Subgroups — C₃×C₅×#3546 #14276580

Order 1920.

2300 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#560	C₂	1	4	yes	maximal, complemented
2	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#550	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#538	C₂	1	4	yes	maximal, complemented
12	C₃×C₅×#537	C₂	1	2	yes	maximal, complemented
13	C₃×C₅×#535	C₂	1	2	yes	maximal, complemented
14	C₃×C₅×#535	C₂	1	2	yes	maximal, complemented
15	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#3546	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
21	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
22	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
23	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
24	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
25	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×#127	C₂²	1	1	yes	characteristic
28	C₃×C₅×#127	C₂²	1	1	yes	characteristic
29	C₃×C₅×#127	C₂²	1	2	yes	complemented
30	C₃×C₅×#127	C₂²	1	4	yes	complemented
31	C₃×C₅×#126	C₂²	1	2	yes	complemented
32	C₃×C₅×#126	C₂²	1	4	yes	complemented
33	C₃×C₅×#126	C₂²	1	4	yes	complemented
34	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#124	C₂²	1	1	yes	characteristic
36	C₃×C₅×#124	C₂²	1	2	yes	—
37	C₃×C₅×#124	C₂²	1	2	yes	complemented
38	C₃×C₅×#124	C₂²	1	2	yes	complemented
39	C₃×C₅×#124	C₂²	1	4	yes	complemented
40	C₃×C₅×#123	C₂²	1	2	yes	complemented
41	C₃×C₅×#123	C₂²	1	4	yes	complemented
42	C₃×C₅×#123	C₂²	1	4	yes	complemented
43	C₃×C₅×#123	C₂²	1	4	yes	complemented
44	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
46	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
47	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
48	C₃×C₅×#121	C₂²	1	1	yes	characteristic
49	C₃×C₅×#121	C₂²	1	1	yes	characteristic
50	C₃×C₅×#121	C₂²	1	2	yes	—
51	C₃×C₅×#121	C₂²	1	2	yes	—
52	C₃×C₅×#121	C₂²	1	2	yes	—
53	C₃×C₅×#121	C₂²	1	2	yes	complemented
54	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×#121	C₂²	1	2	yes	complemented
56	C₃×C₅×#121	C₂²	1	2	yes	complemented
57	C₃×C₅×#121	C₂²	1	4	yes	complemented
58	C₃×C₅×#121	C₂²	1	2	yes	complemented
59	C₃×C₅×#121	C₂²	1	4	yes	complemented
60	C₃×C₅×#121	C₂²	1	4	yes	complemented
61	C₃×C₅×#121	C₂²	1	4	yes	complemented
62	C₃×C₅×#121	C₂²	1	4	yes	complemented
63	C₃×C₅×#121	C₂²	1	4	yes	complemented
64	C₃×C₅×#120	C₂²	1	4	yes	—
65	C₃×C₅×#120	C₂²	1	4	yes	complemented
66	C₃×C₅×#120	C₂²	1	4	yes	complemented
67	C₃×C₅×#120	C₂²	1	4	yes	complemented
68	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
69	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
70	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
71	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
72	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
73	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
74	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
75	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
76	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
77	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
78	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
79	C₃×C₅×#117	C₂²	1	2	yes	complemented
80	C₃×C₅×#117	C₂²	1	2	yes	complemented
81	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
82	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
83	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
84	C₃×#3546	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
85	C₅×#560	C₂×C₃	1	4	yes	complemented
86	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
87	C₅×#553	C₂×C₃	1	2	yes	complemented
88	C₅×#550	C₂×C₃	1	2	yes	complemented
89	C₅×#550	C₂×C₃	1	1	yes	characteristic, complemented
90	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
91	C₅×#546	C₂×C₃	1	2	yes	complemented
92	C₅×#546	C₂×C₃	1	2	yes	complemented
93	C₅×D₄²	C₂×C₃	1	1	yes	characteristic, complemented
94	C₅×#542	C₂×C₃	1	2	yes	complemented
95	C₅×#538	C₂×C₃	1	4	yes	complemented
96	C₅×#537	C₂×C₃	1	2	yes	complemented
97	C₅×#535	C₂×C₃	1	2	yes	complemented
98	C₅×#535	C₂×C₃	1	2	yes	complemented
99	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
100	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
101	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
102	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
103	C₃×C₅×#41	—	4	4	no	—
104	C₃×C₅×#41	—	4	4	no	—
105	C₃×C₅×#41	—	4	4	no	—
106	C₃×C₅×#41	—	4	4	no	—
107	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
109	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
110	C₂×C₃×C₅×D₄	—	4	4	no	—
111	C₂×C₃×C₅×D₄	—	4	4	no	—
112	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
113	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
114	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
115	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
116	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
117	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
118	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
119	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
120	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
121	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
122	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
123	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
124	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
125	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
126	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
127	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
128	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
129	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
130	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
131	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
132	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
133	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
134	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
135	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
136	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
137	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
138	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
140	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
141	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
143	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
144	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
147	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
148	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
149	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
150	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
164	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
165	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
168	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
169	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
170	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
171	C₃×C₄²×C₅	C₂³	1	2	yes	—
172	C₃×C₄²×C₅	C₂³	1	4	yes	—
173	C₃×#560	C₂×C₅	1	4	yes	complemented
174	C₃×#556	C₂×C₅	1	1	yes	characteristic, complemented
175	C₃×#553	C₂×C₅	1	2	yes	complemented
176	C₃×#550	C₂×C₅	1	2	yes	complemented
177	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
178	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
179	C₃×#546	C₂×C₅	1	2	yes	complemented
180	C₃×#546	C₂×C₅	1	2	yes	complemented
181	C₃×D₄²	C₂×C₅	1	1	yes	characteristic, complemented
182	C₃×#542	C₂×C₅	1	2	yes	complemented
183	C₃×#538	C₂×C₅	1	4	yes	complemented
184	C₃×#537	C₂×C₅	1	2	yes	complemented
185	C₃×#535	C₂×C₅	1	2	yes	complemented
186	C₃×#535	C₂×C₅	1	2	yes	complemented
187	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
188	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
189	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
190	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
191	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
192	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
193	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
194	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
195	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
196	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₅×#127	C₂²×C₃	1	1	yes	characteristic
199	C₅×#127	C₂²×C₃	1	1	yes	characteristic
200	C₅×#127	C₂²×C₃	1	2	yes	complemented
201	C₅×#127	C₂²×C₃	1	4	yes	complemented
202	C₅×#126	C₂²×C₃	1	2	yes	complemented
203	C₅×#126	C₂²×C₃	1	4	yes	complemented
204	C₅×#126	C₂²×C₃	1	4	yes	complemented
205	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
206	C₅×#124	C₂²×C₃	1	1	yes	characteristic
207	C₅×#124	C₂²×C₃	1	2	yes	—
208	C₅×#124	C₂²×C₃	1	2	yes	complemented
209	C₅×#124	C₂²×C₃	1	2	yes	complemented
210	C₅×#124	C₂²×C₃	1	4	yes	complemented
211	C₅×#123	C₂²×C₃	1	2	yes	complemented
212	C₅×#123	C₂²×C₃	1	4	yes	complemented
213	C₅×#123	C₂²×C₃	1	4	yes	complemented
214	C₅×#123	C₂²×C₃	1	4	yes	complemented
215	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
216	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
217	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
218	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
219	C₅×#121	C₂²×C₃	1	1	yes	characteristic
220	C₅×#121	C₂²×C₃	1	1	yes	characteristic
221	C₅×#121	C₂²×C₃	1	2	yes	—
222	C₅×#121	C₂²×C₃	1	2	yes	—
223	C₅×#121	C₂²×C₃	1	2	yes	—
224	C₅×#121	C₂²×C₃	1	2	yes	complemented
225	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
226	C₅×#121	C₂²×C₃	1	2	yes	complemented
227	C₅×#121	C₂²×C₃	1	2	yes	complemented
228	C₅×#121	C₂²×C₃	1	4	yes	complemented
229	C₅×#121	C₂²×C₃	1	2	yes	complemented
230	C₅×#121	C₂²×C₃	1	4	yes	complemented
231	C₅×#121	C₂²×C₃	1	4	yes	complemented
232	C₅×#121	C₂²×C₃	1	4	yes	complemented
233	C₅×#121	C₂²×C₃	1	4	yes	complemented
234	C₅×#121	C₂²×C₃	1	4	yes	complemented
235	C₅×#120	C₂²×C₃	1	4	yes	—
236	C₅×#120	C₂²×C₃	1	4	yes	complemented
237	C₅×#120	C₂²×C₃	1	4	yes	complemented
238	C₅×#120	C₂²×C₃	1	4	yes	complemented
239	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
240	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
241	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
242	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
243	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
244	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
245	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
246	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
247	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
248	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
249	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
250	C₅×#117	C₂²×C₃	1	2	yes	complemented
251	C₅×#117	C₂²×C₃	1	2	yes	complemented
252	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
253	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
254	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
255	#3546	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
256	C₂³×C₃×C₅	—	4	4	no	—
257	C₂³×C₃×C₅	—	4	4	no	—
258	C₂³×C₃×C₅	—	4	4	no	—
259	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
260	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
261	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
262	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
263	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
264	C₃×C₅×Q₈	—	2	2	no	—
265	C₃×C₅×Q₈	—	2	4	no	—
266	C₃×C₅×Q₈	—	4	2	no	—
267	C₃×C₅×D₄	—	2	2	no	—
268	C₃×C₅×D₄	—	2	2	no	—
269	C₃×C₅×D₄	—	2	4	no	—
270	C₃×C₅×D₄	—	2	4	no	—
271	C₃×C₅×D₄	—	2	2	no	—
272	C₃×C₅×D₄	—	4	4	no	—
273	C₃×C₅×D₄	—	4	4	no	—
274	C₃×C₅×D₄	—	4	2	no	—
275	C₃×C₅×D₄	—	4	2	no	—
276	C₃×C₅×D₄	—	4	2	no	—
277	C₃×C₅×D₄	—	4	4	no	—
278	C₃×C₅×D₄	—	4	2	no	—
279	C₃×C₅×D₄	—	4	2	no	—
280	C₃×C₅×D₄	—	4	2	no	—
281	C₃×C₅×D₄	—	4	4	no	—
282	C₃×C₅×D₄	—	4	4	no	—
283	C₃×C₅×D₄	—	4	4	no	—
284	C₂×C₃×C₄×C₅	—	2	4	no	—
285	C₂×C₃×C₄×C₅	—	2	4	no	—
286	C₂×C₃×C₄×C₅	—	2	2	no	—
287	C₂×C₃×C₄×C₅	—	2	4	no	—
288	C₂×C₃×C₄×C₅	—	2	2	no	—
289	C₂×C₃×C₄×C₅	—	4	1	no	—
290	C₂×C₃×C₄×C₅	—	4	4	no	—
291	C₂×C₃×C₄×C₅	—	4	4	no	—
292	C₂×C₃×C₄×C₅	—	4	4	no	—
293	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
294	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
295	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
296	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
299	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
300	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
301	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
302	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
303	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
304	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
305	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
306	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
307	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
308	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
309	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
310	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
311	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
312	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
313	C₃×#127	C₂²×C₅	1	1	yes	characteristic
314	C₃×#127	C₂²×C₅	1	1	yes	characteristic
315	C₃×#127	C₂²×C₅	1	4	yes	complemented
316	C₃×#127	C₂²×C₅	1	2	yes	complemented
317	C₃×#126	C₂²×C₅	1	4	yes	complemented
318	C₃×#126	C₂²×C₅	1	4	yes	complemented
319	C₃×#126	C₂²×C₅	1	2	yes	complemented
320	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
321	C₃×#124	C₂²×C₅	1	1	yes	characteristic
322	C₃×#124	C₂²×C₅	1	2	yes	—
323	C₃×#124	C₂²×C₅	1	2	yes	complemented
324	C₃×#124	C₂²×C₅	1	2	yes	complemented
325	C₃×#124	C₂²×C₅	1	4	yes	complemented
326	C₃×#123	C₂²×C₅	1	2	yes	complemented
327	C₃×#123	C₂²×C₅	1	4	yes	complemented
328	C₃×#123	C₂²×C₅	1	4	yes	complemented
329	C₃×#123	C₂²×C₅	1	4	yes	complemented
330	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
331	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
332	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
333	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
334	C₃×#121	C₂²×C₅	1	1	yes	characteristic
335	C₃×#121	C₂²×C₅	1	1	yes	characteristic
336	C₃×#121	C₂²×C₅	1	2	yes	—
337	C₃×#121	C₂²×C₅	1	2	yes	—
338	C₃×#121	C₂²×C₅	1	2	yes	—
339	C₃×#121	C₂²×C₅	1	2	yes	complemented
340	C₃×#121	C₂²×C₅	1	2	yes	complemented
341	C₃×#121	C₂²×C₅	1	4	yes	complemented
342	C₃×#121	C₂²×C₅	1	4	yes	complemented
343	C₃×#121	C₂²×C₅	1	4	yes	complemented
344	C₃×#121	C₂²×C₅	1	4	yes	complemented
345	C₃×#121	C₂²×C₅	1	2	yes	complemented
346	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
347	C₃×#121	C₂²×C₅	1	4	yes	complemented
348	C₃×#121	C₂²×C₅	1	2	yes	complemented
349	C₃×#121	C₂²×C₅	1	4	yes	complemented
350	C₃×#120	C₂²×C₅	1	4	yes	—
351	C₃×#120	C₂²×C₅	1	4	yes	complemented
352	C₃×#120	C₂²×C₅	1	4	yes	complemented
353	C₃×#120	C₂²×C₅	1	4	yes	complemented
354	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
355	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
356	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
357	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
358	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
359	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
360	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
361	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
362	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
363	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
364	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
365	C₃×#117	C₂²×C₅	1	2	yes	complemented
366	C₃×#117	C₂²×C₅	1	2	yes	complemented
367	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
368	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
369	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
370	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
371	C₅×#41	—	4	4	no	—
372	C₅×#41	—	4	4	no	—
373	C₅×#41	—	4	4	no	—
374	C₅×#41	—	4	4	no	—
375	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
376	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
377	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
378	C₂×C₅×D₄	—	4	4	no	—
379	C₂×C₅×D₄	—	4	4	no	—
380	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
381	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
382	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
383	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
384	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
385	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
386	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
387	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
388	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
389	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
390	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
391	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
392	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
393	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
394	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
395	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
396	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
397	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
398	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
399	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
400	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
401	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
402	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
403	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
404	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
405	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
406	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
407	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
408	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
409	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
410	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
411	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
412	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
413	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
414	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
415	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
416	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
417	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
418	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
419	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
420	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
421	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
422	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
423	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
424	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
425	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
426	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
427	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
428	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
429	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
430	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
431	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
432	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
433	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
434	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
435	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
436	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
437	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
438	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
439	C₄²×C₅	C₂³×C₃	1	2	yes	—
440	C₄²×C₅	C₂³×C₃	1	4	yes	—
441	#560	C₂×C₃×C₅	1	4	yes	complemented
442	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
443	#553	C₂×C₃×C₅	1	2	yes	complemented
444	#550	C₂×C₃×C₅	1	2	yes	complemented
445	#550	C₂×C₃×C₅	1	1	yes	characteristic, complemented
446	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
447	#546	C₂×C₃×C₅	1	2	yes	complemented
448	#546	C₂×C₃×C₅	1	2	yes	complemented
449	D₄²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
450	#542	C₂×C₃×C₅	1	2	yes	complemented
451	#538	C₂×C₃×C₅	1	4	yes	complemented
452	#537	C₂×C₃×C₅	1	2	yes	complemented
453	#535	C₂×C₃×C₅	1	2	yes	complemented
454	#535	C₂×C₃×C₅	1	2	yes	complemented
455	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
456	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
457	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
458	C₂²×C₃×C₅	—	2	1	no	—
459	C₂²×C₃×C₅	—	2	1	no	—
460	C₂²×C₃×C₅	—	2	2	no	—
461	C₂²×C₃×C₅	—	2	2	no	—
462	C₂²×C₃×C₅	—	2	2	no	—
463	C₂²×C₃×C₅	—	2	2	no	—
464	C₂²×C₃×C₅	—	2	4	no	—
465	C₂²×C₃×C₅	—	2	4	no	—
466	C₂²×C₃×C₅	—	2	2	no	—
467	C₂²×C₃×C₅	—	2	2	no	—
468	C₂²×C₃×C₅	—	2	1	no	—
469	C₂²×C₃×C₅	—	2	2	no	—
470	C₂²×C₃×C₅	—	2	4	no	—
471	C₂²×C₃×C₅	—	2	2	no	—
472	C₂²×C₃×C₅	—	2	2	no	—
473	C₂²×C₃×C₅	—	8	8	no	—
474	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
475	C₃×C₄×C₅	—	2	1	no	—
476	C₃×C₄×C₅	—	2	2	no	—
477	C₃×C₄×C₅	—	2	2	no	—
478	C₃×C₄×C₅	—	2	2	no	—
479	C₃×C₄×C₅	—	2	1	no	—
480	C₃×C₄×C₅	—	2	4	no	—
481	C₃×C₄×C₅	—	2	2	no	—
482	C₃×C₄×C₅	—	2	1	no	—
483	C₃×C₄×C₅	—	2	1	no	—
484	C₃×C₄×C₅	—	2	2	no	—
485	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
486	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
487	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
488	C₃×#41	—	4	4	no	—
489	C₃×#41	—	4	4	no	—
490	C₃×#41	—	4	4	no	—
491	C₃×#41	—	4	4	no	—
492	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
493	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
494	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
495	C₂×C₃×D₄	—	4	4	no	—
496	C₂×C₃×D₄	—	4	4	no	—
497	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
498	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
499	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
500	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
501	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
502	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
503	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
504	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
505	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
506	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
507	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
508	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
509	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
510	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
511	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
512	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
513	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
514	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
515	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
516	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
517	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
518	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
519	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
520	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
521	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
522	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
523	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
524	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
525	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
526	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
527	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
528	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
529	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
530	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
531	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
532	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
533	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
534	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
535	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
536	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
537	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
538	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
539	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
540	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
541	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
542	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
543	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
544	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
545	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
546	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
547	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
548	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
549	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
550	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
551	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
552	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
553	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
554	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
555	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
556	C₃×C₄²	C₂³×C₅	1	2	yes	—
557	C₃×C₄²	C₂³×C₅	1	4	yes	—
558	C₂³×C₅	—	4	4	no	—
559	C₂³×C₅	—	4	4	no	—
560	C₂³×C₅	—	4	4	no	—
561	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
562	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
563	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
564	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
565	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
566	C₅×Q₈	—	2	2	no	—
567	C₅×Q₈	—	2	4	no	—
568	C₅×Q₈	—	4	2	no	—
569	C₅×D₄	—	2	2	no	—
570	C₅×D₄	—	2	2	no	—
571	C₅×D₄	—	2	4	no	—
572	C₅×D₄	—	2	4	no	—
573	C₅×D₄	—	2	2	no	—
574	C₅×D₄	—	4	4	no	—
575	C₅×D₄	—	4	4	no	—
576	C₅×D₄	—	4	2	no	—
577	C₅×D₄	—	4	2	no	—
578	C₅×D₄	—	4	2	no	—
579	C₅×D₄	—	4	4	no	—
580	C₅×D₄	—	4	2	no	—
581	C₅×D₄	—	4	2	no	—
582	C₅×D₄	—	4	2	no	—
583	C₅×D₄	—	4	4	no	—
584	C₅×D₄	—	4	4	no	—
585	C₅×D₄	—	4	4	no	—
586	C₂×C₄×C₅	—	2	4	no	—
587	C₂×C₄×C₅	—	2	4	no	—
588	C₂×C₄×C₅	—	2	2	no	—
589	C₂×C₄×C₅	—	2	4	no	—
590	C₂×C₄×C₅	—	2	2	no	—
591	C₂×C₄×C₅	—	4	1	no	—
592	C₂×C₄×C₅	—	4	4	no	—
593	C₂×C₄×C₅	—	4	4	no	—
594	C₂×C₄×C₅	—	4	4	no	—
595	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
596	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
597	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
598	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
599	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
600	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
601	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
602	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
603	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
604	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
605	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
606	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
607	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
608	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
609	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
610	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
611	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
612	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
613	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
614	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
615	#127	C₂²×C₃×C₅	1	1	yes	characteristic
616	#127	C₂²×C₃×C₅	1	1	yes	characteristic
617	#127	C₂²×C₃×C₅	1	2	yes	complemented
618	#127	C₂²×C₃×C₅	1	4	yes	complemented
619	#126	C₂²×C₃×C₅	1	2	yes	complemented
620	#126	C₂²×C₃×C₅	1	4	yes	complemented
621	#126	C₂²×C₃×C₅	1	4	yes	complemented
622	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
623	#124	C₂²×C₃×C₅	1	1	yes	characteristic
624	#124	C₂²×C₃×C₅	1	2	yes	—
625	#124	C₂²×C₃×C₅	1	2	yes	complemented
626	#124	C₂²×C₃×C₅	1	2	yes	complemented
627	#124	C₂²×C₃×C₅	1	4	yes	complemented
628	#123	C₂²×C₃×C₅	1	2	yes	complemented
629	#123	C₂²×C₃×C₅	1	4	yes	complemented
630	#123	C₂²×C₃×C₅	1	4	yes	complemented
631	#123	C₂²×C₃×C₅	1	4	yes	complemented
632	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
633	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
634	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
635	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
636	#121	C₂²×C₃×C₅	1	1	yes	characteristic
637	#121	C₂²×C₃×C₅	1	1	yes	characteristic
638	#121	C₂²×C₃×C₅	1	2	yes	—
639	#121	C₂²×C₃×C₅	1	2	yes	—
640	#121	C₂²×C₃×C₅	1	2	yes	—
641	#121	C₂²×C₃×C₅	1	2	yes	complemented
642	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
643	#121	C₂²×C₃×C₅	1	2	yes	complemented
644	#121	C₂²×C₃×C₅	1	2	yes	complemented
645	#121	C₂²×C₃×C₅	1	4	yes	complemented
646	#121	C₂²×C₃×C₅	1	2	yes	complemented
647	#121	C₂²×C₃×C₅	1	4	yes	complemented
648	#121	C₂²×C₃×C₅	1	4	yes	complemented
649	#121	C₂²×C₃×C₅	1	4	yes	complemented
650	#121	C₂²×C₃×C₅	1	4	yes	complemented
651	#121	C₂²×C₃×C₅	1	4	yes	complemented
652	#120	C₂²×C₃×C₅	1	4	yes	—
653	#120	C₂²×C₃×C₅	1	4	yes	complemented
654	#120	C₂²×C₃×C₅	1	4	yes	complemented
655	#120	C₂²×C₃×C₅	1	4	yes	complemented
656	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
657	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
658	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
659	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
660	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
661	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
662	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
663	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
664	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
665	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
666	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
667	#117	C₂²×C₃×C₅	1	2	yes	complemented
668	#117	C₂²×C₃×C₅	1	2	yes	complemented
669	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
670	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
671	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
672	C₂×C₃×C₅	—	4	1	no	—
673	C₂×C₃×C₅	—	4	2	no	—
674	C₂×C₃×C₅	—	4	4	no	—
675	C₂×C₃×C₅	—	4	2	no	—
676	C₂×C₃×C₅	—	4	2	no	—
677	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂×C₃×C₅	#585	1	1	yes	characteristic
680	C₂³×C₃	—	4	4	no	—
681	C₂³×C₃	—	4	4	no	—
682	C₂³×C₃	—	4	4	no	—
683	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
684	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
685	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
686	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
687	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
688	C₃×Q₈	—	2	2	no	—
689	C₃×Q₈	—	2	4	no	—
690	C₃×Q₈	—	4	2	no	—
691	C₃×D₄	—	2	2	no	—
692	C₃×D₄	—	2	2	no	—
693	C₃×D₄	—	2	4	no	—
694	C₃×D₄	—	2	4	no	—
695	C₃×D₄	—	2	2	no	—
696	C₃×D₄	—	4	4	no	—
697	C₃×D₄	—	4	4	no	—
698	C₃×D₄	—	4	2	no	—
699	C₃×D₄	—	4	2	no	—
700	C₃×D₄	—	4	2	no	—
701	C₃×D₄	—	4	4	no	—
702	C₃×D₄	—	4	2	no	—
703	C₃×D₄	—	4	2	no	—
704	C₃×D₄	—	4	2	no	—
705	C₃×D₄	—	4	4	no	—
706	C₃×D₄	—	4	4	no	—
707	C₃×D₄	—	4	4	no	—
708	C₂×C₃×C₄	—	2	4	no	—
709	C₂×C₃×C₄	—	2	4	no	—
710	C₂×C₃×C₄	—	2	2	no	—
711	C₂×C₃×C₄	—	2	4	no	—
712	C₂×C₃×C₄	—	2	2	no	—
713	C₂×C₃×C₄	—	4	1	no	—
714	C₂×C₃×C₄	—	4	4	no	—
715	C₂×C₃×C₄	—	4	4	no	—
716	C₂×C₃×C₄	—	4	4	no	—
717	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
718	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
719	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
720	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
721	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
722	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
723	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
724	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
725	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
726	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
727	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
728	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
729	C₂²×C₅	—	2	1	no	—
730	C₂²×C₅	—	2	1	no	—
731	C₂²×C₅	—	2	2	no	—
732	C₂²×C₅	—	2	2	no	—
733	C₂²×C₅	—	2	2	no	—
734	C₂²×C₅	—	2	2	no	—
735	C₂²×C₅	—	2	4	no	—
736	C₂²×C₅	—	2	4	no	—
737	C₂²×C₅	—	2	2	no	—
738	C₂²×C₅	—	2	2	no	—
739	C₂²×C₅	—	2	1	no	—
740	C₂²×C₅	—	2	2	no	—
741	C₂²×C₅	—	2	4	no	—
742	C₂²×C₅	—	2	2	no	—
743	C₂²×C₅	—	2	2	no	—
744	C₂²×C₅	—	8	8	no	—
745	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
746	C₄×C₅	—	2	1	no	—
747	C₄×C₅	—	2	2	no	—
748	C₄×C₅	—	2	2	no	—
749	C₄×C₅	—	2	2	no	—
750	C₄×C₅	—	2	1	no	—
751	C₄×C₅	—	2	4	no	—
752	C₄×C₅	—	2	2	no	—
753	C₄×C₅	—	2	1	no	—
754	C₄×C₅	—	2	1	no	—
755	C₄×C₅	—	2	2	no	—
756	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
757	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
758	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
759	#41	—	4	4	no	—
760	#41	—	4	4	no	—
761	#41	—	4	4	no	—
762	#41	—	4	4	no	—
763	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
764	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
765	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
766	C₂×D₄	—	4	4	no	—
767	C₂×D₄	—	4	4	no	—
768	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
769	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
770	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
771	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
772	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
773	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
774	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
775	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
776	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
777	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
778	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
779	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
780	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
781	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
782	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
783	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
784	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
785	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
786	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
787	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
788	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
789	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
790	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
791	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
792	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
793	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
794	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
795	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
796	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
797	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
798	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
799	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
800	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
801	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
802	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
803	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
804	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
805	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
806	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
807	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
808	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
809	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
810	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
811	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
812	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
813	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
814	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
815	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
816	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
817	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
818	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
819	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
820	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
821	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
822	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
823	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
824	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
825	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
826	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
827	C₄²	C₂³×C₃×C₅	1	2	yes	—
828	C₄²	C₂³×C₃×C₅	1	4	yes	—
829	C₃×C₅	#3546	1	1	yes	characteristic, direct product factor, Hall
830	C₂²×C₃	—	2	1	no	—
831	C₂²×C₃	—	2	1	no	—
832	C₂²×C₃	—	2	2	no	—
833	C₂²×C₃	—	2	2	no	—
834	C₂²×C₃	—	2	2	no	—
835	C₂²×C₃	—	2	2	no	—
836	C₂²×C₃	—	2	4	no	—
837	C₂²×C₃	—	2	4	no	—
838	C₂²×C₃	—	2	2	no	—
839	C₂²×C₃	—	2	2	no	—
840	C₂²×C₃	—	2	1	no	—
841	C₂²×C₃	—	2	2	no	—
842	C₂²×C₃	—	2	4	no	—
843	C₂²×C₃	—	2	2	no	—
844	C₂²×C₃	—	2	2	no	—
845	C₂²×C₃	—	8	8	no	—
846	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
847	C₃×C₄	—	2	1	no	—
848	C₃×C₄	—	2	2	no	—
849	C₃×C₄	—	2	2	no	—
850	C₃×C₄	—	2	2	no	—
851	C₃×C₄	—	2	1	no	—
852	C₃×C₄	—	2	4	no	—
853	C₃×C₄	—	2	2	no	—
854	C₃×C₄	—	2	1	no	—
855	C₃×C₄	—	2	1	no	—
856	C₃×C₄	—	2	2	no	—
857	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
858	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
859	C₂×C₅	—	4	2	no	—
860	C₂×C₅	—	4	2	no	—
861	C₂×C₅	—	4	4	no	—
862	C₂×C₅	—	4	1	no	—
863	C₂×C₅	—	4	2	no	—
864	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
865	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
866	C₂×C₅	C₃×#585	1	1	yes	characteristic
867	C₂³	—	4	4	no	—
868	C₂³	—	4	4	no	—
869	C₂³	—	4	4	no	—
870	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
871	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
872	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
873	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
874	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
875	Q₈	—	2	2	no	—
876	Q₈	—	2	4	no	—
877	Q₈	—	4	2	no	—
878	D₄	—	2	2	no	—
879	D₄	—	2	2	no	—
880	D₄	—	2	4	no	—
881	D₄	—	2	4	no	—
882	D₄	—	2	2	no	—
883	D₄	—	4	4	no	—
884	D₄	—	4	4	no	—
885	D₄	—	4	2	no	—
886	D₄	—	4	2	no	—
887	D₄	—	4	2	no	—
888	D₄	—	4	4	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	4	no	—
891	D₄	—	4	2	no	—
892	D₄	—	4	2	no	—
893	D₄	—	4	2	no	—
894	D₄	—	4	4	no	—
895	C₂×C₄	—	2	4	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	4	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	1	no	—
904	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
905	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
906	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
907	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
908	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
909	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
910	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
911	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
912	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
913	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
914	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
915	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
916	C₂×C₃	—	4	2	no	—
917	C₂×C₃	—	4	2	no	—
918	C₂×C₃	—	4	4	no	—
919	C₂×C₃	—	4	1	no	—
920	C₂×C₃	—	4	2	no	—
921	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
922	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
923	C₂×C₃	C₅×#585	1	1	yes	characteristic
924	C₅	C₃×#3546	1	1	yes	characteristic, direct product factor, Sylow
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	4	no	—
932	C₂²	—	2	4	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	1	no	—
936	C₂²	—	2	2	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	8	8	no	—
941	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
942	C₄	—	2	1	no	—
943	C₄	—	2	2	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	4	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	2	no	—
952	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
953	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
954	C₃	C₅×#3546	1	1	yes	characteristic, direct product factor, Sylow
955	C₂	—	4	2	no	—
956	C₂	—	4	2	no	—
957	C₂	—	4	4	no	—
958	C₂	—	4	1	no	—
959	C₂	—	4	2	no	—
960	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
961	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
962	C₂	C₃×C₅×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#560	C₂	semidirect
2. C₃×C₅×#556	C₂	semidirect
3. C₃×C₅×#553	C₂	semidirect
4. C₃×C₅×#550	C₂	semidirect
5. C₃×C₅×#550	C₂	semidirect
6. C₃×C₅×#547	C₂	semidirect
7. C₃×C₅×#546	C₂	semidirect
8. C₃×C₅×#546	C₂	semidirect
9. C₃×C₅×D₄²	C₂	semidirect
10. C₃×C₅×#542	C₂	semidirect
11. C₃×C₅×#538	C₂	semidirect
12. C₃×C₅×#537	C₂	semidirect
13. C₃×C₅×#535	C₂	semidirect
14. C₃×C₅×#535	C₂	semidirect
15. C₃×C₅×#532	C₂	semidirect
16. C₃×C₅×#532	C₂	semidirect
17. C₃×C₅×#529	C₂	semidirect
18. C₅×#3546	C₃	direct (N × H)
19. C₂×C₃×C₅×#41	C₂²	semidirect
20. C₂×C₃×C₅×#41	C₂²	semidirect
21. C₂×C₃×C₅×#41	C₂²	semidirect
22. C₂×C₃×C₅×#41	C₂²	semidirect
25. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
26. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
29. C₃×C₅×#127	C₂²	semidirect
30. C₃×C₅×#127	C₂²	semidirect
31. C₃×C₅×#126	C₂²	semidirect
32. C₃×C₅×#126	C₂²	semidirect
33. C₃×C₅×#126	C₂²	semidirect
34. C₃×C₅×#125	C₂²	semidirect
37. C₃×C₅×#124	C₂²	semidirect
38. C₃×C₅×#124	C₂²	semidirect
39. C₃×C₅×#124	C₂²	semidirect
40. C₃×C₅×#123	C₂²	semidirect
41. C₃×C₅×#123	C₂²	semidirect
42. C₃×C₅×#123	C₂²	semidirect
43. C₃×C₅×#123	C₂²	semidirect
44. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
45. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
46. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
47. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
53. C₃×C₅×#121	C₂²	semidirect
54. C₃×C₅×#121	C₂²	semidirect
55. C₃×C₅×#121	C₂²	semidirect
56. C₃×C₅×#121	C₂²	semidirect
57. C₃×C₅×#121	C₂²	semidirect
58. C₃×C₅×#121	C₂²	semidirect
59. C₃×C₅×#121	C₂²	semidirect
60. C₃×C₅×#121	C₂²	semidirect
61. C₃×C₅×#121	C₂²	semidirect
62. C₃×C₅×#121	C₂²	semidirect
63. C₃×C₅×#121	C₂²	semidirect
65. C₃×C₅×#120	C₂²	semidirect
66. C₃×C₅×#120	C₂²	semidirect
67. C₃×C₅×#120	C₂²	semidirect
68. C₃×C₄×C₅×Q₈	C₂²	semidirect
69. C₃×C₄×C₅×Q₈	C₂²	semidirect
72. C₃×C₄×C₅×D₄	C₂²	semidirect
73. C₃×C₄×C₅×D₄	C₂²	semidirect
74. C₃×C₄×C₅×D₄	C₂²	semidirect
75. C₃×C₄×C₅×D₄	C₂²	semidirect
76. C₃×C₄×C₅×D₄	C₂²	semidirect
77. C₃×C₄×C₅×D₄	C₂²	semidirect
78. C₃×C₄×C₅×D₄	C₂²	semidirect
79. C₃×C₅×#117	C₂²	semidirect
80. C₃×C₅×#117	C₂²	semidirect
81. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
82. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
83. C₂×C₃×C₄²×C₅	C₂²	semidirect
84. C₃×#3546	C₅	direct (N × H)
85. C₅×#560	C₂×C₃	semidirect
86. C₅×#556	C₂×C₃	semidirect
87. C₅×#553	C₂×C₃	semidirect
88. C₅×#550	C₂×C₃	semidirect
89. C₅×#550	C₂×C₃	semidirect
90. C₅×#547	C₂×C₃	semidirect
91. C₅×#546	C₂×C₃	semidirect
92. C₅×#546	C₂×C₃	semidirect
93. C₅×D₄²	C₂×C₃	semidirect
94. C₅×#542	C₂×C₃	semidirect
95. C₅×#538	C₂×C₃	semidirect
96. C₅×#537	C₂×C₃	semidirect
97. C₅×#535	C₂×C₃	semidirect
98. C₅×#535	C₂×C₃	semidirect
99. C₅×#532	C₂×C₃	semidirect
100. C₅×#532	C₂×C₃	semidirect
101. C₅×#529	C₂×C₃	semidirect
173. C₃×#560	C₂×C₅	semidirect
174. C₃×#556	C₂×C₅	semidirect
175. C₃×#553	C₂×C₅	semidirect
176. C₃×#550	C₂×C₅	semidirect
177. C₃×#550	C₂×C₅	semidirect
178. C₃×#547	C₂×C₅	semidirect
179. C₃×#546	C₂×C₅	semidirect
180. C₃×#546	C₂×C₅	semidirect
181. C₃×D₄²	C₂×C₅	semidirect
182. C₃×#542	C₂×C₅	semidirect
183. C₃×#538	C₂×C₅	semidirect
184. C₃×#537	C₂×C₅	semidirect
185. C₃×#535	C₂×C₅	semidirect
186. C₃×#535	C₂×C₅	semidirect
187. C₃×#532	C₂×C₅	semidirect
188. C₃×#532	C₂×C₅	semidirect
189. C₃×#529	C₂×C₅	semidirect
190. C₂×C₅×#41	C₂²×C₃	semidirect
191. C₂×C₅×#41	C₂²×C₃	semidirect
192. C₂×C₅×#41	C₂²×C₃	semidirect
193. C₂×C₅×#41	C₂²×C₃	semidirect
196. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
197. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
200. C₅×#127	C₂²×C₃	semidirect
201. C₅×#127	C₂²×C₃	semidirect
202. C₅×#126	C₂²×C₃	semidirect
203. C₅×#126	C₂²×C₃	semidirect
204. C₅×#126	C₂²×C₃	semidirect
205. C₅×#125	C₂²×C₃	semidirect
208. C₅×#124	C₂²×C₃	semidirect
209. C₅×#124	C₂²×C₃	semidirect
210. C₅×#124	C₂²×C₃	semidirect
211. C₅×#123	C₂²×C₃	semidirect
212. C₅×#123	C₂²×C₃	semidirect
213. C₅×#123	C₂²×C₃	semidirect
214. C₅×#123	C₂²×C₃	semidirect
215. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
216. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
217. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
218. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
224. C₅×#121	C₂²×C₃	semidirect
225. C₅×#121	C₂²×C₃	semidirect
226. C₅×#121	C₂²×C₃	semidirect
227. C₅×#121	C₂²×C₃	semidirect
228. C₅×#121	C₂²×C₃	semidirect
229. C₅×#121	C₂²×C₃	semidirect
230. C₅×#121	C₂²×C₃	semidirect
231. C₅×#121	C₂²×C₃	semidirect
232. C₅×#121	C₂²×C₃	semidirect
233. C₅×#121	C₂²×C₃	semidirect
234. C₅×#121	C₂²×C₃	semidirect
236. C₅×#120	C₂²×C₃	semidirect
237. C₅×#120	C₂²×C₃	semidirect
238. C₅×#120	C₂²×C₃	semidirect
239. C₄×C₅×Q₈	C₂²×C₃	semidirect
240. C₄×C₅×Q₈	C₂²×C₃	semidirect
243. C₄×C₅×D₄	C₂²×C₃	semidirect
244. C₄×C₅×D₄	C₂²×C₃	semidirect
245. C₄×C₅×D₄	C₂²×C₃	semidirect
246. C₄×C₅×D₄	C₂²×C₃	semidirect
247. C₄×C₅×D₄	C₂²×C₃	semidirect
248. C₄×C₅×D₄	C₂²×C₃	semidirect
249. C₄×C₅×D₄	C₂²×C₃	semidirect
250. C₅×#117	C₂²×C₃	semidirect
251. C₅×#117	C₂²×C₃	semidirect
252. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
253. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
254. C₂×C₄²×C₅	C₂²×C₃	semidirect
255. #3546	C₃×C₅	direct (N × H)
305. C₂×C₃×#41	C₂²×C₅	semidirect
306. C₂×C₃×#41	C₂²×C₅	semidirect
307. C₂×C₃×#41	C₂²×C₅	semidirect
308. C₂×C₃×#41	C₂²×C₅	semidirect
311. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
312. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
315. C₃×#127	C₂²×C₅	semidirect
316. C₃×#127	C₂²×C₅	semidirect
317. C₃×#126	C₂²×C₅	semidirect
318. C₃×#126	C₂²×C₅	semidirect
319. C₃×#126	C₂²×C₅	semidirect
320. C₃×#125	C₂²×C₅	semidirect
323. C₃×#124	C₂²×C₅	semidirect
324. C₃×#124	C₂²×C₅	semidirect
325. C₃×#124	C₂²×C₅	semidirect
326. C₃×#123	C₂²×C₅	semidirect
327. C₃×#123	C₂²×C₅	semidirect
328. C₃×#123	C₂²×C₅	semidirect
329. C₃×#123	C₂²×C₅	semidirect
330. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
331. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
332. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
333. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
339. C₃×#121	C₂²×C₅	semidirect
340. C₃×#121	C₂²×C₅	semidirect
341. C₃×#121	C₂²×C₅	semidirect
342. C₃×#121	C₂²×C₅	semidirect
343. C₃×#121	C₂²×C₅	semidirect
344. C₃×#121	C₂²×C₅	semidirect
345. C₃×#121	C₂²×C₅	semidirect
346. C₃×#121	C₂²×C₅	semidirect
347. C₃×#121	C₂²×C₅	semidirect
348. C₃×#121	C₂²×C₅	semidirect
349. C₃×#121	C₂²×C₅	semidirect
351. C₃×#120	C₂²×C₅	semidirect
352. C₃×#120	C₂²×C₅	semidirect
353. C₃×#120	C₂²×C₅	semidirect
354. C₃×C₄×Q₈	C₂²×C₅	semidirect
355. C₃×C₄×Q₈	C₂²×C₅	semidirect
358. C₃×C₄×D₄	C₂²×C₅	semidirect
359. C₃×C₄×D₄	C₂²×C₅	semidirect
360. C₃×C₄×D₄	C₂²×C₅	semidirect
361. C₃×C₄×D₄	C₂²×C₅	semidirect
362. C₃×C₄×D₄	C₂²×C₅	semidirect
363. C₃×C₄×D₄	C₂²×C₅	semidirect
364. C₃×C₄×D₄	C₂²×C₅	semidirect
365. C₃×#117	C₂²×C₅	semidirect
366. C₃×#117	C₂²×C₅	semidirect
367. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
368. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
369. C₂×C₃×C₄²	C₂²×C₅	semidirect
441. #560	C₂×C₃×C₅	semidirect
442. #556	C₂×C₃×C₅	semidirect
443. #553	C₂×C₃×C₅	semidirect
444. #550	C₂×C₃×C₅	semidirect
445. #550	C₂×C₃×C₅	semidirect
446. #547	C₂×C₃×C₅	semidirect
447. #546	C₂×C₃×C₅	semidirect
448. #546	C₂×C₃×C₅	semidirect
449. D₄²	C₂×C₃×C₅	semidirect
450. #542	C₂×C₃×C₅	semidirect
451. #538	C₂×C₃×C₅	semidirect
452. #537	C₂×C₃×C₅	semidirect
453. #535	C₂×C₃×C₅	semidirect
454. #535	C₂×C₃×C₅	semidirect
455. #532	C₂×C₃×C₅	semidirect
456. #532	C₂×C₃×C₅	semidirect
457. #529	C₂×C₃×C₅	semidirect
607. C₂×#41	C₂²×C₃×C₅	semidirect
608. C₂×#41	C₂²×C₃×C₅	semidirect
609. C₂×#41	C₂²×C₃×C₅	semidirect
610. C₂×#41	C₂²×C₃×C₅	semidirect
613. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
614. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
617. #127	C₂²×C₃×C₅	semidirect
618. #127	C₂²×C₃×C₅	semidirect
619. #126	C₂²×C₃×C₅	semidirect
620. #126	C₂²×C₃×C₅	semidirect
621. #126	C₂²×C₃×C₅	semidirect
622. #125	C₂²×C₃×C₅	semidirect
625. #124	C₂²×C₃×C₅	semidirect
626. #124	C₂²×C₃×C₅	semidirect
627. #124	C₂²×C₃×C₅	semidirect
628. #123	C₂²×C₃×C₅	semidirect
629. #123	C₂²×C₃×C₅	semidirect
630. #123	C₂²×C₃×C₅	semidirect
631. #123	C₂²×C₃×C₅	semidirect
632. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
633. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
634. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
635. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
641. #121	C₂²×C₃×C₅	semidirect
642. #121	C₂²×C₃×C₅	semidirect
643. #121	C₂²×C₃×C₅	semidirect
644. #121	C₂²×C₃×C₅	semidirect
645. #121	C₂²×C₃×C₅	semidirect
646. #121	C₂²×C₃×C₅	semidirect
647. #121	C₂²×C₃×C₅	semidirect
648. #121	C₂²×C₃×C₅	semidirect
649. #121	C₂²×C₃×C₅	semidirect
650. #121	C₂²×C₃×C₅	semidirect
651. #121	C₂²×C₃×C₅	semidirect
653. #120	C₂²×C₃×C₅	semidirect
654. #120	C₂²×C₃×C₅	semidirect
655. #120	C₂²×C₃×C₅	semidirect
656. C₄×Q₈	C₂²×C₃×C₅	semidirect
657. C₄×Q₈	C₂²×C₃×C₅	semidirect
660. C₄×D₄	C₂²×C₃×C₅	semidirect
661. C₄×D₄	C₂²×C₃×C₅	semidirect
662. C₄×D₄	C₂²×C₃×C₅	semidirect
663. C₄×D₄	C₂²×C₃×C₅	semidirect
664. C₄×D₄	C₂²×C₃×C₅	semidirect
665. C₄×D₄	C₂²×C₃×C₅	semidirect
666. C₄×D₄	C₂²×C₃×C₅	semidirect
667. #117	C₂²×C₃×C₅	semidirect
668. #117	C₂²×C₃×C₅	semidirect
669. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
670. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
671. C₂×C₄²	C₂²×C₃×C₅	semidirect
829. C₃×C₅	#3546	direct (N × H)
924. C₅	C₃×#3546	direct (N × H)
954. C₃	C₅×#3546	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×#560	2
C₃×C₅×#556	2
C₃×C₅×#553	2
C₃×C₅×#550	2
C₃×C₅×#547	2
C₃×C₅×#546	2
C₃×C₅×D₄²	2
C₃×C₅×#542	2
C₃×C₅×#538	2
C₃×C₅×#537	2
C₃×C₅×#535	2
C₃×C₅×#532	2
C₃×C₅×#529	2
C₅×#3546	3
C₃×#3546	5

Subgroups — C3×C5×#3546 #14276580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3546 #14276580