Subgroups — C₃×C₅×#3297 #14276331

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#553	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#447	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3297	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#126	—	2	1	no	—
25	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#124	C₂²	1	1	yes	characteristic
27	C₃×C₅×#123	—	2	1	no	—
28	C₃×C₅×#123	—	2	1	no	—
29	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₃×C₅×#121	—	2	1	no	—
31	C₃×C₅×#121	—	2	1	no	—
32	C₃×C₅×#121	C₂²	1	1	yes	characteristic
33	C₃×C₅×#121	C₂²	1	1	yes	characteristic
34	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#120	—	2	1	no	—
36	C₃×C₄×C₅×D₄	—	2	1	no	—
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
43	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₅×#102	C₂²	1	1	yes	characteristic
51	C₃×C₅×#102	C₂²	1	1	yes	characteristic
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic
56	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3297	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#553	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#546	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#488	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#484	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#482	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#478	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#463	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#447	C₂×C₃	1	1	yes	characteristic, complemented
72	C₄×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×C₅×#102	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂⁴×C₃×C₅	—	2	1	no	—
77	C₃×C₅×#41	—	2	2	no	—
78	C₃×C₅×#41	—	4	1	no	—
79	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	—	2	2	no	—
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	—	2	1	no	—
83	C₂×C₃×C₅×D₄	—	2	1	no	—
84	C₂×C₃×C₅×D₄	—	2	1	no	—
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	—	4	1	no	—
87	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	—	2	1	no	—
92	C₂²×C₃×C₄×C₅	—	2	1	no	—
93	C₂²×C₃×C₄×C₅	—	2	1	no	—
94	C₂²×C₃×C₄×C₅	—	2	1	no	—
95	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
97	C₃×C₅×SD₁₆	—	4	1	no	—
98	C₃×C₅×D₈	—	2	2	no	—
99	C₃×C₅×D₈	—	4	1	no	—
100	C₂×C₃×C₅×C₈	—	4	1	no	—
101	C₂×C₃×C₅×C₈	—	4	1	no	—
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
106	C₃×C₅×C₄⋊C₄	—	2	1	no	—
107	C₃×C₅×C₄⋊C₄	—	2	1	no	—
108	C₃×C₅×C₄⋊C₄	—	2	1	no	—
109	C₃×C₅×C₄⋊C₄	—	2	1	no	—
110	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
111	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
120	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
121	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
122	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
123	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
124	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
125	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
126	C₃×C₄²×C₅	—	2	1	no	—
127	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
128	C₃×#553	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#546	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#488	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#484	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#482	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#478	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#447	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
144	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
148	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
149	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
150	C₅×#126	—	2	1	no	—
151	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₅×#124	C₂²×C₃	1	1	yes	characteristic
153	C₅×#123	—	2	1	no	—
154	C₅×#123	—	2	1	no	—
155	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
156	C₅×#121	—	2	1	no	—
157	C₅×#121	—	2	1	no	—
158	C₅×#121	C₂²×C₃	1	1	yes	characteristic
159	C₅×#121	C₂²×C₃	1	1	yes	characteristic
160	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₅×#120	—	2	1	no	—
162	C₄×C₅×D₄	—	2	1	no	—
163	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
164	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
165	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
169	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₅×#102	C₂²×C₃	1	1	yes	characteristic
177	C₅×#102	C₂²×C₃	1	1	yes	characteristic
178	C₅×#102	C₂²×C₃	1	1	yes	characteristic
179	C₅×#102	C₂²×C₃	1	1	yes	characteristic
180	C₅×#102	C₂²×C₃	1	1	yes	characteristic
181	C₅×#102	C₂²×C₃	1	1	yes	characteristic
182	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
186	#3297	C₃×C₅	1	1	yes	characteristic, direct product factor, 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	—	4	2	no	—
191	C₂³×C₃×C₅	—	4	2	no	—
192	C₂³×C₃×C₅	—	8	1	no	—
193	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
194	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
195	C₃×C₅×Q₈	—	2	1	no	—
196	C₃×C₅×Q₈	—	2	1	no	—
197	C₃×C₅×D₄	—	2	2	no	—
198	C₃×C₅×D₄	—	2	1	no	—
199	C₃×C₅×D₄	—	2	1	no	—
200	C₃×C₅×D₄	—	2	1	no	—
201	C₃×C₅×D₄	—	2	1	no	—
202	C₃×C₅×D₄	—	2	1	no	—
203	C₃×C₅×D₄	—	4	2	no	—
204	C₃×C₅×D₄	—	4	2	no	—
205	C₃×C₅×D₄	—	4	2	no	—
206	C₃×C₅×D₄	—	8	1	no	—
207	C₃×C₅×D₄	—	8	1	no	—
208	C₃×C₅×D₄	#41	1	2	yes	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	2	1	no	—
214	C₂×C₃×C₄×C₅	—	2	1	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	4	2	no	—
219	C₂×C₃×C₄×C₅	—	8	1	no	—
220	C₂×C₃×C₄×C₅	—	8	1	no	—
221	C₂×C₃×C₄×C₅	—	8	1	no	—
222	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
224	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
225	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
226	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
227	C₃×C₅×C₈	—	2	1	no	—
228	C₃×C₅×C₈	—	2	1	no	—
229	C₃×C₅×C₈	—	2	1	no	—
230	C₃×C₅×C₈	—	2	1	no	—
231	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
232	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
234	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
236	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
237	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
238	C₃×#126	—	2	1	no	—
239	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
240	C₃×#124	C₂²×C₅	1	1	yes	characteristic
241	C₃×#123	—	2	1	no	—
242	C₃×#123	—	2	1	no	—
243	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
244	C₃×#121	—	2	1	no	—
245	C₃×#121	—	2	1	no	—
246	C₃×#121	C₂²×C₅	1	1	yes	characteristic
247	C₃×#121	C₂²×C₅	1	1	yes	characteristic
248	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₃×#120	—	2	1	no	—
250	C₃×C₄×D₄	—	2	1	no	—
251	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
252	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
253	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
257	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
258	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
259	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
261	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×#102	C₂²×C₅	1	1	yes	characteristic
265	C₃×#102	C₂²×C₅	1	1	yes	characteristic
266	C₃×#102	C₂²×C₅	1	1	yes	characteristic
267	C₃×#102	C₂²×C₅	1	1	yes	characteristic
268	C₃×#102	C₂²×C₅	1	1	yes	characteristic
269	C₃×#102	C₂²×C₅	1	1	yes	characteristic
270	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₂⁴×C₅	—	2	1	no	—
275	C₅×#41	—	2	2	no	—
276	C₅×#41	—	4	1	no	—
277	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₅×D₄	—	2	2	no	—
279	C₂×C₅×D₄	—	2	1	no	—
280	C₂×C₅×D₄	—	2	1	no	—
281	C₂×C₅×D₄	—	2	1	no	—
282	C₂×C₅×D₄	—	2	1	no	—
283	C₂×C₅×D₄	—	2	1	no	—
284	C₂×C₅×D₄	—	4	1	no	—
285	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
286	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
289	C₂²×C₄×C₅	—	2	1	no	—
290	C₂²×C₄×C₅	—	2	1	no	—
291	C₂²×C₄×C₅	—	2	1	no	—
292	C₂²×C₄×C₅	—	2	1	no	—
293	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
295	C₅×SD₁₆	—	4	1	no	—
296	C₅×D₈	—	2	2	no	—
297	C₅×D₈	—	4	1	no	—
298	C₂×C₅×C₈	—	4	1	no	—
299	C₂×C₅×C₈	—	4	1	no	—
300	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
301	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
303	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
304	C₅×C₄⋊C₄	—	2	1	no	—
305	C₅×C₄⋊C₄	—	2	1	no	—
306	C₅×C₄⋊C₄	—	2	1	no	—
307	C₅×C₄⋊C₄	—	2	1	no	—
308	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
309	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
310	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
311	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
312	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
313	C₅×C₂²⋊C₄	—	2	1	no	—
314	C₅×C₂²⋊C₄	—	2	1	no	—
315	C₅×C₂²⋊C₄	—	2	1	no	—
316	C₅×C₂²⋊C₄	—	2	1	no	—
317	C₅×C₂²⋊C₄	—	2	1	no	—
318	C₅×C₂²⋊C₄	—	2	1	no	—
319	C₅×C₂²⋊C₄	—	2	1	no	—
320	C₅×C₂²⋊C₄	—	2	1	no	—
321	C₅×C₂²⋊C₄	—	2	1	no	—
322	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
323	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
324	C₄²×C₅	—	2	1	no	—
325	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
326	#553	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	#546	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	#488	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	#484	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#482	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	#478	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	#466	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#447	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#416	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	C₂×#102	C₂×C₃×C₅	1	1	yes	characteristic, complemented
341	C₂²×C₃×C₅	—	2	1	no	—
342	C₂²×C₃×C₅	—	2	1	no	—
343	C₂²×C₃×C₅	—	2	1	no	—
344	C₂²×C₃×C₅	—	2	2	no	—
345	C₂²×C₃×C₅	—	2	1	no	—
346	C₂²×C₃×C₅	—	2	1	no	—
347	C₂²×C₃×C₅	—	4	1	no	—
348	C₂²×C₃×C₅	—	4	1	no	—
349	C₂²×C₃×C₅	—	4	1	no	—
350	C₂²×C₃×C₅	—	4	1	no	—
351	C₂²×C₃×C₅	—	4	1	no	—
352	C₂²×C₃×C₅	—	4	1	no	—
353	C₂²×C₃×C₅	—	4	1	no	—
354	C₂²×C₃×C₅	—	4	1	no	—
355	C₂²×C₃×C₅	—	8	4	no	—
356	C₂²×C₃×C₅	#135	1	2	yes	—
357	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
358	C₃×C₄×C₅	—	2	1	no	—
359	C₃×C₄×C₅	—	2	1	no	—
360	C₃×C₄×C₅	—	2	1	no	—
361	C₃×C₄×C₅	—	2	1	no	—
362	C₃×C₄×C₅	—	4	1	no	—
363	C₃×C₄×C₅	—	4	1	no	—
364	C₃×C₄×C₅	—	4	1	no	—
365	C₃×C₄×C₅	—	4	1	no	—
366	C₃×C₄×C₅	—	4	1	no	—
367	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
368	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
369	C₂⁴×C₃	—	2	1	no	—
370	C₃×#41	—	2	2	no	—
371	C₃×#41	—	4	1	no	—
372	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
373	C₂×C₃×D₄	—	2	2	no	—
374	C₂×C₃×D₄	—	2	1	no	—
375	C₂×C₃×D₄	—	2	1	no	—
376	C₂×C₃×D₄	—	2	1	no	—
377	C₂×C₃×D₄	—	2	1	no	—
378	C₂×C₃×D₄	—	2	1	no	—
379	C₂×C₃×D₄	—	4	1	no	—
380	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
381	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
384	C₂²×C₃×C₄	—	2	1	no	—
385	C₂²×C₃×C₄	—	2	1	no	—
386	C₂²×C₃×C₄	—	2	1	no	—
387	C₂²×C₃×C₄	—	2	1	no	—
388	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
390	C₃×SD₁₆	—	4	1	no	—
391	C₃×D₈	—	2	2	no	—
392	C₃×D₈	—	4	1	no	—
393	C₂×C₃×C₈	—	4	1	no	—
394	C₂×C₃×C₈	—	4	1	no	—
395	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
396	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
397	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
398	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
399	C₃×C₄⋊C₄	—	2	1	no	—
400	C₃×C₄⋊C₄	—	2	1	no	—
401	C₃×C₄⋊C₄	—	2	1	no	—
402	C₃×C₄⋊C₄	—	2	1	no	—
403	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
404	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
405	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
406	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
407	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
408	C₃×C₂²⋊C₄	—	2	1	no	—
409	C₃×C₂²⋊C₄	—	2	1	no	—
410	C₃×C₂²⋊C₄	—	2	1	no	—
411	C₃×C₂²⋊C₄	—	2	1	no	—
412	C₃×C₂²⋊C₄	—	2	1	no	—
413	C₃×C₂²⋊C₄	—	2	1	no	—
414	C₃×C₂²⋊C₄	—	2	1	no	—
415	C₃×C₂²⋊C₄	—	2	1	no	—
416	C₃×C₂²⋊C₄	—	2	1	no	—
417	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
418	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
419	C₃×C₄²	—	2	1	no	—
420	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
421	C₂³×C₅	—	2	1	no	—
422	C₂³×C₅	—	2	1	no	—
423	C₂³×C₅	—	2	1	no	—
424	C₂³×C₅	—	4	2	no	—
425	C₂³×C₅	—	4	2	no	—
426	C₂³×C₅	—	8	1	no	—
427	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
428	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
429	C₅×Q₈	—	2	1	no	—
430	C₅×Q₈	—	2	1	no	—
431	C₅×D₄	—	2	2	no	—
432	C₅×D₄	—	2	1	no	—
433	C₅×D₄	—	2	1	no	—
434	C₅×D₄	—	2	1	no	—
435	C₅×D₄	—	2	1	no	—
436	C₅×D₄	—	2	1	no	—
437	C₅×D₄	—	4	2	no	—
438	C₅×D₄	—	4	2	no	—
439	C₅×D₄	—	4	2	no	—
440	C₅×D₄	—	8	1	no	—
441	C₅×D₄	—	8	1	no	—
442	C₅×D₄	C₃×#41	1	2	yes	—
443	C₂×C₄×C₅	—	2	1	no	—
444	C₂×C₄×C₅	—	2	1	no	—
445	C₂×C₄×C₅	—	2	1	no	—
446	C₂×C₄×C₅	—	2	1	no	—
447	C₂×C₄×C₅	—	2	1	no	—
448	C₂×C₄×C₅	—	2	1	no	—
449	C₂×C₄×C₅	—	2	1	no	—
450	C₂×C₄×C₅	—	2	1	no	—
451	C₂×C₄×C₅	—	2	1	no	—
452	C₂×C₄×C₅	—	4	2	no	—
453	C₂×C₄×C₅	—	8	1	no	—
454	C₂×C₄×C₅	—	8	1	no	—
455	C₂×C₄×C₅	—	8	1	no	—
456	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
457	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
458	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
459	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
460	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
461	C₅×C₈	—	2	1	no	—
462	C₅×C₈	—	2	1	no	—
463	C₅×C₈	—	2	1	no	—
464	C₅×C₈	—	2	1	no	—
465	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
466	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
467	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
468	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
469	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
470	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
471	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
472	#126	—	2	1	no	—
473	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
474	#124	C₂²×C₃×C₅	1	1	yes	characteristic
475	#123	—	2	1	no	—
476	#123	—	2	1	no	—
477	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	C₂²×C₃×C₅	1	1	yes	characteristic
481	#121	C₂²×C₃×C₅	1	1	yes	characteristic
482	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
483	#120	—	2	1	no	—
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
486	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
487	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
488	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
489	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
492	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
493	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
494	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
495	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
496	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
497	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
498	#102	C₂²×C₃×C₅	1	1	yes	characteristic
499	#102	C₂²×C₃×C₅	1	1	yes	characteristic
500	#102	C₂²×C₃×C₅	1	1	yes	characteristic
501	#102	C₂²×C₃×C₅	1	1	yes	characteristic
502	#102	C₂²×C₃×C₅	1	1	yes	characteristic
503	#102	C₂²×C₃×C₅	1	1	yes	characteristic
504	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
505	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
506	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
507	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
508	C₂×C₃×C₅	—	2	2	no	—
509	C₂×C₃×C₅	—	4	1	no	—
510	C₂×C₃×C₅	—	4	2	no	—
511	C₂×C₃×C₅	—	8	1	no	—
512	C₂×C₃×C₅	—	8	1	no	—
513	C₂×C₃×C₅	#546	1	1	yes	characteristic
514	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
515	C₂×C₃×C₅	#576	1	1	yes	characteristic
516	C₂³×C₃	—	2	1	no	—
517	C₂³×C₃	—	2	1	no	—
518	C₂³×C₃	—	2	1	no	—
519	C₂³×C₃	—	4	2	no	—
520	C₂³×C₃	—	4	2	no	—
521	C₂³×C₃	—	8	1	no	—
522	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
523	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
524	C₃×Q₈	—	2	1	no	—
525	C₃×Q₈	—	2	1	no	—
526	C₃×D₄	—	2	2	no	—
527	C₃×D₄	—	2	1	no	—
528	C₃×D₄	—	2	1	no	—
529	C₃×D₄	—	2	1	no	—
530	C₃×D₄	—	2	1	no	—
531	C₃×D₄	—	2	1	no	—
532	C₃×D₄	—	4	2	no	—
533	C₃×D₄	—	4	2	no	—
534	C₃×D₄	—	4	2	no	—
535	C₃×D₄	—	8	1	no	—
536	C₃×D₄	—	8	1	no	—
537	C₃×D₄	C₅×#41	1	2	yes	—
538	C₂×C₃×C₄	—	2	1	no	—
539	C₂×C₃×C₄	—	2	1	no	—
540	C₂×C₃×C₄	—	2	1	no	—
541	C₂×C₃×C₄	—	2	1	no	—
542	C₂×C₃×C₄	—	2	1	no	—
543	C₂×C₃×C₄	—	2	1	no	—
544	C₂×C₃×C₄	—	2	1	no	—
545	C₂×C₃×C₄	—	2	1	no	—
546	C₂×C₃×C₄	—	2	1	no	—
547	C₂×C₃×C₄	—	4	2	no	—
548	C₂×C₃×C₄	—	8	1	no	—
549	C₂×C₃×C₄	—	8	1	no	—
550	C₂×C₃×C₄	—	8	1	no	—
551	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
552	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
553	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
554	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
555	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
556	C₃×C₈	—	2	1	no	—
557	C₃×C₈	—	2	1	no	—
558	C₃×C₈	—	2	1	no	—
559	C₃×C₈	—	2	1	no	—
560	C₂²×C₅	—	2	1	no	—
561	C₂²×C₅	—	2	1	no	—
562	C₂²×C₅	—	2	1	no	—
563	C₂²×C₅	—	2	1	no	—
564	C₂²×C₅	—	2	1	no	—
565	C₂²×C₅	—	2	2	no	—
566	C₂²×C₅	—	4	1	no	—
567	C₂²×C₅	—	4	1	no	—
568	C₂²×C₅	—	4	1	no	—
569	C₂²×C₅	—	4	1	no	—
570	C₂²×C₅	—	4	1	no	—
571	C₂²×C₅	—	4	1	no	—
572	C₂²×C₅	—	4	1	no	—
573	C₂²×C₅	—	4	1	no	—
574	C₂²×C₅	—	8	4	no	—
575	C₂²×C₅	C₃×#135	1	2	yes	—
576	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
577	C₄×C₅	—	2	1	no	—
578	C₄×C₅	—	2	1	no	—
579	C₄×C₅	—	2	1	no	—
580	C₄×C₅	—	2	1	no	—
581	C₄×C₅	—	4	1	no	—
582	C₄×C₅	—	4	1	no	—
583	C₄×C₅	—	4	1	no	—
584	C₄×C₅	—	4	1	no	—
585	C₄×C₅	—	4	1	no	—
586	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
587	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
588	C₂⁴	—	2	1	no	—
589	#41	—	2	2	no	—
590	#41	—	4	1	no	—
591	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	4	1	no	—
599	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
600	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
601	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
602	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
608	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
609	SD₁₆	—	4	1	no	—
610	D₈	—	2	2	no	—
611	D₈	—	4	1	no	—
612	C₂×C₈	—	4	1	no	—
613	C₂×C₈	—	4	1	no	—
614	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
615	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
616	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
617	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
623	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
624	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
625	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
626	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	1	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
637	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
638	C₄²	—	2	1	no	—
639	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
640	C₃×C₅	#3297	1	1	yes	characteristic, direct product factor, Hall
641	C₂²×C₃	—	2	1	no	—
642	C₂²×C₃	—	2	1	no	—
643	C₂²×C₃	—	2	1	no	—
644	C₂²×C₃	—	2	2	no	—
645	C₂²×C₃	—	2	1	no	—
646	C₂²×C₃	—	2	1	no	—
647	C₂²×C₃	—	4	1	no	—
648	C₂²×C₃	—	4	1	no	—
649	C₂²×C₃	—	4	1	no	—
650	C₂²×C₃	—	4	1	no	—
651	C₂²×C₃	—	4	1	no	—
652	C₂²×C₃	—	4	1	no	—
653	C₂²×C₃	—	4	1	no	—
654	C₂²×C₃	—	4	1	no	—
655	C₂²×C₃	—	8	4	no	—
656	C₂²×C₃	C₅×#135	1	2	yes	—
657	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
658	C₃×C₄	—	2	1	no	—
659	C₃×C₄	—	2	1	no	—
660	C₃×C₄	—	2	1	no	—
661	C₃×C₄	—	2	1	no	—
662	C₃×C₄	—	4	1	no	—
663	C₃×C₄	—	4	1	no	—
664	C₃×C₄	—	4	1	no	—
665	C₃×C₄	—	4	1	no	—
666	C₃×C₄	—	4	1	no	—
667	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
668	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
669	C₂×C₅	—	2	2	no	—
670	C₂×C₅	—	4	1	no	—
671	C₂×C₅	—	4	2	no	—
672	C₂×C₅	—	8	1	no	—
673	C₂×C₅	—	8	1	no	—
674	C₂×C₅	C₃×#546	1	1	yes	characteristic
675	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
676	C₂×C₅	C₃×#576	1	1	yes	characteristic
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	8	1	no	—
683	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
684	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
685	Q₈	—	2	1	no	—
686	Q₈	—	2	1	no	—
687	D₄	—	2	2	no	—
688	D₄	—	2	1	no	—
689	D₄	—	2	1	no	—
690	D₄	—	2	1	no	—
691	D₄	—	2	1	no	—
692	D₄	—	2	1	no	—
693	D₄	—	4	2	no	—
694	D₄	—	4	2	no	—
695	D₄	—	4	2	no	—
696	D₄	—	8	1	no	—
697	D₄	—	8	1	no	—
698	D₄	C₃×C₅×#41	1	2	yes	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	8	1	no	—
710	C₂×C₄	—	8	1	no	—
711	C₂×C₄	—	8	1	no	—
712	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
713	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
714	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
715	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
716	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
717	C₈	—	2	1	no	—
718	C₈	—	2	1	no	—
719	C₈	—	2	1	no	—
720	C₈	—	2	1	no	—
721	C₂×C₃	—	2	2	no	—
722	C₂×C₃	—	4	1	no	—
723	C₂×C₃	—	4	2	no	—
724	C₂×C₃	—	8	1	no	—
725	C₂×C₃	—	8	1	no	—
726	C₂×C₃	C₅×#546	1	1	yes	characteristic
727	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
728	C₂×C₃	C₅×#576	1	1	yes	characteristic
729	C₅	C₃×#3297	1	1	yes	characteristic, direct product factor, Sylow
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	8	4	no	—
745	C₂²	C₃×C₅×#135	1	2	yes	—
746	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	2	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
757	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
758	C₃	C₅×#3297	1	1	yes	characteristic, direct product factor, Sylow
759	C₂	—	2	2	no	—
760	C₂	—	4	1	no	—
761	C₂	—	4	2	no	—
762	C₂	—	8	1	no	—
763	C₂	—	8	1	no	—
764	C₂	C₃×C₅×#546	1	1	yes	characteristic
765	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
766	C₂	C₃×C₅×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#553	C₂	semidirect
2. C₃×C₅×#546	C₂	semidirect
3. C₃×C₅×#488	C₂	semidirect
4. C₃×C₅×#484	C₂	semidirect
5. C₃×C₅×#482	C₂	semidirect
6. C₃×C₅×#478	C₂	semidirect
7. C₃×C₅×#466	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#463	C₂	semidirect
10. C₃×C₅×#449	C₂	semidirect
11. C₃×C₅×#447	C₂	semidirect
12. C₃×C₄×C₅×D₈	C₂	semidirect
13. C₃×C₅×C₈×D₄	C₂	semidirect
14. C₃×C₅×#416	C₂	semidirect
15. C₂×C₃×C₅×#102	C₂	semidirect
16. C₅×#3297	C₃	direct (N × H)
19. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
23. C₂²×C₃×C₅×C₈	C₂²	semidirect
25. C₃×C₅×#125	C₂²	semidirect
34. C₃×C₅×#121	C₂²	semidirect
39. C₃×C₄×C₅×D₄	C₂²	semidirect
40. C₃×C₅×#117	C₂²	semidirect
43. C₃×C₅×#107	C₂²	semidirect
44. C₃×C₅×#107	C₂²	semidirect
45. C₃×C₅×#106	C₂²	semidirect
46. C₃×C₅×C₄⋊C₈	C₂²	semidirect
47. C₃×C₅×#103	C₂²	semidirect
48. C₃×C₅×#103	C₂²	semidirect
49. C₃×C₅×#103	C₂²	semidirect
56. C₃×C₅×#102	C₂²	semidirect
58. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
59. C₃×C₄×C₅×C₈	C₂²	semidirect
60. C₃×#3297	C₅	direct (N × H)
61. C₅×#553	C₂×C₃	semidirect
62. C₅×#546	C₂×C₃	semidirect
63. C₅×#488	C₂×C₃	semidirect
64. C₅×#484	C₂×C₃	semidirect
65. C₅×#482	C₂×C₃	semidirect
66. C₅×#478	C₂×C₃	semidirect
67. C₅×#466	C₂×C₃	semidirect
68. C₅×#465	C₂×C₃	semidirect
69. C₅×#463	C₂×C₃	semidirect
70. C₅×#449	C₂×C₃	semidirect
71. C₅×#447	C₂×C₃	semidirect
72. C₄×C₅×D₈	C₂×C₃	semidirect
73. C₅×C₈×D₄	C₂×C₃	semidirect
74. C₅×#416	C₂×C₃	semidirect
75. C₂×C₅×#102	C₂×C₃	semidirect
128. C₃×#553	C₂×C₅	semidirect
129. C₃×#546	C₂×C₅	semidirect
130. C₃×#488	C₂×C₅	semidirect
131. C₃×#484	C₂×C₅	semidirect
132. C₃×#482	C₂×C₅	semidirect
133. C₃×#478	C₂×C₅	semidirect
134. C₃×#466	C₂×C₅	semidirect
135. C₃×#465	C₂×C₅	semidirect
136. C₃×#463	C₂×C₅	semidirect
137. C₃×#449	C₂×C₅	semidirect
138. C₃×#447	C₂×C₅	semidirect
139. C₃×C₄×D₈	C₂×C₅	semidirect
140. C₃×C₈×D₄	C₂×C₅	semidirect
141. C₃×#416	C₂×C₅	semidirect
142. C₂×C₃×#102	C₂×C₅	semidirect
145. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
149. C₂²×C₅×C₈	C₂²×C₃	semidirect
151. C₅×#125	C₂²×C₃	semidirect
160. C₅×#121	C₂²×C₃	semidirect
165. C₄×C₅×D₄	C₂²×C₃	semidirect
166. C₅×#117	C₂²×C₃	semidirect
169. C₅×#107	C₂²×C₃	semidirect
170. C₅×#107	C₂²×C₃	semidirect
171. C₅×#106	C₂²×C₃	semidirect
172. C₅×C₄⋊C₈	C₂²×C₃	semidirect
173. C₅×#103	C₂²×C₃	semidirect
174. C₅×#103	C₂²×C₃	semidirect
175. C₅×#103	C₂²×C₃	semidirect
182. C₅×#102	C₂²×C₃	semidirect
184. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
185. C₄×C₅×C₈	C₂²×C₃	semidirect
186. #3297	C₃×C₅	direct (N × H)
233. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
237. C₂²×C₃×C₈	C₂²×C₅	semidirect
239. C₃×#125	C₂²×C₅	semidirect
248. C₃×#121	C₂²×C₅	semidirect
253. C₃×C₄×D₄	C₂²×C₅	semidirect
254. C₃×#117	C₂²×C₅	semidirect
257. C₃×#107	C₂²×C₅	semidirect
258. C₃×#107	C₂²×C₅	semidirect
259. C₃×#106	C₂²×C₅	semidirect
260. C₃×C₄⋊C₈	C₂²×C₅	semidirect
261. C₃×#103	C₂²×C₅	semidirect
262. C₃×#103	C₂²×C₅	semidirect
263. C₃×#103	C₂²×C₅	semidirect
270. C₃×#102	C₂²×C₅	semidirect
272. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
273. C₃×C₄×C₈	C₂²×C₅	semidirect
326. #553	C₂×C₃×C₅	semidirect
327. #546	C₂×C₃×C₅	semidirect
328. #488	C₂×C₃×C₅	semidirect
329. #484	C₂×C₃×C₅	semidirect
330. #482	C₂×C₃×C₅	semidirect
331. #478	C₂×C₃×C₅	semidirect
332. #466	C₂×C₃×C₅	semidirect
333. #465	C₂×C₃×C₅	semidirect
334. #463	C₂×C₃×C₅	semidirect
335. #449	C₂×C₃×C₅	semidirect
336. #447	C₂×C₃×C₅	semidirect
337. C₄×D₈	C₂×C₃×C₅	semidirect
338. C₈×D₄	C₂×C₃×C₅	semidirect
339. #416	C₂×C₃×C₅	semidirect
340. C₂×#102	C₂×C₃×C₅	semidirect
467. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
471. C₂²×C₈	C₂²×C₃×C₅	semidirect
473. #125	C₂²×C₃×C₅	semidirect
482. #121	C₂²×C₃×C₅	semidirect
487. C₄×D₄	C₂²×C₃×C₅	semidirect
488. #117	C₂²×C₃×C₅	semidirect
491. #107	C₂²×C₃×C₅	semidirect
492. #107	C₂²×C₃×C₅	semidirect
493. #106	C₂²×C₃×C₅	semidirect
494. C₄⋊C₈	C₂²×C₃×C₅	semidirect
495. #103	C₂²×C₃×C₅	semidirect
496. #103	C₂²×C₃×C₅	semidirect
497. #103	C₂²×C₃×C₅	semidirect
504. #102	C₂²×C₃×C₅	semidirect
506. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
507. C₄×C₈	C₂²×C₃×C₅	semidirect
640. C₃×C₅	#3297	direct (N × H)
729. C₅	C₃×#3297	direct (N × H)
758. C₃	C₅×#3297	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#553	2
C₃×C₅×#546	2
C₃×C₅×#488	2
C₃×C₅×#484	2
C₃×C₅×#482	2
C₃×C₅×#478	2
C₃×C₅×#466	2
C₃×C₅×#465	2
C₃×C₅×#463	2
C₃×C₅×#449	2
C₃×C₅×#447	2
C₃×C₄×C₅×D₈	2
C₃×C₅×C₈×D₄	2
C₃×C₅×#416	2
C₂×C₃×C₅×#102	2
C₅×#3297	3
C₃×#3297	5

Subgroups — C3×C5×#3297 #14276331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3297 #14276331