Subgroups — C₂×C₅×#5636 #14483787

Order 1920.

2400 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#946	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5636	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
15	C₂×C₅×#878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#878	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#554	—	3	1	no	maximal, Hall
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
21	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
22	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
27	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	8	yes	complemented
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×#217	C₂²	1	1	yes	characteristic
35	C₅×#946	C₂²	1	8	yes	complemented
36	C₅×#944	C₂²	1	8	yes	complemented
37	C₄×C₅×#67	C₂²	1	8	yes	—
38	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
42	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
43	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
54	C₂×C₅×Dic₃⋊C₄	C₂²	1	8	yes	complemented
55	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
58	C₅×#896	C₂²	1	8	yes	complemented
59	C₅×#896	C₂²	1	8	yes	complemented
60	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
61	C₅×#889	C₂²	1	8	yes	complemented
62	C₅×#889	C₂²	1	8	yes	complemented
63	C₅×#887	C₂²	1	8	yes	complemented
64	C₅×#67⋊C₄	C₂²	1	8	yes	—
65	C₅×#67⋊C₄	C₂²	1	8	yes	—
66	C₅×#878	C₂²	1	8	yes	complemented
67	C₅×#878	C₂²	1	8	yes	complemented
68	C₂×#5636	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#554	—	3	16	no	—
70	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
71	C₂×C₅×#125	—	3	1	no	—
72	C₂×C₅×#125	—	3	1	no	—
73	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
74	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
75	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
76	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
77	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
78	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
79	C₂×C₄×C₅×Q₈	—	3	1	no	—
80	C₂×C₄×C₅×D₄	—	3	1	no	—
81	C₂×C₄×C₅×D₄	—	3	1	no	—
82	C₂×C₄×C₅×D₄	—	3	1	no	—
83	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
84	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₅×Q₈	—	4	2	no	—
88	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
89	C₂²×C₃×C₄×C₅	—	4	2	no	—
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
97	C₂×C₅×#67	Q₈	1	8	yes	complemented
98	C₂×C₅×#67	C₂³	1	4	yes	—
99	C₂²×C₅×Dic₃	—	2	4	no	—
100	C₂²×C₅×Dic₃	—	4	2	no	—
101	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
102	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
103	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
104	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
105	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
106	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
107	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
108	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
109	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
110	C₂×C₄×C₅×D₃	—	2	4	no	—
111	C₂×C₄×C₅×D₃	—	4	2	no	—
112	C₂×C₄×C₅×D₃	—	4	2	no	—
113	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
114	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
115	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
116	C₂×C₅×Dic₆	—	2	4	no	—
117	C₂×C₅×Dic₆	—	4	2	no	—
118	C₂×C₅×Dic₆	C₂³	1	4	yes	—
119	C₂×C₅×Dic₆	C₂³	1	4	yes	—
120	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
121	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
122	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
123	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₅×#217	C₂³	1	4	yes	—
126	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
127	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
128	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
129	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
130	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
131	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
132	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
133	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
134	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
135	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
136	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
137	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
138	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
139	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
140	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
141	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
142	C₄×C₅×Dic₃	C₂³	1	4	yes	—
143	C₄×C₅×Dic₃	C₂³	1	4	yes	—
144	C₄×C₅×Dic₃	C₂³	1	4	yes	—
145	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×#946	C₂×C₅	1	1	yes	characteristic, complemented
147	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic
149	C₂²×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
150	#5636	C₂×C₅	1	16	yes	direct product factor
151	C₂×#896	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×#896	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic
158	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic
159	C₂×#878	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×#878	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂²×C₅×Q₈	—	3	1	no	—
162	C₂²×C₅×Q₈	—	3	1	no	—
163	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
164	C₂²×C₅×D₄	—	3	1	no	—
165	C₂³×C₄×C₅	—	3	1	no	—
166	C₂³×C₄×C₅	—	3	1	no	—
167	C₂³×C₄×C₅	—	3	1	no	—
168	C₂³×C₄×C₅	—	3	1	no	—
169	C₂³×C₄×C₅	—	3	1	no	—
170	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
171	C₅×C₄⋊Q₈	—	3	8	no	—
172	C₅×#125	—	3	8	no	—
173	C₅×#125	—	3	8	no	—
174	C₅×C₂²⋊Q₈	—	3	8	no	—
175	C₅×C₂²⋊Q₈	—	3	8	no	—
176	C₅×C₂²⋊Q₈	—	3	8	no	—
177	C₅×C₂²⋊Q₈	—	3	8	no	—
178	C₅×C₂²⋊Q₈	—	3	8	no	—
179	C₅×C₂²⋊Q₈	C₂×D₃	1	8	yes	complemented
180	C₄×C₅×Q₈	—	3	8	no	—
181	C₄×C₅×D₄	—	3	8	no	—
182	C₄×C₅×D₄	—	3	8	no	—
183	C₄×C₅×D₄	—	3	8	no	—
184	C₂×C₅×C₄⋊C₄	—	3	1	no	—
185	C₂×C₅×C₄⋊C₄	—	3	1	no	—
186	C₂×C₅×C₄⋊C₄	—	3	1	no	—
187	C₂×C₅×C₄⋊C₄	—	3	1	no	—
188	C₂×C₅×C₄⋊C₄	—	3	1	no	—
189	C₂×C₅×C₄⋊C₄	—	3	1	no	—
190	C₂×C₅×C₄⋊C₄	—	3	1	no	—
191	C₂×C₅×C₄⋊C₄	—	3	1	no	—
192	C₂×C₅×C₄⋊C₄	—	3	1	no	—
193	C₂×C₅×C₄⋊C₄	—	3	1	no	—
194	C₂×C₅×C₄⋊C₄	—	3	1	no	—
195	C₂×C₅×C₄⋊C₄	—	3	8	no	—
196	C₂×C₅×C₄⋊C₄	—	3	1	no	—
197	C₂×C₅×C₄⋊C₄	—	3	1	no	—
198	C₂×C₅×C₄⋊C₄	—	3	8	no	—
199	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
200	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
201	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
202	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
203	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
204	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
205	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
206	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
207	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
208	C₂×C₄²×C₅	—	3	1	no	—
209	C₂×C₄²×C₅	—	3	1	no	—
210	C₂×C₄²×C₅	—	3	1	no	—
211	C₂×#554	—	3	1	no	Sylow
212	C₂³×C₃×C₅	—	2	2	no	—
213	C₂³×C₃×C₅	—	2	2	no	—
214	C₂³×C₃×C₅	C₂×Q₈	1	4	yes	—
215	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
216	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
217	C₂²×C₅×D₃	—	2	2	no	—
218	C₂²×C₅×D₃	—	2	2	no	—
219	C₂²×C₅×D₃	C₂×Q₈	1	4	yes	—
220	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
221	C₃×C₅×Q₈	—	4	4	no	—
222	C₂×C₃×C₄×C₅	—	2	2	no	—
223	C₂×C₃×C₄×C₅	—	2	2	no	—
224	C₂×C₃×C₄×C₅	—	2	2	no	—
225	C₂×C₃×C₄×C₅	—	2	2	no	—
226	C₂×C₃×C₄×C₅	—	2	2	no	—
227	C₂×C₃×C₄×C₅	—	2	2	no	—
228	C₂×C₃×C₄×C₅	—	4	4	no	—
229	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
230	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
231	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
232	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
233	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
234	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
235	C₅×#67	C₂×Q₈	1	16	yes	complemented
236	C₂×C₅×Dic₃	—	2	2	no	—
237	C₂×C₅×Dic₃	—	2	2	no	—
238	C₂×C₅×Dic₃	—	2	2	no	—
239	C₂×C₅×Dic₃	—	2	2	no	—
240	C₂×C₅×Dic₃	—	2	2	no	—
241	C₂×C₅×Dic₃	—	2	8	no	—
242	C₂×C₅×Dic₃	—	4	4	no	—
243	C₂×C₅×Dic₃	C₂×Q₈	1	4	yes	—
244	C₂×C₅×Dic₃	#41	1	4	yes	—
245	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
246	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
247	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
248	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
249	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
250	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
251	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
252	C₄×C₅×D₃	—	2	8	no	—
253	C₄×C₅×D₃	—	4	4	no	—
254	C₄×C₅×D₃	—	4	4	no	—
255	C₅×Dic₆	—	2	8	no	—
256	C₅×Dic₆	—	4	4	no	—
257	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
258	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
259	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
260	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
261	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
262	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
263	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
264	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
265	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
266	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
267	C₃×C₂²⋊Q₈	C₂²×C₅	1	8	yes	complemented
268	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
273	C₂×#217	C₂²×C₅	1	1	yes	characteristic
274	#946	C₂²×C₅	1	8	yes	complemented
275	#944	C₂²×C₅	1	8	yes	complemented
276	C₄×#67	C₂²×C₅	1	8	yes	—
277	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
278	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
279	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
280	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
282	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
283	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
285	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
286	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
287	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
288	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
289	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
290	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
292	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
293	C₂×Dic₃⋊C₄	C₂²×C₅	1	8	yes	complemented
294	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
295	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
296	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
297	#896	C₂²×C₅	1	8	yes	complemented
298	#896	C₂²×C₅	1	8	yes	complemented
299	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
300	#889	C₂²×C₅	1	8	yes	complemented
301	#889	C₂²×C₅	1	8	yes	complemented
302	#887	C₂²×C₅	1	8	yes	complemented
303	#67⋊C₄	C₂²×C₅	1	8	yes	—
304	#67⋊C₄	C₂²×C₅	1	8	yes	—
305	#878	C₂²×C₅	1	8	yes	complemented
306	#878	C₂²×C₅	1	8	yes	complemented
307	C₂⁴×C₅	—	3	1	no	—
308	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
309	C₂×C₅×Q₈	—	3	4	no	—
310	C₂×C₅×Q₈	—	3	4	no	—
311	C₂×C₅×Q₈	—	4	2	no	—
312	C₂×C₅×Q₈	—	6	4	no	—
313	C₂×C₅×Q₈	—	12	2	no	—
314	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
315	C₂×C₅×D₄	—	3	8	no	—
316	C₂×C₅×D₄	—	3	4	no	—
317	C₂²×C₄×C₅	—	3	1	no	—
318	C₂²×C₄×C₅	—	3	1	no	—
319	C₂²×C₄×C₅	—	3	4	no	—
320	C₂²×C₄×C₅	—	3	1	no	—
321	C₂²×C₄×C₅	—	3	1	no	—
322	C₂²×C₄×C₅	—	3	1	no	—
323	C₂²×C₄×C₅	—	3	1	no	—
324	C₂²×C₄×C₅	—	3	1	no	—
325	C₂²×C₄×C₅	—	3	4	no	—
326	C₂²×C₄×C₅	—	3	4	no	—
327	C₂²×C₄×C₅	—	3	4	no	—
328	C₂²×C₄×C₅	—	3	4	no	—
329	C₂²×C₄×C₅	—	4	2	no	—
330	C₂²×C₄×C₅	—	6	4	no	—
331	C₂²×C₄×C₅	—	6	4	no	—
332	C₂²×C₄×C₅	—	12	2	no	—
333	C₂²×C₄×C₅	—	12	2	no	—
334	C₂²×C₄×C₅	—	12	2	no	—
335	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
336	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
338	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
339	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
340	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
341	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
342	C₅×C₄⋊C₄	—	3	4	no	—
343	C₅×C₄⋊C₄	—	3	4	no	—
344	C₅×C₄⋊C₄	—	3	4	no	—
345	C₅×C₄⋊C₄	—	3	4	no	—
346	C₅×C₄⋊C₄	—	3	4	no	—
347	C₅×C₄⋊C₄	—	3	4	no	—
348	C₅×C₄⋊C₄	—	3	4	no	—
349	C₅×C₄⋊C₄	—	3	4	no	—
350	C₅×C₄⋊C₄	—	3	4	no	—
351	C₅×C₄⋊C₄	—	3	4	no	—
352	C₅×C₄⋊C₄	—	3	4	no	—
353	C₅×C₄⋊C₄	—	3	4	no	—
354	C₅×C₄⋊C₄	—	3	4	no	—
355	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
356	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
357	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
358	C₅×C₂²⋊C₄	—	3	4	no	—
359	C₅×C₂²⋊C₄	—	3	4	no	—
360	C₅×C₂²⋊C₄	—	3	4	no	—
361	C₅×C₂²⋊C₄	—	3	4	no	—
362	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
363	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
364	C₄²×C₅	—	3	4	no	—
365	C₄²×C₅	—	3	4	no	—
366	C₄²×C₅	—	3	4	no	—
367	#554	—	3	16	no	—
368	C₂×C₄⋊Q₈	—	3	1	no	—
369	C₂×#125	—	3	1	no	—
370	C₂×#125	—	3	1	no	—
371	C₂×C₂²⋊Q₈	—	3	1	no	—
372	C₂×C₂²⋊Q₈	—	3	1	no	—
373	C₂×C₂²⋊Q₈	—	3	1	no	—
374	C₂×C₂²⋊Q₈	—	3	1	no	—
375	C₂×C₂²⋊Q₈	—	3	1	no	—
376	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
377	C₂×C₄×Q₈	—	3	1	no	—
378	C₂×C₄×D₄	—	3	1	no	—
379	C₂×C₄×D₄	—	3	1	no	—
380	C₂×C₄×D₄	—	3	1	no	—
381	C₂²×C₄⋊C₄	—	3	1	no	—
382	C₂²×C₄⋊C₄	—	3	1	no	—
383	C₂²×C₃×C₅	—	2	8	no	—
384	C₂²×C₃×C₅	—	2	2	no	—
385	C₂²×C₃×C₅	—	2	2	no	—
386	C₂²×C₃×C₅	C₂²×Q₈	1	4	yes	—
387	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
388	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
389	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
390	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
391	C₂×C₅×D₃	—	2	8	no	—
392	C₂×C₅×D₃	—	2	2	no	—
393	C₂×C₅×D₃	—	2	2	no	—
394	C₂×C₅×D₃	C₂²×Q₈	1	4	yes	—
395	C₃×C₄×C₅	—	2	2	no	—
396	C₃×C₄×C₅	—	2	2	no	—
397	C₃×C₄×C₅	—	2	2	no	—
398	C₃×C₄×C₅	—	2	2	no	—
399	C₃×C₄×C₅	—	2	2	no	—
400	C₃×C₄×C₅	—	2	2	no	—
401	C₅×Dic₃	—	2	2	no	—
402	C₅×Dic₃	—	2	2	no	—
403	C₅×Dic₃	—	2	2	no	—
404	C₅×Dic₃	—	2	2	no	—
405	C₅×Dic₃	—	2	2	no	—
406	C₅×Dic₃	C₂²×Q₈	1	4	yes	—
407	C₅×Dic₃	C₂×#41	1	4	yes	—
408	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
409	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₃×Q₈	—	4	2	no	—
411	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
412	C₂²×C₃×C₄	—	4	2	no	—
413	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
414	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
415	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
416	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
418	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
419	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
420	C₂×#67	C₅×Q₈	1	8	yes	complemented
421	C₂×#67	C₂³×C₅	1	4	yes	—
422	C₂²×Dic₃	—	2	4	no	—
423	C₂²×Dic₃	—	4	2	no	—
424	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
425	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
426	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
427	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
428	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
429	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
430	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
431	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
432	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
433	C₂×C₄×D₃	—	2	4	no	—
434	C₂×C₄×D₃	—	4	2	no	—
435	C₂×C₄×D₃	—	4	2	no	—
436	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
437	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
438	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
439	C₂×Dic₆	—	2	4	no	—
440	C₂×Dic₆	—	4	2	no	—
441	C₂×Dic₆	C₂³×C₅	1	4	yes	—
442	C₂×Dic₆	C₂³×C₅	1	4	yes	—
443	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
444	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
445	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
446	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
447	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
448	#217	C₂³×C₅	1	4	yes	—
449	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
450	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
451	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
452	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
453	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
454	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
455	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
456	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
457	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
458	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
459	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
460	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
461	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
462	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
463	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
464	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
465	C₄×Dic₃	C₂³×C₅	1	4	yes	—
466	C₄×Dic₃	C₂³×C₅	1	4	yes	—
467	C₄×Dic₃	C₂³×C₅	1	4	yes	—
468	C₂³×C₅	—	2	2	no	—
469	C₂³×C₅	—	2	2	no	—
470	C₂³×C₅	—	3	4	no	—
471	C₂³×C₅	—	3	2	no	—
472	C₂³×C₅	—	6	2	no	—
473	C₂³×C₅	—	6	2	no	—
474	C₂³×C₅	D₃×Q₈	1	4	yes	—
475	C₂³×C₅	C₂³×D₃	1	2	yes	—
476	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
477	C₅×Q₈	—	4	4	no	—
478	C₅×Q₈	—	6	8	no	—
479	C₅×Q₈	—	12	4	no	—
480	C₅×D₄	—	3	16	no	—
481	C₂×C₄×C₅	—	2	2	no	—
482	C₂×C₄×C₅	—	2	2	no	—
483	C₂×C₄×C₅	—	2	2	no	—
484	C₂×C₄×C₅	—	2	2	no	—
485	C₂×C₄×C₅	—	2	2	no	—
486	C₂×C₄×C₅	—	2	2	no	—
487	C₂×C₄×C₅	—	3	4	no	—
488	C₂×C₄×C₅	—	3	4	no	—
489	C₂×C₄×C₅	—	3	2	no	—
490	C₂×C₄×C₅	—	3	2	no	—
491	C₂×C₄×C₅	—	3	2	no	—
492	C₂×C₄×C₅	—	3	2	no	—
493	C₂×C₄×C₅	—	3	2	no	—
494	C₂×C₄×C₅	—	3	2	no	—
495	C₂×C₄×C₅	—	3	2	no	—
496	C₂×C₄×C₅	—	4	4	no	—
497	C₂×C₄×C₅	—	6	8	no	—
498	C₂×C₄×C₅	—	6	8	no	—
499	C₂×C₄×C₅	—	6	2	no	—
500	C₂×C₄×C₅	—	6	2	no	—
501	C₂×C₄×C₅	—	6	2	no	—
502	C₂×C₄×C₅	—	6	2	no	—
503	C₂×C₄×C₅	—	6	2	no	—
504	C₂×C₄×C₅	—	12	4	no	—
505	C₂×C₄×C₅	—	12	4	no	—
506	C₂×C₄×C₅	—	12	4	no	—
507	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
508	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
509	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
510	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
511	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
512	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
513	C₂²×Q₈	—	3	1	no	—
514	C₂²×Q₈	—	3	1	no	—
515	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
516	C₂²×D₄	—	3	1	no	—
517	C₂³×C₄	—	3	1	no	—
518	C₂³×C₄	—	3	1	no	—
519	C₂³×C₄	—	3	1	no	—
520	C₂³×C₄	—	3	1	no	—
521	C₂³×C₄	—	3	1	no	—
522	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
523	C₄⋊Q₈	—	3	8	no	—
524	#125	—	3	8	no	—
525	#125	—	3	8	no	—
526	C₂²⋊Q₈	—	3	8	no	—
527	C₂²⋊Q₈	—	3	8	no	—
528	C₂²⋊Q₈	—	3	8	no	—
529	C₂²⋊Q₈	—	3	8	no	—
530	C₂²⋊Q₈	—	3	8	no	—
531	C₂²⋊Q₈	C₂×C₅×D₃	1	8	yes	complemented
532	C₄×Q₈	—	3	8	no	—
533	C₄×D₄	—	3	8	no	—
534	C₄×D₄	—	3	8	no	—
535	C₄×D₄	—	3	8	no	—
536	C₂×C₄⋊C₄	—	3	1	no	—
537	C₂×C₄⋊C₄	—	3	1	no	—
538	C₂×C₄⋊C₄	—	3	1	no	—
539	C₂×C₄⋊C₄	—	3	1	no	—
540	C₂×C₄⋊C₄	—	3	1	no	—
541	C₂×C₄⋊C₄	—	3	1	no	—
542	C₂×C₄⋊C₄	—	3	8	no	—
543	C₂×C₄⋊C₄	—	3	1	no	—
544	C₂×C₄⋊C₄	—	3	1	no	—
545	C₂×C₄⋊C₄	—	3	1	no	—
546	C₂×C₄⋊C₄	—	3	1	no	—
547	C₂×C₄⋊C₄	—	3	1	no	—
548	C₂×C₄⋊C₄	—	3	1	no	—
549	C₂×C₄⋊C₄	—	3	1	no	—
550	C₂×C₄⋊C₄	—	3	8	no	—
551	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
554	C₂×C₂²⋊C₄	—	3	1	no	—
555	C₂×C₂²⋊C₄	—	3	1	no	—
556	C₂×C₂²⋊C₄	—	3	1	no	—
557	C₂×C₂²⋊C₄	—	3	1	no	—
558	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
559	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
560	C₂×C₄²	—	3	1	no	—
561	C₂×C₄²	—	3	1	no	—
562	C₂×C₄²	—	3	1	no	—
563	C₂×C₃×C₅	—	2	4	no	—
564	C₂×C₃×C₅	#554	1	4	yes	complemented
565	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
566	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
567	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
568	C₅×D₃	—	2	4	no	—
569	C₂³×C₃	—	2	2	no	—
570	C₂³×C₃	—	2	2	no	—
571	C₂³×C₃	C₂×C₅×Q₈	1	4	yes	—
572	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
573	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
574	C₂²×D₃	—	2	2	no	—
575	C₂²×D₃	—	2	2	no	—
576	C₂²×D₃	C₂×C₅×Q₈	1	4	yes	—
577	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
578	C₃×Q₈	—	4	4	no	—
579	C₂×C₃×C₄	—	2	2	no	—
580	C₂×C₃×C₄	—	2	2	no	—
581	C₂×C₃×C₄	—	2	2	no	—
582	C₂×C₃×C₄	—	2	2	no	—
583	C₂×C₃×C₄	—	2	2	no	—
584	C₂×C₃×C₄	—	2	2	no	—
585	C₂×C₃×C₄	—	4	4	no	—
586	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
587	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
588	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
589	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
590	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
591	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
592	#67	C₂×C₅×Q₈	1	16	yes	complemented
593	C₂×Dic₃	—	2	2	no	—
594	C₂×Dic₃	—	2	2	no	—
595	C₂×Dic₃	—	2	2	no	—
596	C₂×Dic₃	—	2	2	no	—
597	C₂×Dic₃	—	2	2	no	—
598	C₂×Dic₃	—	2	8	no	—
599	C₂×Dic₃	—	4	4	no	—
600	C₂×Dic₃	C₂×C₅×Q₈	1	4	yes	—
601	C₂×Dic₃	C₅×#41	1	4	yes	—
602	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
603	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
604	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
605	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
606	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
607	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
608	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
609	C₄×D₃	—	2	8	no	—
610	C₄×D₃	—	4	4	no	—
611	C₄×D₃	—	4	4	no	—
612	Dic₆	—	2	8	no	—
613	Dic₆	—	4	4	no	—
614	C₂²×C₅	—	2	8	no	—
615	C₂²×C₅	—	2	2	no	—
616	C₂²×C₅	—	2	2	no	—
617	C₂²×C₅	—	3	4	no	—
618	C₂²×C₅	—	6	8	no	—
619	C₂²×C₅	—	6	2	no	—
620	C₂²×C₅	—	6	2	no	—
621	C₂²×C₅	#1004	1	2	yes	—
622	C₂²×C₅	C₂×D₃×Q₈	1	4	yes	—
623	C₂²×C₅	C₂×D₃×Q₈	1	2	yes	—
624	C₂²×C₅	D₃×#41	1	2	yes	—
625	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
626	C₄×C₅	—	2	2	no	—
627	C₄×C₅	—	2	2	no	—
628	C₄×C₅	—	2	2	no	—
629	C₄×C₅	—	2	2	no	—
630	C₄×C₅	—	2	2	no	—
631	C₄×C₅	—	2	2	no	—
632	C₄×C₅	—	3	4	no	—
633	C₄×C₅	—	3	4	no	—
634	C₄×C₅	—	6	2	no	—
635	C₄×C₅	—	6	2	no	—
636	C₄×C₅	—	6	2	no	—
637	C₄×C₅	—	6	2	no	—
638	C₄×C₅	—	6	2	no	—
639	C₂⁴	—	3	1	no	—
640	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
641	C₂×Q₈	—	3	4	no	—
642	C₂×Q₈	—	3	4	no	—
643	C₂×Q₈	—	4	2	no	—
644	C₂×Q₈	—	6	4	no	—
645	C₂×Q₈	—	12	2	no	—
646	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
647	C₂×D₄	—	3	8	no	—
648	C₂×D₄	—	3	4	no	—
649	C₂²×C₄	—	3	1	no	—
650	C₂²×C₄	—	3	1	no	—
651	C₂²×C₄	—	3	1	no	—
652	C₂²×C₄	—	3	1	no	—
653	C₂²×C₄	—	3	1	no	—
654	C₂²×C₄	—	3	1	no	—
655	C₂²×C₄	—	3	1	no	—
656	C₂²×C₄	—	3	4	no	—
657	C₂²×C₄	—	3	4	no	—
658	C₂²×C₄	—	3	4	no	—
659	C₂²×C₄	—	3	4	no	—
660	C₂²×C₄	—	3	4	no	—
661	C₂²×C₄	—	4	2	no	—
662	C₂²×C₄	—	6	4	no	—
663	C₂²×C₄	—	6	4	no	—
664	C₂²×C₄	—	12	2	no	—
665	C₂²×C₄	—	12	2	no	—
666	C₂²×C₄	—	12	2	no	—
667	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
668	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
669	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
670	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
671	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
672	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
673	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
674	C₄⋊C₄	—	3	4	no	—
675	C₄⋊C₄	—	3	4	no	—
676	C₄⋊C₄	—	3	4	no	—
677	C₄⋊C₄	—	3	4	no	—
678	C₄⋊C₄	—	3	4	no	—
679	C₄⋊C₄	—	3	4	no	—
680	C₄⋊C₄	—	3	4	no	—
681	C₄⋊C₄	—	3	4	no	—
682	C₄⋊C₄	—	3	4	no	—
683	C₄⋊C₄	—	3	4	no	—
684	C₄⋊C₄	—	3	4	no	—
685	C₄⋊C₄	—	3	4	no	—
686	C₄⋊C₄	—	3	4	no	—
687	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
688	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
689	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
690	C₂²⋊C₄	—	3	4	no	—
691	C₂²⋊C₄	—	3	4	no	—
692	C₂²⋊C₄	—	3	4	no	—
693	C₂²⋊C₄	—	3	4	no	—
694	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
695	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
696	C₄²	—	3	4	no	—
697	C₄²	—	3	4	no	—
698	C₄²	—	3	4	no	—
699	C₃×C₅	C₂×#554	1	1	yes	characteristic, complemented, Hall
700	C₂²×C₃	—	2	8	no	—
701	C₂²×C₃	—	2	2	no	—
702	C₂²×C₃	—	2	2	no	—
703	C₂²×C₃	C₂²×C₅×Q₈	1	4	yes	—
704	C₂²×C₃	C₂²×C₅×Q₈	1	2	yes	—
705	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
706	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
707	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
708	C₂×D₃	—	2	8	no	—
709	C₂×D₃	—	2	2	no	—
710	C₂×D₃	—	2	2	no	—
711	C₂×D₃	C₂²×C₅×Q₈	1	4	yes	—
712	C₃×C₄	—	2	2	no	—
713	C₃×C₄	—	2	2	no	—
714	C₃×C₄	—	2	2	no	—
715	C₃×C₄	—	2	2	no	—
716	C₃×C₄	—	2	2	no	—
717	C₃×C₄	—	2	2	no	—
718	Dic₃	—	2	2	no	—
719	Dic₃	—	2	2	no	—
720	Dic₃	—	2	2	no	—
721	Dic₃	—	2	2	no	—
722	Dic₃	—	2	2	no	—
723	Dic₃	C₂²×C₅×Q₈	1	4	yes	—
724	Dic₃	C₂×C₅×#41	1	4	yes	—
725	C₂×C₅	—	2	4	no	—
726	C₂×C₅	—	6	4	no	—
727	C₂×C₅	#5636	1	4	yes	direct product factor
728	C₂×C₅	C₂×#1004	1	1	yes	characteristic
729	C₂×C₅	C₂²×D₃×Q₈	1	1	yes	characteristic
730	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	3	4	no	—
734	C₂³	—	3	2	no	—
735	C₂³	—	6	2	no	—
736	C₂³	—	6	2	no	—
737	C₂³	C₅×D₃×Q₈	1	4	yes	—
738	C₂³	C₂³×C₅×D₃	1	2	yes	—
739	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
740	Q₈	—	4	4	no	—
741	Q₈	—	6	8	no	—
742	Q₈	—	12	4	no	—
743	D₄	—	3	16	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	3	4	no	—
751	C₂×C₄	—	3	4	no	—
752	C₂×C₄	—	3	2	no	—
753	C₂×C₄	—	3	2	no	—
754	C₂×C₄	—	3	2	no	—
755	C₂×C₄	—	3	2	no	—
756	C₂×C₄	—	3	2	no	—
757	C₂×C₄	—	3	2	no	—
758	C₂×C₄	—	3	2	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	6	8	no	—
761	C₂×C₄	—	6	8	no	—
762	C₂×C₄	—	6	2	no	—
763	C₂×C₄	—	6	2	no	—
764	C₂×C₄	—	6	2	no	—
765	C₂×C₄	—	6	2	no	—
766	C₂×C₄	—	6	2	no	—
767	C₂×C₄	—	12	4	no	—
768	C₂×C₄	—	12	4	no	—
769	C₂×C₄	—	12	4	no	—
770	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
771	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
772	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
773	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
774	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
775	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
776	C₂×C₃	—	2	4	no	—
777	C₂×C₃	C₅×#554	1	4	yes	complemented
778	C₂×C₃	C₂³×C₅×Q₈	1	1	yes	characteristic
779	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
780	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
781	D₃	—	2	4	no	—
782	C₅	C₂×#5636	1	1	yes	characteristic, direct product factor, Sylow
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	8	no	—
786	C₂²	—	3	4	no	—
787	C₂²	—	6	2	no	—
788	C₂²	—	6	2	no	—
789	C₂²	—	6	8	no	—
790	C₂²	C₅×#1004	1	2	yes	—
791	C₂²	C₂×C₅×D₃×Q₈	1	4	yes	—
792	C₂²	C₂×C₅×D₃×Q₈	1	2	yes	—
793	C₂²	C₅×D₃×#41	1	2	yes	—
794	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
795	C₄	—	2	2	no	—
796	C₄	—	2	2	no	—
797	C₄	—	2	2	no	—
798	C₄	—	2	2	no	—
799	C₄	—	2	2	no	—
800	C₄	—	2	2	no	—
801	C₄	—	3	4	no	—
802	C₄	—	3	4	no	—
803	C₄	—	6	2	no	—
804	C₄	—	6	2	no	—
805	C₄	—	6	2	no	—
806	C₄	—	6	2	no	—
807	C₄	—	6	2	no	—
808	C₃	C₂×C₅×#554	1	1	yes	characteristic, complemented, Sylow
809	C₂	—	2	4	no	—
810	C₂	—	6	4	no	—
811	C₂	C₅×#5636	1	4	yes	direct product factor
812	C₂	C₂×C₅×#1004	1	1	yes	characteristic
813	C₂	C₂²×C₅×D₃×Q₈	1	1	yes	characteristic
814	C₂	C₂×C₅×D₃×#41	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×C₂²⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#67	C₂²
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#554
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
2. C₂×C₅×#946	C₂	semidirect
3. C₂×C₅×#944	C₂	semidirect
5. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
6. C₅×#5636	C₂	direct (N × H)
7. C₂×C₅×#896	C₂	semidirect
8. C₂×C₅×#896	C₂	semidirect
9. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
10. C₂×C₅×#889	C₂	semidirect
11. C₂×C₅×#889	C₂	semidirect
12. C₂×C₅×#887	C₂	semidirect
15. C₂×C₅×#878	C₂	semidirect
16. C₂×C₅×#878	C₂	semidirect
28. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
35. C₅×#946	C₂²	semidirect
36. C₅×#944	C₂²	semidirect
54. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
58. C₅×#896	C₂²	semidirect
59. C₅×#896	C₂²	semidirect
60. C₅×D₃×C₄⋊C₄	C₂²	semidirect
61. C₅×#889	C₂²	semidirect
62. C₅×#889	C₂²	semidirect
63. C₅×#887	C₂²	semidirect
66. C₅×#878	C₂²	semidirect
67. C₅×#878	C₂²	semidirect
68. C₂×#5636	C₅	direct (N × H)
78. C₂×C₅×C₂²⋊Q₈	D₃	semidirect
97. C₂×C₅×#67	Q₈	semidirect
145. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
146. C₂×#946	C₂×C₅	semidirect
147. C₂×#944	C₂×C₅	semidirect
149. C₂²×Dic₃⋊C₄	C₂×C₅	semidirect
150. #5636	C₂×C₅	direct (N × H)
151. C₂×#896	C₂×C₅	semidirect
152. C₂×#896	C₂×C₅	semidirect
153. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
154. C₂×#889	C₂×C₅	semidirect
155. C₂×#889	C₂×C₅	semidirect
156. C₂×#887	C₂×C₅	semidirect
159. C₂×#878	C₂×C₅	semidirect
160. C₂×#878	C₂×C₅	semidirect
179. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
235. C₅×#67	C₂×Q₈	semidirect
267. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
274. #946	C₂²×C₅	semidirect
275. #944	C₂²×C₅	semidirect
293. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
297. #896	C₂²×C₅	semidirect
298. #896	C₂²×C₅	semidirect
299. D₃×C₄⋊C₄	C₂²×C₅	semidirect
300. #889	C₂²×C₅	semidirect
301. #889	C₂²×C₅	semidirect
302. #887	C₂²×C₅	semidirect
305. #878	C₂²×C₅	semidirect
306. #878	C₂²×C₅	semidirect
376. C₂×C₂²⋊Q₈	C₅×D₃	semidirect
420. C₂×#67	C₅×Q₈	semidirect
531. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
564. C₂×C₃×C₅	#554	semidirect
592. #67	C₂×C₅×Q₈	semidirect
699. C₃×C₅	C₂×#554	semidirect
727. C₂×C₅	#5636	direct (N × H)
777. C₂×C₃	C₅×#554	semidirect
782. C₅	C₂×#5636	direct (N × H)
808. C₃	C₂×C₅×#554	semidirect
811. C₂	C₅×#5636	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×C₅×C₂²⋊Q₈	2
C₂×C₅×#946	2
C₂×C₅×#944	2
C₂×C₄×C₅×#67	2
C₂²×C₅×Dic₃⋊C₄	2
C₅×#5636	2
C₂×C₅×#896	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#889	2
C₂×C₅×#887	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×#878	2
C₂×C₅×#554	3
C₂×#5636	5

Subgroups — C2×C5×#5636 #14483787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5636 #14483787