50	C₂²×C₃×C₂²⋊Q₈	—	5	1	no	maximal, Hall
51	C₂²×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂³×C₄×D₅	C₂×C₃	1	1	yes	characteristic
53	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#4092	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#4070	C₂×C₃	1	1	yes	characteristic, complemented
56	D₅×C₂²⋊Q₈	C₂×C₃	1	16	yes	direct product factor
57	C₂×#4043	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×#4042	C₂×C₃	1	2	yes	complemented
59	C₂×D₅×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
60	C₂×D₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂×D₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
62	C₂×#4024	C₂×C₃	1	2	yes	complemented
63	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
64	C₂³×C₃×D₅	—	2	4	no	—
65	C₂³×C₃×D₅	—	2	4	no	—
66	C₂³×C₃×D₅	Q₈	1	8	yes	complemented
67	C₂³×C₃×D₅	C₂³	1	4	yes	—
68	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
69	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×Q₈	—	2	4	no	—
71	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
72	C₂²×C₃×C₄×C₅	—	2	4	no	—
73	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
76	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×Dic₅	—	2	4	no	—
79	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
80	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
81	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
82	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
84	C₃×Q₈×D₅	—	2	32	no	—
85	C₂×C₃×C₄×D₅	—	2	4	no	—
86	C₂×C₃×C₄×D₅	—	2	8	no	—
87	C₂×C₃×C₄×D₅	—	2	8	no	—
88	C₂×C₃×C₄×D₅	—	2	4	no	—
89	C₂×C₃×C₄×D₅	—	2	4	no	—
90	C₂×C₃×C₄×D₅	—	2	32	no	—
91	C₂×C₃×C₄×D₅	D₄	1	8	yes	—
92	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
93	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
94	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
95	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
96	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
97	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
98	C₂×C₃×Dic₁₀	—	2	4	no	—
99	C₂×C₃×Dic₁₀	—	2	8	no	—
100	C₂×C₃×Dic₁₀	C₂³	1	8	yes	complemented
101	C₂×C₃×Dic₁₀	C₂³	1	4	yes	complemented
102	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
103	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
104	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
106	C₃×#685	C₂³	1	8	yes	—
107	C₃×#685	C₂³	1	8	yes	—
108	C₃×C₄⋊Dic₅	C₂³	1	4	yes	complemented
109	C₃×C₄⋊Dic₅	C₂³	1	8	yes	complemented
110	C₃×#683	C₂³	1	8	yes	complemented
111	C₃×#683	C₂³	1	8	yes	complemented
112	C₃×#683	C₂³	1	8	yes	complemented
113	C₂³×C₃×Q₈	—	5	1	no	—
114	C₂⁴×C₃×C₄	—	5	1	no	—
115	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
116	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
117	C₂×C₃×C₂²⋊Q₈	—	5	16	no	—
118	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
119	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
120	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
121	C₂×C₃×C₂²⋊Q₈	D₅	1	1	yes	characteristic, direct product factor
122	C₂²×C₃×C₄⋊C₄	—	5	1	no	—
123	C₂²×C₃×C₄⋊C₄	—	5	2	no	—
124	C₂²×C₃×C₂²⋊C₄	—	5	2	no	—
125	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
126	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
128	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
129	C₂×Q₈×D₅	—	2	8	no	—
130	C₂×Q₈×D₅	C₂²×C₃	1	8	yes	complemented
131	C₂²×C₄×D₅	—	2	8	no	—
132	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
133	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
134	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
135	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
136	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
137	C₂²×C₄×D₅	C₂²×C₃	1	8	yes	—
138	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
139	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	complemented
140	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
141	C₅×C₂²⋊Q₈	C₂²×C₃	1	8	yes	complemented
142	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
143	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
145	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
146	#4092	C₂²×C₃	1	8	yes	complemented
147	C₂×#685	C₂²×C₃	1	2	yes	—
148	C₂×#685	C₂²×C₃	1	2	yes	—
149	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	complemented
150	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
151	#4070	C₂²×C₃	1	8	yes	complemented
152	C₂×#683	C₂²×C₃	1	2	yes	complemented
153	C₂×#683	C₂²×C₃	1	2	yes	complemented
154	C₂×#683	C₂²×C₃	1	2	yes	complemented
155	#4043	C₂²×C₃	1	8	yes	complemented
156	#4042	C₂²×C₃	1	16	yes	complemented
157	D₅×C₄⋊C₄	C₂²×C₃	1	8	yes	complemented
158	D₅×C₄⋊C₄	C₂²×C₃	1	16	yes	complemented
159	D₅×C₂²⋊C₄	C₂²×C₃	1	16	yes	—
160	#4024	C₂²×C₃	1	16	yes	complemented
161	C₂²×C₂²⋊Q₈	—	5	1	no	Sylow
162	C₂³×C₃×C₅	—	2	2	no	—
163	C₂³×C₃×C₅	—	2	2	no	—
164	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	complemented
165	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
166	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
167	C₂²×C₃×D₅	—	2	2	no	—
168	C₂²×C₃×D₅	—	2	2	no	—
169	C₂²×C₃×D₅	—	2	32	no	—
170	C₂²×C₃×D₅	—	2	8	no	—
171	C₂²×C₃×D₅	—	2	8	no	—
172	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
173	C₂²×C₃×D₅	C₂×Q₈	1	4	yes	—
174	C₂²×C₃×D₅	C₂×Q₈	1	16	yes	complemented
175	C₂²×C₃×D₅	C₂×Q₈	1	4	yes	complemented
176	C₂²×C₃×D₅	#41	1	4	yes	—
177	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
178	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
179	C₃×C₅×Q₈	—	2	8	no	—
180	C₂×C₃×C₄×C₅	—	2	4	no	—
181	C₂×C₃×C₄×C₅	—	2	2	no	—
182	C₂×C₃×C₄×C₅	—	2	4	no	—
183	C₂×C₃×C₄×C₅	—	2	8	no	—
184	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
185	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
186	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
187	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
188	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
189	C₂×C₃×Dic₅	—	2	4	no	—
190	C₂×C₃×Dic₅	—	2	2	no	—
191	C₂×C₃×Dic₅	—	2	4	no	—
192	C₂×C₃×Dic₅	—	2	8	no	—
193	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
194	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
195	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
196	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
197	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
198	C₃×C₄×D₅	—	2	8	no	—
199	C₃×C₄×D₅	—	2	16	no	—
200	C₃×C₄×D₅	—	2	16	no	—
201	C₃×C₄×D₅	—	2	8	no	—
202	C₃×C₄×D₅	—	2	8	no	—
203	C₃×C₄×D₅	C₂×D₄	1	16	yes	—
204	C₃×Dic₁₀	—	2	8	no	—
205	C₃×Dic₁₀	—	2	16	no	—
206	C₂⁵×C₃	—	5	1	no	—
207	C₂²×C₃×Q₈	—	5	8	no	—
208	C₂²×C₃×Q₈	—	5	2	no	—
209	C₂²×C₃×Q₈	—	5	1	no	—
210	C₂²×C₃×Q₈	—	10	8	no	—
211	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
212	C₂³×C₃×C₄	—	5	1	no	—
213	C₂³×C₃×C₄	—	5	1	no	—
214	C₂³×C₃×C₄	—	5	1	no	—
215	C₂³×C₃×C₄	—	5	1	no	—
216	C₂³×C₃×C₄	—	5	8	no	—
217	C₂³×C₃×C₄	—	5	1	no	—
218	C₂³×C₃×C₄	—	5	2	no	—
219	C₂³×C₃×C₄	—	5	2	no	—
220	C₂³×C₃×C₄	—	10	8	no	—
221	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
222	C₃×C₂²⋊Q₈	—	5	8	no	—
223	C₃×C₂²⋊Q₈	—	5	8	no	—
224	C₃×C₂²⋊Q₈	—	5	16	no	—
225	C₃×C₂²⋊Q₈	—	5	8	no	—
226	C₃×C₂²⋊Q₈	—	5	16	no	—
227	C₃×C₂²⋊Q₈	C₂×D₅	1	8	yes	direct product factor
228	C₂×C₃×C₄⋊C₄	—	5	2	no	—
229	C₂×C₃×C₄⋊C₄	—	5	2	no	—
230	C₂×C₃×C₄⋊C₄	—	5	2	no	—
231	C₂×C₃×C₄⋊C₄	—	5	1	no	—
232	C₂×C₃×C₄⋊C₄	—	5	2	no	—
233	C₂×C₃×C₄⋊C₄	—	5	8	no	—
234	C₂×C₃×C₄⋊C₄	—	5	16	no	—
235	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
236	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	complemented
237	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
238	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
239	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
240	C₂×C₃×C₂²⋊C₄	—	5	16	no	—
241	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
242	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
243	C₂³×D₅	—	2	4	no	—
244	C₂³×D₅	—	2	4	no	—
245	C₂³×D₅	C₃×Q₈	1	8	yes	complemented
246	C₂³×D₅	C₂³×C₃	1	4	yes	—
247	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
248	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₅×Q₈	—	2	4	no	—
250	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	complemented
251	C₂²×C₄×C₅	—	2	4	no	—
252	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
253	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
254	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
255	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
256	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
257	C₂²×Dic₅	—	2	4	no	—
258	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
259	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
260	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
261	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
262	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
263	Q₈×D₅	—	2	32	no	—
264	C₂×C₄×D₅	—	2	4	no	—
265	C₂×C₄×D₅	—	2	8	no	—
266	C₂×C₄×D₅	—	2	8	no	—
267	C₂×C₄×D₅	—	2	4	no	—
268	C₂×C₄×D₅	—	2	4	no	—
269	C₂×C₄×D₅	—	2	32	no	—
270	C₂×C₄×D₅	C₃×D₄	1	8	yes	—
271	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
272	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
273	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
274	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
275	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
276	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
277	C₂×Dic₁₀	—	2	4	no	—
278	C₂×Dic₁₀	—	2	8	no	—
279	C₂×Dic₁₀	C₂³×C₃	1	8	yes	complemented
280	C₂×Dic₁₀	C₂³×C₃	1	4	yes	complemented
281	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
282	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
283	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
284	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
285	#685	C₂³×C₃	1	8	yes	—
286	#685	C₂³×C₃	1	8	yes	—
287	C₄⋊Dic₅	C₂³×C₃	1	8	yes	complemented
288	C₄⋊Dic₅	C₂³×C₃	1	4	yes	complemented
289	#683	C₂³×C₃	1	8	yes	complemented
290	#683	C₂³×C₃	1	8	yes	complemented
291	#683	C₂³×C₃	1	8	yes	complemented
292	C₂³×Q₈	—	5	1	no	—
293	C₂⁴×C₄	—	5	1	no	—
294	C₂×C₂²⋊Q₈	—	5	1	no	—
295	C₂×C₂²⋊Q₈	—	5	1	no	—
296	C₂×C₂²⋊Q₈	—	5	16	no	—
297	C₂×C₂²⋊Q₈	—	5	2	no	—
298	C₂×C₂²⋊Q₈	—	5	1	no	—
299	C₂×C₂²⋊Q₈	—	5	2	no	—
300	C₂×C₂²⋊Q₈	C₃×D₅	1	1	yes	characteristic, direct product factor
301	C₂²×C₄⋊C₄	—	5	1	no	—
302	C₂²×C₄⋊C₄	—	5	2	no	—
303	C₂²×C₂²⋊C₄	—	5	2	no	—
304	C₂²×C₃×C₅	—	2	8	no	—
305	C₂²×C₃×C₅	—	2	2	no	—
306	C₂²×C₃×C₅	—	2	2	no	—
307	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
308	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
309	C₂²×C₃×C₅	C₂²×Q₈	1	4	yes	complemented
310	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
311	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
312	C₂×C₃×D₅	—	2	8	no	—
313	C₂×C₃×D₅	—	2	2	no	—
314	C₂×C₃×D₅	—	2	2	no	—
315	C₂×C₃×D₅	—	2	32	no	—
316	C₂×C₃×D₅	C₂²⋊Q₈	1	16	yes	direct product factor
317	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
318	C₂×C₃×D₅	C₂²×Q₈	1	4	yes	—
319	C₂×C₃×D₅	C₂²×Q₈	1	4	yes	complemented
320	C₂×C₃×D₅	C₂×#41	1	4	yes	—
321	C₃×C₄×C₅	—	2	4	no	—
322	C₃×C₄×C₅	—	2	2	no	—
323	C₃×C₄×C₅	—	2	4	no	—
324	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
325	C₃×Dic₅	—	2	4	no	—
326	C₃×Dic₅	—	2	2	no	—
327	C₃×Dic₅	—	2	4	no	—
328	C₃×Dic₅	C₂²×D₄	1	4	yes	—
329	C₂⁴×C₃	—	5	1	no	—
330	C₂⁴×C₃	—	5	8	no	—
331	C₂⁴×C₃	—	5	4	no	—
332	C₂⁴×C₃	—	5	1	no	—
333	C₂⁴×C₃	—	10	4	no	—
334	C₂⁴×C₃	—	10	4	no	—
335	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
336	C₂×C₃×Q₈	—	2	4	no	—
337	C₂×C₃×Q₈	—	5	8	no	—
338	C₂×C₃×Q₈	—	5	4	no	—
339	C₂×C₃×Q₈	—	10	8	no	—
340	C₂×C₃×Q₈	—	10	32	no	—
341	C₂×C₃×Q₈	—	10	4	no	—
342	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	complemented
343	C₂²×C₃×C₄	—	2	4	no	—
344	C₂²×C₃×C₄	—	5	1	no	—
345	C₂²×C₃×C₄	—	5	8	no	—
346	C₂²×C₃×C₄	—	5	4	no	—
347	C₂²×C₃×C₄	—	5	4	no	—
348	C₂²×C₃×C₄	—	5	2	no	—
349	C₂²×C₃×C₄	—	5	2	no	—
350	C₂²×C₃×C₄	—	5	1	no	—
351	C₂²×C₃×C₄	—	5	8	no	—
352	C₂²×C₃×C₄	—	5	8	no	—
353	C₂²×C₃×C₄	—	5	4	no	—
354	C₂²×C₃×C₄	—	5	4	no	—
355	C₂²×C₃×C₄	—	5	4	no	—
356	C₂²×C₃×C₄	—	10	4	no	—
357	C₂²×C₃×C₄	—	10	32	no	—
358	C₂²×C₃×C₄	—	10	8	no	—
359	C₂²×C₃×C₄	—	10	4	no	—
360	C₂²×C₃×C₄	—	10	8	no	—
361	C₂²×C₃×C₄	—	10	4	no	—
362	C₂²×C₃×C₄	—	10	4	no	—
363	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
364	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
365	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
366	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
367	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
368	C₃×C₄⋊C₄	—	5	8	no	—
369	C₃×C₄⋊C₄	—	5	8	no	—
370	C₃×C₄⋊C₄	—	5	8	no	—
371	C₃×C₄⋊C₄	—	5	4	no	—
372	C₃×C₄⋊C₄	—	5	8	no	—
373	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	complemented
374	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	complemented
375	C₃×C₂²⋊C₄	—	5	8	no	—
376	C₃×C₂²⋊C₄	—	5	8	no	—
377	C₃×C₂²⋊C₄	—	5	8	no	—
378	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
379	C₂³×C₅	—	2	2	no	—
380	C₂³×C₅	—	2	2	no	—
381	C₂³×C₅	C₂×C₃×Q₈	1	4	yes	complemented
382	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
383	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
384	C₂²×D₅	—	2	2	no	—
385	C₂²×D₅	—	2	2	no	—
386	C₂²×D₅	—	2	32	no	—
387	C₂²×D₅	—	2	8	no	—
388	C₂²×D₅	—	2	8	no	—
389	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
390	C₂²×D₅	C₂×C₃×Q₈	1	4	yes	—
391	C₂²×D₅	C₂×C₃×Q₈	1	16	yes	complemented
392	C₂²×D₅	C₂×C₃×Q₈	1	4	yes	complemented
393	C₂²×D₅	C₃×#41	1	4	yes	—
394	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
395	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
396	C₅×Q₈	—	2	8	no	—
397	C₂×C₄×C₅	—	2	4	no	—
398	C₂×C₄×C₅	—	2	2	no	—
399	C₂×C₄×C₅	—	2	4	no	—
400	C₂×C₄×C₅	—	2	8	no	—
401	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
402	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
403	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
404	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
405	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
406	C₂×Dic₅	—	2	4	no	—
407	C₂×Dic₅	—	2	2	no	—
408	C₂×Dic₅	—	2	4	no	—
409	C₂×Dic₅	—	2	8	no	—
410	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
411	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
412	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
413	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
414	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
415	C₄×D₅	—	2	8	no	—
416	C₄×D₅	—	2	16	no	—
417	C₄×D₅	—	2	16	no	—
418	C₄×D₅	—	2	8	no	—
419	C₄×D₅	—	2	8	no	—
420	C₄×D₅	C₂×C₃×D₄	1	16	yes	—
421	Dic₁₀	—	2	8	no	—
422	Dic₁₀	—	2	16	no	—
423	C₂⁵	—	5	1	no	—
424	C₂²×Q₈	—	5	8	no	—
425	C₂²×Q₈	—	5	2	no	—
426	C₂²×Q₈	—	5	1	no	—
427	C₂²×Q₈	—	10	8	no	—
428	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
429	C₂³×C₄	—	5	1	no	—
430	C₂³×C₄	—	5	1	no	—
431	C₂³×C₄	—	5	2	no	—
432	C₂³×C₄	—	5	2	no	—
433	C₂³×C₄	—	5	1	no	—
434	C₂³×C₄	—	5	1	no	—
435	C₂³×C₄	—	5	8	no	—
436	C₂³×C₄	—	5	1	no	—
437	C₂³×C₄	—	10	8	no	—
438	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
439	C₂²⋊Q₈	—	5	8	no	—
440	C₂²⋊Q₈	—	5	8	no	—
441	C₂²⋊Q₈	—	5	16	no	—
442	C₂²⋊Q₈	—	5	8	no	—
443	C₂²⋊Q₈	—	5	16	no	—
444	C₂²⋊Q₈	C₂×C₃×D₅	1	8	yes	direct product factor
445	C₂×C₄⋊C₄	—	5	2	no	—
446	C₂×C₄⋊C₄	—	5	2	no	—
447	C₂×C₄⋊C₄	—	5	2	no	—
448	C₂×C₄⋊C₄	—	5	1	no	—
449	C₂×C₄⋊C₄	—	5	2	no	—
450	C₂×C₄⋊C₄	—	5	8	no	—
451	C₂×C₄⋊C₄	—	5	16	no	—
452	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
453	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
454	C₂×C₂²⋊C₄	—	5	2	no	—
455	C₂×C₂²⋊C₄	—	5	2	no	—
456	C₂×C₂²⋊C₄	—	5	2	no	—
457	C₂×C₂²⋊C₄	—	5	16	no	—
458	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
459	C₂×C₃×C₅	—	2	4	no	—
460	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	4	yes	complemented
461	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
462	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
463	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
464	C₃×D₅	—	2	4	no	—
465	C₃×D₅	C₂×C₂²⋊Q₈	1	8	yes	direct product factor
466	C₂³×C₃	—	2	2	no	—
467	C₂³×C₃	—	2	2	no	—
468	C₂³×C₃	—	5	4	no	—
469	C₂³×C₃	—	5	4	no	—
470	C₂³×C₃	—	5	4	no	—
471	C₂³×C₃	—	5	2	no	—
472	C₂³×C₃	—	5	4	no	—
473	C₂³×C₃	—	5	16	no	—
474	C₂³×C₃	—	5	2	no	—
475	C₂³×C₃	—	10	8	no	—
476	C₂³×C₃	—	10	32	no	—
477	C₂³×C₃	—	10	8	no	—
478	C₂³×C₃	—	10	2	no	—
479	C₂³×C₃	—	10	2	no	—
480	C₂³×C₃	Q₈×D₅	1	4	yes	complemented
481	C₂³×C₃	C₂³×D₅	1	2	yes	—
482	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
483	C₃×Q₈	—	2	8	no	—
484	C₃×Q₈	—	10	16	no	—
485	C₃×Q₈	—	10	8	no	—
486	C₂×C₃×C₄	—	2	2	no	—
487	C₂×C₃×C₄	—	2	4	no	—
488	C₂×C₃×C₄	—	2	4	no	—
489	C₂×C₃×C₄	—	2	8	no	—
490	C₂×C₃×C₄	—	5	4	no	—
491	C₂×C₃×C₄	—	5	2	no	—
492	C₂×C₃×C₄	—	5	16	no	—
493	C₂×C₃×C₄	—	5	4	no	—
494	C₂×C₃×C₄	—	5	4	no	—
495	C₂×C₃×C₄	—	5	2	no	—
496	C₂×C₃×C₄	—	10	8	no	—
497	C₂×C₃×C₄	—	10	16	no	—
498	C₂×C₃×C₄	—	10	8	no	—
499	C₂×C₃×C₄	—	10	16	no	—
500	C₂×C₃×C₄	—	10	8	no	—
501	C₂×C₃×C₄	—	10	2	no	—
502	C₂×C₃×C₄	—	10	4	no	—
503	C₂×C₃×C₄	—	10	4	no	—
504	C₂×C₃×C₄	—	10	8	no	—
505	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
506	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
507	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
508	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
509	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
510	C₂²×C₅	—	2	2	no	—
511	C₂²×C₅	—	2	2	no	—
512	C₂²×C₅	—	2	8	no	—
513	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
514	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
515	C₂²×C₅	C₂²×C₃×Q₈	1	4	yes	complemented
516	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
517	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
518	C₂×D₅	—	2	2	no	—
519	C₂×D₅	—	2	2	no	—
520	C₂×D₅	—	2	8	no	—
521	C₂×D₅	—	2	32	no	—
522	C₂×D₅	C₃×C₂²⋊Q₈	1	16	yes	direct product factor
523	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
524	C₂×D₅	C₂²×C₃×Q₈	1	4	yes	—
525	C₂×D₅	C₂²×C₃×Q₈	1	4	yes	complemented
526	C₂×D₅	C₂×C₃×#41	1	4	yes	—
527	C₄×C₅	—	2	4	no	—
528	C₄×C₅	—	2	2	no	—
529	C₄×C₅	—	2	4	no	—
530	C₄×C₅	C₂²×C₃×D₄	1	4	yes	—
531	Dic₅	—	2	4	no	—
532	Dic₅	—	2	2	no	—
533	Dic₅	—	2	4	no	—
534	Dic₅	C₂²×C₃×D₄	1	4	yes	—
535	C₂⁴	—	5	1	no	—
536	C₂⁴	—	5	8	no	—
537	C₂⁴	—	5	4	no	—
538	C₂⁴	—	5	1	no	—
539	C₂⁴	—	10	4	no	—
540	C₂⁴	—	10	4	no	—
541	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
542	C₂×Q₈	—	2	4	no	—
543	C₂×Q₈	—	5	8	no	—
544	C₂×Q₈	—	5	4	no	—
545	C₂×Q₈	—	10	8	no	—
546	C₂×Q₈	—	10	32	no	—
547	C₂×Q₈	—	10	4	no	—
548	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	complemented
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	5	1	no	—
551	C₂²×C₄	—	5	8	no	—
552	C₂²×C₄	—	5	4	no	—
553	C₂²×C₄	—	5	2	no	—
554	C₂²×C₄	—	5	2	no	—
555	C₂²×C₄	—	5	1	no	—
556	C₂²×C₄	—	5	4	no	—
557	C₂²×C₄	—	5	8	no	—
558	C₂²×C₄	—	5	8	no	—
559	C₂²×C₄	—	5	4	no	—
560	C₂²×C₄	—	5	4	no	—
561	C₂²×C₄	—	5	4	no	—
562	C₂²×C₄	—	10	4	no	—
563	C₂²×C₄	—	10	32	no	—
564	C₂²×C₄	—	10	4	no	—
565	C₂²×C₄	—	10	8	no	—
566	C₂²×C₄	—	10	8	no	—
567	C₂²×C₄	—	10	4	no	—
568	C₂²×C₄	—	10	4	no	—
569	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
570	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
571	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
572	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
573	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
574	C₄⋊C₄	—	5	8	no	—
575	C₄⋊C₄	—	5	8	no	—
576	C₄⋊C₄	—	5	8	no	—
577	C₄⋊C₄	—	5	4	no	—
578	C₄⋊C₄	—	5	8	no	—
579	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
580	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	complemented
581	C₂²⋊C₄	—	5	8	no	—
582	C₂²⋊C₄	—	5	8	no	—
583	C₂²⋊C₄	—	5	8	no	—
584	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
585	C₃×C₅	C₂²×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Hall
586	C₂²×C₃	—	2	8	no	—
587	C₂²×C₃	—	2	2	no	—
588	C₂²×C₃	—	2	2	no	—
589	C₂²×C₃	—	5	16	no	—
590	C₂²×C₃	—	5	4	no	—
591	C₂²×C₃	—	5	4	no	—
592	C₂²×C₃	—	5	4	no	—
593	C₂²×C₃	—	5	4	no	—
594	C₂²×C₃	—	10	32	no	—
595	C₂²×C₃	—	10	8	no	—
596	C₂²×C₃	—	10	2	no	—
597	C₂²×C₃	—	10	2	no	—
598	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
599	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
600	C₂²×C₃	C₂×Q₈×D₅	1	4	yes	complemented
601	C₂²×C₃	D₅×#41	1	2	yes	—
602	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
603	C₃×C₄	—	2	2	no	—
604	C₃×C₄	—	2	4	no	—
605	C₃×C₄	—	2	4	no	—
606	C₃×C₄	—	5	4	no	—
607	C₃×C₄	—	10	2	no	—
608	C₃×C₄	—	10	4	no	—
609	C₃×C₄	—	10	4	no	—
610	C₃×C₄	C₂×D₄×D₅	1	4	yes	—
611	C₂×C₅	—	2	4	no	—
612	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	4	yes	complemented
613	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
614	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
615	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
616	D₅	—	2	4	no	—
617	D₅	C₂×C₃×C₂²⋊Q₈	1	8	yes	direct product factor
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	5	4	no	—
621	C₂³	—	5	4	no	—
622	C₂³	—	5	4	no	—
623	C₂³	—	5	2	no	—
624	C₂³	—	5	4	no	—
625	C₂³	—	5	16	no	—
626	C₂³	—	5	2	no	—
627	C₂³	—	10	8	no	—
628	C₂³	—	10	8	no	—
629	C₂³	—	10	32	no	—
630	C₂³	—	10	2	no	—
631	C₂³	—	10	2	no	—
632	C₂³	C₃×Q₈×D₅	1	4	yes	complemented
633	C₂³	C₂³×C₃×D₅	1	2	yes	—
634	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
635	Q₈	—	2	8	no	—
636	Q₈	—	10	16	no	—
637	Q₈	—	10	8	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	8	no	—
642	C₂×C₄	—	5	4	no	—
643	C₂×C₄	—	5	2	no	—
644	C₂×C₄	—	5	16	no	—
645	C₂×C₄	—	5	4	no	—
646	C₂×C₄	—	5	4	no	—
647	C₂×C₄	—	5	2	no	—
648	C₂×C₄	—	10	8	no	—
649	C₂×C₄	—	10	8	no	—
650	C₂×C₄	—	10	16	no	—
651	C₂×C₄	—	10	16	no	—
652	C₂×C₄	—	10	8	no	—
653	C₂×C₄	—	10	2	no	—
654	C₂×C₄	—	10	4	no	—
655	C₂×C₄	—	10	4	no	—
656	C₂×C₄	—	10	8	no	—
657	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
658	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
659	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
660	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
661	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
662	C₂×C₃	—	2	4	no	—
663	C₂×C₃	—	5	8	no	—
664	C₂×C₃	—	10	4	no	—
665	C₂×C₃	D₅×C₂²⋊Q₈	1	4	yes	direct product factor
666	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
667	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
668	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
669	C₅	C₂²×C₃×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	8	no	—
673	C₂²	—	5	4	no	—
674	C₂²	—	5	4	no	—
675	C₂²	—	5	4	no	—
676	C₂²	—	5	16	no	—
677	C₂²	—	5	4	no	—
678	C₂²	—	10	32	no	—
679	C₂²	—	10	2	no	—
680	C₂²	—	10	2	no	—
681	C₂²	—	10	8	no	—
682	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
683	C₂²	C₂×C₃×Q₈×D₅	1	2	yes	—
684	C₂²	C₂×C₃×Q₈×D₅	1	4	yes	complemented
685	C₂²	C₃×D₅×#41	1	2	yes	—
686	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
687	C₄	—	2	2	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	4	no	—
690	C₄	—	5	4	no	—
691	C₄	—	10	2	no	—
692	C₄	—	10	4	no	—
693	C₄	—	10	4	no	—
694	C₄	C₂×C₃×D₄×D₅	1	4	yes	—
695	C₃	C₂×D₅×C₂²⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
696	C₂	—	2	4	no	—
697	C₂	—	5	8	no	—
698	C₂	—	10	4	no	—
699	C₂	C₃×D₅×C₂²⋊Q₈	1	4	yes	direct product factor
700	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
701	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
702	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×C₂²⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×D₅	C₂²
hypercenter	C₂×C₃×C₂²⋊Q₈	D₅
hypocenter	C₅	C₂²×C₃×C₂²⋊Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈×D₅	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
4. C₂×C₃×#4092	C₂	semidirect
5. C₂×C₃×#4070	C₂	semidirect
6. C₃×D₅×C₂²⋊Q₈	C₂	direct (N × H)
7. C₂×C₃×#4043	C₂	semidirect
8. C₂×C₃×#4042	C₂	semidirect
9. C₂×C₃×D₅×C₄⋊C₄	C₂	semidirect
10. C₂×C₃×D₅×C₄⋊C₄	C₂	semidirect
12. C₂×C₃×#4024	C₂	semidirect
13. C₂×D₅×C₂²⋊Q₈	C₃	direct (N × H)
15. C₂²×C₃×C₅×Q₈	C₂²	semidirect
19. C₂×C₃×Q₈×D₅	C₂²	semidirect
28. C₂²×C₃×Dic₁₀	C₂²	semidirect
29. C₂²×C₃×Dic₁₀	C₂²	semidirect
30. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
32. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
35. C₃×#4092	C₂²	semidirect
38. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
39. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
40. C₃×#4070	C₂²	semidirect
41. C₂×C₃×#683	C₂²	semidirect
42. C₂×C₃×#683	C₂²	semidirect
43. C₂×C₃×#683	C₂²	semidirect
44. C₃×#4043	C₂²	semidirect
45. C₃×#4042	C₂²	semidirect
46. C₃×D₅×C₄⋊C₄	C₂²	semidirect
47. C₃×D₅×C₄⋊C₄	C₂²	semidirect
49. C₃×#4024	C₂²	semidirect
51. C₂²×Q₈×D₅	C₂×C₃	semidirect
53. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
54. C₂×#4092	C₂×C₃	semidirect
55. C₂×#4070	C₂×C₃	semidirect
56. D₅×C₂²⋊Q₈	C₂×C₃	direct (N × H)
57. C₂×#4043	C₂×C₃	semidirect
58. C₂×#4042	C₂×C₃	semidirect
59. C₂×D₅×C₄⋊C₄	C₂×C₃	semidirect
60. C₂×D₅×C₄⋊C₄	C₂×C₃	semidirect
62. C₂×#4024	C₂×C₃	semidirect
66. C₂³×C₃×D₅	Q₈	semidirect
71. C₂×C₃×C₅×Q₈	C₂³	semidirect
100. C₂×C₃×Dic₁₀	C₂³	semidirect
101. C₂×C₃×Dic₁₀	C₂³	semidirect
102. C₃×C₅×C₄⋊C₄	C₂³	semidirect
103. C₃×C₅×C₄⋊C₄	C₂³	semidirect
108. C₃×C₄⋊Dic₅	C₂³	semidirect
109. C₃×C₄⋊Dic₅	C₂³	semidirect
110. C₃×#683	C₂³	semidirect
111. C₃×#683	C₂³	semidirect
112. C₃×#683	C₂³	semidirect
121. C₂×C₃×C₂²⋊Q₈	D₅	direct (N × H)
126. C₂²×C₅×Q₈	C₂²×C₃	semidirect
130. C₂×Q₈×D₅	C₂²×C₃	semidirect
139. C₂²×Dic₁₀	C₂²×C₃	semidirect
140. C₂²×Dic₁₀	C₂²×C₃	semidirect
141. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
142. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
143. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
146. #4092	C₂²×C₃	semidirect
149. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
150. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
151. #4070	C₂²×C₃	semidirect
152. C₂×#683	C₂²×C₃	semidirect
153. C₂×#683	C₂²×C₃	semidirect
154. C₂×#683	C₂²×C₃	semidirect
155. #4043	C₂²×C₃	semidirect
156. #4042	C₂²×C₃	semidirect
157. D₅×C₄⋊C₄	C₂²×C₃	semidirect
158. D₅×C₄⋊C₄	C₂²×C₃	semidirect
160. #4024	C₂²×C₃	semidirect
164. C₂³×C₃×C₅	C₂×Q₈	semidirect
174. C₂²×C₃×D₅	C₂×Q₈	semidirect
175. C₂²×C₃×D₅	C₂×Q₈	semidirect
211. C₂²×C₃×Q₈	C₂×D₅	semidirect
227. C₃×C₂²⋊Q₈	C₂×D₅	direct (N × H)
235. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
236. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
245. C₂³×D₅	C₃×Q₈	semidirect
250. C₂×C₅×Q₈	C₂³×C₃	semidirect
279. C₂×Dic₁₀	C₂³×C₃	semidirect
280. C₂×Dic₁₀	C₂³×C₃	semidirect
281. C₅×C₄⋊C₄	C₂³×C₃	semidirect
282. C₅×C₄⋊C₄	C₂³×C₃	semidirect
287. C₄⋊Dic₅	C₂³×C₃	semidirect
288. C₄⋊Dic₅	C₂³×C₃	semidirect
289. #683	C₂³×C₃	semidirect
290. #683	C₂³×C₃	semidirect
291. #683	C₂³×C₃	semidirect
300. C₂×C₂²⋊Q₈	C₃×D₅	direct (N × H)
309. C₂²×C₃×C₅	C₂²×Q₈	semidirect
316. C₂×C₃×D₅	C₂²⋊Q₈	direct (N × H)
319. C₂×C₃×D₅	C₂²×Q₈	semidirect
342. C₂×C₃×Q₈	C₂²×D₅	semidirect
373. C₃×C₄⋊C₄	C₂²×D₅	semidirect
374. C₃×C₄⋊C₄	C₂²×D₅	semidirect
381. C₂³×C₅	C₂×C₃×Q₈	semidirect
391. C₂²×D₅	C₂×C₃×Q₈	semidirect
392. C₂²×D₅	C₂×C₃×Q₈	semidirect
428. C₂²×Q₈	C₂×C₃×D₅	semidirect
444. C₂²⋊Q₈	C₂×C₃×D₅	direct (N × H)
452. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
453. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
460. C₂×C₃×C₅	C₂×C₂²⋊Q₈	semidirect
465. C₃×D₅	C₂×C₂²⋊Q₈	direct (N × H)
480. C₂³×C₃	Q₈×D₅	semidirect
515. C₂²×C₅	C₂²×C₃×Q₈	semidirect
522. C₂×D₅	C₃×C₂²⋊Q₈	direct (N × H)
525. C₂×D₅	C₂²×C₃×Q₈	semidirect
548. C₂×Q₈	C₂²×C₃×D₅	semidirect
579. C₄⋊C₄	C₂²×C₃×D₅	semidirect
580. C₄⋊C₄	C₂²×C₃×D₅	semidirect
585. C₃×C₅	C₂²×C₂²⋊Q₈	semidirect
600. C₂²×C₃	C₂×Q₈×D₅	semidirect
612. C₂×C₅	C₂×C₃×C₂²⋊Q₈	semidirect
617. D₅	C₂×C₃×C₂²⋊Q₈	direct (N × H)
632. C₂³	C₃×Q₈×D₅	semidirect
665. C₂×C₃	D₅×C₂²⋊Q₈	direct (N × H)
669. C₅	C₂²×C₃×C₂²⋊Q₈	semidirect
684. C₂²	C₂×C₃×Q₈×D₅	semidirect
695. C₃	C₂×D₅×C₂²⋊Q₈	direct (N × H)
699. C₂	C₃×D₅×C₂²⋊Q₈	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×Q₈×D₅	2
C₂³×C₃×C₄×D₅	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₃×#4092	2
C₂×C₃×#4070	2
C₃×D₅×C₂²⋊Q₈	2
C₂×C₃×#4043	2
C₂×C₃×#4042	2
C₂×C₃×D₅×C₄⋊C₄	2
C₂×C₃×D₅×C₂²⋊C₄	2
C₂×C₃×#4024	2
C₂×D₅×C₂²⋊Q₈	3
C₂²×C₃×C₂²⋊Q₈	5

Subgroups — C2×C3×D5×C22⋊Q8 #14479409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₅×C₂²⋊Q₈ #14479409