Subgroups — C₂×C₅×#5540 #14483610

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 880 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×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#930	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#929	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5540	C₂	1	16	yes	maximal, direct product factor
9	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#876	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#553	—	3	1	no	maximal, Hall
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
23	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
24	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
25	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
26	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
27	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
28	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
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×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
35	C₂×C₅×#217	C₂²	1	1	yes	characteristic
36	C₂×C₅×#217	C₂²	1	1	yes	characteristic
37	C₅×#939	C₂²	1	8	yes	complemented
38	C₅×#939	C₂²	1	8	yes	complemented
39	C₅×#930	C₂²	1	8	yes	complemented
40	C₅×#929	C₂²	1	8	yes	complemented
41	C₄×C₅×#67	C₂²	1	8	yes	complemented
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×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₅×C₄⋊Dic₃	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	1	yes	characteristic
55	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
56	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×C₅×Dic₃⋊C₄	C₂²	1	8	yes	complemented
58	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
60	C₅×#894	C₂²	1	8	yes	complemented
61	C₅×#889	C₂²	1	8	yes	complemented
62	C₅×#884	C₂²	1	8	yes	complemented
63	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
64	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
65	C₅×#879	C₂²	1	8	yes	complemented
66	C₅×#876	C₂²	1	8	yes	complemented
67	C₅×#872	C₂²	1	8	yes	complemented
68	C₂×#5540	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#553	—	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×#123	—	3	1	no	—
74	C₂×C₅×#123	—	3	1	no	—
75	C₂×C₅×#121	—	3	1	no	—
76	C₂×C₅×#121	—	3	1	no	—
77	C₂×C₅×#121	—	3	1	no	—
78	C₂×C₅×#121	—	3	1	no	—
79	C₂×C₄×C₅×D₄	—	3	1	no	—
80	C₂×C₄×C₅×D₄	—	3	1	no	—
81	C₂×C₄×C₅×D₄	—	3	1	no	—
82	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
83	C₂×C₅×#117	—	3	1	no	—
84	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
87	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
88	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×D₄	—	2	4	no	—
90	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
91	C₂²×C₃×C₄×C₅	—	4	2	no	—
92	C₂²×C₃×C₄×C₅	—	4	2	no	—
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	1	yes	characteristic
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
99	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
100	C₂×C₅×#67	—	2	4	no	—
101	C₂×C₅×#67	—	2	4	no	—
102	C₂×C₅×#67	—	2	4	no	—
103	C₂×C₅×#67	—	4	2	no	—
104	C₂×C₅×#67	C₂³	1	4	yes	—
105	C₂×C₅×#67	C₂³	1	4	yes	—
106	C₂×C₅×#67	C₂³	1	4	yes	—
107	C₂×C₅×#67	C₂³	1	4	yes	—
108	C₂²×C₅×Dic₃	—	2	4	no	—
109	C₂²×C₅×Dic₃	—	4	2	no	—
110	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
111	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
112	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
113	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
114	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
115	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
116	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
117	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
118	C₂×C₅×D₁₂	—	4	2	no	—
119	C₂×C₅×D₁₂	C₂³	1	4	yes	—
120	C₂×C₄×C₅×D₃	—	2	4	no	—
121	C₂×C₄×C₅×D₃	—	4	2	no	—
122	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
123	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
124	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
125	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₃×C₄²×C₅	C₂³	1	4	yes	—
128	C₅×#217	C₂³	1	4	yes	—
129	C₅×#217	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×(C₂×D₃)⋊C₄	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	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
144	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
145	C₄×C₅×Dic₃	C₂³	1	4	yes	—
146	C₄×C₅×Dic₃	C₂³	1	4	yes	—
147	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×#939	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂×#939	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂×#930	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂×#929	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂²×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
154	#5540	C₂×C₅	1	16	yes	direct product factor
155	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂×#884	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×#879	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂×#876	C₂×C₅	1	1	yes	characteristic, complemented
162	C₂×#872	C₂×C₅	1	1	yes	characteristic, complemented
163	C₂²×C₅×D₄	—	3	1	no	—
164	C₂²×C₅×D₄	—	3	1	no	—
165	C₂²×C₅×D₄	—	3	1	no	—
166	C₂²×C₅×D₄	—	3	1	no	—
167	C₂²×C₅×D₄	—	3	1	no	—
168	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
169	C₂³×C₄×C₅	—	3	1	no	—
170	C₂³×C₄×C₅	—	3	1	no	—
171	C₂³×C₄×C₅	—	3	1	no	—
172	C₂³×C₄×C₅	—	3	1	no	—
173	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
174	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
175	C₅×#126	—	3	8	no	—
176	C₅×#126	—	3	8	no	—
177	C₅×#125	—	3	8	no	—
178	C₅×#123	—	3	8	no	—
179	C₅×#123	—	3	8	no	—
180	C₅×#121	—	3	8	no	—
181	C₅×#121	—	3	8	no	—
182	C₅×#121	—	3	8	no	—
183	C₅×#121	—	3	8	no	—
184	C₄×C₅×D₄	—	3	8	no	—
185	C₄×C₅×D₄	—	3	8	no	—
186	C₄×C₅×D₄	—	3	8	no	—
187	C₄×C₅×D₄	C₂×D₃	1	8	yes	complemented
188	C₅×#117	—	3	8	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	1	no	—
196	C₂×C₅×C₄⋊C₄	—	3	1	no	—
197	C₂×C₅×C₄⋊C₄	—	3	8	no	—
198	C₂×C₅×C₄⋊C₄	—	3	1	no	—
199	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
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×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
209	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
210	C₂×C₄²×C₅	—	3	1	no	—
211	C₂×C₄²×C₅	—	3	1	no	—
212	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
213	C₂×#553	—	3	1	no	Sylow
214	C₂³×C₃×C₅	—	2	2	no	—
215	C₂³×C₃×C₅	—	2	2	no	—
216	C₂³×C₃×C₅	—	2	2	no	—
217	C₂³×C₃×C₅	—	2	2	no	—
218	C₂³×C₃×C₅	—	2	2	no	—
219	C₂³×C₃×C₅	#41	1	4	yes	—
220	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
221	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
222	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
223	C₂²×C₅×D₃	—	2	2	no	—
224	C₂²×C₅×D₃	—	2	2	no	—
225	C₂²×C₅×D₃	—	2	2	no	—
226	C₂²×C₅×D₃	—	2	2	no	—
227	C₂²×C₅×D₃	—	2	2	no	—
228	C₂²×C₅×D₃	—	2	2	no	—
229	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
230	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
231	C₃×C₅×D₄	—	2	8	no	—
232	C₂×C₃×C₄×C₅	—	2	2	no	—
233	C₂×C₃×C₄×C₅	—	2	2	no	—
234	C₂×C₃×C₄×C₅	—	2	2	no	—
235	C₂×C₃×C₄×C₅	—	2	2	no	—
236	C₂×C₃×C₄×C₅	—	2	2	no	—
237	C₂×C₃×C₄×C₅	—	4	4	no	—
238	C₂×C₃×C₄×C₅	—	4	4	no	—
239	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
240	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
241	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
242	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
243	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
244	C₅×#67	—	2	8	no	—
245	C₅×#67	—	2	8	no	—
246	C₅×#67	—	2	8	no	—
247	C₅×#67	—	4	4	no	—
248	C₂×C₅×Dic₃	—	2	2	no	—
249	C₂×C₅×Dic₃	—	2	2	no	—
250	C₂×C₅×Dic₃	—	2	2	no	—
251	C₂×C₅×Dic₃	—	2	2	no	—
252	C₂×C₅×Dic₃	—	2	2	no	—
253	C₂×C₅×Dic₃	—	2	8	no	—
254	C₂×C₅×Dic₃	—	4	4	no	—
255	C₂×C₅×Dic₃	#41	1	4	yes	—
256	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
257	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
258	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
259	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
260	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
261	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
262	C₅×D₁₂	—	4	4	no	—
263	C₄×C₅×D₃	—	2	8	no	—
264	C₄×C₅×D₃	—	4	4	no	—
265	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
266	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
269	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
270	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
271	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
272	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
273	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
274	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
275	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
276	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
277	C₃×C₄×D₄	C₂²×C₅	1	8	yes	complemented
278	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
279	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
280	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
282	C₂×#217	C₂²×C₅	1	1	yes	characteristic
283	C₂×#217	C₂²×C₅	1	1	yes	characteristic
284	#939	C₂²×C₅	1	8	yes	complemented
285	#939	C₂²×C₅	1	8	yes	complemented
286	#930	C₂²×C₅	1	8	yes	complemented
287	#929	C₂²×C₅	1	8	yes	complemented
288	C₄×#67	C₂²×C₅	1	8	yes	complemented
289	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
290	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
292	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
293	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
294	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
295	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
296	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
297	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
298	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
299	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
300	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
301	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
302	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
303	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
304	C₂×Dic₃⋊C₄	C₂²×C₅	1	8	yes	complemented
305	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
306	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
307	#894	C₂²×C₅	1	8	yes	complemented
308	#889	C₂²×C₅	1	8	yes	complemented
309	#884	C₂²×C₅	1	8	yes	complemented
310	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
311	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
312	#879	C₂²×C₅	1	8	yes	complemented
313	#876	C₂²×C₅	1	8	yes	complemented
314	#872	C₂²×C₅	1	8	yes	complemented
315	C₂⁴×C₅	—	3	1	no	—
316	C₂⁴×C₅	—	3	1	no	—
317	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
318	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
319	C₂×C₅×D₄	—	2	4	no	—
320	C₂×C₅×D₄	—	3	4	no	—
321	C₂×C₅×D₄	—	3	4	no	—
322	C₂×C₅×D₄	—	3	4	no	—
323	C₂×C₅×D₄	—	3	4	no	—
324	C₂×C₅×D₄	—	3	4	no	—
325	C₂×C₅×D₄	—	6	4	no	—
326	C₂×C₅×D₄	—	6	4	no	—
327	C₂×C₅×D₄	—	6	4	no	—
328	C₂×C₅×D₄	—	12	2	no	—
329	C₂×C₅×D₄	—	12	2	no	—
330	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
331	C₂²×C₄×C₅	—	3	1	no	—
332	C₂²×C₄×C₅	—	3	4	no	—
333	C₂²×C₄×C₅	—	3	1	no	—
334	C₂²×C₄×C₅	—	3	1	no	—
335	C₂²×C₄×C₅	—	3	1	no	—
336	C₂²×C₄×C₅	—	3	1	no	—
337	C₂²×C₄×C₅	—	3	1	no	—
338	C₂²×C₄×C₅	—	3	4	no	—
339	C₂²×C₄×C₅	—	3	4	no	—
340	C₂²×C₄×C₅	—	3	4	no	—
341	C₂²×C₄×C₅	—	4	2	no	—
342	C₂²×C₄×C₅	—	4	2	no	—
343	C₂²×C₄×C₅	—	6	4	no	—
344	C₂²×C₄×C₅	—	6	4	no	—
345	C₂²×C₄×C₅	—	12	2	no	—
346	C₂²×C₄×C₅	—	12	2	no	—
347	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
348	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
349	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
350	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
351	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
352	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
353	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
354	C₅×C₄⋊C₄	—	3	4	no	—
355	C₅×C₄⋊C₄	—	3	4	no	—
356	C₅×C₄⋊C₄	—	3	4	no	—
357	C₅×C₄⋊C₄	—	3	4	no	—
358	C₅×C₄⋊C₄	—	3	4	no	—
359	C₅×C₄⋊C₄	—	3	4	no	—
360	C₅×C₄⋊C₄	—	3	4	no	—
361	C₅×C₄⋊C₄	—	3	4	no	—
362	C₅×C₄⋊C₄	—	3	4	no	—
363	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
364	C₅×C₂²⋊C₄	—	3	4	no	—
365	C₅×C₂²⋊C₄	—	3	4	no	—
366	C₅×C₂²⋊C₄	—	3	4	no	—
367	C₅×C₂²⋊C₄	—	3	4	no	—
368	C₅×C₂²⋊C₄	—	3	4	no	—
369	C₅×C₂²⋊C₄	—	3	4	no	—
370	C₅×C₂²⋊C₄	—	3	4	no	—
371	C₅×C₂²⋊C₄	—	3	4	no	—
372	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
373	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
374	C₄²×C₅	—	3	4	no	—
375	C₄²×C₅	—	3	4	no	—
376	C₄²×C₅	C₂²×D₃	1	4	yes	—
377	#553	—	3	16	no	—
378	C₂×#126	—	3	1	no	—
379	C₂×#126	—	3	1	no	—
380	C₂×#125	—	3	1	no	—
381	C₂×#123	—	3	1	no	—
382	C₂×#123	—	3	1	no	—
383	C₂×#121	—	3	1	no	—
384	C₂×#121	—	3	1	no	—
385	C₂×#121	—	3	1	no	—
386	C₂×#121	—	3	1	no	—
387	C₂×C₄×D₄	—	3	1	no	—
388	C₂×C₄×D₄	—	3	1	no	—
389	C₂×C₄×D₄	—	3	1	no	—
390	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
391	C₂×#117	—	3	1	no	—
392	C₂²×C₄⋊C₄	—	3	1	no	—
393	C₂²×C₃×C₅	—	2	8	no	—
394	C₂²×C₃×C₅	—	2	2	no	—
395	C₂²×C₃×C₅	—	2	2	no	—
396	C₂²×C₃×C₅	—	2	2	no	—
397	C₂²×C₃×C₅	—	2	2	no	—
398	C₂²×C₃×C₅	—	2	2	no	—
399	C₂²×C₃×C₅	—	4	4	no	—
400	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
401	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
402	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
403	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
404	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
405	C₂×C₅×D₃	—	2	2	no	—
406	C₂×C₅×D₃	—	2	2	no	—
407	C₂×C₅×D₃	—	2	2	no	—
408	C₂×C₅×D₃	—	2	2	no	—
409	C₂×C₅×D₃	—	2	2	no	—
410	C₂×C₅×D₃	—	2	2	no	—
411	C₂×C₅×D₃	—	4	4	no	—
412	C₂×C₅×D₃	—	4	4	no	—
413	C₃×C₄×C₅	—	2	2	no	—
414	C₃×C₄×C₅	—	2	2	no	—
415	C₃×C₄×C₅	—	2	2	no	—
416	C₃×C₄×C₅	—	2	2	no	—
417	C₃×C₄×C₅	—	2	2	no	—
418	C₅×Dic₃	—	2	2	no	—
419	C₅×Dic₃	—	2	2	no	—
420	C₅×Dic₃	—	2	2	no	—
421	C₅×Dic₃	—	2	2	no	—
422	C₅×Dic₃	—	2	2	no	—
423	C₅×Dic₃	C₂×#41	1	4	yes	—
424	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
425	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
426	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
427	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
428	C₂×C₃×D₄	—	2	4	no	—
429	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
430	C₂²×C₃×C₄	—	4	2	no	—
431	C₂²×C₃×C₄	—	4	2	no	—
432	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
434	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
435	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
436	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
437	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
438	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
439	C₂×#67	—	2	4	no	—
440	C₂×#67	—	2	4	no	—
441	C₂×#67	—	2	4	no	—
442	C₂×#67	—	4	2	no	—
443	C₂×#67	C₂³×C₅	1	4	yes	—
444	C₂×#67	C₂³×C₅	1	4	yes	—
445	C₂×#67	C₂³×C₅	1	4	yes	—
446	C₂×#67	C₂³×C₅	1	4	yes	—
447	C₂²×Dic₃	—	2	4	no	—
448	C₂²×Dic₃	—	4	2	no	—
449	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
450	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
451	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
452	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
453	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
454	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
455	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
456	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
457	C₂×D₁₂	—	4	2	no	—
458	C₂×D₁₂	C₂³×C₅	1	4	yes	—
459	C₂×C₄×D₃	—	2	4	no	—
460	C₂×C₄×D₃	—	4	2	no	—
461	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
462	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
463	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
464	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
465	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
466	C₃×C₄²	C₂³×C₅	1	4	yes	—
467	#217	C₂³×C₅	1	4	yes	—
468	#217	C₂³×C₅	1	4	yes	—
469	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
470	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
471	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
472	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
473	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
474	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
475	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
476	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
477	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
478	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
479	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
480	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
481	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
482	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
483	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
484	C₄×Dic₃	C₂³×C₅	1	4	yes	—
485	C₄×Dic₃	C₂³×C₅	1	4	yes	—
486	C₂³×C₅	—	2	2	no	—
487	C₂³×C₅	—	2	2	no	—
488	C₂³×C₅	—	2	2	no	—
489	C₂³×C₅	—	2	2	no	—
490	C₂³×C₅	—	2	2	no	—
491	C₂³×C₅	—	3	2	no	—
492	C₂³×C₅	—	3	2	no	—
493	C₂³×C₅	—	6	2	no	—
494	C₂³×C₅	—	6	2	no	—
495	C₂³×C₅	—	6	2	no	—
496	C₂³×C₅	—	6	2	no	—
497	C₂³×C₅	—	6	2	no	—
498	C₂³×C₅	—	6	2	no	—
499	C₂³×C₅	#235	1	4	yes	—
500	C₂³×C₅	C₂³×D₃	1	2	yes	—
501	C₂³×C₅	C₂³×D₃	1	2	yes	—
502	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
503	C₅×D₄	—	2	8	no	—
504	C₅×D₄	—	6	8	no	—
505	C₅×D₄	—	6	8	no	—
506	C₅×D₄	—	6	8	no	—
507	C₅×D₄	—	12	4	no	—
508	C₅×D₄	—	12	4	no	—
509	C₂×C₄×C₅	—	2	2	no	—
510	C₂×C₄×C₅	—	2	2	no	—
511	C₂×C₄×C₅	—	2	2	no	—
512	C₂×C₄×C₅	—	2	2	no	—
513	C₂×C₄×C₅	—	2	2	no	—
514	C₂×C₄×C₅	—	3	4	no	—
515	C₂×C₄×C₅	—	3	2	no	—
516	C₂×C₄×C₅	—	3	2	no	—
517	C₂×C₄×C₅	—	3	2	no	—
518	C₂×C₄×C₅	—	3	2	no	—
519	C₂×C₄×C₅	—	3	2	no	—
520	C₂×C₄×C₅	—	3	2	no	—
521	C₂×C₄×C₅	—	4	4	no	—
522	C₂×C₄×C₅	—	4	4	no	—
523	C₂×C₄×C₅	—	6	8	no	—
524	C₂×C₄×C₅	—	6	8	no	—
525	C₂×C₄×C₅	—	6	2	no	—
526	C₂×C₄×C₅	—	6	2	no	—
527	C₂×C₄×C₅	—	6	2	no	—
528	C₂×C₄×C₅	—	6	2	no	—
529	C₂×C₄×C₅	—	6	2	no	—
530	C₂×C₄×C₅	—	12	4	no	—
531	C₂×C₄×C₅	—	12	4	no	—
532	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
533	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
534	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
535	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
536	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
537	C₂²×D₄	—	3	1	no	—
538	C₂²×D₄	—	3	1	no	—
539	C₂²×D₄	—	3	1	no	—
540	C₂²×D₄	—	3	1	no	—
541	C₂²×D₄	—	3	1	no	—
542	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
543	C₂³×C₄	—	3	1	no	—
544	C₂³×C₄	—	3	1	no	—
545	C₂³×C₄	—	3	1	no	—
546	C₂³×C₄	—	3	1	no	—
547	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
548	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
549	#126	—	3	8	no	—
550	#126	—	3	8	no	—
551	#125	—	3	8	no	—
552	#123	—	3	8	no	—
553	#123	—	3	8	no	—
554	#121	—	3	8	no	—
555	#121	—	3	8	no	—
556	#121	—	3	8	no	—
557	#121	—	3	8	no	—
558	C₄×D₄	—	3	8	no	—
559	C₄×D₄	—	3	8	no	—
560	C₄×D₄	—	3	8	no	—
561	C₄×D₄	C₂×C₅×D₃	1	8	yes	complemented
562	#117	—	3	8	no	—
563	C₂×C₄⋊C₄	—	3	1	no	—
564	C₂×C₄⋊C₄	—	3	1	no	—
565	C₂×C₄⋊C₄	—	3	1	no	—
566	C₂×C₄⋊C₄	—	3	1	no	—
567	C₂×C₄⋊C₄	—	3	8	no	—
568	C₂×C₄⋊C₄	—	3	1	no	—
569	C₂×C₄⋊C₄	—	3	1	no	—
570	C₂×C₄⋊C₄	—	3	1	no	—
571	C₂×C₄⋊C₄	—	3	1	no	—
572	C₂×C₄⋊C₄	—	3	1	no	—
573	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	—	3	1	no	—
575	C₂×C₂²⋊C₄	—	3	1	no	—
576	C₂×C₂²⋊C₄	—	3	1	no	—
577	C₂×C₂²⋊C₄	—	3	1	no	—
578	C₂×C₂²⋊C₄	—	3	1	no	—
579	C₂×C₂²⋊C₄	—	3	1	no	—
580	C₂×C₂²⋊C₄	—	3	1	no	—
581	C₂×C₂²⋊C₄	—	3	1	no	—
582	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
584	C₂×C₄²	—	3	1	no	—
585	C₂×C₄²	—	3	1	no	—
586	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
587	C₂×C₃×C₅	—	2	4	no	—
588	C₂×C₃×C₅	—	4	2	no	—
589	C₂×C₃×C₅	#553	1	4	yes	complemented
590	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
591	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
592	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
593	C₅×D₃	—	4	2	no	—
594	C₅×D₃	—	4	2	no	—
595	C₂³×C₃	—	2	2	no	—
596	C₂³×C₃	—	2	2	no	—
597	C₂³×C₃	—	2	2	no	—
598	C₂³×C₃	—	2	2	no	—
599	C₂³×C₃	—	2	2	no	—
600	C₂³×C₃	C₅×#41	1	4	yes	—
601	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
602	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
603	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
604	C₂²×D₃	—	2	2	no	—
605	C₂²×D₃	—	2	2	no	—
606	C₂²×D₃	—	2	2	no	—
607	C₂²×D₃	—	2	2	no	—
608	C₂²×D₃	—	2	2	no	—
609	C₂²×D₃	—	2	2	no	—
610	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
611	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
612	C₃×D₄	—	2	8	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	2	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	—	4	4	no	—
619	C₂×C₃×C₄	—	4	4	no	—
620	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
621	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
622	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
623	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
624	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
625	#67	—	2	8	no	—
626	#67	—	2	8	no	—
627	#67	—	2	8	no	—
628	#67	—	4	4	no	—
629	C₂×Dic₃	—	2	2	no	—
630	C₂×Dic₃	—	2	2	no	—
631	C₂×Dic₃	—	2	2	no	—
632	C₂×Dic₃	—	2	2	no	—
633	C₂×Dic₃	—	2	2	no	—
634	C₂×Dic₃	—	2	8	no	—
635	C₂×Dic₃	—	4	4	no	—
636	C₂×Dic₃	C₅×#41	1	4	yes	—
637	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
638	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
639	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
640	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
641	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
642	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
643	D₁₂	—	4	4	no	—
644	C₄×D₃	—	2	8	no	—
645	C₄×D₃	—	4	4	no	—
646	C₂²×C₅	—	2	2	no	—
647	C₂²×C₅	—	2	2	no	—
648	C₂²×C₅	—	2	8	no	—
649	C₂²×C₅	—	2	2	no	—
650	C₂²×C₅	—	2	2	no	—
651	C₂²×C₅	—	2	2	no	—
652	C₂²×C₅	—	4	4	no	—
653	C₂²×C₅	—	6	2	no	—
654	C₂²×C₅	—	6	2	no	—
655	C₂²×C₅	—	6	2	no	—
656	C₂²×C₅	—	6	2	no	—
657	C₂²×C₅	—	6	2	no	—
658	C₂²×C₅	—	6	2	no	—
659	C₂²×C₅	—	12	4	no	—
660	C₂²×C₅	—	12	4	no	—
661	C₂²×C₅	C₂×#235	1	4	yes	—
662	C₂²×C₅	C₂×#235	1	2	yes	—
663	C₂²×C₅	#1004	1	2	yes	—
664	C₂²×C₅	D₃×#41	1	2	yes	—
665	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
666	C₄×C₅	—	2	2	no	—
667	C₄×C₅	—	2	2	no	—
668	C₄×C₅	—	2	2	no	—
669	C₄×C₅	—	2	2	no	—
670	C₄×C₅	—	2	2	no	—
671	C₄×C₅	—	3	4	no	—
672	C₄×C₅	—	6	2	no	—
673	C₄×C₅	—	6	2	no	—
674	C₄×C₅	—	6	2	no	—
675	C₄×C₅	—	6	2	no	—
676	C₄×C₅	—	6	2	no	—
677	C₂⁴	—	3	1	no	—
678	C₂⁴	—	3	1	no	—
679	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
680	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	3	4	no	—
683	C₂×D₄	—	3	4	no	—
684	C₂×D₄	—	3	4	no	—
685	C₂×D₄	—	3	4	no	—
686	C₂×D₄	—	3	4	no	—
687	C₂×D₄	—	6	4	no	—
688	C₂×D₄	—	6	4	no	—
689	C₂×D₄	—	6	4	no	—
690	C₂×D₄	—	12	2	no	—
691	C₂×D₄	—	12	2	no	—
692	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
693	C₂²×C₄	—	3	1	no	—
694	C₂²×C₄	—	3	1	no	—
695	C₂²×C₄	—	3	1	no	—
696	C₂²×C₄	—	3	1	no	—
697	C₂²×C₄	—	3	1	no	—
698	C₂²×C₄	—	3	1	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	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	6	4	no	—
706	C₂²×C₄	—	6	4	no	—
707	C₂²×C₄	—	12	2	no	—
708	C₂²×C₄	—	12	2	no	—
709	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
710	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
711	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
712	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
713	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
714	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
715	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
716	C₄⋊C₄	—	3	4	no	—
717	C₄⋊C₄	—	3	4	no	—
718	C₄⋊C₄	—	3	4	no	—
719	C₄⋊C₄	—	3	4	no	—
720	C₄⋊C₄	—	3	4	no	—
721	C₄⋊C₄	—	3	4	no	—
722	C₄⋊C₄	—	3	4	no	—
723	C₄⋊C₄	—	3	4	no	—
724	C₄⋊C₄	—	3	4	no	—
725	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
726	C₂²⋊C₄	—	3	4	no	—
727	C₂²⋊C₄	—	3	4	no	—
728	C₂²⋊C₄	—	3	4	no	—
729	C₂²⋊C₄	—	3	4	no	—
730	C₂²⋊C₄	—	3	4	no	—
731	C₂²⋊C₄	—	3	4	no	—
732	C₂²⋊C₄	—	3	4	no	—
733	C₂²⋊C₄	—	3	4	no	—
734	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
735	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
736	C₄²	—	3	4	no	—
737	C₄²	—	3	4	no	—
738	C₄²	C₂²×C₅×D₃	1	4	yes	—
739	C₃×C₅	C₂×#553	1	1	yes	characteristic, complemented, Hall
740	C₂²×C₃	—	2	8	no	—
741	C₂²×C₃	—	2	2	no	—
742	C₂²×C₃	—	2	2	no	—
743	C₂²×C₃	—	2	2	no	—
744	C₂²×C₃	—	2	2	no	—
745	C₂²×C₃	—	2	2	no	—
746	C₂²×C₃	—	4	4	no	—
747	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
748	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
749	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
750	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
751	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
752	C₂×D₃	—	2	2	no	—
753	C₂×D₃	—	2	2	no	—
754	C₂×D₃	—	2	2	no	—
755	C₂×D₃	—	2	2	no	—
756	C₂×D₃	—	2	2	no	—
757	C₂×D₃	—	2	2	no	—
758	C₂×D₃	—	4	4	no	—
759	C₂×D₃	—	4	4	no	—
760	C₃×C₄	—	2	2	no	—
761	C₃×C₄	—	2	2	no	—
762	C₃×C₄	—	2	2	no	—
763	C₃×C₄	—	2	2	no	—
764	C₃×C₄	—	2	2	no	—
765	Dic₃	—	2	2	no	—
766	Dic₃	—	2	2	no	—
767	Dic₃	—	2	2	no	—
768	Dic₃	—	2	2	no	—
769	Dic₃	—	2	2	no	—
770	Dic₃	C₂×C₅×#41	1	4	yes	—
771	C₂×C₅	—	2	4	no	—
772	C₂×C₅	—	4	2	no	—
773	C₂×C₅	—	12	2	no	—
774	C₂×C₅	—	12	2	no	—
775	C₂×C₅	#5540	1	4	yes	direct product factor
776	C₂×C₅	C₂²×#235	1	1	yes	characteristic
777	C₂×C₅	C₂×#1004	1	1	yes	characteristic
778	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	3	2	no	—
785	C₂³	—	3	2	no	—
786	C₂³	—	6	2	no	—
787	C₂³	—	6	2	no	—
788	C₂³	—	6	2	no	—
789	C₂³	—	6	2	no	—
790	C₂³	—	6	2	no	—
791	C₂³	—	6	2	no	—
792	C₂³	C₅×#235	1	4	yes	—
793	C₂³	C₂³×C₅×D₃	1	2	yes	—
794	C₂³	C₂³×C₅×D₃	1	2	yes	—
795	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
796	D₄	—	2	8	no	—
797	D₄	—	6	8	no	—
798	D₄	—	6	8	no	—
799	D₄	—	6	8	no	—
800	D₄	—	12	4	no	—
801	D₄	—	12	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	3	4	no	—
808	C₂×C₄	—	3	2	no	—
809	C₂×C₄	—	3	2	no	—
810	C₂×C₄	—	3	2	no	—
811	C₂×C₄	—	3	2	no	—
812	C₂×C₄	—	3	2	no	—
813	C₂×C₄	—	3	2	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	6	8	no	—
817	C₂×C₄	—	6	8	no	—
818	C₂×C₄	—	6	2	no	—
819	C₂×C₄	—	6	2	no	—
820	C₂×C₄	—	6	2	no	—
821	C₂×C₄	—	6	2	no	—
822	C₂×C₄	—	6	2	no	—
823	C₂×C₄	—	12	4	no	—
824	C₂×C₄	—	12	4	no	—
825	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
826	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
827	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
828	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
829	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
830	C₂×C₃	—	2	4	no	—
831	C₂×C₃	—	4	2	no	—
832	C₂×C₃	C₅×#553	1	4	yes	complemented
833	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
834	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
835	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
836	D₃	—	4	2	no	—
837	D₃	—	4	2	no	—
838	C₅	C₂×#5540	1	1	yes	characteristic, direct product factor, Sylow
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	8	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	4	4	no	—
846	C₂²	—	6	2	no	—
847	C₂²	—	6	2	no	—
848	C₂²	—	6	2	no	—
849	C₂²	—	6	2	no	—
850	C₂²	—	6	2	no	—
851	C₂²	—	6	2	no	—
852	C₂²	—	12	4	no	—
853	C₂²	—	12	4	no	—
854	C₂²	C₂×C₅×#235	1	4	yes	—
855	C₂²	C₂×C₅×#235	1	2	yes	—
856	C₂²	C₅×#1004	1	2	yes	—
857	C₂²	C₅×D₃×#41	1	2	yes	—
858	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	3	4	no	—
865	C₄	—	6	2	no	—
866	C₄	—	6	2	no	—
867	C₄	—	6	2	no	—
868	C₄	—	6	2	no	—
869	C₄	—	6	2	no	—
870	C₃	C₂×C₅×#553	1	1	yes	characteristic, complemented, Sylow
871	C₂	—	2	4	no	—
872	C₂	—	4	2	no	—
873	C₂	—	12	2	no	—
874	C₂	—	12	2	no	—
875	C₂	C₅×#5540	1	4	yes	direct product factor
876	C₂	C₂²×C₅×#235	1	1	yes	characteristic
877	C₂	C₂×C₅×#1004	1	1	yes	characteristic
878	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×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₂×C₅×#553
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
2. C₂×C₅×#939	C₂	semidirect
3. C₂×C₅×#939	C₂	semidirect
4. C₂×C₅×#930	C₂	semidirect
5. C₂×C₅×#929	C₂	semidirect
6. C₂×C₄×C₅×#67	C₂	semidirect
7. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
8. C₅×#5540	C₂	direct (N × H)
9. C₂×C₅×#894	C₂	semidirect
10. C₂×C₅×#889	C₂	semidirect
11. C₂×C₅×#884	C₂	semidirect
12. C₂×C₅×#67⋊C₄	C₂	semidirect
13. C₂×C₅×#67⋊C₄	C₂	semidirect
14. C₂×C₅×#879	C₂	semidirect
15. C₂×C₅×#876	C₂	semidirect
16. C₂×C₅×#872	C₂	semidirect
30. C₃×C₄×C₅×D₄	C₂²	semidirect
37. C₅×#939	C₂²	semidirect
38. C₅×#939	C₂²	semidirect
39. C₅×#930	C₂²	semidirect
40. C₅×#929	C₂²	semidirect
41. C₄×C₅×#67	C₂²	semidirect
57. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
60. C₅×#894	C₂²	semidirect
61. C₅×#889	C₂²	semidirect
62. C₅×#884	C₂²	semidirect
63. C₅×#67⋊C₄	C₂²	semidirect
64. C₅×#67⋊C₄	C₂²	semidirect
65. C₅×#879	C₂²	semidirect
66. C₅×#876	C₂²	semidirect
67. C₅×#872	C₂²	semidirect
68. C₂×#5540	C₅	direct (N × H)
82. C₂×C₄×C₅×D₄	D₃	semidirect
147. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
148. C₂×#939	C₂×C₅	semidirect
149. C₂×#939	C₂×C₅	semidirect
150. C₂×#930	C₂×C₅	semidirect
151. C₂×#929	C₂×C₅	semidirect
152. C₂×C₄×#67	C₂×C₅	semidirect
153. C₂²×Dic₃⋊C₄	C₂×C₅	semidirect
154. #5540	C₂×C₅	direct (N × H)
155. C₂×#894	C₂×C₅	semidirect
156. C₂×#889	C₂×C₅	semidirect
157. C₂×#884	C₂×C₅	semidirect
158. C₂×#67⋊C₄	C₂×C₅	semidirect
159. C₂×#67⋊C₄	C₂×C₅	semidirect
160. C₂×#879	C₂×C₅	semidirect
161. C₂×#876	C₂×C₅	semidirect
162. C₂×#872	C₂×C₅	semidirect
187. C₄×C₅×D₄	C₂×D₃	semidirect
277. C₃×C₄×D₄	C₂²×C₅	semidirect
284. #939	C₂²×C₅	semidirect
285. #939	C₂²×C₅	semidirect
286. #930	C₂²×C₅	semidirect
287. #929	C₂²×C₅	semidirect
288. C₄×#67	C₂²×C₅	semidirect
304. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
307. #894	C₂²×C₅	semidirect
308. #889	C₂²×C₅	semidirect
309. #884	C₂²×C₅	semidirect
310. #67⋊C₄	C₂²×C₅	semidirect
311. #67⋊C₄	C₂²×C₅	semidirect
312. #879	C₂²×C₅	semidirect
313. #876	C₂²×C₅	semidirect
314. #872	C₂²×C₅	semidirect
390. C₂×C₄×D₄	C₅×D₃	semidirect
561. C₄×D₄	C₂×C₅×D₃	semidirect
589. C₂×C₃×C₅	#553	semidirect
739. C₃×C₅	C₂×#553	semidirect
775. C₂×C₅	#5540	direct (N × H)
832. C₂×C₃	C₅×#553	semidirect
838. C₅	C₂×#5540	direct (N × H)
870. C₃	C₂×C₅×#553	semidirect
875. C₂	C₅×#5540	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×D₄	2
C₂×C₅×#939	2
C₂×C₅×#930	2
C₂×C₅×#929	2
C₂×C₄×C₅×#67	2
C₂²×C₅×Dic₃⋊C₄	2
C₅×#5540	2
C₂×C₅×#894	2
C₂×C₅×#889	2
C₂×C₅×#884	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×#879	2
C₂×C₅×#876	2
C₂×C₅×#872	2
C₂×C₅×#553	3
C₂×#5540	5

Subgroups — C2×C5×#5540 #14483610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5540 #14483610