Subgroups — C₃×C₅×#3198 #14276232

Order 1920.

844 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3198	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#127	—	2	1	no	—
27	C₃×C₅×#124	—	2	1	no	—
28	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
29	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#121	—	2	1	no	—
32	C₃×C₅×#121	—	2	1	no	—
33	C₃×C₅×#121	—	2	1	no	—
34	C₃×C₅×#121	C₂²	1	1	yes	characteristic
35	C₃×C₅×#121	C₂²	1	1	yes	characteristic
36	C₃×C₅×#121	C₂²	1	1	yes	characteristic
37	C₃×C₅×#121	C₂²	1	1	yes	characteristic
38	C₃×C₅×#121	C₂²	1	1	yes	characteristic
39	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#120	—	2	1	no	—
41	C₃×C₅×#120	—	2	1	no	—
42	C₃×C₅×#117	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×#106	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, complemented
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
56	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3198	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#537	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#485	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#482	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#481	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#480	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#469	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#468	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#447	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂⁴×C₃×C₅	—	2	1	no	—
77	C₃×C₅×#41	—	4	1	no	—
78	C₃×C₅×#41	—	4	1	no	—
79	C₃×C₅×#41	—	4	1	no	—
80	C₃×C₅×#41	—	4	1	no	—
81	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
82	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
87	C₂×C₃×C₅×D₄	—	2	1	no	—
88	C₂×C₃×C₅×D₄	—	2	1	no	—
89	C₂×C₃×C₅×D₄	—	2	1	no	—
90	C₂×C₃×C₅×D₄	—	2	1	no	—
91	C₂×C₃×C₅×D₄	—	4	1	no	—
92	C₂×C₃×C₅×D₄	—	4	1	no	—
93	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
94	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
95	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
96	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	—	2	1	no	—
100	C₂²×C₃×C₄×C₅	—	2	1	no	—
101	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
103	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
104	C₃×C₅×SD₁₆	—	4	1	no	—
105	C₃×C₅×SD₁₆	—	4	1	no	—
106	C₃×C₅×D₈	—	4	1	no	—
107	C₃×C₅×D₈	—	4	1	no	—
108	C₃×C₅×M₁₆	—	4	1	no	—
109	C₂×C₃×C₅×C₈	—	4	1	no	—
110	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
111	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
112	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	—	2	1	no	—
115	C₃×C₅×C₄⋊C₄	—	2	1	no	—
116	C₃×C₅×C₄⋊C₄	—	2	1	no	—
117	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
125	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
126	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
127	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
128	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
129	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
130	C₃×C₄²×C₅	—	2	1	no	—
131	C₃×#537	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#485	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#482	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#481	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#480	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#469	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#468	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#447	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
148	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
154	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₅×#127	—	2	1	no	—
156	C₅×#124	—	2	1	no	—
157	C₅×C₂²⋊Q₈	—	2	1	no	—
158	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
160	C₅×#121	—	2	1	no	—
161	C₅×#121	—	2	1	no	—
162	C₅×#121	—	2	1	no	—
163	C₅×#121	C₂²×C₃	1	1	yes	characteristic
164	C₅×#121	C₂²×C₃	1	1	yes	characteristic
165	C₅×#121	C₂²×C₃	1	1	yes	characteristic
166	C₅×#121	C₂²×C₃	1	1	yes	characteristic
167	C₅×#121	C₂²×C₃	1	1	yes	characteristic
168	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₅×#120	—	2	1	no	—
170	C₅×#120	—	2	1	no	—
171	C₅×#117	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
178	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
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
183	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
186	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
187	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
189	#3198	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	4	2	no	—
194	C₂³×C₃×C₅	—	8	1	no	—
195	C₂³×C₃×C₅	—	8	1	no	—
196	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
198	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
199	C₃×C₅×Q₈	—	2	1	no	—
200	C₃×C₅×Q₈	—	2	1	no	—
201	C₃×C₅×Q₈	—	4	1	no	—
202	C₃×C₅×D₄	—	2	1	no	—
203	C₃×C₅×D₄	—	2	1	no	—
204	C₃×C₅×D₄	—	2	1	no	—
205	C₃×C₅×D₄	—	2	1	no	—
206	C₃×C₅×D₄	—	2	1	no	—
207	C₃×C₅×D₄	—	2	1	no	—
208	C₃×C₅×D₄	—	4	1	no	—
209	C₃×C₅×D₄	—	4	1	no	—
210	C₃×C₅×D₄	—	4	1	no	—
211	C₃×C₅×D₄	—	4	2	no	—
212	C₃×C₅×D₄	—	4	2	no	—
213	C₃×C₅×D₄	—	8	1	no	—
214	C₃×C₅×D₄	—	8	1	no	—
215	C₃×C₅×D₄	—	8	1	no	—
216	C₃×C₅×D₄	—	8	1	no	—
217	C₃×C₅×D₄	—	8	1	no	—
218	C₃×C₅×D₄	—	8	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	2	no	—
231	C₂×C₃×C₄×C₅	—	8	1	no	—
232	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
233	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
235	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
236	C₃×C₅×C₈	—	2	1	no	—
237	C₃×C₅×C₈	—	2	1	no	—
238	C₃×C₅×C₈	—	2	1	no	—
239	C₃×C₅×C₈	—	2	1	no	—
240	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
248	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₃×#127	—	2	1	no	—
250	C₃×#124	—	2	1	no	—
251	C₃×C₂²⋊Q₈	—	2	1	no	—
252	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
253	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₃×#121	—	2	1	no	—
255	C₃×#121	—	2	1	no	—
256	C₃×#121	—	2	1	no	—
257	C₃×#121	C₂²×C₅	1	1	yes	characteristic
258	C₃×#121	C₂²×C₅	1	1	yes	characteristic
259	C₃×#121	C₂²×C₅	1	1	yes	characteristic
260	C₃×#121	C₂²×C₅	1	1	yes	characteristic
261	C₃×#121	C₂²×C₅	1	1	yes	characteristic
262	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×#120	—	2	1	no	—
264	C₃×#120	—	2	1	no	—
265	C₃×#117	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₃×#102	C₂²×C₅	1	1	yes	characteristic
274	C₃×#102	C₂²×C₅	1	1	yes	characteristic
275	C₃×#102	C₂²×C₅	1	1	yes	characteristic
276	C₃×#102	C₂²×C₅	1	1	yes	characteristic
277	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
280	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
281	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
283	C₂⁴×C₅	—	2	1	no	—
284	C₅×#41	—	4	1	no	—
285	C₅×#41	—	4	1	no	—
286	C₅×#41	—	4	1	no	—
287	C₅×#41	—	4	1	no	—
288	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
289	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₅×D₄	—	2	1	no	—
291	C₂×C₅×D₄	—	2	1	no	—
292	C₂×C₅×D₄	—	2	1	no	—
293	C₂×C₅×D₄	—	2	1	no	—
294	C₂×C₅×D₄	—	2	1	no	—
295	C₂×C₅×D₄	—	2	1	no	—
296	C₂×C₅×D₄	—	2	1	no	—
297	C₂×C₅×D₄	—	2	1	no	—
298	C₂×C₅×D₄	—	4	1	no	—
299	C₂×C₅×D₄	—	4	1	no	—
300	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
301	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
302	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
303	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
304	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
306	C₂²×C₄×C₅	—	2	1	no	—
307	C₂²×C₄×C₅	—	2	1	no	—
308	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
309	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
310	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
311	C₅×SD₁₆	—	4	1	no	—
312	C₅×SD₁₆	—	4	1	no	—
313	C₅×D₈	—	4	1	no	—
314	C₅×D₈	—	4	1	no	—
315	C₅×M₁₆	—	4	1	no	—
316	C₂×C₅×C₈	—	4	1	no	—
317	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
318	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
319	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
320	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
321	C₅×C₄⋊C₄	—	2	1	no	—
322	C₅×C₄⋊C₄	—	2	1	no	—
323	C₅×C₄⋊C₄	—	2	1	no	—
324	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
325	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
326	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
327	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
328	C₅×C₂²⋊C₄	—	2	1	no	—
329	C₅×C₂²⋊C₄	—	2	1	no	—
330	C₅×C₂²⋊C₄	—	2	1	no	—
331	C₅×C₂²⋊C₄	—	2	1	no	—
332	C₅×C₂²⋊C₄	—	2	1	no	—
333	C₅×C₂²⋊C₄	—	2	1	no	—
334	C₅×C₂²⋊C₄	—	2	1	no	—
335	C₅×C₂²⋊C₄	—	2	1	no	—
336	C₅×C₂²⋊C₄	—	2	1	no	—
337	C₄²×C₅	—	2	1	no	—
338	#537	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	#485	C₂×C₃×C₅	1	1	yes	characteristic, complemented
341	#482	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	#481	C₂×C₃×C₅	1	1	yes	characteristic, complemented
343	#480	C₂×C₃×C₅	1	1	yes	characteristic, complemented
344	#469	C₂×C₃×C₅	1	1	yes	characteristic, complemented
345	#468	C₂×C₃×C₅	1	1	yes	characteristic, complemented
346	#466	C₂×C₃×C₅	1	1	yes	characteristic, complemented
347	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
348	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
349	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
350	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
351	#447	C₂×C₃×C₅	1	1	yes	characteristic, complemented
352	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
353	C₂²×C₃×C₅	—	2	1	no	—
354	C₂²×C₃×C₅	—	2	1	no	—
355	C₂²×C₃×C₅	—	2	1	no	—
356	C₂²×C₃×C₅	—	2	1	no	—
357	C₂²×C₃×C₅	—	2	1	no	—
358	C₂²×C₃×C₅	—	2	1	no	—
359	C₂²×C₃×C₅	—	2	1	no	—
360	C₂²×C₃×C₅	—	2	1	no	—
361	C₂²×C₃×C₅	—	2	1	no	—
362	C₂²×C₃×C₅	—	4	1	no	—
363	C₂²×C₃×C₅	—	4	1	no	—
364	C₂²×C₃×C₅	—	4	1	no	—
365	C₂²×C₃×C₅	—	4	1	no	—
366	C₂²×C₃×C₅	—	4	1	no	—
367	C₂²×C₃×C₅	—	4	1	no	—
368	C₂²×C₃×C₅	—	4	1	no	—
369	C₂²×C₃×C₅	—	4	1	no	—
370	C₂²×C₃×C₅	—	4	1	no	—
371	C₂²×C₃×C₅	—	8	4	no	—
372	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
373	C₃×C₄×C₅	—	2	1	no	—
374	C₃×C₄×C₅	—	2	1	no	—
375	C₃×C₄×C₅	—	2	1	no	—
376	C₃×C₄×C₅	—	4	1	no	—
377	C₃×C₄×C₅	—	4	1	no	—
378	C₃×C₄×C₅	—	4	1	no	—
379	C₃×C₄×C₅	—	4	1	no	—
380	C₃×C₄×C₅	—	4	1	no	—
381	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
382	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
383	C₂⁴×C₃	—	2	1	no	—
384	C₃×#41	—	4	1	no	—
385	C₃×#41	—	4	1	no	—
386	C₃×#41	—	4	1	no	—
387	C₃×#41	—	4	1	no	—
388	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
389	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₃×D₄	—	2	1	no	—
391	C₂×C₃×D₄	—	2	1	no	—
392	C₂×C₃×D₄	—	2	1	no	—
393	C₂×C₃×D₄	—	2	1	no	—
394	C₂×C₃×D₄	—	2	1	no	—
395	C₂×C₃×D₄	—	2	1	no	—
396	C₂×C₃×D₄	—	2	1	no	—
397	C₂×C₃×D₄	—	2	1	no	—
398	C₂×C₃×D₄	—	4	1	no	—
399	C₂×C₃×D₄	—	4	1	no	—
400	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
401	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
402	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
403	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
404	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
406	C₂²×C₃×C₄	—	2	1	no	—
407	C₂²×C₃×C₄	—	2	1	no	—
408	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
409	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
410	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
411	C₃×SD₁₆	—	4	1	no	—
412	C₃×SD₁₆	—	4	1	no	—
413	C₃×D₈	—	4	1	no	—
414	C₃×D₈	—	4	1	no	—
415	C₃×M₁₆	—	4	1	no	—
416	C₂×C₃×C₈	—	4	1	no	—
417	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
419	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
421	C₃×C₄⋊C₄	—	2	1	no	—
422	C₃×C₄⋊C₄	—	2	1	no	—
423	C₃×C₄⋊C₄	—	2	1	no	—
424	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
425	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
426	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
427	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
428	C₃×C₂²⋊C₄	—	2	1	no	—
429	C₃×C₂²⋊C₄	—	2	1	no	—
430	C₃×C₂²⋊C₄	—	2	1	no	—
431	C₃×C₂²⋊C₄	—	2	1	no	—
432	C₃×C₂²⋊C₄	—	2	1	no	—
433	C₃×C₂²⋊C₄	—	2	1	no	—
434	C₃×C₂²⋊C₄	—	2	1	no	—
435	C₃×C₂²⋊C₄	—	2	1	no	—
436	C₃×C₂²⋊C₄	—	2	1	no	—
437	C₃×C₄²	—	2	1	no	—
438	C₂³×C₅	—	2	1	no	—
439	C₂³×C₅	—	2	1	no	—
440	C₂³×C₅	—	2	1	no	—
441	C₂³×C₅	—	4	2	no	—
442	C₂³×C₅	—	8	1	no	—
443	C₂³×C₅	—	8	1	no	—
444	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
445	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
446	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
447	C₅×Q₈	—	2	1	no	—
448	C₅×Q₈	—	2	1	no	—
449	C₅×Q₈	—	4	1	no	—
450	C₅×D₄	—	2	1	no	—
451	C₅×D₄	—	2	1	no	—
452	C₅×D₄	—	2	1	no	—
453	C₅×D₄	—	2	1	no	—
454	C₅×D₄	—	2	1	no	—
455	C₅×D₄	—	2	1	no	—
456	C₅×D₄	—	4	1	no	—
457	C₅×D₄	—	4	1	no	—
458	C₅×D₄	—	4	1	no	—
459	C₅×D₄	—	4	2	no	—
460	C₅×D₄	—	4	2	no	—
461	C₅×D₄	—	8	1	no	—
462	C₅×D₄	—	8	1	no	—
463	C₅×D₄	—	8	1	no	—
464	C₅×D₄	—	8	1	no	—
465	C₅×D₄	—	8	1	no	—
466	C₅×D₄	—	8	1	no	—
467	C₂×C₄×C₅	—	2	1	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	2	1	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	2	1	no	—
473	C₂×C₄×C₅	—	2	1	no	—
474	C₂×C₄×C₅	—	2	1	no	—
475	C₂×C₄×C₅	—	2	1	no	—
476	C₂×C₄×C₅	—	2	1	no	—
477	C₂×C₄×C₅	—	2	1	no	—
478	C₂×C₄×C₅	—	4	2	no	—
479	C₂×C₄×C₅	—	8	1	no	—
480	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
481	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
482	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
483	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
484	C₅×C₈	—	2	1	no	—
485	C₅×C₈	—	2	1	no	—
486	C₅×C₈	—	2	1	no	—
487	C₅×C₈	—	2	1	no	—
488	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
489	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
490	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
491	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
492	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
493	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
494	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
495	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
496	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
497	#127	—	2	1	no	—
498	#124	—	2	1	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
501	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	—	2	1	no	—
505	#121	C₂²×C₃×C₅	1	1	yes	characteristic
506	#121	C₂²×C₃×C₅	1	1	yes	characteristic
507	#121	C₂²×C₃×C₅	1	1	yes	characteristic
508	#121	C₂²×C₃×C₅	1	1	yes	characteristic
509	#121	C₂²×C₃×C₅	1	1	yes	characteristic
510	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
511	#120	—	2	1	no	—
512	#120	—	2	1	no	—
513	#117	C₂²×C₃×C₅	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
515	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
516	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
517	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
518	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
519	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
520	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
521	#102	C₂²×C₃×C₅	1	1	yes	characteristic
522	#102	C₂²×C₃×C₅	1	1	yes	characteristic
523	#102	C₂²×C₃×C₅	1	1	yes	characteristic
524	#102	C₂²×C₃×C₅	1	1	yes	characteristic
525	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
526	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
527	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
528	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
529	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
530	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
531	C₂×C₃×C₅	—	4	1	no	—
532	C₂×C₃×C₅	—	4	1	no	—
533	C₂×C₃×C₅	—	4	1	no	—
534	C₂×C₃×C₅	—	8	1	no	—
535	C₂×C₃×C₅	—	8	1	no	—
536	C₂×C₃×C₅	—	8	1	no	—
537	C₂×C₃×C₅	#534	1	1	yes	characteristic
538	C₂×C₃×C₅	#576	1	1	yes	characteristic
539	C₂×C₃×C₅	#577	1	1	yes	characteristic
540	C₂³×C₃	—	2	1	no	—
541	C₂³×C₃	—	2	1	no	—
542	C₂³×C₃	—	2	1	no	—
543	C₂³×C₃	—	4	2	no	—
544	C₂³×C₃	—	8	1	no	—
545	C₂³×C₃	—	8	1	no	—
546	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
547	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
548	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
549	C₃×Q₈	—	2	1	no	—
550	C₃×Q₈	—	2	1	no	—
551	C₃×Q₈	—	4	1	no	—
552	C₃×D₄	—	2	1	no	—
553	C₃×D₄	—	2	1	no	—
554	C₃×D₄	—	2	1	no	—
555	C₃×D₄	—	2	1	no	—
556	C₃×D₄	—	2	1	no	—
557	C₃×D₄	—	2	1	no	—
558	C₃×D₄	—	4	1	no	—
559	C₃×D₄	—	4	1	no	—
560	C₃×D₄	—	4	1	no	—
561	C₃×D₄	—	4	2	no	—
562	C₃×D₄	—	4	2	no	—
563	C₃×D₄	—	8	1	no	—
564	C₃×D₄	—	8	1	no	—
565	C₃×D₄	—	8	1	no	—
566	C₃×D₄	—	8	1	no	—
567	C₃×D₄	—	8	1	no	—
568	C₃×D₄	—	8	1	no	—
569	C₂×C₃×C₄	—	2	1	no	—
570	C₂×C₃×C₄	—	2	1	no	—
571	C₂×C₃×C₄	—	2	1	no	—
572	C₂×C₃×C₄	—	2	1	no	—
573	C₂×C₃×C₄	—	2	1	no	—
574	C₂×C₃×C₄	—	2	1	no	—
575	C₂×C₃×C₄	—	2	1	no	—
576	C₂×C₃×C₄	—	2	1	no	—
577	C₂×C₃×C₄	—	2	1	no	—
578	C₂×C₃×C₄	—	2	1	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	4	2	no	—
581	C₂×C₃×C₄	—	8	1	no	—
582	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
583	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
584	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
585	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
586	C₃×C₈	—	2	1	no	—
587	C₃×C₈	—	2	1	no	—
588	C₃×C₈	—	2	1	no	—
589	C₃×C₈	—	2	1	no	—
590	C₂²×C₅	—	2	1	no	—
591	C₂²×C₅	—	2	1	no	—
592	C₂²×C₅	—	2	1	no	—
593	C₂²×C₅	—	2	1	no	—
594	C₂²×C₅	—	2	1	no	—
595	C₂²×C₅	—	2	1	no	—
596	C₂²×C₅	—	2	1	no	—
597	C₂²×C₅	—	2	1	no	—
598	C₂²×C₅	—	2	1	no	—
599	C₂²×C₅	—	4	1	no	—
600	C₂²×C₅	—	4	1	no	—
601	C₂²×C₅	—	4	1	no	—
602	C₂²×C₅	—	4	1	no	—
603	C₂²×C₅	—	4	1	no	—
604	C₂²×C₅	—	4	1	no	—
605	C₂²×C₅	—	4	1	no	—
606	C₂²×C₅	—	4	1	no	—
607	C₂²×C₅	—	4	1	no	—
608	C₂²×C₅	—	8	4	no	—
609	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
610	C₄×C₅	—	2	1	no	—
611	C₄×C₅	—	2	1	no	—
612	C₄×C₅	—	2	1	no	—
613	C₄×C₅	—	4	1	no	—
614	C₄×C₅	—	4	1	no	—
615	C₄×C₅	—	4	1	no	—
616	C₄×C₅	—	4	1	no	—
617	C₄×C₅	—	4	1	no	—
618	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
619	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
620	C₂⁴	—	2	1	no	—
621	#41	—	4	1	no	—
622	#41	—	4	1	no	—
623	#41	—	4	1	no	—
624	#41	—	4	1	no	—
625	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
626	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂×D₄	—	4	1	no	—
637	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
638	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
639	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
640	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
641	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
642	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
646	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
647	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
648	SD₁₆	—	4	1	no	—
649	SD₁₆	—	4	1	no	—
650	D₈	—	4	1	no	—
651	D₈	—	4	1	no	—
652	M₁₆	—	4	1	no	—
653	C₂×C₈	—	4	1	no	—
654	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
655	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
656	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
657	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
662	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
663	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
664	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
665	C₂²⋊C₄	—	2	1	no	—
666	C₂²⋊C₄	—	2	1	no	—
667	C₂²⋊C₄	—	2	1	no	—
668	C₂²⋊C₄	—	2	1	no	—
669	C₂²⋊C₄	—	2	1	no	—
670	C₂²⋊C₄	—	2	1	no	—
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	1	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₄²	—	2	1	no	—
675	C₃×C₅	#3198	1	1	yes	characteristic, direct product factor, Hall
676	C₂²×C₃	—	2	1	no	—
677	C₂²×C₃	—	2	1	no	—
678	C₂²×C₃	—	2	1	no	—
679	C₂²×C₃	—	2	1	no	—
680	C₂²×C₃	—	2	1	no	—
681	C₂²×C₃	—	2	1	no	—
682	C₂²×C₃	—	2	1	no	—
683	C₂²×C₃	—	2	1	no	—
684	C₂²×C₃	—	2	1	no	—
685	C₂²×C₃	—	4	1	no	—
686	C₂²×C₃	—	4	1	no	—
687	C₂²×C₃	—	4	1	no	—
688	C₂²×C₃	—	4	1	no	—
689	C₂²×C₃	—	4	1	no	—
690	C₂²×C₃	—	4	1	no	—
691	C₂²×C₃	—	4	1	no	—
692	C₂²×C₃	—	4	1	no	—
693	C₂²×C₃	—	4	1	no	—
694	C₂²×C₃	—	8	4	no	—
695	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
696	C₃×C₄	—	2	1	no	—
697	C₃×C₄	—	2	1	no	—
698	C₃×C₄	—	2	1	no	—
699	C₃×C₄	—	4	1	no	—
700	C₃×C₄	—	4	1	no	—
701	C₃×C₄	—	4	1	no	—
702	C₃×C₄	—	4	1	no	—
703	C₃×C₄	—	4	1	no	—
704	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
705	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂×C₅	—	4	1	no	—
707	C₂×C₅	—	4	1	no	—
708	C₂×C₅	—	4	1	no	—
709	C₂×C₅	—	8	1	no	—
710	C₂×C₅	—	8	1	no	—
711	C₂×C₅	—	8	1	no	—
712	C₂×C₅	C₃×#534	1	1	yes	characteristic
713	C₂×C₅	C₃×#576	1	1	yes	characteristic
714	C₂×C₅	C₃×#577	1	1	yes	characteristic
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	4	2	no	—
719	C₂³	—	8	1	no	—
720	C₂³	—	8	1	no	—
721	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
722	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
723	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
724	Q₈	—	2	1	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	4	1	no	—
727	D₄	—	2	1	no	—
728	D₄	—	2	1	no	—
729	D₄	—	2	1	no	—
730	D₄	—	2	1	no	—
731	D₄	—	2	1	no	—
732	D₄	—	2	1	no	—
733	D₄	—	4	1	no	—
734	D₄	—	4	1	no	—
735	D₄	—	4	1	no	—
736	D₄	—	4	2	no	—
737	D₄	—	4	2	no	—
738	D₄	—	8	1	no	—
739	D₄	—	8	1	no	—
740	D₄	—	8	1	no	—
741	D₄	—	8	1	no	—
742	D₄	—	8	1	no	—
743	D₄	—	8	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	8	1	no	—
757	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
758	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
759	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
760	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
761	C₈	—	2	1	no	—
762	C₈	—	2	1	no	—
763	C₈	—	2	1	no	—
764	C₈	—	2	1	no	—
765	C₂×C₃	—	4	1	no	—
766	C₂×C₃	—	4	1	no	—
767	C₂×C₃	—	4	1	no	—
768	C₂×C₃	—	8	1	no	—
769	C₂×C₃	—	8	1	no	—
770	C₂×C₃	—	8	1	no	—
771	C₂×C₃	C₅×#534	1	1	yes	characteristic
772	C₂×C₃	C₅×#576	1	1	yes	characteristic
773	C₂×C₃	C₅×#577	1	1	yes	characteristic
774	C₅	C₃×#3198	1	1	yes	characteristic, direct product factor, Sylow
775	C₂²	—	2	1	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	1	no	—
779	C₂²	—	2	1	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	2	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	8	4	no	—
794	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	2	1	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	1	no	—
803	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
804	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
805	C₃	C₅×#3198	1	1	yes	characteristic, direct product factor, Sylow
806	C₂	—	4	1	no	—
807	C₂	—	4	1	no	—
808	C₂	—	4	1	no	—
809	C₂	—	8	1	no	—
810	C₂	—	8	1	no	—
811	C₂	—	8	1	no	—
812	C₂	C₃×C₅×#534	1	1	yes	characteristic
813	C₂	C₃×C₅×#576	1	1	yes	characteristic
814	C₂	C₃×C₅×#577	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 ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#537	C₂	semidirect
2. C₃×C₅×#535	C₂	semidirect
3. C₃×C₅×#485	C₂	semidirect
4. C₃×C₅×#482	C₂	semidirect
5. C₃×C₅×#481	C₂	semidirect
6. C₃×C₅×#480	C₂	semidirect
7. C₃×C₅×#469	C₂	semidirect
8. C₃×C₅×#468	C₂	semidirect
9. C₃×C₅×#466	C₂	semidirect
10. C₃×C₅×#465	C₂	semidirect
11. C₃×C₅×#450	C₂	semidirect
12. C₃×C₅×#449	C₂	semidirect
13. C₃×C₅×#449	C₂	semidirect
14. C₃×C₅×#447	C₂	semidirect
15. C₃×C₅×#408	C₂	semidirect
16. C₅×#3198	C₃	direct (N × H)
18. C₂×C₃×C₅×#41	C₂²	semidirect
24. C₂×C₃×C₅×M₁₆	C₂²	semidirect
25. C₂²×C₃×C₅×C₈	C₂²	semidirect
30. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
39. C₃×C₅×#121	C₂²	semidirect
43. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
44. C₃×C₅×#107	C₂²	semidirect
45. C₃×C₅×#107	C₂²	semidirect
46. C₃×C₅×#106	C₂²	semidirect
47. C₃×C₅×#106	C₂²	semidirect
48. C₃×C₅×#103	C₂²	semidirect
49. C₃×C₅×#103	C₂²	semidirect
54. C₃×C₅×#102	C₂²	semidirect
55. C₃×C₅×#102	C₂²	semidirect
58. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
59. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
60. C₃×#3198	C₅	direct (N × H)
61. C₅×#537	C₂×C₃	semidirect
62. C₅×#535	C₂×C₃	semidirect
63. C₅×#485	C₂×C₃	semidirect
64. C₅×#482	C₂×C₃	semidirect
65. C₅×#481	C₂×C₃	semidirect
66. C₅×#480	C₂×C₃	semidirect
67. C₅×#469	C₂×C₃	semidirect
68. C₅×#468	C₂×C₃	semidirect
69. C₅×#466	C₂×C₃	semidirect
70. C₅×#465	C₂×C₃	semidirect
71. C₅×#450	C₂×C₃	semidirect
72. C₅×#449	C₂×C₃	semidirect
73. C₅×#449	C₂×C₃	semidirect
74. C₅×#447	C₂×C₃	semidirect
75. C₅×#408	C₂×C₃	semidirect
131. C₃×#537	C₂×C₅	semidirect
132. C₃×#535	C₂×C₅	semidirect
133. C₃×#485	C₂×C₅	semidirect
134. C₃×#482	C₂×C₅	semidirect
135. C₃×#481	C₂×C₅	semidirect
136. C₃×#480	C₂×C₅	semidirect
137. C₃×#469	C₂×C₅	semidirect
138. C₃×#468	C₂×C₅	semidirect
139. C₃×#466	C₂×C₅	semidirect
140. C₃×#465	C₂×C₅	semidirect
141. C₃×#450	C₂×C₅	semidirect
142. C₃×#449	C₂×C₅	semidirect
143. C₃×#449	C₂×C₅	semidirect
144. C₃×#447	C₂×C₅	semidirect
145. C₃×#408	C₂×C₅	semidirect
147. C₂×C₅×#41	C₂²×C₃	semidirect
153. C₂×C₅×M₁₆	C₂²×C₃	semidirect
154. C₂²×C₅×C₈	C₂²×C₃	semidirect
159. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
168. C₅×#121	C₂²×C₃	semidirect
172. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
173. C₅×#107	C₂²×C₃	semidirect
174. C₅×#107	C₂²×C₃	semidirect
175. C₅×#106	C₂²×C₃	semidirect
176. C₅×#106	C₂²×C₃	semidirect
177. C₅×#103	C₂²×C₃	semidirect
178. C₅×#103	C₂²×C₃	semidirect
183. C₅×#102	C₂²×C₃	semidirect
184. C₅×#102	C₂²×C₃	semidirect
187. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
188. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
189. #3198	C₃×C₅	direct (N × H)
241. C₂×C₃×#41	C₂²×C₅	semidirect
247. C₂×C₃×M₁₆	C₂²×C₅	semidirect
248. C₂²×C₃×C₈	C₂²×C₅	semidirect
253. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
262. C₃×#121	C₂²×C₅	semidirect
266. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
267. C₃×#107	C₂²×C₅	semidirect
268. C₃×#107	C₂²×C₅	semidirect
269. C₃×#106	C₂²×C₅	semidirect
270. C₃×#106	C₂²×C₅	semidirect
271. C₃×#103	C₂²×C₅	semidirect
272. C₃×#103	C₂²×C₅	semidirect
277. C₃×#102	C₂²×C₅	semidirect
278. C₃×#102	C₂²×C₅	semidirect
281. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
282. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
338. #537	C₂×C₃×C₅	semidirect
339. #535	C₂×C₃×C₅	semidirect
340. #485	C₂×C₃×C₅	semidirect
341. #482	C₂×C₃×C₅	semidirect
342. #481	C₂×C₃×C₅	semidirect
343. #480	C₂×C₃×C₅	semidirect
344. #469	C₂×C₃×C₅	semidirect
345. #468	C₂×C₃×C₅	semidirect
346. #466	C₂×C₃×C₅	semidirect
347. #465	C₂×C₃×C₅	semidirect
348. #450	C₂×C₃×C₅	semidirect
349. #449	C₂×C₃×C₅	semidirect
350. #449	C₂×C₃×C₅	semidirect
351. #447	C₂×C₃×C₅	semidirect
352. #408	C₂×C₃×C₅	semidirect
489. C₂×#41	C₂²×C₃×C₅	semidirect
495. C₂×M₁₆	C₂²×C₃×C₅	semidirect
496. C₂²×C₈	C₂²×C₃×C₅	semidirect
501. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
510. #121	C₂²×C₃×C₅	semidirect
514. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
515. #107	C₂²×C₃×C₅	semidirect
516. #107	C₂²×C₃×C₅	semidirect
517. #106	C₂²×C₃×C₅	semidirect
518. #106	C₂²×C₃×C₅	semidirect
519. #103	C₂²×C₃×C₅	semidirect
520. #103	C₂²×C₃×C₅	semidirect
525. #102	C₂²×C₃×C₅	semidirect
526. #102	C₂²×C₃×C₅	semidirect
529. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
530. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
675. C₃×C₅	#3198	direct (N × H)
774. C₅	C₃×#3198	direct (N × H)
805. C₃	C₅×#3198	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×#537	2
C₃×C₅×#535	2
C₃×C₅×#485	2
C₃×C₅×#482	2
C₃×C₅×#481	2
C₃×C₅×#480	2
C₃×C₅×#469	2
C₃×C₅×#468	2
C₃×C₅×#466	2
C₃×C₅×#465	2
C₃×C₅×#450	2
C₃×C₅×#449	2
C₃×C₅×#447	2
C₃×C₅×#408	2
C₅×#3198	3
C₃×#3198	5

Subgroups — C3×C5×#3198 #14276232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3198 #14276232