Subgroups — C₃⋊(C₅⋊(C₅⋊#64424)) #36348048

Order 22050.

720 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₅⋊(C₅⋊(C₇⋊D₇)))	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊(C₅⋊#64424)	—	3	1	no	maximal
4	C₃⋊(C₅⋊#64424)	—	5	1	no	maximal
5	C₃⋊(C₅⋊#64424)	—	5	1	no	maximal
6	C₃⋊(C₅⋊#64424)	—	5	1	no	maximal
7	C₃⋊(C₅⋊#64424)	—	5	1	no	maximal
8	C₃⋊(C₅⋊#64424)	—	5	1	no	maximal
9	C₃⋊(C₅⋊#64424)	—	5	1	no	maximal
10	C₅²×#3861	—	2	1	no	—
11	C₅²×#3861	D₃	1	1	yes	characteristic, complemented
12	C₃×C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	—	7	1	no	maximal
14	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	—	7	1	no	maximal
15	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	—	7	1	no	maximal
16	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	—	7	1	no	maximal
17	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	—	7	1	no	maximal
18	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	—	7	3	no	maximal
19	C₅⋊(C₅⋊(C₇⋊D₇))	—	3	1	no	Hall
20	C₃×C₅×#3861	D₅	1	1	yes	characteristic, complemented
21	C₃×C₅×#3861	D₅	1	1	yes	characteristic, complemented
22	C₃×C₅×#3861	D₅	1	1	yes	characteristic, complemented
23	C₃×C₅×#3861	D₅	1	1	yes	characteristic, complemented
24	C₃×C₅×#3861	D₅	1	1	yes	characteristic, complemented
25	C₃×C₅×#3861	D₅	1	1	yes	characteristic, complemented
26	C₃×C₅²×ΓL(1,𝔽₈)	—	7	1	no	—
27	C₃×C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
28	C₃×C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
29	C₃×C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
30	C₃×C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
31	C₃×C₅²×ΓL(1,𝔽₈)	—	14	3	no	—
32	C₃⋊(C₅⋊(C₇⋊D₇))	—	5	1	no	—
33	C₃⋊(C₅⋊(C₇⋊D₇))	—	5	1	no	—
34	C₃⋊(C₅⋊(C₇⋊D₇))	—	5	1	no	—
35	C₃⋊(C₅⋊(C₇⋊D₇))	—	5	1	no	—
36	C₃⋊(C₅⋊(C₇⋊D₇))	—	5	1	no	—
37	C₃⋊(C₅⋊(C₇⋊D₇))	—	5	1	no	—
38	C₅⋊#64424	—	15	1	no	—
39	C₅⋊#64424	—	15	1	no	—
40	C₅⋊#64424	—	15	1	no	—
41	C₅⋊#64424	—	15	1	no	—
42	C₅⋊#64424	—	15	1	no	—
43	C₅⋊#64424	—	15	1	no	—
44	C₅²×C₇²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
45	C₃⋊(C₅⋊D₃₅)	—	7	1	no	—
46	C₃⋊(C₅⋊D₃₅)	—	7	1	no	—
47	C₃⋊(C₅⋊D₃₅)	—	7	1	no	—
48	C₃⋊(C₅⋊D₃₅)	—	7	1	no	—
49	C₃⋊(C₅⋊D₃₅)	—	7	1	no	—
50	C₃⋊(C₅⋊D₃₅)	—	7	3	no	—
51	C₅⋊(C₅⋊AGL(1,𝔽₇))	—	21	1	no	—
52	C₅⋊(C₅⋊AGL(1,𝔽₇))	—	21	1	no	—
53	C₅⋊(C₅⋊AGL(1,𝔽₇))	—	21	1	no	—
54	C₅⋊(C₅⋊AGL(1,𝔽₇))	—	21	1	no	—
55	C₅⋊(C₅⋊AGL(1,𝔽₇))	—	21	1	no	—
56	C₅⋊(C₅⋊AGL(1,𝔽₇))	—	21	3	no	—
57	C₃⋊#64424	—	25	1	no	Hall
58	C₃×C₅×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
59	C₃×C₅×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
60	C₃×C₅×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
61	C₃×C₅×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
62	C₃×C₅×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
63	C₃×C₅×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
64	C₅×#3861	—	2	1	no	—
65	C₅×#3861	—	2	1	no	—
66	C₅×#3861	—	2	1	no	—
67	C₅×#3861	—	2	1	no	—
68	C₅×#3861	—	2	1	no	—
69	C₅×#3861	—	2	1	no	—
70	C₅×#3861	D₁₅	1	1	yes	characteristic, complemented
71	C₅×#3861	D₁₅	1	1	yes	characteristic, complemented
72	C₅×#3861	D₁₅	1	1	yes	characteristic, complemented
73	C₅×#3861	D₁₅	1	1	yes	characteristic, complemented
74	C₅×#3861	D₁₅	1	1	yes	characteristic, complemented
75	C₅×#3861	D₁₅	1	1	yes	characteristic, complemented
76	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
77	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
78	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
79	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
80	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
81	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
82	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
83	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
84	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
85	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
86	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
87	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
88	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
89	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
90	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
91	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
92	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
93	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
94	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
95	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
96	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
97	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	3	no	—
98	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
99	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	3	no	—
100	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	3	no	—
101	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
102	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
103	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	3	no	—
104	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
105	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
106	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
107	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
108	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
109	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	1	no	—
110	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	3	no	—
111	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	35	3	no	—
112	C₃×C₅²×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
113	C₃×C₅²×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
114	C₃×C₅²×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
115	C₃×C₅²×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
116	C₃×C₅²×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
117	C₃×C₅²×C₇	AGL(1,𝔽₇)	1	3	yes	complemented
118	C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
119	C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
120	C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
121	C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
122	C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
123	C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
124	C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
125	C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
126	C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
127	C₅²×ΓL(1,𝔽₈)	—	14	3	no	—
128	C₅²×ΓL(1,𝔽₈)	—	14	1	no	—
129	C₅²×ΓL(1,𝔽₈)	—	14	3	no	—
130	C₅⋊(C₇⋊D₇)	—	15	1	no	—
131	C₅⋊(C₇⋊D₇)	—	15	1	no	—
132	C₅⋊(C₇⋊D₇)	—	15	1	no	—
133	C₅⋊(C₇⋊D₇)	—	15	1	no	—
134	C₅⋊(C₇⋊D₇)	—	15	1	no	—
135	C₅⋊(C₇⋊D₇)	—	15	1	no	—
136	C₃×C₃⋊(C₅⋊D₅)	—	49	1	no	Hall
137	C₃×#3861	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
138	C₅⋊D₃₅	—	21	1	no	—
139	C₅⋊D₃₅	—	21	1	no	—
140	C₅⋊D₃₅	—	21	1	no	—
141	C₅⋊D₃₅	—	21	1	no	—
142	C₅⋊D₃₅	—	21	1	no	—
143	C₅⋊D₃₅	—	21	3	no	—
144	C₃×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
145	C₃×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
146	C₃×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
147	C₃×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
148	C₃×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
149	C₃×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
150	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
151	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
152	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
153	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
154	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
155	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
156	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
157	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
158	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
159	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
160	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
161	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
162	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
163	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
164	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
165	C₃×C₅×ΓL(1,𝔽₈)	—	14	3	no	—
166	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
167	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
168	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
169	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
170	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
171	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
172	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
173	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
174	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
175	C₃×C₅×ΓL(1,𝔽₈)	—	14	3	no	—
176	C₃×C₅×ΓL(1,𝔽₈)	—	14	3	no	—
177	C₃×C₅×ΓL(1,𝔽₈)	—	14	3	no	—
178	C₃×C₅×ΓL(1,𝔽₈)	—	14	3	no	—
179	C₃×C₅×ΓL(1,𝔽₈)	—	14	3	no	—
180	C₃⋊(C₇⋊D₇)	—	25	1	no	—
181	#64424	—	75	1	no	—
182	C₅×C₇²	C₃×D₁₅	1	1	yes	characteristic, complemented
183	C₅×C₇²	C₃×D₁₅	1	1	yes	characteristic, complemented
184	C₅×C₇²	C₃×D₁₅	1	1	yes	characteristic, complemented
185	C₅×C₇²	C₃×D₁₅	1	1	yes	characteristic, complemented
186	C₅×C₇²	C₃×D₁₅	1	1	yes	characteristic, complemented
187	C₅×C₇²	C₃×D₁₅	1	1	yes	characteristic, complemented
188	C₃²×C₅²	—	98	1	no	Hall
189	D₁₀₅	—	35	1	no	—
190	D₁₀₅	—	35	1	no	—
191	D₁₀₅	—	35	1	no	—
192	D₁₀₅	—	35	1	no	—
193	D₁₀₅	—	35	1	no	—
194	D₁₀₅	—	35	1	no	—
195	D₁₀₅	—	35	1	no	—
196	D₁₀₅	—	35	1	no	—
197	D₁₀₅	—	35	1	no	—
198	D₁₀₅	—	35	1	no	—
199	D₁₀₅	—	35	1	no	—
200	D₁₀₅	—	35	1	no	—
201	D₁₀₅	—	35	1	no	—
202	D₁₀₅	—	35	1	no	—
203	D₁₀₅	—	35	1	no	—
204	D₁₀₅	—	35	1	no	—
205	D₁₀₅	—	35	1	no	—
206	D₁₀₅	—	35	1	no	—
207	D₁₀₅	—	35	1	no	—
208	D₁₀₅	—	35	1	no	—
209	D₁₀₅	—	35	1	no	—
210	D₁₀₅	—	35	3	no	—
211	D₁₀₅	—	35	1	no	—
212	D₁₀₅	—	35	3	no	—
213	D₁₀₅	—	35	3	no	—
214	D₁₀₅	—	35	1	no	—
215	D₁₀₅	—	35	1	no	—
216	D₁₀₅	—	35	3	no	—
217	D₁₀₅	—	35	1	no	—
218	D₁₀₅	—	35	1	no	—
219	D₁₀₅	—	35	1	no	—
220	D₁₀₅	—	35	1	no	—
221	D₁₀₅	—	35	1	no	—
222	D₁₀₅	—	35	1	no	—
223	D₁₀₅	—	35	3	no	—
224	D₁₀₅	—	35	3	no	—
225	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
226	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
227	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
228	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
229	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
230	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
231	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
232	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
233	C₅⋊AGL(1,𝔽₇)	—	105	3	no	—
234	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
235	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
236	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
237	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
238	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
239	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
240	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
241	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
242	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
243	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
244	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
245	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
246	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
247	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
248	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
249	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
250	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
251	C₅⋊AGL(1,𝔽₇)	—	105	3	no	—
252	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
253	C₅⋊AGL(1,𝔽₇)	—	105	3	no	—
254	C₅⋊AGL(1,𝔽₇)	—	105	3	no	—
255	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
256	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
257	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
258	C₅⋊AGL(1,𝔽₇)	—	105	3	no	—
259	C₅⋊AGL(1,𝔽₇)	—	105	1	no	—
260	C₅⋊AGL(1,𝔽₇)	—	105	3	no	—
261	C₅²×C₇	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
262	C₅²×C₇	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
263	C₅²×C₇	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
264	C₅²×C₇	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
265	C₅²×C₇	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
266	C₅²×C₇	C₃⋊AGL(1,𝔽₇)	1	3	yes	complemented
267	C₃⋊(C₅⋊D₅)	—	49	1	no	—
268	C₃×C₅⋊D₅	—	147	1	no	—
269	C₃×C₇²	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
270	#3861	—	2	1	no	—
271	#3861	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented
272	C₃⋊AGL(1,𝔽₇)	—	175	1	no	—
273	C₃⋊AGL(1,𝔽₇)	—	175	1	no	—
274	C₃⋊AGL(1,𝔽₇)	—	175	1	no	—
275	C₃⋊AGL(1,𝔽₇)	—	175	1	no	—
276	C₃⋊AGL(1,𝔽₇)	—	175	1	no	—
277	C₃⋊AGL(1,𝔽₇)	—	175	3	no	—
278	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
279	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
280	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
281	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
282	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
283	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
284	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
285	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
286	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
287	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
288	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
289	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
290	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
291	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
292	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
293	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
294	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
295	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
296	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
297	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
298	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
299	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	3	yes	complemented
300	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
301	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	3	yes	complemented
302	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	3	yes	complemented
303	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
304	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
305	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	3	yes	complemented
306	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
307	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
308	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
309	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
310	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
311	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
312	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	3	yes	complemented
313	C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	3	yes	complemented
314	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
315	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
316	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
317	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
318	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
319	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
320	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
321	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
322	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
323	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
324	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
325	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
326	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
327	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
328	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
329	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
330	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
331	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
332	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
333	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
334	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
335	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
336	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
337	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
338	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
339	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
340	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
341	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
342	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
343	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
344	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
345	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
346	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
347	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
348	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
349	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
350	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
351	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
352	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
353	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
354	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
355	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
356	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
357	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
358	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
359	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
360	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
361	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
362	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
363	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
364	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
365	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
366	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
367	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
368	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
369	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
370	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
371	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
372	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
373	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
374	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
375	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
376	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
377	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
378	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
379	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
380	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
381	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
382	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
383	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
384	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
385	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
386	C₇⋊D₇	—	75	1	no	Hall
387	C₃×D₁₅	—	245	1	no	—
388	C₃×D₁₅	—	245	1	no	—
389	C₃×D₁₅	—	245	1	no	—
390	C₃×D₁₅	—	245	1	no	—
391	C₃×D₁₅	—	245	1	no	—
392	C₃×D₁₅	—	245	1	no	—
393	C₃×C₅²	—	98	1	no	—
394	C₃×C₅²	—	98	1	no	—
395	C₃×C₅²	#64424	1	1	yes	characteristic, complemented
396	D₃₅	—	105	1	no	—
397	D₃₅	—	105	1	no	—
398	D₃₅	—	105	1	no	—
399	D₃₅	—	105	1	no	—
400	D₃₅	—	105	1	no	—
401	D₃₅	—	105	1	no	—
402	D₃₅	—	105	1	no	—
403	D₃₅	—	105	1	no	—
404	D₃₅	—	105	3	no	—
405	D₃₅	—	105	1	no	—
406	D₃₅	—	105	1	no	—
407	D₃₅	—	105	1	no	—
408	D₃₅	—	105	1	no	—
409	D₃₅	—	105	1	no	—
410	D₃₅	—	105	1	no	—
411	D₃₅	—	105	1	no	—
412	D₃₅	—	105	1	no	—
413	D₃₅	—	105	1	no	—
414	D₃₅	—	105	1	no	—
415	D₃₅	—	105	1	no	—
416	D₃₅	—	105	1	no	—
417	D₃₅	—	105	1	no	—
418	D₃₅	—	105	1	no	—
419	D₃₅	—	105	1	no	—
420	D₃₅	—	105	1	no	—
421	D₃₅	—	105	1	no	—
422	D₃₅	—	105	3	no	—
423	D₃₅	—	105	1	no	—
424	D₃₅	—	105	3	no	—
425	D₃₅	—	105	3	no	—
426	D₃₅	—	105	1	no	—
427	D₃₅	—	105	1	no	—
428	D₃₅	—	105	1	no	—
429	D₃₅	—	105	3	no	—
430	D₃₅	—	105	1	no	—
431	D₃₅	—	105	3	no	—
432	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
433	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
434	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
435	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
436	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
437	C₃×ΓL(1,𝔽₈)	—	14	3	no	—
438	C₅⋊D₅	—	147	1	no	Hall
439	C₇²	C₃×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Sylow
440	C₃²×C₅	—	98	1	no	—
441	C₃²×C₅	—	98	1	no	—
442	C₃²×C₅	—	98	1	no	—
443	C₃²×C₅	—	98	1	no	—
444	C₃²×C₅	—	98	1	no	—
445	C₃²×C₅	—	98	1	no	—
446	D₂₁	—	175	1	no	—
447	D₂₁	—	175	1	no	—
448	D₂₁	—	175	1	no	—
449	D₂₁	—	175	1	no	—
450	D₂₁	—	175	1	no	—
451	D₂₁	—	175	3	no	—
452	AGL(1,𝔽₇)	—	525	1	no	—
453	AGL(1,𝔽₇)	—	525	1	no	—
454	AGL(1,𝔽₇)	—	525	1	no	—
455	AGL(1,𝔽₇)	—	525	1	no	—
456	AGL(1,𝔽₇)	—	525	1	no	—
457	AGL(1,𝔽₇)	—	525	3	no	—
458	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
459	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
460	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
461	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
462	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
463	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
464	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
465	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
466	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	3	yes	complemented
467	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
468	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
469	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
470	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
471	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
472	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
473	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
474	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
475	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
476	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
477	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
478	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
479	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
480	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
481	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
482	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
483	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
484	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	3	yes	complemented
485	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
486	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	3	yes	complemented
487	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	3	yes	complemented
488	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
489	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
490	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
491	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	3	yes	complemented
492	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
493	C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	3	yes	complemented
494	D₁₅	—	245	1	no	—
495	D₁₅	—	245	1	no	—
496	D₁₅	—	245	1	no	—
497	D₁₅	—	245	1	no	—
498	D₁₅	—	245	1	no	—
499	D₁₅	—	245	1	no	—
500	C₃×D₅	—	735	1	no	—
501	C₃×D₅	—	735	1	no	—
502	C₃×D₅	—	735	1	no	—
503	C₃×D₅	—	735	1	no	—
504	C₃×D₅	—	735	1	no	—
505	C₃×D₅	—	735	1	no	—
506	C₅²	C₃⋊#64424	1	1	yes	characteristic, complemented, Sylow
507	C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
508	C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
509	C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
510	C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
511	C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
512	C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	1	3	yes	complemented
513	ΓL(1,𝔽₈)	—	7	1	no	—
514	ΓL(1,𝔽₈)	—	7	1	no	—
515	ΓL(1,𝔽₈)	—	14	1	no	—
516	ΓL(1,𝔽₈)	—	14	1	no	—
517	ΓL(1,𝔽₈)	—	14	1	no	—
518	ΓL(1,𝔽₈)	—	14	1	no	—
519	ΓL(1,𝔽₈)	—	14	1	no	—
520	ΓL(1,𝔽₈)	—	14	3	no	—
521	ΓL(1,𝔽₈)	—	14	1	no	—
522	ΓL(1,𝔽₈)	—	14	1	no	—
523	ΓL(1,𝔽₈)	—	14	1	no	—
524	ΓL(1,𝔽₈)	—	14	3	no	—
525	C₃×D₃	—	1225	1	no	Hall
526	C₃×C₅	—	49	1	no	—
527	C₃×C₅	—	98	1	no	—
528	C₃×C₅	—	98	1	no	—
529	C₃×C₅	—	98	1	no	—
530	C₃×C₅	—	98	1	no	—
531	C₃×C₅	—	98	1	no	—
532	C₃×C₅	—	98	1	no	—
533	C₃×C₅	—	98	1	no	—
534	C₃×C₅	—	98	1	no	—
535	C₃×C₅	—	98	1	no	—
536	C₃×C₅	—	98	1	no	—
537	C₃×C₅	—	98	1	no	—
538	C₃×C₅	C₅⋊#64424	1	1	yes	characteristic, complemented
539	C₃×C₅	C₅⋊#64424	1	1	yes	characteristic, complemented
540	C₃×C₅	C₅⋊#64424	1	1	yes	characteristic, complemented
541	C₃×C₅	C₅⋊#64424	1	1	yes	characteristic, complemented
542	C₃×C₅	C₅⋊#64424	1	1	yes	characteristic, complemented
543	C₃×C₅	C₅⋊#64424	1	1	yes	characteristic, complemented
544	D₇	—	525	1	no	—
545	D₇	—	525	1	no	—
546	D₇	—	525	1	no	—
547	D₇	—	525	1	no	—
548	D₇	—	525	1	no	—
549	D₇	—	525	3	no	—
550	D₅	—	735	1	no	—
551	D₅	—	735	1	no	—
552	D₅	—	735	1	no	—
553	D₅	—	735	1	no	—
554	D₅	—	735	1	no	—
555	D₅	—	735	1	no	—
556	C₃²	—	98	1	no	Sylow
557	C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	1	1	yes	characteristic, complemented
558	C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	1	1	yes	characteristic, complemented
559	C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	1	1	yes	characteristic, complemented
560	C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	1	1	yes	characteristic, complemented
561	C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	1	1	yes	characteristic, complemented
562	C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	1	3	yes	complemented
563	C₂×C₃	—	3675	1	no	—
564	D₃	—	1225	1	no	—
565	C₅	C₃⋊(C₅⋊#64424)	1	1	yes	characteristic, complemented
566	C₅	C₃⋊(C₅⋊#64424)	1	1	yes	characteristic, complemented
567	C₅	C₃⋊(C₅⋊#64424)	1	1	yes	characteristic, complemented
568	C₅	C₃⋊(C₅⋊#64424)	1	1	yes	characteristic, complemented
569	C₅	C₃⋊(C₅⋊#64424)	1	1	yes	characteristic, complemented
570	C₅	C₃⋊(C₅⋊#64424)	1	1	yes	characteristic, complemented
571	C₃	—	98	1	no	—
572	C₃	—	98	1	no	—
573	C₃	C₅⋊(C₅⋊#64424)	1	1	yes	characteristic, complemented
574	C₂	—	3675	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²×C₇²	C₂×C₃
LCS	G ▷ C₃×C₅²×C₇²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×#3861	C₂	semidirect
2. C₃⋊(C₅⋊(C₅⋊(C₇⋊D₇)))	C₃	semidirect
11. C₅²×#3861	D₃	semidirect
12. C₃×C₅²×C₇²	C₂×C₃	semidirect
20. C₃×C₅×#3861	D₅	semidirect
21. C₃×C₅×#3861	D₅	semidirect
22. C₃×C₅×#3861	D₅	semidirect
23. C₃×C₅×#3861	D₅	semidirect
24. C₃×C₅×#3861	D₅	semidirect
25. C₃×C₅×#3861	D₅	semidirect
44. C₅²×C₇²	C₃×D₃	semidirect
58. C₃×C₅×C₇²	C₃×D₅	semidirect
59. C₃×C₅×C₇²	C₃×D₅	semidirect
60. C₃×C₅×C₇²	C₃×D₅	semidirect
61. C₃×C₅×C₇²	C₃×D₅	semidirect
62. C₃×C₅×C₇²	C₃×D₅	semidirect
63. C₃×C₅×C₇²	C₃×D₅	semidirect
70. C₅×#3861	D₁₅	semidirect
71. C₅×#3861	D₁₅	semidirect
72. C₅×#3861	D₁₅	semidirect
73. C₅×#3861	D₁₅	semidirect
74. C₅×#3861	D₁₅	semidirect
75. C₅×#3861	D₁₅	semidirect
112. C₃×C₅²×C₇	AGL(1,𝔽₇)	semidirect
113. C₃×C₅²×C₇	AGL(1,𝔽₇)	semidirect
114. C₃×C₅²×C₇	AGL(1,𝔽₇)	semidirect
115. C₃×C₅²×C₇	AGL(1,𝔽₇)	semidirect
116. C₃×C₅²×C₇	AGL(1,𝔽₇)	semidirect
117. C₃×C₅²×C₇	AGL(1,𝔽₇)	semidirect
137. C₃×#3861	C₅⋊D₅	semidirect
182. C₅×C₇²	C₃×D₁₅	semidirect
183. C₅×C₇²	C₃×D₁₅	semidirect
184. C₅×C₇²	C₃×D₁₅	semidirect
185. C₅×C₇²	C₃×D₁₅	semidirect
186. C₅×C₇²	C₃×D₁₅	semidirect
187. C₅×C₇²	C₃×D₁₅	semidirect
261. C₅²×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
262. C₅²×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
263. C₅²×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
264. C₅²×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
265. C₅²×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
266. C₅²×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
269. C₃×C₇²	C₃×C₅⋊D₅	semidirect
271. #3861	C₃⋊(C₅⋊D₅)	semidirect
278. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
279. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
280. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
281. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
282. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
283. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
284. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
285. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
286. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
287. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
288. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
289. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
290. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
291. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
292. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
293. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
294. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
295. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
296. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
297. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
298. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
299. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
300. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
301. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
302. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
303. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
304. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
305. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
306. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
307. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
308. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
309. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
310. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
311. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
312. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
313. C₃×C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
395. C₃×C₅²	#64424	semidirect
439. C₇²	C₃×C₃⋊(C₅⋊D₅)	semidirect
458. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
459. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
460. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
461. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
462. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
463. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
464. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
465. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
466. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
467. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
468. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
469. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
470. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
471. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
472. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
473. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
474. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
475. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
476. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
477. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
478. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
479. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
480. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
481. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
482. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
483. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
484. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
485. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
486. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
487. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
488. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
489. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
490. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
491. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
492. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
493. C₅×C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
506. C₅²	C₃⋊#64424	semidirect
507. C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	semidirect
508. C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	semidirect
509. C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	semidirect
510. C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	semidirect
511. C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	semidirect
512. C₃×C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	semidirect
538. C₃×C₅	C₅⋊#64424	semidirect
539. C₃×C₅	C₅⋊#64424	semidirect
540. C₃×C₅	C₅⋊#64424	semidirect
541. C₃×C₅	C₅⋊#64424	semidirect
542. C₃×C₅	C₅⋊#64424	semidirect
543. C₃×C₅	C₅⋊#64424	semidirect
557. C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	semidirect
558. C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	semidirect
559. C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	semidirect
560. C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	semidirect
561. C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	semidirect
562. C₇	C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	semidirect
565. C₅	C₃⋊(C₅⋊#64424)	semidirect
566. C₅	C₃⋊(C₅⋊#64424)	semidirect
567. C₅	C₃⋊(C₅⋊#64424)	semidirect
568. C₅	C₃⋊(C₅⋊#64424)	semidirect
569. C₅	C₃⋊(C₅⋊#64424)	semidirect
570. C₅	C₃⋊(C₅⋊#64424)	semidirect
573. C₃	C₅⋊(C₅⋊#64424)	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×#3861	2
C₃⋊(C₅⋊(C₅⋊(C₇⋊D₇)))	3
C₅⋊(C₅⋊#64424)	3
C₃⋊(C₅⋊#64424)	5
C₃⋊(C₅⋊(C₅⋊AGL(1,𝔽₇)))	7

Subgroups — C3⋊(C5⋊(C5⋊#64424)) #36348048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₅⋊(C₅⋊#64424)) #36348048