Subgroups — #34058298

Order 19072.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750358	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750331	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750330	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750320	C₂	1	2	yes	maximal, complemented
5	#23750319	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750304	C₂	1	2	yes	maximal, complemented
7	#23750300	C₂	1	2	yes	maximal, complemented
8	#23750272	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750271	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750264	C₂	1	2	yes	maximal, complemented
11	#23750259	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750170	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750160	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750158	C₂	1	2	yes	maximal, complemented
15	#23750156	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750135	C₂	1	2	yes	maximal, complemented
17	#23750133	C₂	1	2	yes	maximal, complemented
18	#23750093	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#14558735	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#18011873	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₁₄₉	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558736	C₂²	1	1	yes	characteristic
25	C₂×#14558735	C₂²	1	1	yes	characteristic
26	C₂×#14558735	C₂²	1	2	yes	complemented
27	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₁₄₉	C₂²	1	2	yes	—
29	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	complemented
31	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	complemented
32	#18011910	C₂²	1	1	yes	characteristic, complemented
33	#18011907	C₂²	1	1	yes	characteristic
34	#18011906	C₂²	1	2	yes	complemented
35	#18011905	C₂²	1	2	yes	complemented
36	#18011904	C₂²	1	2	yes	complemented
37	#18011902	C₂²	1	1	yes	characteristic, complemented
38	#18011901	C₂²	1	2	yes	complemented
39	#18011899	C₂²	1	1	yes	characteristic, complemented
40	#18011898	C₂²	1	1	yes	characteristic, complemented
41	#18011897	C₂²	1	2	yes	complemented
42	#18011897	C₂²	1	2	yes	complemented
43	#18011896	C₂²	1	2	yes	complemented
44	#18011896	C₂²	1	2	yes	complemented
45	#18011894	C₂²	1	2	yes	complemented
46	#18011893	C₂²	1	2	yes	complemented
47	#18011893	C₂²	1	2	yes	complemented
48	#18011893	C₂²	1	2	yes	complemented
49	#18011892	C₂²	1	2	yes	complemented
50	#18011891	C₂²	1	1	yes	characteristic, complemented
51	#18011891	C₂²	1	2	yes	complemented
52	#18011890	C₂²	1	1	yes	characteristic, complemented
53	#18011890	C₂²	1	2	yes	complemented
54	#18011889	C₂²	1	2	yes	complemented
55	#18011889	C₂²	1	2	yes	complemented
56	#18011889	C₂²	1	2	yes	complemented
57	#18011886	C₂²	1	1	yes	characteristic
58	#18011885	C₂²	1	1	yes	characteristic, complemented
59	#18011884	C₂²	1	2	yes	—
60	#18011884	C₂²	1	2	yes	complemented
61	#18011884	C₂²	1	2	yes	complemented
62	#18011883	C₂²	1	2	yes	complemented
63	#18011882	C₂²	1	2	yes	complemented
64	#18011881	C₂²	1	2	yes	—
65	#18011879	C₂²	1	2	yes	—
66	#18011879	C₂²	1	2	yes	complemented
67	#18011879	C₂²	1	2	yes	complemented
68	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
69	#18011876	C₂²	1	1	yes	characteristic, complemented
70	#18011876	C₂²	1	1	yes	characteristic, complemented
71	#18011876	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
73	C₄×D₅₉₆	C₂²	1	2	yes	complemented
74	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
75	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
76	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
77	#18011873	C₂²	1	1	yes	characteristic
78	#18011873	C₂²	1	1	yes	characteristic
79	#18011873	C₂²	1	1	yes	characteristic
80	#18011873	C₂²	1	2	yes	complemented
81	#18011873	C₂²	1	1	yes	characteristic, complemented
82	#18011873	C₂²	1	2	yes	complemented
83	#18011873	C₂²	1	2	yes	complemented
84	#18011873	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
88	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
89	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
90	#18011871	C₂²	1	1	yes	characteristic
91	#18011871	C₂²	1	2	yes	complemented
92	#18011871	C₂²	1	2	yes	complemented
93	#18011871	C₂²	1	2	yes	complemented
94	#18011871	C₂²	1	1	yes	characteristic, complemented
95	#18011871	C₂²	1	2	yes	complemented
96	#18011869	C₂²	1	2	yes	complemented
97	#18011869	C₂²	1	1	yes	characteristic, complemented
98	#18011868	C₂²	1	2	yes	complemented
99	#18011867	C₂²	1	2	yes	complemented
100	#18011867	C₂²	1	1	yes	characteristic, complemented
101	#18011867	C₂²	1	1	yes	characteristic, complemented
102	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
104	C₂×#14558713	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
108	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
110	C₄²×D₁₄₉	C₂²	1	2	yes	complemented
111	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
112	#126×C₁₄₉	C₂²	1	2	yes	complemented
113	#125×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
114	#123×C₁₄₉	C₂²	1	2	yes	complemented
115	#121×C₁₄₉	C₂²	1	1	yes	characteristic
116	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₄₉	C₂²	1	2	yes	complemented
118	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
120	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
121	#117×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₄₉	C₂³	1	2	yes	—
124	C₂³×D₁₄₉	C₂³	1	2	yes	—
125	#14558736	—	2	4	no	—
126	#14558735	—	2	4	no	—
127	#14558735	—	4	4	no	—
128	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₉₈	C₂³	1	2	yes	—
131	C₂×D₅₉₆	—	2	4	no	—
132	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
133	C₂×D₅₉₆	C₂³	1	2	yes	—
134	C₂×D₅₉₆	C₂³	1	2	yes	—
135	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
143	D₄×D₁₄₉	—	2	4	no	—
144	D₄×D₁₄₉	—	2	8	no	—
145	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
147	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
149	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₄₉	—	4	4	no	—
151	C₂×C₄×D₁₄₉	—	4	4	no	—
152	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
154	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
155	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
156	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
159	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
160	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
161	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
162	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
163	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
164	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
165	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
167	#14558715	C₂³	1	2	yes	—
168	#14558715	C₂³	1	2	yes	—
169	#14558715	C₂³	1	1	yes	characteristic
170	#14558715	C₂³	1	2	yes	—
171	#14558715	C₂³	1	2	yes	—
172	#14558715	C₂³	1	2	yes	—
173	#14558715	C₂³	1	1	yes	characteristic
174	#14558715	C₂³	1	1	yes	characteristic
175	#14558715	C₂³	1	1	yes	characteristic
176	#14558715	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
183	#14558713	C₂³	1	2	yes	—
184	#14558713	C₂³	1	2	yes	—
185	#14558713	C₂³	1	2	yes	—
186	#14558713	C₂³	1	2	yes	—
187	#14558713	C₂³	1	2	yes	—
188	#14558713	C₂³	1	1	yes	characteristic
189	#14558713	C₂³	1	2	yes	—
190	#14558713	C₂³	1	2	yes	—
191	#14558713	C₂³	1	2	yes	—
192	#14558713	C₂³	1	2	yes	—
193	#14558713	C₂³	1	2	yes	—
194	#14558713	C₂³	1	1	yes	characteristic
195	#14558713	C₂³	1	2	yes	—
196	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₄₉	C₂³	1	2	yes	—
202	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₄₉	C₂³	1	2	yes	—
204	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
205	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
206	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
209	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
211	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
214	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
228	C₄²×C₁₄₉	C₂³	1	2	yes	—
229	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
230	C₂²×D₁₄₉	—	2	4	no	—
231	C₂²×D₁₄₉	—	2	4	no	—
232	C₂²×D₁₄₉	—	2	4	no	—
233	C₂²×D₁₄₉	—	2	4	no	—
234	C₂²×D₁₄₉	—	4	2	no	—
235	C₂²×D₁₄₉	—	4	2	no	—
236	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
237	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
238	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
239	Dic₂₉₈	—	2	2	no	—
240	Dic₂₉₈	—	2	2	no	—
241	Dic₂₉₈	—	4	2	no	—
242	D₅₉₆	—	2	4	no	—
243	D₅₉₆	—	2	4	no	—
244	D₅₉₆	—	2	2	no	—
245	D₅₉₆	#41	1	4	yes	complemented
246	C₂²⋊D₁₄₉	—	2	4	no	—
247	C₂²⋊D₁₄₉	—	2	2	no	—
248	C₂²⋊D₁₄₉	—	2	4	no	—
249	C₂²⋊D₁₄₉	—	2	4	no	—
250	C₂²⋊D₁₄₉	—	4	2	no	—
251	C₂²⋊D₁₄₉	—	4	2	no	—
252	C₂²⋊D₁₄₉	#41	1	4	yes	complemented
253	C₂×Dic₁₄₉	—	2	2	no	—
254	C₂×Dic₁₄₉	—	2	2	no	—
255	C₂×Dic₁₄₉	—	2	2	no	—
256	C₂×Dic₁₄₉	—	2	4	no	—
257	C₂×Dic₁₄₉	—	2	2	no	—
258	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
260	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
263	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
267	C₄×D₁₄₉	—	2	2	no	—
268	C₄×D₁₄₉	—	2	4	no	—
269	C₄×D₁₄₉	—	2	2	no	—
270	C₄×D₁₄₉	—	2	4	no	—
271	C₄×D₁₄₉	—	2	2	no	—
272	C₄×D₁₄₉	—	2	4	no	—
273	C₄×D₁₄₉	—	2	4	no	—
274	C₄×D₁₄₉	—	4	2	no	—
275	C₄×D₁₄₉	—	4	2	no	—
276	C₄×D₁₄₉	—	4	2	no	—
277	C₄×D₁₄₉	—	4	2	no	—
278	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
279	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
280	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
281	D₄×C₁₄₉	—	2	4	no	—
282	D₄×C₁₄₉	—	2	2	no	—
283	D₄×C₁₄₉	—	2	2	no	—
284	D₄×C₁₄₉	—	4	2	no	—
285	C₂×C₄×C₁₄₉	—	2	2	no	—
286	C₂×C₄×C₁₄₉	—	2	2	no	—
287	C₂×C₄×C₁₄₉	—	4	2	no	—
288	C₂×C₄×C₁₄₉	—	4	2	no	—
289	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
291	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
292	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
293	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
294	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
295	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
297	C₂²×C₁₄₉	—	2	1	no	—
298	C₂²×C₁₄₉	—	2	1	no	—
299	C₂²×C₁₄₉	—	2	1	no	—
300	C₂²×C₁₄₉	—	2	1	no	—
301	C₂²×C₁₄₉	—	2	2	no	—
302	C₂²×C₁₄₉	—	2	2	no	—
303	C₂²×C₁₄₉	—	2	2	no	—
304	C₂²×C₁₄₉	—	2	1	no	—
305	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
306	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
307	C₂×D₁₄₉	—	2	1	no	—
308	C₂×D₁₄₉	—	2	2	no	—
309	C₂×D₁₄₉	—	2	1	no	—
310	C₂×D₁₄₉	—	2	2	no	—
311	C₂×D₁₄₉	—	2	2	no	—
312	C₂×D₁₄₉	—	2	2	no	—
313	C₂×D₁₄₉	—	2	2	no	—
314	C₂×D₁₄₉	—	4	8	no	—
315	C₂×D₁₄₉	—	4	8	no	—
316	C₂×D₁₄₉	C₂×#41	1	4	yes	—
317	C₂×D₁₄₉	C₂×#41	1	2	yes	—
318	C₄×C₁₄₉	—	2	1	no	—
319	C₄×C₁₄₉	—	2	1	no	—
320	C₄×C₁₄₉	—	2	2	no	—
321	C₄×C₁₄₉	—	2	1	no	—
322	C₄×C₁₄₉	—	2	1	no	—
323	C₄×C₁₄₉	—	2	2	no	—
324	C₄×C₁₄₉	—	2	2	no	—
325	C₄×C₁₄₉	C₂×#41	1	2	yes	—
326	Dic₁₄₉	—	2	1	no	—
327	Dic₁₄₉	—	2	1	no	—
328	Dic₁₄₉	—	2	2	no	—
329	Dic₁₄₉	—	2	1	no	—
330	Dic₁₄₉	—	2	1	no	—
331	Dic₁₄₉	—	2	2	no	—
332	Dic₁₄₉	—	2	1	no	—
333	Dic₁₄₉	C₂×#41	1	2	yes	—
334	Dic₁₄₉	H(5,𝔽₂)	1	2	yes	—
335	C₂×C₁₄₉	—	2	2	no	—
336	C₂×C₁₄₉	—	4	2	no	—
337	C₂×C₁₄₉	—	4	1	no	—
338	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
339	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
340	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
341	D₁₄₉	—	2	2	no	—
342	D₁₄₉	—	2	4	no	—
343	D₁₄₉	—	4	2	no	—
344	C₁₄₉	#3481	1	1	yes	characteristic, complemented, Sylow
345	#3481	—	149	1	no	maximal, Sylow
346	#559	—	149	1	no	—
347	#554	—	149	1	no	—
348	#554	—	149	1	no	—
349	#553	—	149	2	no	—
350	#553	—	149	1	no	—
351	#553	D₁₄₉	1	1	yes	characteristic, complemented
352	#551	—	149	2	no	—
353	#551	—	149	2	no	—
354	#546	—	149	2	no	—
355	#546	—	149	1	no	—
356	#546	—	149	1	no	—
357	D₄²	—	149	1	no	—
358	#532	—	149	1	no	—
359	#529	—	149	2	no	—
360	#529	—	149	1	no	—
361	#529	—	149	1	no	—
362	#525	—	149	2	no	—
363	#525	—	149	2	no	—
364	C₄×#41	—	149	1	no	—
365	C₄×#41	—	149	1	no	—
366	C₂×C₄×D₄	—	149	2	no	—
367	C₂×C₄×D₄	—	149	1	no	—
368	C₂×C₄×D₄	—	149	1	no	—
369	C₂×#41	—	149	1	no	—
370	C₂×#41	—	149	2	no	—
371	C₂×#41	—	149	1	no	—
372	C₂²×D₄	—	149	1	no	—
373	C₂²×D₄	—	149	2	no	—
374	C₂²×D₄	—	149	1	no	—
375	C₂³×C₄	—	149	2	no	—
376	C₂³×C₄	—	149	2	no	—
377	C₄⋊Q₈	—	149	1	no	—
378	#127	—	149	1	no	—
379	#126	—	149	2	no	—
380	#126	—	149	2	no	—
381	#126	—	149	2	no	—
382	#126	C₂×D₁₄₉	1	2	yes	complemented
383	#125	—	149	2	no	—
384	#125	—	149	1	no	—
385	#125	C₂×D₁₄₉	1	1	yes	characteristic, complemented
386	#124	—	149	1	no	—
387	#124	—	149	2	no	—
388	#124	—	149	2	no	—
389	#124	—	149	1	no	—
390	#123	—	149	2	no	—
391	#123	—	149	2	no	—
392	#123	—	149	2	no	—
393	#123	—	149	2	no	—
394	#123	—	149	2	no	—
395	#123	—	149	2	no	—
396	#123	—	149	2	no	—
397	#123	C₂×D₁₄₉	1	2	yes	complemented
398	C₂²⋊Q₈	—	149	2	no	—
399	C₂²⋊Q₈	—	149	1	no	—
400	C₂²⋊Q₈	—	149	2	no	—
401	C₂²⋊Q₈	—	149	2	no	—
402	C₂²⋊Q₈	—	149	2	no	—
403	C₂²⋊Q₈	—	149	2	no	—
404	C₂²⋊Q₈	—	149	1	no	—
405	#121	—	149	2	no	—
406	#121	—	149	2	no	—
407	#121	—	149	1	no	—
408	#121	—	149	1	no	—
409	#121	—	149	2	no	—
410	#121	—	149	2	no	—
411	#121	—	149	2	no	—
412	#121	C₂×D₁₄₉	1	1	yes	characteristic
413	#121	C₂×D₁₄₉	1	2	yes	complemented
414	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
415	#120	—	149	2	no	—
416	#120	—	149	2	no	—
417	#120	—	149	2	no	—
418	#120	—	149	2	no	—
419	C₄×Q₈	—	149	1	no	—
420	C₄×Q₈	—	149	1	no	—
421	C₄×Q₈	—	149	1	no	—
422	C₄×Q₈	—	149	1	no	—
423	C₄×D₄	—	149	2	no	—
424	C₄×D₄	—	149	1	no	—
425	C₄×D₄	—	149	1	no	—
426	C₄×D₄	—	149	2	no	—
427	C₄×D₄	—	149	2	no	—
428	C₄×D₄	—	149	2	no	—
429	C₄×D₄	—	149	1	no	—
430	C₄×D₄	—	149	1	no	—
431	C₄×D₄	—	149	1	no	—
432	C₄×D₄	—	149	2	no	—
433	C₄×D₄	—	149	2	no	—
434	C₄×D₄	—	149	1	no	—
435	C₄×D₄	—	149	1	no	—
436	C₄×D₄	—	149	2	no	—
437	C₄×D₄	—	149	1	no	—
438	C₄×D₄	—	149	1	no	—
439	C₄×D₄	—	149	1	no	—
440	C₄×D₄	—	149	2	no	—
441	C₄×D₄	—	149	2	no	—
442	C₄×D₄	—	149	1	no	—
443	C₄×D₄	—	149	2	no	—
444	C₄×D₄	—	149	2	no	—
445	C₄×D₄	—	149	1	no	—
446	C₄×D₄	—	149	2	no	—
447	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
448	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
449	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
450	#117	—	149	1	no	—
451	#117	—	149	2	no	—
452	#117	—	149	1	no	—
453	#117	—	149	1	no	—
454	#117	—	149	2	no	—
455	#117	—	149	2	no	—
456	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
457	C₂×C₄⋊C₄	—	149	2	no	—
458	C₂×C₄⋊C₄	—	149	1	no	—
459	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
460	C₂×C₂²⋊C₄	—	149	2	no	—
461	C₂×C₂²⋊C₄	—	149	2	no	—
462	C₂×C₂²⋊C₄	—	149	2	no	—
463	C₂×C₂²⋊C₄	—	149	2	no	—
464	C₂×C₄²	—	149	1	no	—
465	C₂×C₄²	—	149	1	no	—
466	C₂×C₄²	—	149	1	no	—
467	C₂×C₄²	—	149	2	no	—
468	C₂⁴	—	149	2	no	—
469	C₂⁴	—	149	2	no	—
470	#41	—	298	4	no	—
471	#41	—	298	4	no	—
472	#41	—	596	4	no	—
473	C₂×Q₈	—	149	1	no	—
474	C₂×Q₈	—	149	1	no	—
475	C₂×Q₈	—	149	2	no	—
476	C₂×D₄	—	298	4	no	—
477	C₂×D₄	—	298	8	no	—
478	C₂×D₄	—	298	4	no	—
479	C₂×D₄	—	149	1	no	—
480	C₂×D₄	—	149	2	no	—
481	C₂×D₄	—	149	2	no	—
482	C₂×D₄	—	149	2	no	—
483	C₂×D₄	—	149	2	no	—
484	C₂×D₄	—	149	2	no	—
485	C₂×D₄	—	149	1	no	—
486	C₂×D₄	—	149	2	no	—
487	C₂×D₄	—	149	2	no	—
488	C₂×D₄	—	149	1	no	—
489	C₂×D₄	—	149	1	no	—
490	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
491	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
492	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
493	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
494	C₂²×C₄	—	596	4	no	—
495	C₂²×C₄	—	596	4	no	—
496	C₂²×C₄	—	149	1	no	—
497	C₂²×C₄	—	149	1	no	—
498	C₂²×C₄	—	149	1	no	—
499	C₂²×C₄	—	149	1	no	—
500	C₂²×C₄	—	149	2	no	—
501	C₂²×C₄	—	149	1	no	—
502	C₂²×C₄	—	149	2	no	—
503	C₂²×C₄	—	149	2	no	—
504	C₂²×C₄	—	149	1	no	—
505	C₂²×C₄	—	149	1	no	—
506	C₂²×C₄	—	149	2	no	—
507	C₂²×C₄	—	149	2	no	—
508	C₂²×C₄	—	149	2	no	—
509	C₂²×C₄	—	149	2	no	—
510	C₂²×C₄	—	149	2	no	—
511	C₂²×C₄	—	149	2	no	—
512	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
515	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
516	C₄⋊C₄	—	149	1	no	—
517	C₄⋊C₄	—	149	2	no	—
518	C₄⋊C₄	—	149	1	no	—
519	C₄⋊C₄	—	149	2	no	—
520	C₄⋊C₄	—	149	2	no	—
521	C₄⋊C₄	—	149	1	no	—
522	C₄⋊C₄	—	149	1	no	—
523	C₄⋊C₄	—	149	2	no	—
524	C₄⋊C₄	—	149	1	no	—
525	C₄⋊C₄	—	149	2	no	—
526	C₄⋊C₄	—	149	1	no	—
527	C₄⋊C₄	—	149	2	no	—
528	C₄⋊C₄	—	149	2	no	—
529	C₄⋊C₄	—	149	2	no	—
530	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
532	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
533	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
534	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
536	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
537	C₂²⋊C₄	—	149	2	no	—
538	C₂²⋊C₄	—	149	2	no	—
539	C₂²⋊C₄	—	149	2	no	—
540	C₂²⋊C₄	—	149	1	no	—
541	C₂²⋊C₄	—	149	1	no	—
542	C₂²⋊C₄	—	149	2	no	—
543	C₂²⋊C₄	—	149	2	no	—
544	C₂²⋊C₄	—	149	1	no	—
545	C₂²⋊C₄	—	149	2	no	—
546	C₂²⋊C₄	—	149	2	no	—
547	C₂²⋊C₄	—	149	2	no	—
548	C₂²⋊C₄	—	149	2	no	—
549	C₂²⋊C₄	—	149	2	no	—
550	C₂²⋊C₄	—	149	2	no	—
551	C₂²⋊C₄	—	149	2	no	—
552	C₂²⋊C₄	—	149	1	no	—
553	C₂²⋊C₄	—	149	2	no	—
554	C₂²⋊C₄	—	149	2	no	—
555	C₂²⋊C₄	—	149	2	no	—
556	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
557	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
562	C₄²	—	149	1	no	—
563	C₄²	—	149	1	no	—
564	C₄²	—	149	1	no	—
565	C₄²	—	149	1	no	—
566	C₄²	—	149	2	no	—
567	C₄²	—	149	1	no	—
568	C₄²	—	149	1	no	—
569	C₄²	—	149	1	no	—
570	C₄²	—	149	1	no	—
571	C₄²	—	149	2	no	—
572	C₄²	—	149	1	no	—
573	C₄²	C₂²×D₁₄₉	1	2	yes	—
574	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
575	C₂³	—	298	4	no	—
576	C₂³	—	298	4	no	—
577	C₂³	—	298	4	no	—
578	C₂³	—	298	4	no	—
579	C₂³	—	596	2	no	—
580	C₂³	—	596	2	no	—
581	C₂³	—	149	2	no	—
582	C₂³	—	149	2	no	—
583	C₂³	—	149	1	no	—
584	C₂³	C₂³×D₁₄₉	1	2	yes	—
585	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
586	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
587	Q₈	—	298	2	no	—
588	Q₈	—	298	2	no	—
589	Q₈	—	596	2	no	—
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	2	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	298	4	no	—
595	D₄	—	298	4	no	—
596	D₄	—	298	4	no	—
597	D₄	—	298	4	no	—
598	D₄	—	298	2	no	—
599	D₄	—	298	4	no	—
600	D₄	—	298	2	no	—
601	D₄	—	596	2	no	—
602	D₄	—	596	2	no	—
603	D₄	—	149	4	no	—
604	D₄	—	149	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	298	4	no	—
610	C₂×C₄	—	298	2	no	—
611	C₂×C₄	—	298	2	no	—
612	C₂×C₄	—	298	4	no	—
613	C₂×C₄	—	298	4	no	—
614	C₂×C₄	—	298	4	no	—
615	C₂×C₄	—	298	2	no	—
616	C₂×C₄	—	298	2	no	—
617	C₂×C₄	—	298	4	no	—
618	C₂×C₄	—	298	2	no	—
619	C₂×C₄	—	298	2	no	—
620	C₂×C₄	—	298	2	no	—
621	C₂×C₄	—	596	2	no	—
622	C₂×C₄	—	596	2	no	—
623	C₂×C₄	—	596	2	no	—
624	C₂×C₄	—	596	2	no	—
625	C₂×C₄	—	149	1	no	—
626	C₂×C₄	—	149	2	no	—
627	C₂×C₄	—	149	1	no	—
628	C₂×C₄	—	149	1	no	—
629	C₂×C₄	—	149	1	no	—
630	C₂×C₄	—	149	1	no	—
631	C₂×C₄	—	149	2	no	—
632	C₂×C₄	—	149	1	no	—
633	C₂×C₄	—	149	1	no	—
634	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
638	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
640	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
641	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	298	2	no	—
651	C₂²	—	298	1	no	—
652	C₂²	—	298	2	no	—
653	C₂²	—	298	1	no	—
654	C₂²	—	298	2	no	—
655	C₂²	—	298	2	no	—
656	C₂²	—	298	2	no	—
657	C₂²	—	596	8	no	—
658	C₂²	—	596	8	no	—
659	C₂²	—	149	2	no	—
660	C₂²	—	149	4	no	—
661	C₂²	#41×D₁₄₉	1	2	yes	—
662	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	298	1	no	—
671	C₄	—	298	1	no	—
672	C₄	—	298	1	no	—
673	C₄	—	298	2	no	—
674	C₄	—	298	1	no	—
675	C₄	—	298	2	no	—
676	C₄	—	298	1	no	—
677	C₄	—	149	2	no	—
678	C₄	—	149	2	no	—
679	C₄	#41×D₁₄₉	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	4	2	no	—
682	C₂	—	4	1	no	—
683	C₂	—	298	4	no	—
684	C₂	—	298	2	no	—
685	C₂	—	596	2	no	—
686	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
687	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
688	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#553×C₁₄₉	C₂
hypercenter	#553	D₁₄₉
hypocenter	C₁₄₉	#3481
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #23750358	C₂	semidirect
2. #23750331	C₂	semidirect
3. #23750330	C₂	semidirect
4. #23750320	C₂	semidirect
5. #23750319	C₂	semidirect
6. #23750304	C₂	semidirect
7. #23750300	C₂	semidirect
8. #23750272	C₂	semidirect
9. #23750271	C₂	semidirect
10. #23750264	C₂	semidirect
11. #23750259	C₂	semidirect
12. #23750170	C₂	semidirect
13. #23750160	C₂	semidirect
14. #23750158	C₂	semidirect
15. #23750156	C₂	semidirect
16. #23750135	C₂	semidirect
17. #23750133	C₂	semidirect
18. #23750093	C₂	semidirect
19. C₄×#14558735	C₂	semidirect
20. C₂×#18011873	C₂	semidirect
21. C₄×D₄×D₁₄₉	C₂	semidirect
22. C₄×D₄×D₁₄₉	C₂	semidirect
23. #553×C₁₄₉	C₂	semidirect
26. C₂×#14558735	C₂²	semidirect
30. C₂²×C₄×D₁₄₉	C₂²	semidirect
31. C₂²×C₄×D₁₄₉	C₂²	semidirect
32. #18011910	C₂²	semidirect
34. #18011906	C₂²	semidirect
35. #18011905	C₂²	semidirect
36. #18011904	C₂²	semidirect
37. #18011902	C₂²	semidirect
38. #18011901	C₂²	semidirect
39. #18011899	C₂²	semidirect
40. #18011898	C₂²	semidirect
41. #18011897	C₂²	semidirect
42. #18011897	C₂²	semidirect
43. #18011896	C₂²	semidirect
44. #18011896	C₂²	semidirect
45. #18011894	C₂²	semidirect
46. #18011893	C₂²	semidirect
47. #18011893	C₂²	semidirect
48. #18011893	C₂²	semidirect
49. #18011892	C₂²	semidirect
50. #18011891	C₂²	semidirect
51. #18011891	C₂²	semidirect
52. #18011890	C₂²	semidirect
53. #18011890	C₂²	semidirect
54. #18011889	C₂²	semidirect
55. #18011889	C₂²	semidirect
56. #18011889	C₂²	semidirect
58. #18011885	C₂²	semidirect
60. #18011884	C₂²	semidirect
61. #18011884	C₂²	semidirect
62. #18011883	C₂²	semidirect
63. #18011882	C₂²	semidirect
66. #18011879	C₂²	semidirect
67. #18011879	C₂²	semidirect
68. C₄×Dic₂₉₈	C₂²	semidirect
69. #18011876	C₂²	semidirect
70. #18011876	C₂²	semidirect
71. #18011876	C₂²	semidirect
73. C₄×D₅₉₆	C₂²	semidirect
74. D₄×Dic₁₄₉	C₂²	semidirect
75. D₄×Dic₁₄₉	C₂²	semidirect
76. D₄×Dic₁₄₉	C₂²	semidirect
80. #18011873	C₂²	semidirect
81. #18011873	C₂²	semidirect
82. #18011873	C₂²	semidirect
83. #18011873	C₂²	semidirect
84. #18011873	C₂²	semidirect
87. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
88. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
89. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
91. #18011871	C₂²	semidirect
92. #18011871	C₂²	semidirect
93. #18011871	C₂²	semidirect
94. #18011871	C₂²	semidirect
95. #18011871	C₂²	semidirect
96. #18011869	C₂²	semidirect
97. #18011869	C₂²	semidirect
98. #18011868	C₂²	semidirect
99. #18011867	C₂²	semidirect
100. #18011867	C₂²	semidirect
101. #18011867	C₂²	semidirect
102. C₄⋊C₄×D₁₄₉	C₂²	semidirect
103. C₄⋊C₄×D₁₄₉	C₂²	semidirect
104. C₂×#14558713	C₂²	semidirect
105. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
106. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
107. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
108. C₂×C₄×Dic₁₄₉	C₂²	semidirect
109. C₂×C₄×Dic₁₄₉	C₂²	semidirect
110. C₄²×D₁₄₉	C₂²	semidirect
111. C₄²×D₁₄₉	C₂²	semidirect
112. #126×C₁₄₉	C₂²	semidirect
113. #125×C₁₄₉	C₂²	semidirect
114. #123×C₁₄₉	C₂²	semidirect
116. #121×C₁₄₉	C₂²	semidirect
117. #121×C₁₄₉	C₂²	semidirect
118. C₄×D₄×C₁₄₉	C₂²	semidirect
119. C₄×D₄×C₁₄₉	C₂²	semidirect
120. C₄×D₄×C₁₄₉	C₂²	semidirect
121. #117×C₁₄₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
245. D₅₉₆	#41	semidirect
252. C₂²⋊D₁₄₉	#41	semidirect
344. C₁₄₉	#3481	semidirect
351. #553	D₁₄₉	semidirect
382. #126	C₂×D₁₄₉	semidirect
385. #125	C₂×D₁₄₉	semidirect
397. #123	C₂×D₁₄₉	semidirect
413. #121	C₂×D₁₄₉	semidirect
414. #121	C₂×D₁₄₉	semidirect
447. C₄×D₄	C₂×D₁₄₉	semidirect
448. C₄×D₄	C₂×D₁₄₉	semidirect
449. C₄×D₄	C₂×D₁₄₉	semidirect
456. #117	C₂×D₁₄₉	semidirect
459. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750358	2
#23750331	2
#23750330	2
#23750320	2
#23750319	2
#23750304	2
#23750300	2
#23750272	2
#23750271	2
#23750264	2
#23750259	2
#23750170	2
#23750160	2
#23750158	2
#23750156	2
#23750135	2
#23750133	2
#23750093	2
C₄×#14558735	2
C₂×#18011873	2
C₄×D₄×D₁₄₉	2
#553×C₁₄₉	2
#3481	149