Subgroups — C₂×C₅×#5692 #14480935

Order 1920.

2288 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5692	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#898	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#897	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#876	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#539	—	3	1	no	maximal, Hall
18	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×C₅×D₃	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	C₃×C₅×#125	C₂²	1	8	yes	complemented
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
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×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
46	C₂×C₅×C₄⋊Dic₃	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×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
54	C₅×#898	C₂²	1	8	yes	complemented
55	C₅×#897	C₂²	1	8	yes	complemented
56	C₅×#896	C₂²	1	8	yes	complemented
57	C₅×#896	C₂²	1	8	yes	complemented
58	C₅×#895	C₂²	1	8	yes	—
59	C₅×#894	C₂²	1	8	yes	complemented
60	C₅×#894	C₂²	1	8	yes	complemented
61	C₅×#894	C₂²	1	8	yes	complemented
62	C₅×#894	C₂²	1	8	yes	complemented
63	C₅×#893	C₂²	1	8	yes	complemented
64	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
65	C₅×#889	C₂²	1	8	yes	complemented
66	C₅×#876	C₂²	1	8	yes	complemented
67	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
68	C₂×#5692	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#539	—	3	16	no	—
70	C₂×C₅×#126	—	3	1	no	—
71	C₂×C₅×#126	—	3	1	no	—
72	C₂×C₅×#125	—	3	1	no	—
73	C₂×C₅×#125	D₃	1	1	yes	characteristic, complemented
74	C₂×C₅×#123	—	3	1	no	—
75	C₂×C₅×#123	—	3	1	no	—
76	C₂×C₅×#123	—	3	1	no	—
77	C₂×C₅×#123	—	3	1	no	—
78	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
79	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
80	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
81	C₂×C₅×#121	—	3	1	no	—
82	C₂×C₄×C₅×D₄	—	3	1	no	—
83	C₂×C₄×C₅×D₄	—	3	1	no	—
84	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
86	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
87	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
100	C₂×C₅×D₁₂	—	2	4	no	—
101	C₂×C₅×D₁₂	—	2	4	no	—
102	C₂×C₅×D₁₂	—	4	2	no	—
103	C₂×C₅×D₁₂	C₂³	1	4	yes	—
104	C₂×C₅×D₁₂	C₂³	1	4	yes	—
105	C₂×C₅×D₁₂	C₂³	1	4	yes	—
106	C₂×C₄×C₅×D₃	—	2	4	no	—
107	C₂×C₄×C₅×D₃	—	4	2	no	—
108	C₂×C₄×C₅×D₃	—	4	2	no	—
109	C₂×C₄×C₅×D₃	—	4	2	no	—
110	C₂×C₄×C₅×D₃	—	4	2	no	—
111	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
112	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
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	—	4	2	no	—
117	C₂×C₅×Dic₆	C₂³	1	4	yes	—
118	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
119	C₃×C₅×C₄⋊C₄	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×C₄⋊C₄	C₂³	1	4	yes	—
124	C₃×C₄²×C₅	C₂³	1	4	yes	—
125	C₅×(C₂×D₃)⋊C₄	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×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
130	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
131	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
132	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
133	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
134	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
135	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
136	C₅×C₄⋊Dic₃	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	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
143	C₄×C₅×Dic₃	C₂³	1	4	yes	—
144	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
145	#5692	C₂×C₅	1	16	yes	direct product factor
146	C₂×#898	C₂×C₅	1	1	yes	characteristic, complemented
147	C₂×#897	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×#896	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂×#896	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂×#895	C₂×C₅	1	1	yes	characteristic
151	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂×#876	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂²×C₅×Q₈	—	3	1	no	—
161	C₂²×C₅×D₄	—	3	1	no	—
162	C₂²×C₅×D₄	—	3	1	no	—
163	C₂²×C₅×D₄	—	3	1	no	—
164	C₂³×C₄×C₅	—	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	C₅×#126	—	3	8	no	—
170	C₅×#126	—	3	8	no	—
171	C₅×#125	—	3	8	no	—
172	C₅×#125	C₂×D₃	1	8	yes	complemented
173	C₅×#123	—	3	8	no	—
174	C₅×#123	—	3	8	no	—
175	C₅×#123	—	3	8	no	—
176	C₅×#123	—	3	8	no	—
177	C₅×C₂²⋊Q₈	—	3	8	no	—
178	C₅×C₂²⋊Q₈	—	3	8	no	—
179	C₅×C₂²⋊Q₈	—	3	8	no	—
180	C₅×#121	—	3	8	no	—
181	C₄×C₅×D₄	—	3	8	no	—
182	C₄×C₅×D₄	—	3	8	no	—
183	C₂×C₅×C₄⋊C₄	—	3	1	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	8	no	—
192	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
193	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
194	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
195	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
196	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
197	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
198	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
199	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
200	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
201	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
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	—	3	1	no	—
207	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
208	C₂×C₄²×C₅	—	3	1	no	—
209	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
210	C₂×#539	—	3	1	no	Sylow
211	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
212	C₂²×C₅×D₃	—	2	2	no	—
213	C₂²×C₅×D₃	—	2	2	no	—
214	C₂²×C₅×D₃	—	2	2	no	—
215	C₂²×C₅×D₃	—	2	2	no	—
216	C₂²×C₅×D₃	—	2	2	no	—
217	C₂²×C₅×D₃	—	2	2	no	—
218	C₂²×C₅×D₃	—	2	2	no	—
219	C₂²×C₅×D₃	—	2	2	no	—
220	C₂²×C₅×D₃	#41	1	4	yes	—
221	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
222	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
223	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
229	C₂×C₃×C₄×C₅	—	2	2	no	—
230	C₂×C₃×C₄×C₅	—	2	2	no	—
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	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
236	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
237	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
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	2	no	—
242	C₂×C₅×Dic₃	—	2	2	no	—
243	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
244	C₂×C₅×Dic₃	C₂⁴	1	2	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	C₅×D₁₂	—	2	8	no	—
249	C₅×D₁₂	—	2	8	no	—
250	C₅×D₁₂	—	4	4	no	—
251	C₄×C₅×D₃	—	2	8	no	—
252	C₄×C₅×D₃	—	4	4	no	—
253	C₄×C₅×D₃	—	4	4	no	—
254	C₄×C₅×D₃	—	4	4	no	—
255	C₄×C₅×D₃	—	4	4	no	—
256	C₅×Dic₆	—	4	4	no	—
257	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
258	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
259	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
260	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
261	C₂²×C₄×D₃	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	C₃×#125	C₂²×C₅	1	8	yes	complemented
267	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
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×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
274	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
275	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
276	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
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×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
282	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
283	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
285	C₂×C₄⋊Dic₃	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×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
293	#898	C₂²×C₅	1	8	yes	complemented
294	#897	C₂²×C₅	1	8	yes	complemented
295	#896	C₂²×C₅	1	8	yes	complemented
296	#896	C₂²×C₅	1	8	yes	complemented
297	#895	C₂²×C₅	1	8	yes	—
298	#894	C₂²×C₅	1	8	yes	complemented
299	#894	C₂²×C₅	1	8	yes	complemented
300	#894	C₂²×C₅	1	8	yes	complemented
301	#894	C₂²×C₅	1	8	yes	complemented
302	#893	C₂²×C₅	1	8	yes	complemented
303	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
304	#889	C₂²×C₅	1	8	yes	complemented
305	#876	C₂²×C₅	1	8	yes	complemented
306	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
307	C₂⁴×C₅	—	3	1	no	—
308	C₂⁴×C₅	—	3	1	no	—
309	C₂⁴×C₅	—	3	1	no	—
310	C₂×C₅×Q₈	—	3	4	no	—
311	C₂×C₅×Q₈	—	12	2	no	—
312	C₂×C₅×D₄	—	3	4	no	—
313	C₂×C₅×D₄	—	3	4	no	—
314	C₂×C₅×D₄	—	3	4	no	—
315	C₂×C₅×D₄	—	6	4	no	—
316	C₂×C₅×D₄	—	6	4	no	—
317	C₂×C₅×D₄	—	12	2	no	—
318	C₂²×C₄×C₅	—	3	1	no	—
319	C₂²×C₄×C₅	—	3	1	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	4	no	—
324	C₂²×C₄×C₅	—	3	4	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	—	6	4	no	—
329	C₂²×C₄×C₅	—	12	2	no	—
330	C₂²×C₄×C₅	—	12	2	no	—
331	C₂²×C₄×C₅	—	12	2	no	—
332	C₂²×C₄×C₅	—	12	2	no	—
333	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
334	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
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	C₅×C₄⋊C₄	—	3	4	no	—
341	C₅×C₄⋊C₄	—	3	4	no	—
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	C₂²×D₃	1	4	yes	—
349	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
350	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
351	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
352	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
353	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
354	C₅×C₂²⋊C₄	—	3	4	no	—
355	C₅×C₂²⋊C₄	—	3	4	no	—
356	C₅×C₂²⋊C₄	—	3	4	no	—
357	C₅×C₂²⋊C₄	—	3	4	no	—
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	—	3	4	no	—
363	C₅×C₂²⋊C₄	—	3	4	no	—
364	C₄²×C₅	—	3	4	no	—
365	C₄²×C₅	C₂²×D₃	1	4	yes	—
366	#539	—	3	16	no	—
367	C₂×#126	—	3	1	no	—
368	C₂×#126	—	3	1	no	—
369	C₂×#125	—	3	1	no	—
370	C₂×#125	C₅×D₃	1	1	yes	characteristic, complemented
371	C₂×#123	—	3	1	no	—
372	C₂×#123	—	3	1	no	—
373	C₂×#123	—	3	1	no	—
374	C₂×#123	—	3	1	no	—
375	C₂×C₂²⋊Q₈	—	3	1	no	—
376	C₂×C₂²⋊Q₈	—	3	1	no	—
377	C₂×C₂²⋊Q₈	—	3	1	no	—
378	C₂×#121	—	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×C₃×C₅	C₂×#41	1	2	yes	—
383	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
384	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
385	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
386	C₂×C₅×D₃	—	2	8	no	—
387	C₂×C₅×D₃	—	2	2	no	—
388	C₂×C₅×D₃	—	2	2	no	—
389	C₂×C₅×D₃	—	2	2	no	—
390	C₂×C₅×D₃	—	2	2	no	—
391	C₂×C₅×D₃	—	2	2	no	—
392	C₂×C₅×D₃	—	2	2	no	—
393	C₂×C₅×D₃	—	2	2	no	—
394	C₂×C₅×D₃	—	2	2	no	—
395	C₂×C₅×D₃	—	4	4	no	—
396	C₂×C₅×D₃	—	4	4	no	—
397	C₂×C₅×D₃	C₂×#41	1	4	yes	—
398	C₃×C₄×C₅	—	2	2	no	—
399	C₃×C₄×C₅	—	2	2	no	—
400	C₃×C₄×C₅	—	2	2	no	—
401	C₃×C₄×C₅	—	2	2	no	—
402	C₃×C₄×C₅	—	2	2	no	—
403	C₃×C₄×C₅	—	2	2	no	—
404	C₃×C₄×C₅	—	2	2	no	—
405	C₅×Dic₃	—	2	2	no	—
406	C₅×Dic₃	—	2	2	no	—
407	C₅×Dic₃	—	2	2	no	—
408	C₅×Dic₃	—	2	2	no	—
409	C₅×Dic₃	—	2	2	no	—
410	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
411	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
412	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
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	1	yes	characteristic
420	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
421	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
422	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
423	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
424	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
425	C₂×D₁₂	—	2	4	no	—
426	C₂×D₁₂	—	2	4	no	—
427	C₂×D₁₂	—	4	2	no	—
428	C₂×D₁₂	C₂³×C₅	1	4	yes	—
429	C₂×D₁₂	C₂³×C₅	1	4	yes	—
430	C₂×D₁₂	C₂³×C₅	1	4	yes	—
431	C₂×C₄×D₃	—	2	4	no	—
432	C₂×C₄×D₃	—	4	2	no	—
433	C₂×C₄×D₃	—	4	2	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×C₄×D₃	C₂³×C₅	1	4	yes	—
440	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
441	C₂×Dic₆	—	4	2	no	—
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×C₄⋊C₄	C₂³×C₅	1	4	yes	—
447	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
448	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
449	C₃×C₄²	C₂³×C₅	1	4	yes	—
450	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
451	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
452	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
453	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
454	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
455	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
456	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
457	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
458	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
459	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
460	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
461	C₄⋊Dic₃	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	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
466	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
467	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
468	C₄×Dic₃	C₂³×C₅	1	4	yes	—
469	C₂³×C₅	—	3	4	no	—
470	C₂³×C₅	—	3	2	no	—
471	C₂³×C₅	—	3	2	no	—
472	C₂³×C₅	—	3	2	no	—
473	C₂³×C₅	—	6	2	no	—
474	C₂³×C₅	—	6	2	no	—
475	C₂³×C₅	—	6	2	no	—
476	C₂³×C₅	—	6	2	no	—
477	C₂³×C₅	—	6	2	no	—
478	C₂³×C₅	—	6	2	no	—
479	C₂³×C₅	—	6	2	no	—
480	C₂³×C₅	—	6	2	no	—
481	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
482	C₅×Q₈	—	12	4	no	—
483	C₅×D₄	—	6	8	no	—
484	C₅×D₄	—	6	8	no	—
485	C₅×D₄	—	12	4	no	—
486	C₂×C₄×C₅	—	2	2	no	—
487	C₂×C₄×C₅	—	2	2	no	—
488	C₂×C₄×C₅	—	2	2	no	—
489	C₂×C₄×C₅	—	2	2	no	—
490	C₂×C₄×C₅	—	2	2	no	—
491	C₂×C₄×C₅	—	2	2	no	—
492	C₂×C₄×C₅	—	2	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	—	3	2	no	—
497	C₂×C₄×C₅	—	3	2	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	—	12	4	no	—
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	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
514	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
515	C₂²×Q₈	—	3	1	no	—
516	C₂²×D₄	—	3	1	no	—
517	C₂²×D₄	—	3	1	no	—
518	C₂²×D₄	—	3	1	no	—
519	C₂³×C₄	—	3	1	no	—
520	C₂³×C₄	—	3	1	no	—
521	C₂³×C₄	—	3	1	no	—
522	C₂³×C₄	—	3	1	no	—
523	C₂³×C₄	—	3	1	no	—
524	#126	—	3	8	no	—
525	#126	—	3	8	no	—
526	#125	—	3	8	no	—
527	#125	C₂×C₅×D₃	1	8	yes	complemented
528	#123	—	3	8	no	—
529	#123	—	3	8	no	—
530	#123	—	3	8	no	—
531	#123	—	3	8	no	—
532	C₂²⋊Q₈	—	3	8	no	—
533	C₂²⋊Q₈	—	3	8	no	—
534	C₂²⋊Q₈	—	3	8	no	—
535	#121	—	3	8	no	—
536	C₄×D₄	—	3	8	no	—
537	C₄×D₄	—	3	8	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	1	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	8	no	—
547	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	—	3	1	no	—
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	—	3	1	no	—
559	C₂×C₂²⋊C₄	—	3	1	no	—
560	C₂×C₂²⋊C₄	—	3	1	no	—
561	C₂×C₂²⋊C₄	—	3	1	no	—
562	C₂×C₂²⋊C₄	—	3	1	no	—
563	C₂×C₄²	—	3	1	no	—
564	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
565	C₂×C₃×C₅	#539	1	4	yes	complemented
566	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
567	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
569	C₅×D₃	—	2	4	no	—
570	C₅×D₃	—	4	2	no	—
571	C₅×D₃	—	4	2	no	—
572	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
573	C₂²×D₃	—	2	2	no	—
574	C₂²×D₃	—	2	2	no	—
575	C₂²×D₃	—	2	2	no	—
576	C₂²×D₃	—	2	2	no	—
577	C₂²×D₃	—	2	2	no	—
578	C₂²×D₃	—	2	2	no	—
579	C₂²×D₃	—	2	2	no	—
580	C₂²×D₃	—	2	2	no	—
581	C₂²×D₃	C₅×#41	1	4	yes	—
582	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
583	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
584	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
585	C₂×C₃×C₄	—	2	2	no	—
586	C₂×C₃×C₄	—	2	2	no	—
587	C₂×C₃×C₄	—	2	2	no	—
588	C₂×C₃×C₄	—	2	2	no	—
589	C₂×C₃×C₄	—	2	2	no	—
590	C₂×C₃×C₄	—	2	2	no	—
591	C₂×C₃×C₄	—	2	2	no	—
592	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
593	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
594	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
595	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
596	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
597	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
598	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
599	C₂×Dic₃	—	2	2	no	—
600	C₂×Dic₃	—	2	2	no	—
601	C₂×Dic₃	—	2	2	no	—
602	C₂×Dic₃	—	2	2	no	—
603	C₂×Dic₃	—	2	2	no	—
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	D₁₂	—	2	8	no	—
610	D₁₂	—	2	8	no	—
611	D₁₂	—	4	4	no	—
612	C₄×D₃	—	2	8	no	—
613	C₄×D₃	—	4	4	no	—
614	C₄×D₃	—	4	4	no	—
615	C₄×D₃	—	4	4	no	—
616	C₄×D₃	—	4	4	no	—
617	Dic₆	—	4	4	no	—
618	C₂²×C₅	—	3	4	no	—
619	C₂²×C₅	—	6	8	no	—
620	C₂²×C₅	—	6	2	no	—
621	C₂²×C₅	—	6	2	no	—
622	C₂²×C₅	—	6	2	no	—
623	C₂²×C₅	—	6	2	no	—
624	C₂²×C₅	—	6	2	no	—
625	C₂²×C₅	—	6	2	no	—
626	C₂²×C₅	—	6	2	no	—
627	C₂²×C₅	—	6	2	no	—
628	C₂²×C₅	—	12	4	no	—
629	C₂²×C₅	—	12	4	no	—
630	C₂²×C₅	#1007	1	2	yes	—
631	C₂²×C₅	D₃×#41	1	2	yes	—
632	C₂²×C₅	#1009	1	2	yes	—
633	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
634	C₄×C₅	—	2	2	no	—
635	C₄×C₅	—	2	2	no	—
636	C₄×C₅	—	2	2	no	—
637	C₄×C₅	—	2	2	no	—
638	C₄×C₅	—	2	2	no	—
639	C₄×C₅	—	2	2	no	—
640	C₄×C₅	—	2	2	no	—
641	C₄×C₅	—	6	2	no	—
642	C₄×C₅	—	6	2	no	—
643	C₄×C₅	—	6	2	no	—
644	C₄×C₅	—	6	2	no	—
645	C₄×C₅	—	6	2	no	—
646	C₂⁴	—	3	1	no	—
647	C₂⁴	—	3	1	no	—
648	C₂⁴	—	3	1	no	—
649	C₂×Q₈	—	3	4	no	—
650	C₂×Q₈	—	12	2	no	—
651	C₂×D₄	—	3	4	no	—
652	C₂×D₄	—	3	4	no	—
653	C₂×D₄	—	3	4	no	—
654	C₂×D₄	—	6	4	no	—
655	C₂×D₄	—	6	4	no	—
656	C₂×D₄	—	12	2	no	—
657	C₂²×C₄	—	3	1	no	—
658	C₂²×C₄	—	3	1	no	—
659	C₂²×C₄	—	3	1	no	—
660	C₂²×C₄	—	3	1	no	—
661	C₂²×C₄	—	3	1	no	—
662	C₂²×C₄	—	3	4	no	—
663	C₂²×C₄	—	3	4	no	—
664	C₂²×C₄	—	3	4	no	—
665	C₂²×C₄	—	3	4	no	—
666	C₂²×C₄	—	3	4	no	—
667	C₂²×C₄	—	6	4	no	—
668	C₂²×C₄	—	12	2	no	—
669	C₂²×C₄	—	12	2	no	—
670	C₂²×C₄	—	12	2	no	—
671	C₂²×C₄	—	12	2	no	—
672	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
673	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
674	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
675	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
676	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
677	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
678	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
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	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
691	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
692	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
693	C₂²⋊C₄	—	3	4	no	—
694	C₂²⋊C₄	—	3	4	no	—
695	C₂²⋊C₄	—	3	4	no	—
696	C₂²⋊C₄	—	3	4	no	—
697	C₂²⋊C₄	—	3	4	no	—
698	C₂²⋊C₄	—	3	4	no	—
699	C₂²⋊C₄	—	3	4	no	—
700	C₂²⋊C₄	—	3	4	no	—
701	C₂²⋊C₄	—	3	4	no	—
702	C₂²⋊C₄	—	3	4	no	—
703	C₄²	—	3	4	no	—
704	C₄²	C₂²×C₅×D₃	1	4	yes	—
705	C₃×C₅	C₂×#539	1	1	yes	characteristic, complemented, Hall
706	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
707	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
708	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
709	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
710	C₂×D₃	—	2	8	no	—
711	C₂×D₃	—	2	2	no	—
712	C₂×D₃	—	2	2	no	—
713	C₂×D₃	—	2	2	no	—
714	C₂×D₃	—	2	2	no	—
715	C₂×D₃	—	2	2	no	—
716	C₂×D₃	—	2	2	no	—
717	C₂×D₃	—	2	2	no	—
718	C₂×D₃	—	2	2	no	—
719	C₂×D₃	—	4	4	no	—
720	C₂×D₃	—	4	4	no	—
721	C₂×D₃	C₂×C₅×#41	1	4	yes	—
722	C₃×C₄	—	2	2	no	—
723	C₃×C₄	—	2	2	no	—
724	C₃×C₄	—	2	2	no	—
725	C₃×C₄	—	2	2	no	—
726	C₃×C₄	—	2	2	no	—
727	C₃×C₄	—	2	2	no	—
728	C₃×C₄	—	2	2	no	—
729	Dic₃	—	2	2	no	—
730	Dic₃	—	2	2	no	—
731	Dic₃	—	2	2	no	—
732	Dic₃	—	2	2	no	—
733	Dic₃	—	2	2	no	—
734	C₂×C₅	—	6	4	no	—
735	C₂×C₅	—	12	2	no	—
736	C₂×C₅	—	12	2	no	—
737	C₂×C₅	#5692	1	4	yes	direct product factor
738	C₂×C₅	C₂×#1007	1	1	yes	characteristic
739	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
740	C₂×C₅	C₂×#1009	1	1	yes	characteristic
741	C₂³	—	3	4	no	—
742	C₂³	—	3	2	no	—
743	C₂³	—	3	2	no	—
744	C₂³	—	3	2	no	—
745	C₂³	—	6	2	no	—
746	C₂³	—	6	2	no	—
747	C₂³	—	6	2	no	—
748	C₂³	—	6	2	no	—
749	C₂³	—	6	2	no	—
750	C₂³	—	6	2	no	—
751	C₂³	—	6	2	no	—
752	C₂³	—	6	2	no	—
753	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
754	Q₈	—	12	4	no	—
755	D₄	—	6	8	no	—
756	D₄	—	6	8	no	—
757	D₄	—	12	4	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	3	2	no	—
766	C₂×C₄	—	3	2	no	—
767	C₂×C₄	—	3	2	no	—
768	C₂×C₄	—	3	2	no	—
769	C₂×C₄	—	3	2	no	—
770	C₂×C₄	—	6	8	no	—
771	C₂×C₄	—	6	2	no	—
772	C₂×C₄	—	6	2	no	—
773	C₂×C₄	—	6	2	no	—
774	C₂×C₄	—	6	2	no	—
775	C₂×C₄	—	6	2	no	—
776	C₂×C₄	—	12	4	no	—
777	C₂×C₄	—	12	4	no	—
778	C₂×C₄	—	12	4	no	—
779	C₂×C₄	—	12	4	no	—
780	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
781	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
782	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
783	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
784	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
785	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
786	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
787	C₂×C₃	C₅×#539	1	4	yes	complemented
788	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
789	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
790	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
791	D₃	—	2	4	no	—
792	D₃	—	4	2	no	—
793	D₃	—	4	2	no	—
794	C₅	C₂×#5692	1	1	yes	characteristic, direct product factor, Sylow
795	C₂²	—	3	4	no	—
796	C₂²	—	6	8	no	—
797	C₂²	—	6	2	no	—
798	C₂²	—	6	2	no	—
799	C₂²	—	6	2	no	—
800	C₂²	—	6	2	no	—
801	C₂²	—	6	2	no	—
802	C₂²	—	6	2	no	—
803	C₂²	—	6	2	no	—
804	C₂²	—	6	2	no	—
805	C₂²	—	12	4	no	—
806	C₂²	—	12	4	no	—
807	C₂²	C₅×#1007	1	2	yes	—
808	C₂²	C₅×D₃×#41	1	2	yes	—
809	C₂²	C₅×#1009	1	2	yes	—
810	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
811	C₄	—	2	2	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	6	2	no	—
819	C₄	—	6	2	no	—
820	C₄	—	6	2	no	—
821	C₄	—	6	2	no	—
822	C₄	—	6	2	no	—
823	C₃	C₂×C₅×#539	1	1	yes	characteristic, complemented, Sylow
824	C₂	—	6	4	no	—
825	C₂	—	12	2	no	—
826	C₂	—	12	2	no	—
827	C₂	C₅×#5692	1	4	yes	direct product factor
828	C₂	C₂×C₅×#1007	1	1	yes	characteristic
829	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
830	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×C₅×#125	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#895	C₂
hypercenter	C₂×C₅×#125	D₃
hypocenter	C₃	C₂×C₅×#539
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#125

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
2. C₅×#5692	C₂	direct (N × H)
3. C₂×C₅×#898	C₂	semidirect
4. C₂×C₅×#897	C₂	semidirect
5. C₂×C₅×#896	C₂	semidirect
6. C₂×C₅×#896	C₂	semidirect
8. C₂×C₅×#894	C₂	semidirect
9. C₂×C₅×#894	C₂	semidirect
10. C₂×C₅×#894	C₂	semidirect
11. C₂×C₅×#894	C₂	semidirect
12. C₂×C₅×#893	C₂	semidirect
13. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
14. C₂×C₅×#889	C₂	semidirect
15. C₂×C₅×#876	C₂	semidirect
16. C₂×C₄×C₅×D₁₂	C₂	semidirect
27. C₃×C₅×#125	C₂²	semidirect
54. C₅×#898	C₂²	semidirect
55. C₅×#897	C₂²	semidirect
56. C₅×#896	C₂²	semidirect
57. C₅×#896	C₂²	semidirect
59. C₅×#894	C₂²	semidirect
60. C₅×#894	C₂²	semidirect
61. C₅×#894	C₂²	semidirect
62. C₅×#894	C₂²	semidirect
63. C₅×#893	C₂²	semidirect
64. C₅×D₃×C₄⋊C₄	C₂²	semidirect
65. C₅×#889	C₂²	semidirect
66. C₅×#876	C₂²	semidirect
67. C₄×C₅×D₁₂	C₂²	semidirect
68. C₂×#5692	C₅	direct (N × H)
73. C₂×C₅×#125	D₃	semidirect
144. C₂×C₃×#125	C₂×C₅	semidirect
145. #5692	C₂×C₅	direct (N × H)
146. C₂×#898	C₂×C₅	semidirect
147. C₂×#897	C₂×C₅	semidirect
148. C₂×#896	C₂×C₅	semidirect
149. C₂×#896	C₂×C₅	semidirect
151. C₂×#894	C₂×C₅	semidirect
152. C₂×#894	C₂×C₅	semidirect
153. C₂×#894	C₂×C₅	semidirect
154. C₂×#894	C₂×C₅	semidirect
155. C₂×#893	C₂×C₅	semidirect
156. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
157. C₂×#889	C₂×C₅	semidirect
158. C₂×#876	C₂×C₅	semidirect
159. C₂×C₄×D₁₂	C₂×C₅	semidirect
172. C₅×#125	C₂×D₃	semidirect
266. C₃×#125	C₂²×C₅	semidirect
293. #898	C₂²×C₅	semidirect
294. #897	C₂²×C₅	semidirect
295. #896	C₂²×C₅	semidirect
296. #896	C₂²×C₅	semidirect
298. #894	C₂²×C₅	semidirect
299. #894	C₂²×C₅	semidirect
300. #894	C₂²×C₅	semidirect
301. #894	C₂²×C₅	semidirect
302. #893	C₂²×C₅	semidirect
303. D₃×C₄⋊C₄	C₂²×C₅	semidirect
304. #889	C₂²×C₅	semidirect
305. #876	C₂²×C₅	semidirect
306. C₄×D₁₂	C₂²×C₅	semidirect
370. C₂×#125	C₅×D₃	semidirect
527. #125	C₂×C₅×D₃	semidirect
565. C₂×C₃×C₅	#539	semidirect
705. C₃×C₅	C₂×#539	semidirect
737. C₂×C₅	#5692	direct (N × H)
787. C₂×C₃	C₅×#539	semidirect
794. C₅	C₂×#5692	direct (N × H)
823. C₃	C₂×C₅×#539	semidirect
827. C₂	C₅×#5692	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×#125	2
C₅×#5692	2
C₂×C₅×#898	2
C₂×C₅×#897	2
C₂×C₅×#896	2
C₂×C₅×#895	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#889	2
C₂×C₅×#876	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#539	3
C₂×#5692	5

Subgroups — C2×C5×#5692 #14480935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5692 #14480935