Subgroups — #553×D₁₅₁ #34082625

Order 19328.

1252 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23752915	C₂	1	1	yes	maximal, characteristic, complemented
2	#23752914	C₂	1	1	yes	maximal, characteristic, complemented
3	#23752913	C₂	1	2	yes	maximal, complemented
4	#23752912	C₂	1	1	yes	maximal, characteristic, complemented
5	#23752911	C₂	1	2	yes	maximal, complemented
6	#23752910	C₂	1	1	yes	maximal, characteristic, complemented
7	#23752909	C₂	1	1	yes	maximal, characteristic, complemented
8	#23752908	C₂	1	1	yes	maximal, characteristic, complemented
9	#23752907	C₂	1	2	yes	maximal, complemented
10	#23752906	C₂	1	1	yes	maximal, characteristic, complemented
11	#23752905	C₂	1	2	yes	maximal, complemented
12	#126×D₁₅₁	C₂	1	2	yes	maximal, complemented
13	#125×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#123×D₁₅₁	C₂	1	2	yes	maximal, complemented
15	#121×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#121×D₁₅₁	C₂	1	2	yes	maximal, complemented
17	#121×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₄×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×D₄×D₁₅₁	C₂	1	2	yes	maximal, complemented
21	#117×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₄×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₄×D₁₅₁	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₁₅₁	C₂²	1	2	yes	—
26	C₂×D₄×D₁₅₁	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₅₁	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₅₁	C₂²	1	2	yes	—
31	C₂²×C₄×D₁₅₁	C₂²	1	2	yes	—
32	#18012734	C₂²	1	2	yes	complemented
33	#18012734	C₂²	1	2	yes	complemented
34	#18012734	C₂²	1	2	yes	complemented
35	#18012733	C₂²	1	2	yes	complemented
36	#18012732	C₂²	1	2	yes	complemented
37	#18012732	C₂²	1	2	yes	complemented
38	#18012732	C₂²	1	2	yes	complemented
39	#18012731	C₂²	1	1	yes	characteristic, complemented
40	#18012730	C₂²	1	1	yes	characteristic, complemented
41	#18012730	C₂²	1	1	yes	characteristic, complemented
42	#18012729	C₂²	1	2	yes	complemented
43	#18012729	C₂²	1	2	yes	complemented
44	#18012724	C₂²	1	2	yes	complemented
45	#18012724	C₂²	1	2	yes	complemented
46	#18012723	C₂²	1	2	yes	complemented
47	#18012722	C₂²	1	2	yes	complemented
48	#18012721	C₂²	1	2	yes	complemented
49	#18012721	C₂²	1	2	yes	complemented
50	#18012720	C₂²	1	2	yes	complemented
51	#18012714	C₂²	1	1	yes	characteristic, complemented
52	#18012714	C₂²	1	1	yes	characteristic, complemented
53	#18012714	C₂²	1	2	yes	complemented
54	#18012713	C₂²	1	1	yes	characteristic, complemented
55	#18012713	C₂²	1	1	yes	characteristic, complemented
56	#18012713	C₂²	1	2	yes	complemented
57	#18012712	C₂²	1	2	yes	complemented
58	#18012712	C₂²	1	2	yes	complemented
59	#18012712	C₂²	1	2	yes	complemented
60	#18012712	C₂²	1	2	yes	complemented
61	#18012711	C₂²	1	2	yes	complemented
62	#18012711	C₂²	1	2	yes	complemented
63	#18012711	C₂²	1	2	yes	complemented
64	#18012711	C₂²	1	2	yes	complemented
65	#18012710	C₂²	1	2	yes	complemented
66	#18012710	C₂²	1	1	yes	characteristic, complemented
67	#18012710	C₂²	1	1	yes	characteristic, complemented
68	C₄×D₆₀₄	C₂²	1	2	yes	complemented
69	C₄×D₆₀₄	C₂²	1	1	yes	characteristic, complemented
70	C₄×D₆₀₄	C₂²	1	1	yes	characteristic, complemented
71	D₄×Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₁₅₁	C₂²	1	2	yes	complemented
73	D₄×Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
74	#18012701	C₂²	1	1	yes	characteristic, complemented
75	#18012701	C₂²	1	2	yes	complemented
76	#18012701	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₁₅₁	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₁₅₁	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₁₅₁	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₁₅₁	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₁₅₁	C₂²	1	1	yes	characteristic, complemented
82	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	2	yes	complemented
83	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
84	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	2	yes	complemented
85	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	2	yes	complemented
86	(C₂²⋊D₁₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	#18012698	C₂²	1	1	yes	characteristic, complemented
88	#18012697	C₂²	1	1	yes	characteristic, complemented
89	#18012697	C₂²	1	1	yes	characteristic, complemented
90	#18012696	C₂²	1	2	yes	complemented
91	#18012695	C₂²	1	2	yes	complemented
92	C₂×C₄⋊Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
93	C₂×Dic₁₅₁⋊C₄	C₂²	1	2	yes	complemented
94	C₄⋊C₄×D₁₅₁	C₂²	1	2	yes	—
95	C₄⋊C₄×D₁₅₁	C₂²	1	2	yes	—
96	C₄⋊C₄×D₁₅₁	C₂²	1	2	yes	—
97	C₄⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic
98	C₄⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic
99	C₄⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic
100	C₄⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic
101	C₄⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic, complemented
102	C₄⋊C₄×D₁₅₁	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic, complemented
104	C₂²⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic
105	C₂²⋊C₄×D₁₅₁	C₂²	1	2	yes	—
106	C₂²⋊C₄×D₁₅₁	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₁₅₁	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₁₅₁	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₁₅₁	C₂²	1	1	yes	characteristic
110	C₄²×D₁₅₁	C₂²	1	1	yes	characteristic
111	C₄²×D₁₅₁	C₂²	1	2	yes	—
112	#126×C₁₅₁	C₂²	1	2	yes	complemented
113	#125×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
114	#123×C₁₅₁	C₂²	1	2	yes	complemented
115	#121×C₁₅₁	C₂²	1	2	yes	complemented
116	#121×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₅₁	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
121	#117×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₅₁	C₂³	1	1	yes	characteristic
124	C₂³×D₁₅₁	C₂³	1	2	yes	—
125	C₂³×D₁₅₁	C₂³	1	1	yes	characteristic
126	C₂×D₆₀₄	C₂³	1	2	yes	—
127	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
128	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
129	C₂×D₆₀₄	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₅₁	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₅₁	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₅₁	C₂³	1	2	yes	—
137	D₄×D₁₅₁	—	2	4	no	—
138	D₄×D₁₅₁	—	2	8	no	—
139	D₄×D₁₅₁	—	2	4	no	—
140	D₄×D₁₅₁	—	4	4	no	—
141	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
142	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
143	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
144	C₂²×Dic₁₅₁	C₂³	1	2	yes	—
145	C₂×C₄×D₁₅₁	—	2	4	no	—
146	C₂×C₄×D₁₅₁	—	2	4	no	—
147	C₂×C₄×D₁₅₁	—	4	4	no	—
148	C₂×C₄×D₁₅₁	—	4	4	no	—
149	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
152	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
154	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
156	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
161	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
162	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
163	C₂×C₄×D₁₅₁	C₂³	1	2	yes	—
164	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
168	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
170	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₁₅₁	C₂³	1	2	yes	—
172	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
173	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
174	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
175	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
176	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
177	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
178	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
179	Dic₁₅₁⋊C₄	C₂³	1	1	yes	characteristic
180	Dic₁₅₁⋊C₄	C₂³	1	1	yes	characteristic
181	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
182	Dic₁₅₁⋊C₄	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₅₁	C₂³	1	2	yes	—
189	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₁₅₁)⋊C₄	C₂³	1	2	yes	—
201	C₄×Dic₁₅₁	C₂³	1	2	yes	—
202	C₄×Dic₁₅₁	C₂³	1	2	yes	—
203	C₄×Dic₁₅₁	C₂³	1	2	yes	—
204	C₄×Dic₁₅₁	C₂³	1	1	yes	characteristic
205	C₄×Dic₁₅₁	C₂³	1	1	yes	characteristic
206	C₄×Dic₁₅₁	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₁₅₁	C₂³	1	2	yes	—
210	C₂×D₄×C₁₅₁	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
214	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
218	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
220	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₁₅₁	C₂³	1	2	yes	—
228	C₄²×C₁₅₁	C₂³	1	2	yes	—
229	C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
230	C₂²×D₁₅₁	—	2	2	no	—
231	C₂²×D₁₅₁	—	2	2	no	—
232	C₂²×D₁₅₁	—	2	2	no	—
233	C₂²×D₁₅₁	—	2	2	no	—
234	C₂²×D₁₅₁	—	2	4	no	—
235	C₂²×D₁₅₁	—	2	4	no	—
236	C₂²×D₁₅₁	—	2	4	no	—
237	C₂²×D₁₅₁	—	2	2	no	—
238	C₂²×D₁₅₁	#41	1	4	yes	—
239	C₂²×D₁₅₁	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₅₁	C₂⁴	1	2	yes	—
241	C₂²×D₁₅₁	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₅₁	C₂⁴	1	1	yes	characteristic
243	D₆₀₄	—	2	4	no	—
244	D₆₀₄	—	2	2	no	—
245	D₆₀₄	—	2	2	no	—
246	D₆₀₄	—	4	2	no	—
247	C₂²⋊D₁₅₁	—	2	4	no	—
248	C₂²⋊D₁₅₁	—	2	2	no	—
249	C₂²⋊D₁₅₁	—	2	2	no	—
250	C₂²⋊D₁₅₁	—	2	4	no	—
251	C₂²⋊D₁₅₁	—	2	4	no	—
252	C₂²⋊D₁₅₁	—	4	2	no	—
253	C₂²⋊D₁₅₁	—	4	2	no	—
254	C₂×Dic₁₅₁	—	2	2	no	—
255	C₂×Dic₁₅₁	—	2	2	no	—
256	C₂×Dic₁₅₁	—	4	2	no	—
257	C₂×Dic₁₅₁	—	4	2	no	—
258	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
260	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
262	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
265	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
266	C₄×D₁₅₁	—	2	2	no	—
267	C₄×D₁₅₁	—	2	2	no	—
268	C₄×D₁₅₁	—	2	2	no	—
269	C₄×D₁₅₁	—	2	4	no	—
270	C₄×D₁₅₁	—	2	2	no	—
271	C₄×D₁₅₁	—	2	4	no	—
272	C₄×D₁₅₁	—	2	4	no	—
273	C₄×D₁₅₁	—	2	2	no	—
274	C₄×D₁₅₁	—	2	2	no	—
275	C₄×D₁₅₁	—	2	2	no	—
276	C₄×D₁₅₁	—	2	2	no	—
277	C₄×D₁₅₁	—	4	2	no	—
278	C₄×D₁₅₁	—	4	2	no	—
279	C₄×D₁₅₁	—	4	2	no	—
280	C₄×D₁₅₁	—	4	2	no	—
281	C₄×D₁₅₁	#41	1	4	yes	—
282	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
283	C₂³×C₁₅₁	C₂⁴	1	2	yes	—
284	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
285	D₄×C₁₅₁	—	2	2	no	—
286	D₄×C₁₅₁	—	2	4	no	—
287	D₄×C₁₅₁	—	2	2	no	—
288	D₄×C₁₅₁	—	4	2	no	—
289	C₂×C₄×C₁₅₁	—	2	2	no	—
290	C₂×C₄×C₁₅₁	—	2	2	no	—
291	C₂×C₄×C₁₅₁	—	4	2	no	—
292	C₂×C₄×C₁₅₁	—	4	2	no	—
293	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
294	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
295	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
297	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
298	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
299	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
300	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
301	C₂²×C₁₅₁	—	2	1	no	—
302	C₂²×C₁₅₁	—	2	1	no	—
303	C₂²×C₁₅₁	—	2	1	no	—
304	C₂²×C₁₅₁	—	2	1	no	—
305	C₂²×C₁₅₁	—	2	2	no	—
306	C₂²×C₁₅₁	—	2	2	no	—
307	C₂²×C₁₅₁	—	2	2	no	—
308	C₂²×C₁₅₁	—	2	1	no	—
309	C₂²×C₁₅₁	C₂×#41	1	2	yes	—
310	C₂²×C₁₅₁	C₂⁵	1	1	yes	characteristic
311	C₂×D₁₅₁	—	2	1	no	—
312	C₂×D₁₅₁	—	2	1	no	—
313	C₂×D₁₅₁	—	2	8	no	—
314	C₂×D₁₅₁	—	2	1	no	—
315	C₂×D₁₅₁	—	2	1	no	—
316	C₂×D₁₅₁	—	2	2	no	—
317	C₂×D₁₅₁	—	2	2	no	—
318	C₂×D₁₅₁	—	2	2	no	—
319	C₂×D₁₅₁	—	2	1	no	—
320	C₂×D₁₅₁	—	4	4	no	—
321	C₂×D₁₅₁	—	4	8	no	—
322	C₂×D₁₅₁	C₂×#41	1	2	yes	—
323	C₂×D₁₅₁	C₂×#41	1	2	yes	—
324	C₂×D₁₅₁	C₂×#41	1	2	yes	—
325	C₂×D₁₅₁	H(5,𝔽₂)	1	2	yes	—
326	C₄×C₁₅₁	—	2	1	no	—
327	C₄×C₁₅₁	—	2	1	no	—
328	C₄×C₁₅₁	—	2	2	no	—
329	C₄×C₁₅₁	—	2	1	no	—
330	C₄×C₁₅₁	—	2	1	no	—
331	C₄×C₁₅₁	—	2	2	no	—
332	C₄×C₁₅₁	—	2	2	no	—
333	C₄×C₁₅₁	C₂×#41	1	2	yes	—
334	Dic₁₅₁	—	2	1	no	—
335	Dic₁₅₁	—	2	1	no	—
336	Dic₁₅₁	—	2	2	no	—
337	Dic₁₅₁	—	2	1	no	—
338	Dic₁₅₁	—	2	1	no	—
339	Dic₁₅₁	—	2	2	no	—
340	Dic₁₅₁	—	2	2	no	—
341	Dic₁₅₁	C₂×#41	1	2	yes	—
342	C₂×C₁₅₁	—	2	2	no	—
343	C₂×C₁₅₁	—	4	1	no	—
344	C₂×C₁₅₁	—	4	2	no	—
345	C₂×C₁₅₁	C₂²×#41	1	1	yes	characteristic
346	C₂×C₁₅₁	C₂²×#41	1	1	yes	characteristic
347	C₂×C₁₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	D₁₅₁	—	2	2	no	—
349	D₁₅₁	—	4	1	no	—
350	D₁₅₁	—	4	2	no	—
351	D₁₅₁	#553	1	4	yes	direct product factor
352	C₁₅₁	C₂×#553	1	1	yes	characteristic, complemented, Sylow
353	C₂×#553	—	151	1	no	maximal, Sylow
354	#553	—	151	2	no	—
355	#553	—	151	1	no	—
356	#553	—	151	2	no	—
357	#553	—	151	2	no	—
358	#553	—	151	1	no	—
359	#553	—	151	1	no	—
360	#553	—	151	1	no	—
361	#553	—	151	2	no	—
362	#553	—	151	1	no	—
363	#553	—	151	1	no	—
364	#553	—	151	1	no	—
365	#553	D₁₅₁	1	1	yes	characteristic, direct product factor
366	C₂×#126	—	151	2	no	—
367	C₂×#125	—	151	1	no	—
368	C₂×#123	—	151	2	no	—
369	C₂×#121	—	151	2	no	—
370	C₂×#121	—	151	1	no	—
371	C₂×#121	—	151	1	no	—
372	C₂×C₄×D₄	—	151	2	no	—
373	C₂×C₄×D₄	—	151	1	no	—
374	C₂×C₄×D₄	—	151	1	no	—
375	C₂×#117	—	151	1	no	—
376	C₂²×C₄⋊C₄	—	151	1	no	—
377	C₂²×D₄	—	151	2	no	—
378	C₂²×D₄	—	151	1	no	—
379	C₂²×D₄	—	151	1	no	—
380	C₂²×D₄	—	151	2	no	—
381	C₂³×C₄	—	151	1	no	—
382	C₂³×C₄	—	151	1	no	—
383	C₂³×C₄	—	151	2	no	—
384	C₂³×C₄	—	151	2	no	—
385	#126	—	151	2	no	—
386	#126	—	151	2	no	—
387	#126	—	151	2	no	—
388	#126	—	151	2	no	—
389	#126	—	151	2	no	—
390	#126	—	151	2	no	—
391	#126	—	151	2	no	—
392	#126	C₂×D₁₅₁	1	2	yes	complemented
393	#125	—	151	2	no	—
394	#125	—	151	2	no	—
395	#125	—	151	1	no	—
396	#125	—	151	1	no	—
397	#125	—	151	1	no	—
398	#125	C₂×D₁₅₁	1	1	yes	characteristic, complemented
399	#123	—	151	2	no	—
400	#123	—	151	2	no	—
401	#123	—	151	2	no	—
402	#123	—	151	2	no	—
403	#123	—	151	2	no	—
404	#123	—	151	2	no	—
405	#123	—	151	2	no	—
406	#123	C₂×D₁₅₁	1	2	yes	complemented
407	#121	—	151	2	no	—
408	#121	—	151	1	no	—
409	#121	—	151	1	no	—
410	#121	—	151	2	no	—
411	#121	—	151	2	no	—
412	#121	—	151	2	no	—
413	#121	—	151	2	no	—
414	#121	—	151	2	no	—
415	#121	—	151	1	no	—
416	#121	—	151	1	no	—
417	#121	—	151	2	no	—
418	#121	—	151	1	no	—
419	#121	—	151	1	no	—
420	#121	—	151	2	no	—
421	#121	—	151	2	no	—
422	#121	—	151	2	no	—
423	#121	—	151	2	no	—
424	#121	C₂×D₁₅₁	1	2	yes	complemented
425	#121	C₂×D₁₅₁	1	1	yes	characteristic, complemented
426	#121	C₂×D₁₅₁	1	1	yes	characteristic, complemented
427	C₄×D₄	—	151	2	no	—
428	C₄×D₄	—	151	1	no	—
429	C₄×D₄	—	151	1	no	—
430	C₄×D₄	—	151	2	no	—
431	C₄×D₄	—	151	2	no	—
432	C₄×D₄	—	151	1	no	—
433	C₄×D₄	—	151	2	no	—
434	C₄×D₄	—	151	1	no	—
435	C₄×D₄	—	151	2	no	—
436	C₄×D₄	—	151	1	no	—
437	C₄×D₄	—	151	1	no	—
438	C₄×D₄	—	151	2	no	—
439	C₄×D₄	—	151	2	no	—
440	C₄×D₄	—	151	1	no	—
441	C₄×D₄	—	151	2	no	—
442	C₄×D₄	—	151	1	no	—
443	C₄×D₄	—	151	2	no	—
444	C₄×D₄	—	151	1	no	—
445	C₄×D₄	—	151	1	no	—
446	C₄×D₄	C₂×D₁₅₁	1	2	yes	complemented
447	C₄×D₄	C₂×D₁₅₁	1	1	yes	characteristic, complemented
448	C₄×D₄	C₂×D₁₅₁	1	1	yes	characteristic, complemented
449	#117	—	151	1	no	—
450	#117	—	151	1	no	—
451	#117	—	151	1	no	—
452	#117	—	151	2	no	—
453	#117	—	151	2	no	—
454	#117	C₂×D₁₅₁	1	1	yes	characteristic, complemented
455	C₂×C₄⋊C₄	—	151	2	no	—
456	C₂×C₄⋊C₄	—	151	1	no	—
457	C₂×C₄⋊C₄	—	151	1	no	—
458	C₂×C₄⋊C₄	—	151	1	no	—
459	C₂×C₄⋊C₄	—	151	2	no	—
460	C₂×C₄⋊C₄	—	151	2	no	—
461	C₂×C₄⋊C₄	—	151	1	no	—
462	C₂×C₄⋊C₄	—	151	1	no	—
463	C₂×C₄⋊C₄	—	151	1	no	—
464	C₂×C₄⋊C₄	—	151	2	no	—
465	C₂×C₄⋊C₄	—	151	1	no	—
466	C₂×C₄⋊C₄	—	151	2	no	—
467	C₂×C₄⋊C₄	C₂×D₁₅₁	1	1	yes	characteristic, complemented
468	C₂×C₂²⋊C₄	—	151	2	no	—
469	C₂×C₂²⋊C₄	—	151	1	no	—
470	C₂×C₂²⋊C₄	—	151	2	no	—
471	C₂×C₂²⋊C₄	—	151	2	no	—
472	C₂×C₂²⋊C₄	—	151	1	no	—
473	C₂×C₂²⋊C₄	—	151	2	no	—
474	C₂×C₄²	—	151	2	no	—
475	C₂×C₄²	—	151	1	no	—
476	C₂⁴	—	151	1	no	—
477	C₂⁴	—	151	2	no	—
478	C₂⁴	—	151	1	no	—
479	C₂×D₄	—	302	8	no	—
480	C₂×D₄	—	302	4	no	—
481	C₂×D₄	—	302	4	no	—
482	C₂×D₄	—	604	4	no	—
483	C₂×D₄	—	151	2	no	—
484	C₂×D₄	—	151	1	no	—
485	C₂×D₄	—	151	2	no	—
486	C₂×D₄	—	151	1	no	—
487	C₂×D₄	—	151	2	no	—
488	C₂×D₄	—	151	2	no	—
489	C₂×D₄	—	151	2	no	—
490	C₂×D₄	—	151	2	no	—
491	C₂×D₄	—	151	1	no	—
492	C₂×D₄	—	151	1	no	—
493	C₂×D₄	—	151	2	no	—
494	C₂×D₄	C₂²×D₁₅₁	1	2	yes	—
495	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₁₅₁	1	2	yes	—
498	C₂²×C₄	—	302	4	no	—
499	C₂²×C₄	—	302	4	no	—
500	C₂²×C₄	—	604	4	no	—
501	C₂²×C₄	—	604	4	no	—
502	C₂²×C₄	—	151	1	no	—
503	C₂²×C₄	—	151	1	no	—
504	C₂²×C₄	—	151	1	no	—
505	C₂²×C₄	—	151	2	no	—
506	C₂²×C₄	—	151	1	no	—
507	C₂²×C₄	—	151	2	no	—
508	C₂²×C₄	—	151	1	no	—
509	C₂²×C₄	—	151	1	no	—
510	C₂²×C₄	—	151	2	no	—
511	C₂²×C₄	—	151	1	no	—
512	C₂²×C₄	—	151	1	no	—
513	C₂²×C₄	—	151	1	no	—
514	C₂²×C₄	—	151	1	no	—
515	C₂²×C₄	—	151	2	no	—
516	C₂²×C₄	—	151	2	no	—
517	C₂²×C₄	—	151	2	no	—
518	C₂²×C₄	—	151	2	no	—
519	C₂²×C₄	—	151	2	no	—
520	C₂²×C₄	—	151	2	no	—
521	C₂²×C₄	—	151	1	no	—
522	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
525	C₂²×C₄	C₂²×D₁₅₁	1	2	yes	—
526	C₄⋊C₄	—	151	2	no	—
527	C₄⋊C₄	—	151	2	no	—
528	C₄⋊C₄	—	151	2	no	—
529	C₄⋊C₄	—	151	2	no	—
530	C₄⋊C₄	—	151	2	no	—
531	C₄⋊C₄	—	151	2	no	—
532	C₄⋊C₄	—	151	2	no	—
533	C₄⋊C₄	—	151	1	no	—
534	C₄⋊C₄	—	151	1	no	—
535	C₄⋊C₄	—	151	2	no	—
536	C₄⋊C₄	—	151	2	no	—
537	C₄⋊C₄	—	151	1	no	—
538	C₄⋊C₄	—	151	1	no	—
539	C₄⋊C₄	—	151	2	no	—
540	C₄⋊C₄	—	151	1	no	—
541	C₄⋊C₄	—	151	2	no	—
542	C₄⋊C₄	—	151	1	no	—
543	C₄⋊C₄	—	151	2	no	—
544	C₄⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₁₅₁	1	2	yes	—
547	C₄⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₁₅₁	1	2	yes	—
549	C₄⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
550	C₄⋊C₄	C₂²×D₁₅₁	1	2	yes	—
551	C₂²⋊C₄	—	151	2	no	—
552	C₂²⋊C₄	—	151	1	no	—
553	C₂²⋊C₄	—	151	2	no	—
554	C₂²⋊C₄	—	151	2	no	—
555	C₂²⋊C₄	—	151	1	no	—
556	C₂²⋊C₄	—	151	2	no	—
557	C₂²⋊C₄	—	151	2	no	—
558	C₂²⋊C₄	—	151	2	no	—
559	C₂²⋊C₄	—	151	1	no	—
560	C₂²⋊C₄	—	151	1	no	—
561	C₂²⋊C₄	—	151	2	no	—
562	C₂²⋊C₄	—	151	2	no	—
563	C₂²⋊C₄	—	151	2	no	—
564	C₂²⋊C₄	—	151	2	no	—
565	C₂²⋊C₄	—	151	1	no	—
566	C₂²⋊C₄	—	151	1	no	—
567	C₂²⋊C₄	—	151	2	no	—
568	C₂²⋊C₄	—	151	2	no	—
569	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
570	C₂²⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
571	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
573	C₂²⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₁₅₁	1	2	yes	—
575	C₄²	—	151	2	no	—
576	C₄²	—	151	2	no	—
577	C₄²	—	151	2	no	—
578	C₄²	—	151	1	no	—
579	C₄²	—	151	1	no	—
580	C₄²	—	151	1	no	—
581	C₄²	C₂²×D₁₅₁	1	2	yes	—
582	C₄²	C₂²×D₁₅₁	1	1	yes	characteristic
583	C₂³	—	302	2	no	—
584	C₂³	—	302	2	no	—
585	C₂³	—	302	2	no	—
586	C₂³	—	302	4	no	—
587	C₂³	—	302	2	no	—
588	C₂³	—	302	4	no	—
589	C₂³	—	302	4	no	—
590	C₂³	—	302	2	no	—
591	C₂³	—	151	1	no	—
592	C₂³	—	151	2	no	—
593	C₂³	—	151	4	no	—
594	C₂³	—	151	1	no	—
595	C₂³	—	151	1	no	—
596	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
597	C₂³	C₂³×D₁₅₁	1	2	yes	—
598	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
599	D₄	—	2	4	no	—
600	D₄	—	2	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	4	2	no	—
603	D₄	—	302	4	no	—
604	D₄	—	302	2	no	—
605	D₄	—	302	4	no	—
606	D₄	—	302	2	no	—
607	D₄	—	302	4	no	—
608	D₄	—	302	2	no	—
609	D₄	—	302	4	no	—
610	D₄	—	302	2	no	—
611	D₄	—	604	2	no	—
612	D₄	—	604	2	no	—
613	D₄	—	604	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	302	2	no	—
619	C₂×C₄	—	302	2	no	—
620	C₂×C₄	—	302	2	no	—
621	C₂×C₄	—	302	4	no	—
622	C₂×C₄	—	302	4	no	—
623	C₂×C₄	—	302	4	no	—
624	C₂×C₄	—	302	2	no	—
625	C₂×C₄	—	302	2	no	—
626	C₂×C₄	—	302	2	no	—
627	C₂×C₄	—	302	2	no	—
628	C₂×C₄	—	302	2	no	—
629	C₂×C₄	—	302	2	no	—
630	C₂×C₄	—	302	2	no	—
631	C₂×C₄	—	604	2	no	—
632	C₂×C₄	—	604	2	no	—
633	C₂×C₄	—	604	2	no	—
634	C₂×C₄	—	604	2	no	—
635	C₂×C₄	—	604	2	no	—
636	C₂×C₄	—	604	2	no	—
637	C₂×C₄	—	151	1	no	—
638	C₂×C₄	—	151	2	no	—
639	C₂×C₄	—	151	1	no	—
640	C₂×C₄	—	151	2	no	—
641	C₂×C₄	—	151	1	no	—
642	C₂×C₄	—	151	1	no	—
643	C₂×C₄	—	151	2	no	—
644	C₂×C₄	—	151	1	no	—
645	C₂×C₄	—	151	4	no	—
646	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
648	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
650	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
653	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	302	8	no	—
663	C₂²	—	302	1	no	—
664	C₂²	—	302	1	no	—
665	C₂²	—	302	1	no	—
666	C₂²	—	302	1	no	—
667	C₂²	—	302	2	no	—
668	C₂²	—	302	2	no	—
669	C₂²	—	302	2	no	—
670	C₂²	—	302	1	no	—
671	C₂²	—	604	4	no	—
672	C₂²	—	604	8	no	—
673	C₂²	—	151	2	no	—
674	C₂²	—	151	2	no	—
675	C₂²	—	151	2	no	—
676	C₂²	—	151	2	no	—
677	C₂²	#41×D₁₅₁	1	2	yes	—
678	C₂²	C₂⁴×D₁₅₁	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	302	1	no	—
687	C₄	—	302	1	no	—
688	C₄	—	302	2	no	—
689	C₄	—	302	1	no	—
690	C₄	—	302	1	no	—
691	C₄	—	302	2	no	—
692	C₄	—	302	2	no	—
693	C₄	—	151	2	no	—
694	C₄	#41×D₁₅₁	1	2	yes	—
695	C₂	—	2	2	no	—
696	C₂	—	4	1	no	—
697	C₂	—	4	2	no	—
698	C₂	—	302	2	no	—
699	C₂	—	604	1	no	—
700	C₂	—	604	2	no	—
701	C₂	—	151	4	no	—
702	C₂	C₂×#41×D₁₅₁	1	1	yes	characteristic
703	C₂	C₂×#41×D₁₅₁	1	1	yes	characteristic
704	C₂	H(5,𝔽₂)×D₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₅₁
commutator, socle, cosocle	C₂²×C₁₅₁	C₂⁵
Fitting	#553×C₁₅₁	C₂
hypercenter	#553	D₁₅₁
hypocenter	C₁₅₁	C₂×#553
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #23752915	C₂	semidirect
2. #23752914	C₂	semidirect
3. #23752913	C₂	semidirect
4. #23752912	C₂	semidirect
5. #23752911	C₂	semidirect
6. #23752910	C₂	semidirect
7. #23752909	C₂	semidirect
8. #23752908	C₂	semidirect
9. #23752907	C₂	semidirect
10. #23752906	C₂	semidirect
11. #23752905	C₂	semidirect
12. #126×D₁₅₁	C₂	semidirect
13. #125×D₁₅₁	C₂	semidirect
14. #123×D₁₅₁	C₂	semidirect
15. #121×D₁₅₁	C₂	semidirect
16. #121×D₁₅₁	C₂	semidirect
17. #121×D₁₅₁	C₂	semidirect
18. C₄×D₄×D₁₅₁	C₂	semidirect
19. C₄×D₄×D₁₅₁	C₂	semidirect
20. C₄×D₄×D₁₅₁	C₂	semidirect
21. #117×D₁₅₁	C₂	semidirect
22. C₂×C₄⋊C₄×D₁₅₁	C₂	semidirect
23. #553×C₁₅₁	C₂	semidirect
32. #18012734	C₂²	semidirect
33. #18012734	C₂²	semidirect
34. #18012734	C₂²	semidirect
35. #18012733	C₂²	semidirect
36. #18012732	C₂²	semidirect
37. #18012732	C₂²	semidirect
38. #18012732	C₂²	semidirect
39. #18012731	C₂²	semidirect
40. #18012730	C₂²	semidirect
41. #18012730	C₂²	semidirect
42. #18012729	C₂²	semidirect
43. #18012729	C₂²	semidirect
44. #18012724	C₂²	semidirect
45. #18012724	C₂²	semidirect
46. #18012723	C₂²	semidirect
47. #18012722	C₂²	semidirect
48. #18012721	C₂²	semidirect
49. #18012721	C₂²	semidirect
50. #18012720	C₂²	semidirect
51. #18012714	C₂²	semidirect
52. #18012714	C₂²	semidirect
53. #18012714	C₂²	semidirect
54. #18012713	C₂²	semidirect
55. #18012713	C₂²	semidirect
56. #18012713	C₂²	semidirect
57. #18012712	C₂²	semidirect
58. #18012712	C₂²	semidirect
59. #18012712	C₂²	semidirect
60. #18012712	C₂²	semidirect
61. #18012711	C₂²	semidirect
62. #18012711	C₂²	semidirect
63. #18012711	C₂²	semidirect
64. #18012711	C₂²	semidirect
65. #18012710	C₂²	semidirect
66. #18012710	C₂²	semidirect
67. #18012710	C₂²	semidirect
68. C₄×D₆₀₄	C₂²	semidirect
69. C₄×D₆₀₄	C₂²	semidirect
70. C₄×D₆₀₄	C₂²	semidirect
71. D₄×Dic₁₅₁	C₂²	semidirect
72. D₄×Dic₁₅₁	C₂²	semidirect
73. D₄×Dic₁₅₁	C₂²	semidirect
74. #18012701	C₂²	semidirect
75. #18012701	C₂²	semidirect
76. #18012701	C₂²	semidirect
77. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
78. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
79. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
80. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
81. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
82. (C₂²⋊D₁₅₁)⋊C₄	C₂²	semidirect
83. (C₂²⋊D₁₅₁)⋊C₄	C₂²	semidirect
84. (C₂²⋊D₁₅₁)⋊C₄	C₂²	semidirect
85. (C₂²⋊D₁₅₁)⋊C₄	C₂²	semidirect
86. (C₂²⋊D₁₅₁)⋊C₄	C₂²	semidirect
87. #18012698	C₂²	semidirect
88. #18012697	C₂²	semidirect
89. #18012697	C₂²	semidirect
90. #18012696	C₂²	semidirect
91. #18012695	C₂²	semidirect
92. C₂×C₄⋊Dic₁₅₁	C₂²	semidirect
93. C₂×Dic₁₅₁⋊C₄	C₂²	semidirect
101. C₄⋊C₄×D₁₅₁	C₂²	semidirect
102. C₄⋊C₄×D₁₅₁	C₂²	semidirect
103. C₄⋊C₄×D₁₅₁	C₂²	semidirect
112. #126×C₁₅₁	C₂²	semidirect
113. #125×C₁₅₁	C₂²	semidirect
114. #123×C₁₅₁	C₂²	semidirect
115. #121×C₁₅₁	C₂²	semidirect
116. #121×C₁₅₁	C₂²	semidirect
117. #121×C₁₅₁	C₂²	semidirect
118. C₄×D₄×C₁₅₁	C₂²	semidirect
119. C₄×D₄×C₁₅₁	C₂²	semidirect
120. C₄×D₄×C₁₅₁	C₂²	semidirect
121. #117×C₁₅₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₅₁	C₂²	semidirect
351. D₁₅₁	#553	direct (N × H)
352. C₁₅₁	C₂×#553	semidirect
365. #553	D₁₅₁	direct (N × H)
392. #126	C₂×D₁₅₁	semidirect
398. #125	C₂×D₁₅₁	semidirect
406. #123	C₂×D₁₅₁	semidirect
424. #121	C₂×D₁₅₁	semidirect
425. #121	C₂×D₁₅₁	semidirect
426. #121	C₂×D₁₅₁	semidirect
446. C₄×D₄	C₂×D₁₅₁	semidirect
447. C₄×D₄	C₂×D₁₅₁	semidirect
448. C₄×D₄	C₂×D₁₅₁	semidirect
454. #117	C₂×D₁₅₁	semidirect
467. C₂×C₄⋊C₄	C₂×D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#23752915	2
#23752914	2
#23752913	2
#23752912	2
#23752911	2
#23752910	2
#23752909	2
#23752908	2
#23752907	2
#23752906	2
#23752905	2
#126×D₁₅₁	2
#125×D₁₅₁	2
#123×D₁₅₁	2
#121×D₁₅₁	2
C₄×D₄×D₁₅₁	2
#117×D₁₅₁	2
C₂×C₄⋊C₄×D₁₅₁	2
#553×C₁₅₁	2
C₂×#553	151

Subgroups — #553×D151 #34082625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #553×D₁₅₁ #34082625