Subgroups — C₅×#74667 #14324365

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#940	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5220	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5213	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4958	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4956	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4956	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4665	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4665	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4650	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4648	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2328	—	3	1	no	maximal, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
20	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
21	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
23	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
24	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
25	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×#217	C₂²	1	1	yes	characteristic
31	C₂×C₅×#217	C₂²	1	1	yes	characteristic
32	C₂×C₅×#217	C₂²	1	1	yes	characteristic
33	C₅×#940	C₄	1	8	yes	complemented
34	C₄×C₅×#67	—	2	4	no	—
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×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
46	C₅×#67⋊C₄	—	2	4	no	—
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic
49	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
50	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
53	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
54	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
55	#74667	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
56	C₂×C₅×#127	—	3	1	no	—
57	C₂×C₄×C₅×D₄	—	3	1	no	—
58	C₂×C₄×C₅×D₄	—	3	1	no	—
59	C₅×#390	—	3	1	no	—
60	C₅×#390	—	3	1	no	—
61	C₅×#386	—	3	1	no	—
62	C₅×#386	—	3	1	no	—
63	C₅×#386	—	3	1	no	—
64	C₅×#386	—	3	1	no	—
65	C₅×#386	—	3	1	no	—
66	C₅×#386	—	3	1	no	—
67	C₅×#386	—	3	1	no	—
68	C₅×#386	D₃	1	1	yes	characteristic, complemented
69	C₅×#382	—	3	1	no	—
70	C₅×#376	—	3	1	no	—
71	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
73	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
74	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₅×D₄	—	4	1	no	—
76	C₂×C₃×C₅×D₄	—	4	1	no	—
77	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
78	C₂²×C₃×C₄×C₅	—	2	2	no	—
79	C₂²×C₃×C₄×C₅	—	4	1	no	—
80	C₂²×C₃×C₄×C₅	—	4	1	no	—
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂×C₅×#67	—	2	2	no	—
87	C₂×C₅×#67	—	2	2	no	—
88	C₂×C₅×#67	—	2	2	no	—
89	C₂×C₅×#67	—	2	2	no	—
90	C₂×C₅×#67	—	4	1	no	—
91	C₂×C₅×#67	—	4	1	no	—
92	C₂×C₅×#67	—	4	1	no	—
93	C₂×C₅×#67	—	4	1	no	—
94	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
95	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
96	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
97	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
98	C₂²×C₅×Dic₃	—	2	2	no	—
99	C₂²×C₅×Dic₃	—	4	1	no	—
100	C₂²×C₅×Dic₃	—	4	1	no	—
101	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
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	C₂×C₅×D₁₂	—	4	1	no	—
108	C₂×C₅×D₁₂	—	4	1	no	—
109	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	complemented
110	C₂×C₄×C₅×D₃	—	2	2	no	—
111	C₂×C₄×C₅×D₃	—	2	2	no	—
112	C₂×C₄×C₅×D₃	—	4	1	no	—
113	C₂×C₄×C₅×D₃	—	4	1	no	—
114	C₂×C₄×C₅×D₃	—	4	1	no	—
115	C₂×C₄×C₅×D₃	—	4	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
117	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
119	C₅×#217	—	2	2	no	—
120	C₅×#217	—	4	1	no	—
121	C₅×#217	—	4	1	no	—
122	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
123	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
124	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
125	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
126	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
127	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
128	C₅×Dic₃⋊C₄	—	2	2	no	—
129	C₅×Dic₃⋊C₄	—	2	2	no	—
130	C₄×C₅×Dic₃	—	2	2	no	—
131	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
132	C₄×C₅×Dic₃	D₄	1	4	yes	complemented
133	C₂×#940	C₂×C₅	1	1	yes	characteristic
134	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
137	#5220	C₂×C₅	1	1	yes	characteristic, complemented
138	#5213	C₂×C₅	1	1	yes	characteristic, complemented
139	#4958	C₂×C₅	1	1	yes	characteristic, complemented
140	#4957	C₂×C₅	1	1	yes	characteristic, complemented
141	#4957	C₂×C₅	1	1	yes	characteristic, complemented
142	#4956	C₂×C₅	1	1	yes	characteristic, complemented
143	#4956	C₂×C₅	1	1	yes	characteristic, complemented
144	#4665	C₂×C₅	1	1	yes	characteristic, complemented
145	#4665	C₂×C₅	1	1	yes	characteristic, complemented
146	#4650	C₂×C₅	1	1	yes	characteristic, complemented
147	#4648	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂²×C₅×D₄	—	3	1	no	—
149	C₂²×C₅×D₄	—	3	1	no	—
150	C₂²×C₅×D₄	—	3	1	no	—
151	C₂²×C₅×D₄	—	3	1	no	—
152	C₂²×C₅×D₄	—	3	1	no	—
153	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
154	C₂³×C₄×C₅	—	3	1	no	—
155	C₂³×C₄×C₅	—	3	1	no	—
156	C₂³×C₄×C₅	—	3	1	no	—
157	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
158	C₅×#127	—	3	8	no	—
159	C₄×C₅×D₄	—	6	4	no	—
160	C₄×C₅×D₄	—	6	4	no	—
161	C₂×C₅×C₄⋊C₄	—	3	1	no	—
162	C₂×C₅×C₄⋊C₄	—	3	1	no	—
163	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
164	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
165	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
166	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
167	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
168	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
169	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
170	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
171	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
172	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
173	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
175	C₂×C₄²×C₅	—	3	1	no	—
176	C₂×C₄²×C₅	—	3	1	no	—
177	C₂×C₄²×C₅	—	3	1	no	—
178	C₅×#95	—	3	1	no	—
179	C₅×#95	—	3	1	no	—
180	C₅×#95	—	3	1	no	—
181	C₅×#95	—	3	1	no	—
182	C₅×#95	—	3	1	no	—
183	C₅×#95	—	3	1	no	—
184	C₅×#95	C₂×D₃	1	1	yes	characteristic
185	C₅×#95	C₂×D₃	1	1	yes	characteristic
186	#2328	—	3	1	no	Sylow
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	—	2	1	no	—
189	C₂³×C₃×C₅	—	2	1	no	—
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂³×C₃×C₅	—	2	1	no	—
194	C₂³×C₃×C₅	—	2	1	no	—
195	C₂³×C₃×C₅	—	2	1	no	—
196	C₂³×C₃×C₅	—	2	1	no	—
197	C₂³×C₃×C₅	—	2	1	no	—
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
200	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
201	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
202	C₂²×C₅×D₃	—	2	1	no	—
203	C₂²×C₅×D₃	—	2	1	no	—
204	C₂²×C₅×D₃	—	2	1	no	—
205	C₂²×C₅×D₃	—	2	1	no	—
206	C₂²×C₅×D₃	—	2	1	no	—
207	C₂²×C₅×D₃	—	2	1	no	—
208	C₂²×C₅×D₃	—	2	1	no	—
209	C₂²×C₅×D₃	—	2	1	no	—
210	C₂²×C₅×D₃	—	2	1	no	—
211	C₂²×C₅×D₃	—	2	1	no	—
212	C₂²×C₅×D₃	—	2	1	no	—
213	C₂²×C₅×D₃	—	2	1	no	—
214	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
215	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
216	C₃×C₅×D₄	—	4	4	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	—	2	1	no	—
226	C₂×C₃×C₄×C₅	—	2	1	no	—
227	C₂×C₃×C₄×C₅	—	2	1	no	—
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	—	2	1	no	—
230	C₂×C₃×C₄×C₅	—	4	4	no	—
231	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
232	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
233	C₅×#67	—	2	8	no	—
234	C₅×#67	—	2	8	no	—
235	C₅×#67	—	4	4	no	—
236	C₅×#67	—	4	4	no	—
237	C₂×C₅×Dic₃	—	2	1	no	—
238	C₂×C₅×Dic₃	—	2	1	no	—
239	C₂×C₅×Dic₃	—	2	1	no	—
240	C₂×C₅×Dic₃	—	2	1	no	—
241	C₂×C₅×Dic₃	—	2	1	no	—
242	C₂×C₅×Dic₃	—	2	1	no	—
243	C₂×C₅×Dic₃	—	2	1	no	—
244	C₂×C₅×Dic₃	—	2	1	no	—
245	C₂×C₅×Dic₃	—	2	1	no	—
246	C₂×C₅×Dic₃	—	2	1	no	—
247	C₂×C₅×Dic₃	—	2	1	no	—
248	C₂×C₅×Dic₃	—	2	1	no	—
249	C₂×C₅×Dic₃	—	2	1	no	—
250	C₂×C₅×Dic₃	—	4	4	no	—
251	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
252	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
253	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
254	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
255	C₂×C₅×Dic₃	#41	1	2	yes	—
256	C₅×D₁₂	—	4	4	no	—
257	C₄×C₅×D₃	—	4	4	no	—
258	C₄×C₅×D₃	—	4	4	no	—
259	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
260	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
261	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
262	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
263	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
264	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
265	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
266	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
267	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
268	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	C₂×#217	C₂²×C₅	1	1	yes	characteristic
273	C₂×#217	C₂²×C₅	1	1	yes	characteristic
274	C₂×#217	C₂²×C₅	1	1	yes	characteristic
275	#940	C₄×C₅	1	8	yes	complemented
276	C₄×#67	—	2	4	no	—
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×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
285	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
286	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
287	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
288	#67⋊C₄	—	2	4	no	—
289	C₃×#95	C₂²×C₅	1	1	yes	characteristic
290	C₃×#95	C₂²×C₅	1	1	yes	characteristic
291	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
292	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
293	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
294	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
295	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
296	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
297	C₂⁴×C₅	—	3	1	no	—
298	C₂⁴×C₅	—	3	1	no	—
299	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
300	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
301	C₂×C₅×D₄	—	3	4	no	—
302	C₂×C₅×D₄	—	3	4	no	—
303	C₂×C₅×D₄	—	3	4	no	—
304	C₂×C₅×D₄	—	3	4	no	—
305	C₂×C₅×D₄	—	3	4	no	—
306	C₂×C₅×D₄	—	4	1	no	—
307	C₂×C₅×D₄	—	4	1	no	—
308	C₂×C₅×D₄	—	6	2	no	—
309	C₂×C₅×D₄	—	6	2	no	—
310	C₂×C₅×D₄	—	6	2	no	—
311	C₂×C₅×D₄	—	6	2	no	—
312	C₂×C₅×D₄	—	12	1	no	—
313	C₂×C₅×D₄	—	12	1	no	—
314	C₂×C₅×D₄	—	12	1	no	—
315	C₂×C₅×D₄	—	12	1	no	—
316	C₂×C₅×D₄	—	12	1	no	—
317	C₂×C₅×D₄	—	12	1	no	—
318	C₂×C₅×D₄	C₄×D₃	1	4	yes	complemented
319	C₂²×C₄×C₅	—	2	2	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	1	no	—
326	C₂²×C₄×C₅	—	4	1	no	—
327	C₂²×C₄×C₅	—	4	1	no	—
328	C₂²×C₄×C₅	—	6	2	no	—
329	C₂²×C₄×C₅	—	6	2	no	—
330	C₂²×C₄×C₅	—	6	2	no	—
331	C₂²×C₄×C₅	—	12	1	no	—
332	C₂²×C₄×C₅	—	12	1	no	—
333	C₂²×C₄×C₅	—	12	1	no	—
334	C₂²×C₄×C₅	—	12	1	no	—
335	C₂²×C₄×C₅	—	12	1	no	—
336	C₂²×C₄×C₅	—	12	1	no	—
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	1	yes	characteristic
342	C₅×C₄⋊C₄	—	6	2	no	—
343	C₅×C₄⋊C₄	—	6	2	no	—
344	C₅×C₂²⋊C₄	—	2	2	no	—
345	C₅×C₂²⋊C₄	—	4	1	no	—
346	C₅×C₂²⋊C₄	—	4	1	no	—
347	C₅×C₂²⋊C₄	—	6	2	no	—
348	C₅×C₂²⋊C₄	—	6	2	no	—
349	C₅×C₂²⋊C₄	—	6	2	no	—
350	C₅×C₂²⋊C₄	—	12	1	no	—
351	C₅×C₂²⋊C₄	—	12	1	no	—
352	C₅×C₂²⋊C₄	—	12	1	no	—
353	C₅×C₂²⋊C₄	—	12	1	no	—
354	C₅×C₂²⋊C₄	—	12	1	no	—
355	C₅×C₂²⋊C₄	—	12	1	no	—
356	C₄²×C₅	—	3	4	no	—
357	C₄²×C₅	—	3	4	no	—
358	C₄²×C₅	—	6	2	no	—
359	C₂×#127	—	3	1	no	—
360	C₂×C₄×D₄	—	3	1	no	—
361	C₂×C₄×D₄	—	3	1	no	—
362	#390	—	3	1	no	—
363	#390	—	3	1	no	—
364	#386	—	3	1	no	—
365	#386	—	3	1	no	—
366	#386	—	3	1	no	—
367	#386	—	3	1	no	—
368	#386	—	3	1	no	—
369	#386	—	3	1	no	—
370	#386	—	3	1	no	—
371	#386	C₅×D₃	1	1	yes	characteristic, complemented
372	#382	—	3	1	no	—
373	#376	—	3	1	no	—
374	C₂²×C₃×C₅	—	2	2	no	—
375	C₂²×C₃×C₅	—	2	2	no	—
376	C₂²×C₃×C₅	—	2	2	no	—
377	C₂²×C₃×C₅	—	2	2	no	—
378	C₂²×C₃×C₅	—	2	2	no	—
379	C₂²×C₃×C₅	—	2	2	no	—
380	C₂²×C₃×C₅	—	4	1	no	—
381	C₂²×C₃×C₅	—	4	1	no	—
382	C₂²×C₃×C₅	—	4	1	no	—
383	C₂²×C₃×C₅	—	4	1	no	—
384	C₂²×C₃×C₅	—	4	1	no	—
385	C₂²×C₃×C₅	—	4	1	no	—
386	C₂²×C₃×C₅	—	4	1	no	—
387	C₂²×C₃×C₅	—	4	1	no	—
388	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
389	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
390	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
391	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
392	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
393	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
394	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
395	C₂×C₅×D₃	—	2	2	no	—
396	C₂×C₅×D₃	—	2	2	no	—
397	C₂×C₅×D₃	—	2	2	no	—
398	C₂×C₅×D₃	—	2	2	no	—
399	C₂×C₅×D₃	—	2	2	no	—
400	C₂×C₅×D₃	—	2	2	no	—
401	C₂×C₅×D₃	—	4	1	no	—
402	C₂×C₅×D₃	—	4	1	no	—
403	C₂×C₅×D₃	—	4	1	no	—
404	C₂×C₅×D₃	—	4	1	no	—
405	C₂×C₅×D₃	—	4	1	no	—
406	C₂×C₅×D₃	—	4	1	no	—
407	C₂×C₅×D₃	—	4	1	no	—
408	C₂×C₅×D₃	—	4	1	no	—
409	C₃×C₄×C₅	—	2	2	no	—
410	C₃×C₄×C₅	—	2	2	no	—
411	C₃×C₄×C₅	—	4	1	no	—
412	C₃×C₄×C₅	—	4	1	no	—
413	C₃×C₄×C₅	—	4	1	no	—
414	C₅×Dic₃	—	2	2	no	—
415	C₅×Dic₃	—	2	2	no	—
416	C₅×Dic₃	—	4	1	no	—
417	C₅×Dic₃	—	4	1	no	—
418	C₅×Dic₃	—	4	1	no	—
419	C₅×Dic₃	C₄×D₄	1	4	yes	—
420	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
421	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
422	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
423	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₃×D₄	—	4	1	no	—
425	C₂×C₃×D₄	—	4	1	no	—
426	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
427	C₂²×C₃×C₄	—	2	2	no	—
428	C₂²×C₃×C₄	—	4	1	no	—
429	C₂²×C₃×C₄	—	4	1	no	—
430	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
431	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	C₂×#67	—	2	2	no	—
436	C₂×#67	—	2	2	no	—
437	C₂×#67	—	2	2	no	—
438	C₂×#67	—	2	2	no	—
439	C₂×#67	—	4	1	no	—
440	C₂×#67	—	4	1	no	—
441	C₂×#67	—	4	1	no	—
442	C₂×#67	—	4	1	no	—
443	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
444	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
445	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
446	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
447	C₂²×Dic₃	—	2	2	no	—
448	C₂²×Dic₃	—	4	1	no	—
449	C₂²×Dic₃	—	4	1	no	—
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	1	yes	characteristic
456	C₂×D₁₂	—	4	1	no	—
457	C₂×D₁₂	—	4	1	no	—
458	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	complemented
459	C₂×C₄×D₃	—	2	2	no	—
460	C₂×C₄×D₃	—	2	2	no	—
461	C₂×C₄×D₃	—	4	1	no	—
462	C₂×C₄×D₃	—	4	1	no	—
463	C₂×C₄×D₃	—	4	1	no	—
464	C₂×C₄×D₃	—	4	1	no	—
465	C₃×C₂²⋊C₄	—	2	2	no	—
466	C₃×C₂²⋊C₄	—	4	1	no	—
467	C₃×C₂²⋊C₄	—	4	1	no	—
468	#217	—	2	2	no	—
469	#217	—	4	1	no	—
470	#217	—	4	1	no	—
471	(C₂×D₃)⋊C₄	—	2	2	no	—
472	(C₂×D₃)⋊C₄	—	2	2	no	—
473	(C₂×D₃)⋊C₄	—	4	1	no	—
474	(C₂×D₃)⋊C₄	—	4	1	no	—
475	(C₂×D₃)⋊C₄	—	4	1	no	—
476	(C₂×D₃)⋊C₄	—	4	1	no	—
477	Dic₃⋊C₄	—	2	2	no	—
478	Dic₃⋊C₄	—	2	2	no	—
479	C₄×Dic₃	—	2	2	no	—
480	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
481	C₄×Dic₃	C₅×D₄	1	4	yes	complemented
482	C₂³×C₅	—	2	1	no	—
483	C₂³×C₅	—	2	1	no	—
484	C₂³×C₅	—	2	1	no	—
485	C₂³×C₅	—	2	1	no	—
486	C₂³×C₅	—	2	1	no	—
487	C₂³×C₅	—	2	1	no	—
488	C₂³×C₅	—	2	1	no	—
489	C₂³×C₅	—	2	1	no	—
490	C₂³×C₅	—	2	1	no	—
491	C₂³×C₅	—	2	1	no	—
492	C₂³×C₅	—	2	1	no	—
493	C₂³×C₅	—	2	1	no	—
494	C₂³×C₅	—	3	2	no	—
495	C₂³×C₅	—	3	2	no	—
496	C₂³×C₅	—	6	1	no	—
497	C₂³×C₅	—	6	1	no	—
498	C₂³×C₅	—	6	1	no	—
499	C₂³×C₅	—	6	1	no	—
500	C₂³×C₅	—	6	1	no	—
501	C₂³×C₅	—	6	1	no	—
502	C₂³×C₅	—	6	1	no	—
503	C₂³×C₅	—	6	1	no	—
504	C₂³×C₅	—	6	1	no	—
505	C₂³×C₅	—	6	1	no	—
506	C₂³×C₅	—	6	1	no	—
507	C₂³×C₅	—	6	1	no	—
508	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
509	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
510	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
511	C₅×D₄	—	4	4	no	—
512	C₅×D₄	—	6	8	no	—
513	C₅×D₄	—	6	8	no	—
514	C₅×D₄	—	12	4	no	—
515	C₅×D₄	—	12	4	no	—
516	C₅×D₄	—	12	4	no	—
517	C₂×C₄×C₅	—	2	1	no	—
518	C₂×C₄×C₅	—	2	1	no	—
519	C₂×C₄×C₅	—	2	1	no	—
520	C₂×C₄×C₅	—	2	1	no	—
521	C₂×C₄×C₅	—	2	1	no	—
522	C₂×C₄×C₅	—	2	1	no	—
523	C₂×C₄×C₅	—	2	1	no	—
524	C₂×C₄×C₅	—	2	1	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	1	no	—
527	C₂×C₄×C₅	—	2	1	no	—
528	C₂×C₄×C₅	—	2	1	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	3	2	no	—
531	C₂×C₄×C₅	—	3	2	no	—
532	C₂×C₄×C₅	—	3	2	no	—
533	C₂×C₄×C₅	—	3	2	no	—
534	C₂×C₄×C₅	—	3	2	no	—
535	C₂×C₄×C₅	—	4	4	no	—
536	C₂×C₄×C₅	—	6	1	no	—
537	C₂×C₄×C₅	—	6	1	no	—
538	C₂×C₄×C₅	—	6	1	no	—
539	C₂×C₄×C₅	—	6	1	no	—
540	C₂×C₄×C₅	—	6	1	no	—
541	C₂×C₄×C₅	—	6	1	no	—
542	C₂×C₄×C₅	—	6	1	no	—
543	C₂×C₄×C₅	—	6	1	no	—
544	C₂×C₄×C₅	—	6	1	no	—
545	C₂×C₄×C₅	—	6	1	no	—
546	C₂×C₄×C₅	—	6	1	no	—
547	C₂×C₄×C₅	—	6	1	no	—
548	C₂×C₄×C₅	—	6	1	no	—
549	C₂×C₄×C₅	—	12	4	no	—
550	C₂×C₄×C₅	—	12	4	no	—
551	C₂×C₄×C₅	—	12	4	no	—
552	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
553	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
554	C₂²×D₄	—	3	1	no	—
555	C₂²×D₄	—	3	1	no	—
556	C₂²×D₄	—	3	1	no	—
557	C₂²×D₄	—	3	1	no	—
558	C₂²×D₄	—	3	1	no	—
559	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
560	C₂³×C₄	—	3	1	no	—
561	C₂³×C₄	—	3	1	no	—
562	C₂³×C₄	—	3	1	no	—
563	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
564	#127	—	3	8	no	—
565	C₄×D₄	—	6	4	no	—
566	C₄×D₄	—	6	4	no	—
567	C₂×C₄⋊C₄	—	3	1	no	—
568	C₂×C₄⋊C₄	—	3	1	no	—
569	C₂×C₂²⋊C₄	—	3	1	no	—
570	C₂×C₂²⋊C₄	—	3	1	no	—
571	C₂×C₂²⋊C₄	—	3	1	no	—
572	C₂×C₂²⋊C₄	—	3	1	no	—
573	C₂×C₂²⋊C₄	—	3	1	no	—
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	C₂×C₅×D₃	1	1	yes	characteristic
579	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
581	C₂×C₄²	—	3	1	no	—
582	C₂×C₄²	—	3	1	no	—
583	C₂×C₄²	—	3	1	no	—
584	#95	—	3	1	no	—
585	#95	—	3	1	no	—
586	#95	—	3	1	no	—
587	#95	—	3	1	no	—
588	#95	—	3	1	no	—
589	#95	—	3	1	no	—
590	#95	C₂×C₅×D₃	1	1	yes	characteristic
591	#95	C₂×C₅×D₃	1	1	yes	characteristic
592	C₂×C₃×C₅	—	4	2	no	—
593	C₂×C₃×C₅	—	4	2	no	—
594	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
595	C₂×C₃×C₅	#518	1	1	yes	characteristic
596	C₂×C₃×C₅	#518	1	1	yes	characteristic
597	C₂×C₃×C₅	#535	1	1	yes	characteristic
598	C₂×C₃×C₅	#535	1	1	yes	characteristic
599	C₂×C₃×C₅	#540	1	1	yes	characteristic
600	C₂×C₃×C₅	#540	1	1	yes	characteristic
601	C₅×D₃	—	4	2	no	—
602	C₅×D₃	—	4	2	no	—
603	C₂³×C₃	—	2	1	no	—
604	C₂³×C₃	—	2	1	no	—
605	C₂³×C₃	—	2	1	no	—
606	C₂³×C₃	—	2	1	no	—
607	C₂³×C₃	—	2	1	no	—
608	C₂³×C₃	—	2	1	no	—
609	C₂³×C₃	—	2	1	no	—
610	C₂³×C₃	—	2	1	no	—
611	C₂³×C₃	—	2	1	no	—
612	C₂³×C₃	—	2	1	no	—
613	C₂³×C₃	—	2	1	no	—
614	C₂³×C₃	—	2	1	no	—
615	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
616	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
617	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
618	C₂²×D₃	—	2	1	no	—
619	C₂²×D₃	—	2	1	no	—
620	C₂²×D₃	—	2	1	no	—
621	C₂²×D₃	—	2	1	no	—
622	C₂²×D₃	—	2	1	no	—
623	C₂²×D₃	—	2	1	no	—
624	C₂²×D₃	—	2	1	no	—
625	C₂²×D₃	—	2	1	no	—
626	C₂²×D₃	—	2	1	no	—
627	C₂²×D₃	—	2	1	no	—
628	C₂²×D₃	—	2	1	no	—
629	C₂²×D₃	—	2	1	no	—
630	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
631	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
632	C₃×D₄	—	4	4	no	—
633	C₂×C₃×C₄	—	2	1	no	—
634	C₂×C₃×C₄	—	2	1	no	—
635	C₂×C₃×C₄	—	2	1	no	—
636	C₂×C₃×C₄	—	2	1	no	—
637	C₂×C₃×C₄	—	2	1	no	—
638	C₂×C₃×C₄	—	2	1	no	—
639	C₂×C₃×C₄	—	2	1	no	—
640	C₂×C₃×C₄	—	2	1	no	—
641	C₂×C₃×C₄	—	2	1	no	—
642	C₂×C₃×C₄	—	2	1	no	—
643	C₂×C₃×C₄	—	2	1	no	—
644	C₂×C₃×C₄	—	2	1	no	—
645	C₂×C₃×C₄	—	2	1	no	—
646	C₂×C₃×C₄	—	4	4	no	—
647	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
648	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
649	#67	—	2	8	no	—
650	#67	—	2	8	no	—
651	#67	—	4	4	no	—
652	#67	—	4	4	no	—
653	C₂×Dic₃	—	2	1	no	—
654	C₂×Dic₃	—	2	1	no	—
655	C₂×Dic₃	—	2	1	no	—
656	C₂×Dic₃	—	2	1	no	—
657	C₂×Dic₃	—	2	1	no	—
658	C₂×Dic₃	—	2	1	no	—
659	C₂×Dic₃	—	2	1	no	—
660	C₂×Dic₃	—	2	1	no	—
661	C₂×Dic₃	—	2	1	no	—
662	C₂×Dic₃	—	2	1	no	—
663	C₂×Dic₃	—	2	1	no	—
664	C₂×Dic₃	—	2	1	no	—
665	C₂×Dic₃	—	2	1	no	—
666	C₂×Dic₃	—	4	4	no	—
667	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
668	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
669	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
670	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
671	C₂×Dic₃	C₅×#41	1	2	yes	—
672	D₁₂	—	4	4	no	—
673	C₄×D₃	—	4	4	no	—
674	C₄×D₃	—	4	4	no	—
675	C₂²×C₅	—	2	2	no	—
676	C₂²×C₅	—	2	2	no	—
677	C₂²×C₅	—	2	2	no	—
678	C₂²×C₅	—	2	2	no	—
679	C₂²×C₅	—	2	2	no	—
680	C₂²×C₅	—	2	2	no	—
681	C₂²×C₅	—	4	1	no	—
682	C₂²×C₅	—	4	1	no	—
683	C₂²×C₅	—	4	1	no	—
684	C₂²×C₅	—	4	1	no	—
685	C₂²×C₅	—	4	1	no	—
686	C₂²×C₅	—	4	1	no	—
687	C₂²×C₅	—	4	1	no	—
688	C₂²×C₅	—	4	1	no	—
689	C₂²×C₅	—	6	2	no	—
690	C₂²×C₅	—	6	2	no	—
691	C₂²×C₅	—	6	2	no	—
692	C₂²×C₅	—	6	2	no	—
693	C₂²×C₅	—	6	2	no	—
694	C₂²×C₅	—	6	2	no	—
695	C₂²×C₅	—	12	1	no	—
696	C₂²×C₅	—	12	1	no	—
697	C₂²×C₅	—	12	1	no	—
698	C₂²×C₅	—	12	1	no	—
699	C₂²×C₅	—	12	1	no	—
700	C₂²×C₅	—	12	1	no	—
701	C₂²×C₅	—	12	1	no	—
702	C₂²×C₅	—	12	1	no	—
703	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
704	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
705	C₂²×C₅	#1004	1	1	yes	characteristic
706	C₂²×C₅	#1004	1	1	yes	characteristic
707	C₂²×C₅	#1004	1	1	yes	characteristic
708	C₂²×C₅	D₃×#41	1	1	yes	characteristic
709	C₂²×C₅	#1009	1	1	yes	characteristic
710	C₄×C₅	—	2	2	no	—
711	C₄×C₅	—	2	2	no	—
712	C₄×C₅	—	3	4	no	—
713	C₄×C₅	—	4	1	no	—
714	C₄×C₅	—	4	1	no	—
715	C₄×C₅	—	4	1	no	—
716	C₄×C₅	—	6	2	no	—
717	C₄×C₅	—	6	2	no	—
718	C₄×C₅	—	12	1	no	—
719	C₄×C₅	—	12	1	no	—
720	C₄×C₅	—	12	1	no	—
721	C₂⁴	—	3	1	no	—
722	C₂⁴	—	3	1	no	—
723	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
724	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
725	C₂×D₄	—	3	4	no	—
726	C₂×D₄	—	3	4	no	—
727	C₂×D₄	—	3	4	no	—
728	C₂×D₄	—	3	4	no	—
729	C₂×D₄	—	3	4	no	—
730	C₂×D₄	—	4	1	no	—
731	C₂×D₄	—	4	1	no	—
732	C₂×D₄	—	6	2	no	—
733	C₂×D₄	—	6	2	no	—
734	C₂×D₄	—	6	2	no	—
735	C₂×D₄	—	6	2	no	—
736	C₂×D₄	—	12	1	no	—
737	C₂×D₄	—	12	1	no	—
738	C₂×D₄	—	12	1	no	—
739	C₂×D₄	—	12	1	no	—
740	C₂×D₄	—	12	1	no	—
741	C₂×D₄	—	12	1	no	—
742	C₂×D₄	C₄×C₅×D₃	1	4	yes	complemented
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	3	1	no	—
745	C₂²×C₄	—	3	1	no	—
746	C₂²×C₄	—	3	1	no	—
747	C₂²×C₄	—	3	1	no	—
748	C₂²×C₄	—	3	1	no	—
749	C₂²×C₄	—	3	1	no	—
750	C₂²×C₄	—	4	1	no	—
751	C₂²×C₄	—	4	1	no	—
752	C₂²×C₄	—	6	2	no	—
753	C₂²×C₄	—	6	2	no	—
754	C₂²×C₄	—	6	2	no	—
755	C₂²×C₄	—	12	1	no	—
756	C₂²×C₄	—	12	1	no	—
757	C₂²×C₄	—	12	1	no	—
758	C₂²×C₄	—	12	1	no	—
759	C₂²×C₄	—	12	1	no	—
760	C₂²×C₄	—	12	1	no	—
761	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
762	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
763	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
764	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
765	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
766	C₄⋊C₄	—	6	2	no	—
767	C₄⋊C₄	—	6	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	4	1	no	—
770	C₂²⋊C₄	—	4	1	no	—
771	C₂²⋊C₄	—	6	2	no	—
772	C₂²⋊C₄	—	6	2	no	—
773	C₂²⋊C₄	—	6	2	no	—
774	C₂²⋊C₄	—	12	1	no	—
775	C₂²⋊C₄	—	12	1	no	—
776	C₂²⋊C₄	—	12	1	no	—
777	C₂²⋊C₄	—	12	1	no	—
778	C₂²⋊C₄	—	12	1	no	—
779	C₂²⋊C₄	—	12	1	no	—
780	C₄²	—	3	4	no	—
781	C₄²	—	3	4	no	—
782	C₄²	—	6	2	no	—
783	C₃×C₅	#2328	1	1	yes	characteristic, complemented, Hall
784	C₂²×C₃	—	2	2	no	—
785	C₂²×C₃	—	2	2	no	—
786	C₂²×C₃	—	2	2	no	—
787	C₂²×C₃	—	2	2	no	—
788	C₂²×C₃	—	2	2	no	—
789	C₂²×C₃	—	2	2	no	—
790	C₂²×C₃	—	4	1	no	—
791	C₂²×C₃	—	4	1	no	—
792	C₂²×C₃	—	4	1	no	—
793	C₂²×C₃	—	4	1	no	—
794	C₂²×C₃	—	4	1	no	—
795	C₂²×C₃	—	4	1	no	—
796	C₂²×C₃	—	4	1	no	—
797	C₂²×C₃	—	4	1	no	—
798	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
799	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
800	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
801	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
802	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
803	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
804	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
805	C₂×D₃	—	2	2	no	—
806	C₂×D₃	—	2	2	no	—
807	C₂×D₃	—	2	2	no	—
808	C₂×D₃	—	2	2	no	—
809	C₂×D₃	—	2	2	no	—
810	C₂×D₃	—	2	2	no	—
811	C₂×D₃	—	4	1	no	—
812	C₂×D₃	—	4	1	no	—
813	C₂×D₃	—	4	1	no	—
814	C₂×D₃	—	4	1	no	—
815	C₂×D₃	—	4	1	no	—
816	C₂×D₃	—	4	1	no	—
817	C₂×D₃	—	4	1	no	—
818	C₂×D₃	—	4	1	no	—
819	C₃×C₄	—	2	2	no	—
820	C₃×C₄	—	2	2	no	—
821	C₃×C₄	—	4	1	no	—
822	C₃×C₄	—	4	1	no	—
823	C₃×C₄	—	4	1	no	—
824	Dic₃	—	2	2	no	—
825	Dic₃	—	2	2	no	—
826	Dic₃	—	4	1	no	—
827	Dic₃	—	4	1	no	—
828	Dic₃	—	4	1	no	—
829	Dic₃	C₄×C₅×D₄	1	4	yes	—
830	C₂×C₅	—	4	2	no	—
831	C₂×C₅	—	4	2	no	—
832	C₂×C₅	—	12	2	no	—
833	C₂×C₅	—	12	2	no	—
834	C₂×C₅	#5486	1	1	yes	characteristic
835	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
836	C₂×C₅	#5545	1	1	yes	characteristic
837	C₂×C₅	#5592	1	1	yes	characteristic
838	C₂×C₅	#5607	1	1	yes	characteristic
839	C₂×C₅	#5615	1	1	yes	characteristic
840	C₂×C₅	#5663	1	1	yes	characteristic
841	C₂³	—	2	1	no	—
842	C₂³	—	2	1	no	—
843	C₂³	—	2	1	no	—
844	C₂³	—	2	1	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	1	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	1	no	—
852	C₂³	—	2	1	no	—
853	C₂³	—	3	2	no	—
854	C₂³	—	3	2	no	—
855	C₂³	—	6	1	no	—
856	C₂³	—	6	1	no	—
857	C₂³	—	6	1	no	—
858	C₂³	—	6	1	no	—
859	C₂³	—	6	1	no	—
860	C₂³	—	6	1	no	—
861	C₂³	—	6	1	no	—
862	C₂³	—	6	1	no	—
863	C₂³	—	6	1	no	—
864	C₂³	—	6	1	no	—
865	C₂³	—	6	1	no	—
866	C₂³	—	6	1	no	—
867	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
868	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
869	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
870	D₄	—	4	4	no	—
871	D₄	—	6	8	no	—
872	D₄	—	6	8	no	—
873	D₄	—	12	4	no	—
874	D₄	—	12	4	no	—
875	D₄	—	12	4	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	3	2	no	—
890	C₂×C₄	—	3	2	no	—
891	C₂×C₄	—	3	2	no	—
892	C₂×C₄	—	3	2	no	—
893	C₂×C₄	—	3	2	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	6	1	no	—
896	C₂×C₄	—	6	1	no	—
897	C₂×C₄	—	6	1	no	—
898	C₂×C₄	—	6	1	no	—
899	C₂×C₄	—	6	1	no	—
900	C₂×C₄	—	6	1	no	—
901	C₂×C₄	—	6	1	no	—
902	C₂×C₄	—	6	1	no	—
903	C₂×C₄	—	6	1	no	—
904	C₂×C₄	—	6	1	no	—
905	C₂×C₄	—	6	1	no	—
906	C₂×C₄	—	6	1	no	—
907	C₂×C₄	—	6	1	no	—
908	C₂×C₄	—	12	4	no	—
909	C₂×C₄	—	12	4	no	—
910	C₂×C₄	—	12	4	no	—
911	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
912	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
913	C₂×C₃	—	4	2	no	—
914	C₂×C₃	—	4	2	no	—
915	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
916	C₂×C₃	C₅×#518	1	1	yes	characteristic
917	C₂×C₃	C₅×#518	1	1	yes	characteristic
918	C₂×C₃	C₅×#535	1	1	yes	characteristic
919	C₂×C₃	C₅×#535	1	1	yes	characteristic
920	C₂×C₃	C₅×#540	1	1	yes	characteristic
921	C₂×C₃	C₅×#540	1	1	yes	characteristic
922	D₃	—	4	2	no	—
923	D₃	—	4	2	no	—
924	C₅	#74667	1	1	yes	characteristic, direct product factor, Sylow
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	4	1	no	—
932	C₂²	—	4	1	no	—
933	C₂²	—	4	1	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	6	2	no	—
940	C₂²	—	6	2	no	—
941	C₂²	—	6	2	no	—
942	C₂²	—	6	2	no	—
943	C₂²	—	6	2	no	—
944	C₂²	—	6	2	no	—
945	C₂²	—	12	1	no	—
946	C₂²	—	12	1	no	—
947	C₂²	—	12	1	no	—
948	C₂²	—	12	1	no	—
949	C₂²	—	12	1	no	—
950	C₂²	—	12	1	no	—
951	C₂²	—	12	1	no	—
952	C₂²	—	12	1	no	—
953	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
954	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
955	C₂²	C₅×#1004	1	1	yes	characteristic
956	C₂²	C₅×#1004	1	1	yes	characteristic
957	C₂²	C₅×#1004	1	1	yes	characteristic
958	C₂²	C₅×D₃×#41	1	1	yes	characteristic
959	C₂²	C₅×#1009	1	1	yes	characteristic
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	3	4	no	—
963	C₄	—	4	1	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₄	—	6	2	no	—
967	C₄	—	6	2	no	—
968	C₄	—	12	1	no	—
969	C₄	—	12	1	no	—
970	C₄	—	12	1	no	—
971	C₃	C₅×#2328	1	1	yes	characteristic, complemented, Sylow
972	C₂	—	4	2	no	—
973	C₂	—	4	2	no	—
974	C₂	—	12	2	no	—
975	C₂	—	12	2	no	—
976	C₂	C₅×#5486	1	1	yes	characteristic
977	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
978	C₂	C₅×#5545	1	1	yes	characteristic
979	C₂	C₅×#5592	1	1	yes	characteristic
980	C₂	C₅×#5607	1	1	yes	characteristic
981	C₂	C₅×#5615	1	1	yes	characteristic
982	C₂	C₅×#5663	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#386	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#940	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#386	D₃
hypocenter	C₃	C₅×#2328
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#386

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×#67	C₂	semidirect
3. C₂×C₅×#67⋊C₄	C₂	semidirect
4. C₃×C₅×#386	C₂	semidirect
5. C₅×#5220	C₂	semidirect
6. C₅×#5213	C₂	semidirect
7. C₅×#4958	C₂	semidirect
8. C₅×#4957	C₂	semidirect
9. C₅×#4957	C₂	semidirect
10. C₅×#4956	C₂	semidirect
11. C₅×#4956	C₂	semidirect
12. C₅×#4665	C₂	semidirect
13. C₅×#4665	C₂	semidirect
14. C₅×#4650	C₂	semidirect
15. C₅×#4648	C₂	semidirect
33. C₅×#940	C₄	semidirect
55. #74667	C₅	direct (N × H)
68. C₅×#386	D₃	semidirect
77. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
94. C₂×C₅×#67	C₂×C₄	semidirect
95. C₂×C₅×#67	C₂×C₄	semidirect
96. C₂×C₅×#67	C₂×C₄	semidirect
97. C₂×C₅×#67	C₂×C₄	semidirect
109. C₂×C₅×D₁₂	C₂×C₄	semidirect
131. C₄×C₅×Dic₃	C₂×C₄	semidirect
132. C₄×C₅×Dic₃	D₄	semidirect
134. C₂×C₄×#67	C₂×C₅	semidirect
135. C₂×#67⋊C₄	C₂×C₅	semidirect
136. C₃×#386	C₂×C₅	semidirect
137. #5220	C₂×C₅	semidirect
138. #5213	C₂×C₅	semidirect
139. #4958	C₂×C₅	semidirect
140. #4957	C₂×C₅	semidirect
141. #4957	C₂×C₅	semidirect
142. #4956	C₂×C₅	semidirect
143. #4956	C₂×C₅	semidirect
144. #4665	C₂×C₅	semidirect
145. #4665	C₂×C₅	semidirect
146. #4650	C₂×C₅	semidirect
147. #4648	C₂×C₅	semidirect
275. #940	C₄×C₅	semidirect
318. C₂×C₅×D₄	C₄×D₃	semidirect
371. #386	C₅×D₃	semidirect
426. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
443. C₂×#67	C₂×C₄×C₅	semidirect
444. C₂×#67	C₂×C₄×C₅	semidirect
445. C₂×#67	C₂×C₄×C₅	semidirect
446. C₂×#67	C₂×C₄×C₅	semidirect
458. C₂×D₁₂	C₂×C₄×C₅	semidirect
480. C₄×Dic₃	C₂×C₄×C₅	semidirect
481. C₄×Dic₃	C₅×D₄	semidirect
742. C₂×D₄	C₄×C₅×D₃	semidirect
783. C₃×C₅	#2328	semidirect
924. C₅	#74667	direct (N × H)
971. C₃	C₅×#2328	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#940	2
C₂×C₄×C₅×#67	2
C₂×C₅×#67⋊C₄	2
C₃×C₅×#386	2
C₅×#5220	2
C₅×#5213	2
C₅×#4958	2
C₅×#4957	2
C₅×#4956	2
C₅×#4665	2
C₅×#4650	2
C₅×#4648	2
C₅×#2328	3
#74667	5

Subgroups — C5×#74667 #14324365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#74667 #14324365