Subgroups — #34058716

Order 19072.

1252 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750338	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750330	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750328	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750326	C₂	1	2	yes	maximal, complemented
5	#23750293	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750271	C₂	1	2	yes	maximal, complemented
7	#23750271	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750270	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750267	C₂	1	2	yes	maximal, complemented
10	#23750259	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750259	C₂	1	2	yes	maximal, complemented
12	#23750227	C₂	1	2	yes	maximal, complemented
13	#23750214	C₂	1	2	yes	maximal, complemented
14	#23750212	C₂	1	2	yes	maximal, complemented
15	#23750172	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750160	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750137	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750135	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#18011886	C₂	1	1	yes	maximal, characteristic, complemented
20	#121×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750097	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	2	yes	complemented
25	C₂×#14558736	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14558735	C₂²	1	1	yes	characteristic, complemented
27	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₅₉₆	C₂²	1	2	yes	complemented
29	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₁₄₉	C₂²	1	2	yes	—
31	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
32	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
35	#18011910	C₂²	1	1	yes	characteristic, complemented
36	#18011907	C₂²	1	1	yes	characteristic, complemented
37	#18011907	C₂²	1	2	yes	complemented
38	#18011906	C₂²	1	2	yes	complemented
39	#18011906	C₂²	1	2	yes	complemented
40	#18011901	C₂²	1	2	yes	complemented
41	#18011899	C₂²	1	1	yes	characteristic, complemented
42	#18011899	C₂²	1	2	yes	complemented
43	#18011897	C₂²	1	2	yes	complemented
44	#18011897	C₂²	1	2	yes	complemented
45	#18011896	C₂²	1	2	yes	complemented
46	#18011896	C₂²	1	2	yes	complemented
47	#18011896	C₂²	1	2	yes	complemented
48	#18011895	C₂²	1	2	yes	complemented
49	#18011895	C₂²	1	2	yes	complemented
50	#18011893	C₂²	1	2	yes	complemented
51	#18011891	C₂²	1	1	yes	characteristic, complemented
52	#18011891	C₂²	1	1	yes	characteristic, complemented
53	#18011890	C₂²	1	2	yes	complemented
54	#18011890	C₂²	1	1	yes	characteristic, complemented
55	#18011889	C₂²	1	2	yes	complemented
56	#18011886	C₂²	1	1	yes	characteristic
57	#18011886	C₂²	1	1	yes	characteristic, complemented
58	#18011886	C₂²	1	2	yes	complemented
59	#18011886	C₂²	1	2	yes	complemented
60	#18011886	C₂²	1	1	yes	characteristic, complemented
61	#18011886	C₂²	1	2	yes	complemented
62	#18011886	C₂²	1	1	yes	characteristic, complemented
63	#18011886	C₂²	1	1	yes	characteristic, complemented
64	#18011885	C₂²	1	2	yes	complemented
65	#18011885	C₂²	1	1	yes	characteristic, complemented
66	#18011884	C₂²	1	2	yes	complemented
67	#18011884	C₂²	1	2	yes	complemented
68	#18011884	C₂²	1	2	yes	complemented
69	#18011884	C₂²	1	2	yes	complemented
70	#18011884	C₂²	1	2	yes	complemented
71	#18011884	C₂²	1	2	yes	complemented
72	#18011883	C₂²	1	2	yes	complemented
73	#18011883	C₂²	1	2	yes	complemented
74	#18011882	C₂²	1	1	yes	characteristic, complemented
75	#18011881	C₂²	1	2	yes	complemented
76	#18011881	C₂²	1	2	yes	complemented
77	#18011881	C₂²	1	2	yes	complemented
78	#18011879	C₂²	1	2	yes	complemented
79	#18011879	C₂²	1	2	yes	complemented
80	#18011879	C₂²	1	2	yes	complemented
81	#18011876	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₅₉₆	C₂²	1	2	yes	complemented
84	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₅₉₆	C₂²	1	2	yes	complemented
86	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
87	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
88	#18011873	C₂²	1	2	yes	complemented
89	#18011873	C₂²	1	1	yes	characteristic, complemented
90	#18011873	C₂²	1	1	yes	characteristic, complemented
91	#18011873	C₂²	1	2	yes	complemented
92	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
95	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
96	#18011871	C₂²	1	1	yes	characteristic
97	#18011871	C₂²	1	1	yes	characteristic, complemented
98	#18011871	C₂²	1	2	yes	complemented
99	#18011871	C₂²	1	2	yes	complemented
100	#18011869	C₂²	1	2	yes	complemented
101	#18011869	C₂²	1	1	yes	characteristic, complemented
102	#18011868	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
105	C₂×#14558713	C₂²	1	2	yes	complemented
106	C₂×#14558713	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
109	C₂²⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
110	C₂²⋊C₄×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	2	yes	complemented
116	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₁₄₉	C₂²	1	2	yes	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	1	yes	characteristic
124	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
125	C₂³×D₁₄₉	C₂³	1	2	yes	—
126	C₂³×D₁₄₉	C₂³	1	2	yes	—
127	#14558736	—	4	2	no	—
128	#14558736	—	4	4	no	—
129	#14558735	—	4	2	no	—
130	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
131	C₂×Dic₂₉₈	C₂³	1	2	yes	—
132	C₂×D₅₉₆	—	4	2	no	—
133	C₂×D₅₉₆	—	4	4	no	—
134	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
135	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
136	C₂×D₅₉₆	C₂³	1	2	yes	—
137	C₂×D₅₉₆	C₂³	1	2	yes	—
138	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
139	C₂×D₅₉₆	C₂³	1	2	yes	—
140	C₂×D₅₉₆	C₂³	1	2	yes	—
141	C₂×D₅₉₆	C₂³	1	2	yes	—
142	C₂×D₅₉₆	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
152	D₄×D₁₄₉	—	2	4	no	—
153	D₄×D₁₄₉	—	2	8	no	—
154	D₄×D₁₄₉	—	4	2	no	—
155	D₄×D₁₄₉	—	4	4	no	—
156	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
157	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
158	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
159	C₂×C₄×D₁₄₉	—	4	2	no	—
160	C₂×C₄×D₁₄₉	—	4	2	no	—
161	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
166	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
172	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
173	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
174	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
176	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
177	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
178	#14558715	C₂³	1	2	yes	—
179	#14558715	C₂³	1	2	yes	—
180	#14558715	C₂³	1	2	yes	—
181	#14558715	C₂³	1	1	yes	characteristic
182	#14558715	C₂³	1	1	yes	characteristic
183	#14558715	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
188	#14558713	C₂³	1	2	yes	—
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	2	yes	—
195	#14558713	C₂³	1	1	yes	characteristic
196	#14558713	C₂³	1	2	yes	—
197	#14558713	C₂³	1	1	yes	characteristic
198	#14558713	C₂³	1	1	yes	characteristic
199	#14558713	C₂³	1	1	yes	characteristic
200	#14558713	C₂³	1	2	yes	—
201	#14558713	C₂³	1	2	yes	—
202	#14558713	C₂³	1	2	yes	—
203	#14558713	C₂³	1	2	yes	—
204	#14558713	C₂³	1	2	yes	—
205	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
206	C₄×Dic₁₄₉	C₂³	1	2	yes	—
207	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
208	C₄×Dic₁₄₉	C₂³	1	2	yes	—
209	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
213	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
214	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
217	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
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	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
224	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
229	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
230	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
231	C₄²×C₁₄₉	C₂³	1	2	yes	—
232	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
233	C₂²×D₁₄₉	—	2	2	no	—
234	C₂²×D₁₄₉	—	2	4	no	—
235	C₂²×D₁₄₉	—	2	2	no	—
236	C₂²×D₁₄₉	—	2	2	no	—
237	C₂²×D₁₄₉	—	2	2	no	—
238	C₂²×D₁₄₉	—	2	4	no	—
239	C₂²×D₁₄₉	—	4	1	no	—
240	C₂²×D₁₄₉	—	4	1	no	—
241	C₂²×D₁₄₉	—	4	2	no	—
242	C₂²×D₁₄₉	—	4	2	no	—
243	C₂²×D₁₄₉	—	4	2	no	—
244	C₂²×D₁₄₉	—	4	2	no	—
245	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
246	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
247	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
248	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
249	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
250	Dic₂₉₈	—	2	2	no	—
251	Dic₂₉₈	—	4	2	no	—
252	D₅₉₆	—	2	2	no	—
253	D₅₉₆	—	2	4	no	—
254	D₅₉₆	—	2	4	no	—
255	D₅₉₆	—	2	4	no	—
256	D₅₉₆	—	2	2	no	—
257	D₅₉₆	—	2	2	no	—
258	D₅₉₆	—	4	2	no	—
259	D₅₉₆	—	4	2	no	—
260	D₅₉₆	—	4	2	no	—
261	C₂²⋊D₁₄₉	—	2	4	no	—
262	C₂²⋊D₁₄₉	—	2	2	no	—
263	C₂²⋊D₁₄₉	—	2	4	no	—
264	C₂²⋊D₁₄₉	—	4	2	no	—
265	C₂²⋊D₁₄₉	—	4	2	no	—
266	C₂²⋊D₁₄₉	—	4	2	no	—
267	C₂²⋊D₁₄₉	—	4	2	no	—
268	C₂²⋊D₁₄₉	—	4	2	no	—
269	C₂²⋊D₁₄₉	#41	1	4	yes	complemented
270	C₂×Dic₁₄₉	—	4	1	no	—
271	C₂×Dic₁₄₉	—	4	1	no	—
272	C₂×Dic₁₄₉	—	4	2	no	—
273	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
277	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
278	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
280	C₄×D₁₄₉	—	2	2	no	—
281	C₄×D₁₄₉	—	2	2	no	—
282	C₄×D₁₄₉	—	2	2	no	—
283	C₄×D₁₄₉	—	2	2	no	—
284	C₄×D₁₄₉	—	2	2	no	—
285	C₄×D₁₄₉	—	2	4	no	—
286	C₄×D₁₄₉	—	4	1	no	—
287	C₄×D₁₄₉	—	4	1	no	—
288	C₄×D₁₄₉	—	4	1	no	—
289	C₄×D₁₄₉	—	4	1	no	—
290	C₄×D₁₄₉	—	4	2	no	—
291	C₄×D₁₄₉	—	4	2	no	—
292	C₄×D₁₄₉	—	4	2	no	—
293	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
294	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
295	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
296	D₄×C₁₄₉	—	2	2	no	—
297	D₄×C₁₄₉	—	2	4	no	—
298	D₄×C₁₄₉	—	2	2	no	—
299	D₄×C₁₄₉	—	4	2	no	—
300	C₂×C₄×C₁₄₉	—	2	2	no	—
301	C₂×C₄×C₁₄₉	—	2	2	no	—
302	C₂×C₄×C₁₄₉	—	4	2	no	—
303	C₂×C₄×C₁₄₉	—	4	2	no	—
304	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
305	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
306	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
307	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
308	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
309	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
310	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
311	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₁₄₉	—	2	1	no	—
313	C₂²×C₁₄₉	—	2	1	no	—
314	C₂²×C₁₄₉	—	2	1	no	—
315	C₂²×C₁₄₉	—	2	2	no	—
316	C₂²×C₁₄₉	—	2	1	no	—
317	C₂²×C₁₄₉	—	2	2	no	—
318	C₂²×C₁₄₉	—	2	2	no	—
319	C₂²×C₁₄₉	—	2	1	no	—
320	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
321	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
322	C₂×D₁₄₉	—	2	1	no	—
323	C₂×D₁₄₉	—	2	1	no	—
324	C₂×D₁₄₉	—	2	1	no	—
325	C₂×D₁₄₉	—	2	1	no	—
326	C₂×D₁₄₉	—	2	2	no	—
327	C₂×D₁₄₉	—	2	1	no	—
328	C₂×D₁₄₉	—	2	2	no	—
329	C₂×D₁₄₉	—	2	1	no	—
330	C₂×D₁₄₉	—	2	2	no	—
331	C₂×D₁₄₉	—	2	2	no	—
332	C₂×D₁₄₉	—	2	2	no	—
333	C₂×D₁₄₉	—	2	2	no	—
334	C₂×D₁₄₉	—	2	1	no	—
335	C₂×D₁₄₉	—	4	4	no	—
336	C₂×D₁₄₉	—	4	4	no	—
337	C₂×D₁₄₉	—	8	4	no	—
338	C₂×D₁₄₉	—	8	4	no	—
339	C₂×D₁₄₉	C₂×#41	1	2	yes	—
340	C₂×D₁₄₉	H(5,𝔽₂)	1	2	yes	—
341	C₄×C₁₄₉	—	2	1	no	—
342	C₄×C₁₄₉	—	2	2	no	—
343	C₄×C₁₄₉	—	2	1	no	—
344	C₄×C₁₄₉	—	2	1	no	—
345	C₄×C₁₄₉	—	2	1	no	—
346	C₄×C₁₄₉	—	2	2	no	—
347	C₄×C₁₄₉	—	2	2	no	—
348	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
349	Dic₁₄₉	—	2	1	no	—
350	Dic₁₄₉	—	2	1	no	—
351	Dic₁₄₉	—	2	1	no	—
352	Dic₁₄₉	—	2	1	no	—
353	Dic₁₄₉	—	2	2	no	—
354	Dic₁₄₉	—	2	2	no	—
355	Dic₁₄₉	C₂×#41	1	2	yes	—
356	C₂×C₁₄₉	—	2	2	no	—
357	C₂×C₁₄₉	—	4	1	no	—
358	C₂×C₁₄₉	—	4	2	no	—
359	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
360	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
362	D₁₄₉	—	2	2	no	—
363	D₁₄₉	—	2	2	no	—
364	D₁₄₉	—	4	1	no	—
365	D₁₄₉	—	4	2	no	—
366	D₁₄₉	—	4	2	no	—
367	C₁₄₉	#3519	1	1	yes	characteristic, complemented, Sylow
368	#3519	—	149	1	no	maximal, Sylow
369	#555	—	149	1	no	—
370	#554	—	149	1	no	—
371	#553	—	149	2	no	—
372	#553	—	149	1	no	—
373	#553	D₁₄₉	1	1	yes	characteristic, complemented
374	#550	—	149	1	no	—
375	#546	—	149	2	no	—
376	#546	—	149	1	no	—
377	#546	—	149	2	no	—
378	#546	—	149	1	no	—
379	D₄²	—	149	1	no	—
380	D₄²	—	149	2	no	—
381	#540	—	149	2	no	—
382	#538	—	149	2	no	—
383	#538	—	149	2	no	—
384	#532	—	149	1	no	—
385	#529	—	149	1	no	—
386	#525	—	149	1	no	—
387	#525	—	149	1	no	—
388	C₂×#121	—	149	1	no	—
389	C₂×#121	—	149	1	no	—
390	#518	—	149	2	no	—
391	C₂×C₄×D₄	—	149	1	no	—
392	C₂×#41	—	149	1	no	—
393	C₂×#41	—	149	1	no	—
394	C₂×#41	—	149	2	no	—
395	C₂²×D₄	—	149	1	no	—
396	C₂²×D₄	—	149	2	no	—
397	C₂²×D₄	—	149	1	no	—
398	C₂²×D₄	—	149	2	no	—
399	C₂²×D₄	—	149	1	no	—
400	C₂²×D₄	—	149	2	no	—
401	C₂³×C₄	—	149	1	no	—
402	C₂³×C₄	—	149	1	no	—
403	C₄⋊Q₈	—	149	1	no	—
404	#127	—	149	1	no	—
405	#127	—	149	2	no	—
406	#126	—	149	2	no	—
407	#126	—	149	2	no	—
408	#126	C₂×D₁₄₉	1	2	yes	complemented
409	#125	—	149	2	no	—
410	#125	C₂×D₁₄₉	1	1	yes	characteristic, complemented
411	#124	—	149	2	no	—
412	#124	—	149	2	no	—
413	#124	—	149	1	no	—
414	#124	—	149	2	no	—
415	#123	—	149	2	no	—
416	#123	—	149	2	no	—
417	#123	—	149	2	no	—
418	#123	—	149	2	no	—
419	#123	—	149	2	no	—
420	#123	—	149	2	no	—
421	#123	C₂×D₁₄₉	1	2	yes	complemented
422	C₂²⋊Q₈	—	149	1	no	—
423	C₂²⋊Q₈	—	149	2	no	—
424	C₂²⋊Q₈	—	149	1	no	—
425	C₂²⋊Q₈	—	149	1	no	—
426	C₂²⋊Q₈	—	149	2	no	—
427	#121	—	149	1	no	—
428	#121	—	149	2	no	—
429	#121	—	149	2	no	—
430	#121	—	149	1	no	—
431	#121	—	149	2	no	—
432	#121	—	149	1	no	—
433	#121	—	149	1	no	—
434	#121	—	149	2	no	—
435	#121	—	149	2	no	—
436	#121	—	149	1	no	—
437	#121	—	149	1	no	—
438	#121	—	149	1	no	—
439	#121	—	149	2	no	—
440	#121	—	149	2	no	—
441	#121	—	149	2	no	—
442	#121	—	149	2	no	—
443	#121	—	149	2	no	—
444	#121	—	149	2	no	—
445	#121	—	149	2	no	—
446	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
447	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
448	#121	C₂×D₁₄₉	1	2	yes	complemented
449	#120	—	149	2	no	—
450	#120	—	149	2	no	—
451	#120	—	149	2	no	—
452	#120	—	149	2	no	—
453	#120	—	149	2	no	—
454	#120	—	149	2	no	—
455	C₄×Q₈	—	149	1	no	—
456	C₄×D₄	—	149	1	no	—
457	C₄×D₄	—	149	2	no	—
458	C₄×D₄	—	149	1	no	—
459	C₄×D₄	—	149	1	no	—
460	C₄×D₄	—	149	2	no	—
461	C₄×D₄	—	149	2	no	—
462	C₄×D₄	—	149	1	no	—
463	C₄×D₄	—	149	2	no	—
464	C₄×D₄	—	149	2	no	—
465	C₄×D₄	—	149	1	no	—
466	C₄×D₄	—	149	1	no	—
467	C₄×D₄	—	149	1	no	—
468	C₄×D₄	—	149	2	no	—
469	C₄×D₄	—	149	2	no	—
470	C₄×D₄	—	149	1	no	—
471	C₄×D₄	—	149	2	no	—
472	C₄×D₄	—	149	2	no	—
473	C₄×D₄	—	149	1	no	—
474	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
475	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
476	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
477	#117	—	149	2	no	—
478	#117	—	149	1	no	—
479	#117	—	149	2	no	—
480	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
481	C₂×C₄⋊C₄	—	149	1	no	—
482	C₂×C₄⋊C₄	—	149	1	no	—
483	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
484	C₂×C₂²⋊C₄	—	149	2	no	—
485	C₂×C₂²⋊C₄	—	149	2	no	—
486	C₂×C₂²⋊C₄	—	149	1	no	—
487	C₂×C₂²⋊C₄	—	149	1	no	—
488	C₂×C₂²⋊C₄	—	149	2	no	—
489	C₂×C₂²⋊C₄	—	149	2	no	—
490	C₂×C₄²	—	149	1	no	—
491	C₂⁴	—	149	1	no	—
492	C₂⁴	—	149	1	no	—
493	C₂⁴	—	149	2	no	—
494	C₂⁴	—	149	2	no	—
495	#41	—	596	2	no	—
496	#41	—	596	4	no	—
497	#41	—	596	2	no	—
498	C₂×Q₈	—	149	1	no	—
499	C₂×Q₈	—	149	2	no	—
500	C₂×D₄	—	298	4	no	—
501	C₂×D₄	—	298	8	no	—
502	C₂×D₄	—	596	2	no	—
503	C₂×D₄	—	596	4	no	—
504	C₂×D₄	—	596	2	no	—
505	C₂×D₄	—	596	4	no	—
506	C₂×D₄	—	149	1	no	—
507	C₂×D₄	—	149	2	no	—
508	C₂×D₄	—	149	2	no	—
509	C₂×D₄	—	149	2	no	—
510	C₂×D₄	—	149	2	no	—
511	C₂×D₄	—	149	2	no	—
512	C₂×D₄	—	149	2	no	—
513	C₂×D₄	—	149	2	no	—
514	C₂×D₄	—	149	1	no	—
515	C₂×D₄	—	149	1	no	—
516	C₂×D₄	—	149	2	no	—
517	C₂×D₄	—	149	2	no	—
518	C₂×D₄	—	149	2	no	—
519	C₂×D₄	—	149	1	no	—
520	C₂×D₄	—	149	1	no	—
521	C₂×D₄	—	149	2	no	—
522	C₂×D₄	—	149	2	no	—
523	C₂×D₄	—	149	2	no	—
524	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
525	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
526	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
527	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
528	C₂²×C₄	—	596	2	no	—
529	C₂²×C₄	—	596	2	no	—
530	C₂²×C₄	—	149	1	no	—
531	C₂²×C₄	—	149	1	no	—
532	C₂²×C₄	—	149	1	no	—
533	C₂²×C₄	—	149	1	no	—
534	C₂²×C₄	—	149	2	no	—
535	C₂²×C₄	—	149	1	no	—
536	C₂²×C₄	—	149	1	no	—
537	C₂²×C₄	—	149	2	no	—
538	C₂²×C₄	—	149	1	no	—
539	C₂²×C₄	—	149	1	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	2	no	—
545	C₂²×C₄	—	149	1	no	—
546	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
547	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
548	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
549	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
550	C₄⋊C₄	—	149	1	no	—
551	C₄⋊C₄	—	149	1	no	—
552	C₄⋊C₄	—	149	1	no	—
553	C₄⋊C₄	—	149	1	no	—
554	C₄⋊C₄	—	149	2	no	—
555	C₄⋊C₄	—	149	2	no	—
556	C₄⋊C₄	—	149	2	no	—
557	C₄⋊C₄	—	149	2	no	—
558	C₄⋊C₄	—	149	2	no	—
559	C₄⋊C₄	—	149	2	no	—
560	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
561	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
562	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
563	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
564	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
565	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
566	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
567	C₂²⋊C₄	—	149	1	no	—
568	C₂²⋊C₄	—	149	2	no	—
569	C₂²⋊C₄	—	149	2	no	—
570	C₂²⋊C₄	—	149	1	no	—
571	C₂²⋊C₄	—	149	1	no	—
572	C₂²⋊C₄	—	149	2	no	—
573	C₂²⋊C₄	—	149	2	no	—
574	C₂²⋊C₄	—	149	2	no	—
575	C₂²⋊C₄	—	149	2	no	—
576	C₂²⋊C₄	—	149	1	no	—
577	C₂²⋊C₄	—	149	2	no	—
578	C₂²⋊C₄	—	149	2	no	—
579	C₂²⋊C₄	—	149	1	no	—
580	C₂²⋊C₄	—	149	2	no	—
581	C₂²⋊C₄	—	149	1	no	—
582	C₂²⋊C₄	—	149	2	no	—
583	C₂²⋊C₄	—	149	2	no	—
584	C₂²⋊C₄	—	149	2	no	—
585	C₂²⋊C₄	—	149	2	no	—
586	C₂²⋊C₄	—	149	2	no	—
587	C₂²⋊C₄	—	149	2	no	—
588	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
589	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
590	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
591	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
592	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
593	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
594	C₄²	—	149	1	no	—
595	C₄²	—	149	1	no	—
596	C₄²	—	149	1	no	—
597	C₄²	—	149	2	no	—
598	C₄²	—	149	2	no	—
599	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
600	C₄²	C₂²×D₁₄₉	1	2	yes	—
601	C₂³	—	298	2	no	—
602	C₂³	—	298	2	no	—
603	C₂³	—	298	2	no	—
604	C₂³	—	298	4	no	—
605	C₂³	—	298	2	no	—
606	C₂³	—	298	4	no	—
607	C₂³	—	596	1	no	—
608	C₂³	—	596	1	no	—
609	C₂³	—	596	2	no	—
610	C₂³	—	596	2	no	—
611	C₂³	—	596	2	no	—
612	C₂³	—	596	2	no	—
613	C₂³	—	149	2	no	—
614	C₂³	—	149	2	no	—
615	C₂³	—	149	1	no	—
616	C₂³	—	149	1	no	—
617	C₂³	—	149	1	no	—
618	C₂³	C₂³×D₁₄₉	1	2	yes	—
619	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
620	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
621	Q₈	—	298	2	no	—
622	Q₈	—	596	2	no	—
623	D₄	—	2	2	no	—
624	D₄	—	2	4	no	—
625	D₄	—	2	2	no	—
626	D₄	—	4	2	no	—
627	D₄	—	298	2	no	—
628	D₄	—	298	4	no	—
629	D₄	—	298	4	no	—
630	D₄	—	298	4	no	—
631	D₄	—	298	4	no	—
632	D₄	—	298	2	no	—
633	D₄	—	298	4	no	—
634	D₄	—	298	2	no	—
635	D₄	—	298	2	no	—
636	D₄	—	596	2	no	—
637	D₄	—	596	2	no	—
638	D₄	—	596	2	no	—
639	D₄	—	596	2	no	—
640	D₄	—	596	2	no	—
641	D₄	—	596	2	no	—
642	D₄	—	596	2	no	—
643	D₄	—	596	2	no	—
644	D₄	—	149	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	4	2	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	298	2	no	—
650	C₂×C₄	—	298	2	no	—
651	C₂×C₄	—	298	4	no	—
652	C₂×C₄	—	298	2	no	—
653	C₂×C₄	—	298	2	no	—
654	C₂×C₄	—	298	2	no	—
655	C₂×C₄	—	596	1	no	—
656	C₂×C₄	—	596	1	no	—
657	C₂×C₄	—	596	1	no	—
658	C₂×C₄	—	596	1	no	—
659	C₂×C₄	—	596	2	no	—
660	C₂×C₄	—	596	2	no	—
661	C₂×C₄	—	596	2	no	—
662	C₂×C₄	—	596	1	no	—
663	C₂×C₄	—	596	1	no	—
664	C₂×C₄	—	596	2	no	—
665	C₂×C₄	—	149	1	no	—
666	C₂×C₄	—	149	1	no	—
667	C₂×C₄	—	149	1	no	—
668	C₂×C₄	—	149	2	no	—
669	C₂×C₄	—	149	2	no	—
670	C₂×C₄	—	149	1	no	—
671	C₂×C₄	—	149	1	no	—
672	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
673	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
674	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
675	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
676	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
677	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
678	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
679	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	298	1	no	—
689	C₂²	—	298	1	no	—
690	C₂²	—	298	1	no	—
691	C₂²	—	298	1	no	—
692	C₂²	—	298	2	no	—
693	C₂²	—	298	1	no	—
694	C₂²	—	298	2	no	—
695	C₂²	—	298	2	no	—
696	C₂²	—	298	2	no	—
697	C₂²	—	298	1	no	—
698	C₂²	—	298	1	no	—
699	C₂²	—	298	2	no	—
700	C₂²	—	298	2	no	—
701	C₂²	—	596	4	no	—
702	C₂²	—	596	4	no	—
703	C₂²	—	149	2	no	—
704	C₂²	—	149	2	no	—
705	C₂²	—	1192	4	no	—
706	C₂²	—	1192	4	no	—
707	C₂²	#41×D₁₄₉	1	2	yes	—
708	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
709	C₄	—	2	1	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	1	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	298	1	no	—
717	C₄	—	298	2	no	—
718	C₄	—	298	1	no	—
719	C₄	—	298	1	no	—
720	C₄	—	298	1	no	—
721	C₄	—	298	2	no	—
722	C₄	—	149	2	no	—
723	C₄	#18011957	1	2	yes	—
724	C₂	—	2	2	no	—
725	C₂	—	4	1	no	—
726	C₂	—	4	2	no	—
727	C₂	—	298	2	no	—
728	C₂	—	298	2	no	—
729	C₂	—	596	1	no	—
730	C₂	—	596	2	no	—
731	C₂	—	596	2	no	—
732	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
733	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic
734	C₂	C₂×#18011957	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	#3519
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. #23750338	C₂	semidirect
2. #23750330	C₂	semidirect
3. #23750328	C₂	semidirect
4. #23750326	C₂	semidirect
5. #23750293	C₂	semidirect
6. #23750271	C₂	semidirect
7. #23750271	C₂	semidirect
8. #23750270	C₂	semidirect
9. #23750267	C₂	semidirect
10. #23750259	C₂	semidirect
11. #23750259	C₂	semidirect
12. #23750227	C₂	semidirect
13. #23750214	C₂	semidirect
14. #23750212	C₂	semidirect
15. #23750172	C₂	semidirect
16. #23750160	C₂	semidirect
17. #23750137	C₂	semidirect
18. #23750135	C₂	semidirect
19. C₂×#18011886	C₂	semidirect
20. #121×D₁₄₉	C₂	semidirect
21. #23750097	C₂	semidirect
22. C₄×D₄×D₁₄₉	C₂	semidirect
23. #553×C₁₄₉	C₂	semidirect
24. C₂×#14558736	C₂²	semidirect
25. C₂×#14558736	C₂²	semidirect
26. C₂×#14558735	C₂²	semidirect
27. C₂²×D₅₉₆	C₂²	semidirect
28. C₂²×D₅₉₆	C₂²	semidirect
31. C₂×D₄×D₁₄₉	C₂²	semidirect
32. C₂×D₄×D₁₄₉	C₂²	semidirect
33. C₂²×C₄×D₁₄₉	C₂²	semidirect
34. C₂²×C₄×D₁₄₉	C₂²	semidirect
35. #18011910	C₂²	semidirect
36. #18011907	C₂²	semidirect
37. #18011907	C₂²	semidirect
38. #18011906	C₂²	semidirect
39. #18011906	C₂²	semidirect
40. #18011901	C₂²	semidirect
41. #18011899	C₂²	semidirect
42. #18011899	C₂²	semidirect
43. #18011897	C₂²	semidirect
44. #18011897	C₂²	semidirect
45. #18011896	C₂²	semidirect
46. #18011896	C₂²	semidirect
47. #18011896	C₂²	semidirect
48. #18011895	C₂²	semidirect
49. #18011895	C₂²	semidirect
50. #18011893	C₂²	semidirect
51. #18011891	C₂²	semidirect
52. #18011891	C₂²	semidirect
53. #18011890	C₂²	semidirect
54. #18011890	C₂²	semidirect
55. #18011889	C₂²	semidirect
57. #18011886	C₂²	semidirect
58. #18011886	C₂²	semidirect
59. #18011886	C₂²	semidirect
60. #18011886	C₂²	semidirect
61. #18011886	C₂²	semidirect
62. #18011886	C₂²	semidirect
63. #18011886	C₂²	semidirect
64. #18011885	C₂²	semidirect
65. #18011885	C₂²	semidirect
66. #18011884	C₂²	semidirect
67. #18011884	C₂²	semidirect
68. #18011884	C₂²	semidirect
69. #18011884	C₂²	semidirect
70. #18011884	C₂²	semidirect
71. #18011884	C₂²	semidirect
72. #18011883	C₂²	semidirect
73. #18011883	C₂²	semidirect
74. #18011882	C₂²	semidirect
75. #18011881	C₂²	semidirect
76. #18011881	C₂²	semidirect
77. #18011881	C₂²	semidirect
78. #18011879	C₂²	semidirect
79. #18011879	C₂²	semidirect
80. #18011879	C₂²	semidirect
81. #18011876	C₂²	semidirect
82. C₄×D₅₉₆	C₂²	semidirect
83. C₄×D₅₉₆	C₂²	semidirect
84. C₄×D₅₉₆	C₂²	semidirect
85. C₄×D₅₉₆	C₂²	semidirect
86. D₄×Dic₁₄₉	C₂²	semidirect
87. D₄×Dic₁₄₉	C₂²	semidirect
88. #18011873	C₂²	semidirect
89. #18011873	C₂²	semidirect
90. #18011873	C₂²	semidirect
91. #18011873	C₂²	semidirect
94. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
95. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
97. #18011871	C₂²	semidirect
98. #18011871	C₂²	semidirect
99. #18011871	C₂²	semidirect
100. #18011869	C₂²	semidirect
101. #18011869	C₂²	semidirect
102. #18011868	C₂²	semidirect
103. C₄⋊C₄×D₁₄₉	C₂²	semidirect
104. C₄⋊C₄×D₁₄₉	C₂²	semidirect
105. C₂×#14558713	C₂²	semidirect
106. C₂×#14558713	C₂²	semidirect
107. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
108. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
109. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
110. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
111. C₄²×D₁₄₉	C₂²	semidirect
112. #126×C₁₄₉	C₂²	semidirect
113. #125×C₁₄₉	C₂²	semidirect
114. #123×C₁₄₉	C₂²	semidirect
115. #121×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
269. C₂²⋊D₁₄₉	#41	semidirect
367. C₁₄₉	#3519	semidirect
373. #553	D₁₄₉	semidirect
408. #126	C₂×D₁₄₉	semidirect
410. #125	C₂×D₁₄₉	semidirect
421. #123	C₂×D₁₄₉	semidirect
446. #121	C₂×D₁₄₉	semidirect
447. #121	C₂×D₁₄₉	semidirect
448. #121	C₂×D₁₄₉	semidirect
474. C₄×D₄	C₂×D₁₄₉	semidirect
475. C₄×D₄	C₂×D₁₄₉	semidirect
476. C₄×D₄	C₂×D₁₄₉	semidirect
480. #117	C₂×D₁₄₉	semidirect
483. 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
#23750338	2
#23750330	2
#23750328	2
#23750326	2
#23750293	2
#23750271	2
#23750270	2
#23750267	2
#23750259	2
#23750227	2
#23750214	2
#23750212	2
#23750172	2
#23750160	2
#23750137	2
#23750135	2
C₂×#18011886	2
#121×D₁₄₉	2
#23750097	2
C₄×D₄×D₁₄₉	2
#553×C₁₄₉	2
#3519	149