Subgroups — #34058351

Order 19072.

1658 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18011956	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14558735	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750295	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750293	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750284	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750281	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750270	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750269	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750264	C₂	1	2	yes	maximal, complemented
10	#23750262	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊D₁₄₉	C₂	1	2	yes	maximal, complemented
13	#23750257	C₂	1	2	yes	maximal, complemented
14	#23750204	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750202	C₂	1	2	yes	maximal, complemented
16	#23750190	C₂	1	2	yes	maximal, complemented
17	#23750188	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750134	C₂	1	1	yes	maximal, characteristic, complemented
19	#23750131	C₂	1	2	yes	maximal, complemented
20	C₂×#18011883	C₂	1	2	yes	maximal, complemented
21	#121×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#23750104	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄²×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	#18011956	—	2	8	no	—
25	C₂×#14558736	C₂²	1	1	yes	characteristic, complemented
26	C₂×#14558736	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14558735	—	2	8	no	—
28	C₂×#14558735	C₂²	1	1	yes	characteristic
29	C₂×#14558735	C₂²	1	1	yes	characteristic, complemented
30	C₂×#14558735	C₂²	1	2	yes	complemented
31	C₂×#14558735	C₂²	1	2	yes	complemented
32	C₂×#14558735	C₂²	1	1	yes	characteristic, complemented
33	C₂×#14558735	C₂²	1	1	yes	characteristic, complemented
34	C₂×#14558735	C₂²	1	2	yes	complemented
35	C₂×#14558735	C₂²	1	1	yes	characteristic, complemented
36	C₂²×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
38	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
39	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
40	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
41	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
43	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
45	C₂³×Dic₁₄₉	C₂²	1	2	yes	complemented
46	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
47	#18011907	C₂²	1	1	yes	characteristic, complemented
48	#18011907	C₂²	1	2	yes	complemented
49	#18011907	C₂²	1	2	yes	complemented
50	#18011899	C₂²	1	1	yes	characteristic, complemented
51	#18011898	C₂²	1	1	yes	characteristic, complemented
52	#18011897	C₂²	1	2	yes	complemented
53	#18011897	C₂²	1	2	yes	complemented
54	#18011896	C₂²	1	1	yes	characteristic, complemented
55	#18011895	C₂²	1	2	yes	complemented
56	#18011893	C₂²	1	1	yes	characteristic, complemented
57	#18011892	C₂²	1	2	yes	complemented
58	#18011891	C₂²	1	1	yes	characteristic, complemented
59	#18011890	C₂²	1	1	yes	characteristic, complemented
60	#18011889	C₂²	1	1	yes	characteristic, complemented
61	#18011889	C₂²	1	2	yes	complemented
62	#18011888	C₂²	1	2	yes	complemented
63	#18011888	C₂²	1	2	yes	complemented
64	#18011888	C₂²	1	1	yes	characteristic, complemented
65	#18011886	C₂²	1	1	yes	characteristic, complemented
66	#18011885	C₂²	1	2	yes	complemented
67	#18011885	C₂²	1	1	yes	characteristic, complemented
68	#18011884	C₂²	1	1	yes	characteristic, 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	#18011883	C₂²	1	2	yes	complemented
75	#18011883	C₂²	1	2	yes	complemented
76	#18011883	C₂²	1	2	yes	complemented
77	#18011883	C₂²	1	2	yes	complemented
78	#18011883	C₂²	1	2	yes	complemented
79	#18011883	C₂²	1	2	yes	complemented
80	#18011883	C₂²	1	2	yes	complemented
81	#18011883	C₂²	1	2	yes	complemented
82	#18011883	C₂²	1	2	yes	complemented
83	#18011883	C₂²	1	1	yes	characteristic, complemented
84	#18011882	C₂²	1	2	yes	complemented
85	#18011882	C₂²	1	1	yes	characteristic, complemented
86	#18011882	C₂²	1	1	yes	characteristic, complemented
87	#18011881	C₂²	1	2	yes	complemented
88	#18011881	C₂²	1	1	yes	characteristic, complemented
89	#18011880	C₂²	1	2	yes	complemented
90	#18011880	C₂²	1	2	yes	complemented
91	#18011879	C₂²	1	2	yes	complemented
92	#18011879	C₂²	1	2	yes	complemented
93	#18011879	C₂²	1	2	yes	complemented
94	#18011879	C₂²	1	1	yes	characteristic, complemented
95	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
96	#18011876	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
98	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
99	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
100	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic, complemented
104	#18011871	C₂²	1	2	yes	complemented
105	#18011871	C₂²	1	2	yes	complemented
106	#18011871	C₂²	1	2	yes	complemented
107	#18011868	C₂²	1	1	yes	characteristic, complemented
108	#18011867	C₂²	1	2	yes	complemented
109	C₂×#14558715	C₂²	1	2	yes	complemented
110	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₂²⋊Dic₁₄₉	C₂²	1	2	yes	complemented
112	C₂×#14558713	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
114	C₂²×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
115	C₂²×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
116	C₂²×D₄×C₁₄₉	C₂²	1	2	yes	complemented
117	#127×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
118	#121×C₁₄₉	C₂²	1	2	yes	complemented
119	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
120	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
121	#120×C₁₄₉	C₂²	1	2	yes	complemented
122	#120×C₁₄₉	C₂²	1	2	yes	complemented
123	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
124	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
125	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
126	C₂³×D₁₄₉	C₂³	1	2	yes	—
127	C₂³×D₁₄₉	C₂³	1	2	yes	—
128	#14558736	—	2	4	no	—
129	#14558736	—	2	4	no	—
130	#14558735	—	2	4	no	—
131	#14558735	—	2	4	no	—
132	#14558735	—	2	8	no	—
133	#14558735	—	2	8	no	—
134	#14558735	—	2	8	no	—
135	#14558735	—	2	4	no	—
136	#14558735	—	2	4	no	—
137	#14558735	D₄	1	8	yes	complemented
138	C₂×Dic₂₉₈	—	2	4	no	—
139	C₂×Dic₂₉₈	C₂³	1	2	yes	—
140	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
141	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
142	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
143	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
144	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
145	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
146	C₂×D₅₉₆	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₁₄₉	—	2	8	no	—
148	C₂×C₂²⋊D₁₄₉	—	2	8	no	—
149	C₂×C₂²⋊D₁₄₉	—	2	8	no	—
150	C₂×C₂²⋊D₁₄₉	—	4	4	no	—
151	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
163	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
167	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
168	D₄×D₁₄₉	—	2	8	no	—
169	D₄×D₁₄₉	—	2	4	no	—
170	D₄×D₁₄₉	—	2	4	no	—
171	D₄×D₁₄₉	—	4	4	no	—
172	C₂²×Dic₁₄₉	—	2	8	no	—
173	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
174	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
175	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
176	C₂²×Dic₁₄₉	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	2	yes	—
181	C₂×C₄×D₁₄₉	—	2	4	no	—
182	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
185	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
186	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
187	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
188	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
192	#14558715	C₂³	1	2	yes	—
193	#14558715	C₂³	1	1	yes	characteristic
194	#14558715	C₂³	1	2	yes	—
195	#14558715	C₂³	1	2	yes	—
196	#14558715	C₂³	1	1	yes	characteristic
197	#14558715	C₂³	1	1	yes	characteristic
198	#14558715	C₂³	1	2	yes	—
199	#14558715	C₂³	1	1	yes	characteristic
200	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
201	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
202	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
203	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
204	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
205	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
206	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
207	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
208	#14558713	C₂³	1	2	yes	—
209	#14558713	C₂³	1	2	yes	—
210	#14558713	C₂³	1	1	yes	characteristic
211	#14558713	C₂³	1	2	yes	—
212	#14558713	C₂³	1	2	yes	—
213	#14558713	C₂³	1	1	yes	characteristic
214	#14558713	C₂³	1	1	yes	characteristic
215	#14558713	C₂³	1	2	yes	—
216	#14558713	C₂³	1	1	yes	characteristic
217	#14558713	C₂³	1	1	yes	characteristic
218	#14558713	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₄₉	C₂³	1	2	yes	—
220	C₄×Dic₁₄₉	C₂³	1	2	yes	—
221	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
222	C₂⁴×C₁₄₉	C₂³	1	2	yes	—
223	C₂⁴×C₁₄₉	C₂³	1	2	yes	—
224	C₂×D₄×C₁₄₉	—	2	4	no	—
225	C₂×D₄×C₁₄₉	—	2	4	no	—
226	C₂×D₄×C₁₄₉	—	4	4	no	—
227	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
228	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
229	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
230	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
231	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
232	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
233	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
234	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
235	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
236	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
237	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
238	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
239	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
240	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
241	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
242	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
243	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
244	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
245	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
246	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
247	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
248	C₂²×D₁₄₉	—	2	2	no	—
249	C₂²×D₁₄₉	—	2	4	no	—
250	C₂²×D₁₄₉	—	2	2	no	—
251	C₂²×D₁₄₉	—	2	4	no	—
252	C₂²×D₁₄₉	—	4	1	no	—
253	C₂²×D₁₄₉	—	4	2	no	—
254	C₂²×D₁₄₉	—	4	2	no	—
255	C₂²×D₁₄₉	—	4	2	no	—
256	C₂²×D₁₄₉	—	4	2	no	—
257	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
258	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
259	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
260	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
261	Dic₂₉₈	—	2	2	no	—
262	Dic₂₉₈	—	2	4	no	—
263	Dic₂₉₈	—	2	2	no	—
264	Dic₂₉₈	C₂×D₄	1	4	yes	complemented
265	D₅₉₆	—	2	2	no	—
266	D₅₉₆	—	2	2	no	—
267	D₅₉₆	—	4	2	no	—
268	D₅₉₆	—	4	1	no	—
269	C₂²⋊D₁₄₉	—	2	4	no	—
270	C₂²⋊D₁₄₉	—	2	4	no	—
271	C₂²⋊D₁₄₉	—	2	4	no	—
272	C₂²⋊D₁₄₉	—	2	2	no	—
273	C₂²⋊D₁₄₉	—	2	2	no	—
274	C₂²⋊D₁₄₉	—	2	4	no	—
275	C₂²⋊D₁₄₉	—	2	4	no	—
276	C₂²⋊D₁₄₉	—	2	4	no	—
277	C₂²⋊D₁₄₉	—	2	2	no	—
278	C₂²⋊D₁₄₉	—	2	4	no	—
279	C₂²⋊D₁₄₉	—	2	4	no	—
280	C₂²⋊D₁₄₉	—	4	2	no	—
281	C₂²⋊D₁₄₉	—	4	2	no	—
282	C₂²⋊D₁₄₉	—	4	2	no	—
283	C₂²⋊D₁₄₉	—	4	1	no	—
284	C₂²⋊D₁₄₉	—	4	2	no	—
285	C₂²⋊D₁₄₉	C₂×D₄	1	8	yes	complemented
286	C₂×Dic₁₄₉	—	2	4	no	—
287	C₂×Dic₁₄₉	—	2	2	no	—
288	C₂×Dic₁₄₉	—	2	4	no	—
289	C₂×Dic₁₄₉	—	2	4	no	—
290	C₂×Dic₁₄₉	—	2	4	no	—
291	C₂×Dic₁₄₉	—	2	4	no	—
292	C₂×Dic₁₄₉	—	4	2	no	—
293	C₂×Dic₁₄₉	C₂×D₄	1	8	yes	complemented
294	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
295	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
296	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
297	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
298	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
301	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
302	C₄×D₁₄₉	—	2	2	no	—
303	C₄×D₁₄₉	—	2	2	no	—
304	C₄×D₁₄₉	—	2	2	no	—
305	C₄×D₁₄₉	—	2	2	no	—
306	C₄×D₁₄₉	—	2	4	no	—
307	C₄×D₁₄₉	—	4	2	no	—
308	C₄×D₁₄₉	C₂×D₄	1	4	yes	complemented
309	C₂³×C₁₄₉	—	2	4	no	—
310	C₂³×C₁₄₉	—	2	4	no	—
311	C₂³×C₁₄₉	—	2	4	no	—
312	C₂³×C₁₄₉	—	4	2	no	—
313	C₂³×C₁₄₉	—	4	2	no	—
314	C₂³×C₁₄₉	—	4	2	no	—
315	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
316	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
317	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
318	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
319	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
320	D₄×C₁₄₉	—	2	4	no	—
321	D₄×C₁₄₉	—	2	4	no	—
322	D₄×C₁₄₉	—	2	4	no	—
323	D₄×C₁₄₉	—	2	2	no	—
324	D₄×C₁₄₉	—	2	2	no	—
325	D₄×C₁₄₉	—	2	2	no	—
326	D₄×C₁₄₉	—	4	2	no	—
327	D₄×C₁₄₉	—	4	2	no	—
328	D₄×C₁₄₉	—	4	2	no	—
329	D₄×C₁₄₉	C₂×D₄	1	4	yes	complemented
330	C₂×C₄×C₁₄₉	—	2	2	no	—
331	C₂×C₄×C₁₄₉	—	2	2	no	—
332	C₂×C₄×C₁₄₉	—	4	2	no	—
333	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
334	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
335	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
336	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
337	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
338	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
339	C₂²×C₁₄₉	—	2	1	no	—
340	C₂²×C₁₄₉	—	2	2	no	—
341	C₂²×C₁₄₉	—	2	1	no	—
342	C₂²×C₁₄₉	—	2	2	no	—
343	C₂²×C₁₄₉	—	2	1	no	—
344	C₂²×C₁₄₉	—	2	2	no	—
345	C₂²×C₁₄₉	—	2	2	no	—
346	C₂²×C₁₄₉	—	2	1	no	—
347	C₂²×C₁₄₉	—	2	2	no	—
348	C₂²×C₁₄₉	—	2	2	no	—
349	C₂²×C₁₄₉	—	2	2	no	—
350	C₂²×C₁₄₉	—	2	2	no	—
351	C₂²×C₁₄₉	—	2	1	no	—
352	C₂²×C₁₄₉	—	4	8	no	—
353	C₂²×C₁₄₉	—	8	4	no	—
354	C₂²×C₁₄₉	C₂²×D₄	1	4	yes	—
355	C₂²×C₁₄₉	H(5,𝔽₂)	1	2	yes	complemented
356	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
357	C₂×D₁₄₉	—	2	1	no	—
358	C₂×D₁₄₉	—	2	1	no	—
359	C₂×D₁₄₉	—	2	1	no	—
360	C₂×D₁₄₉	—	2	1	no	—
361	C₂×D₁₄₉	—	2	2	no	—
362	C₂×D₁₄₉	—	2	1	no	—
363	C₂×D₁₄₉	—	2	2	no	—
364	C₂×D₁₄₉	—	2	1	no	—
365	C₂×D₁₄₉	—	2	1	no	—
366	C₂×D₁₄₉	—	2	2	no	—
367	C₂×D₁₄₉	—	2	1	no	—
368	C₂×D₁₄₉	—	4	4	no	—
369	C₂×D₁₄₉	—	8	4	no	—
370	C₂×D₁₄₉	—	8	4	no	—
371	C₂×D₁₄₉	C₂²×D₄	1	2	yes	—
372	C₄×C₁₄₉	—	2	1	no	—
373	C₄×C₁₄₉	—	2	1	no	—
374	C₄×C₁₄₉	—	2	1	no	—
375	C₄×C₁₄₉	—	2	2	no	—
376	C₄×C₁₄₉	—	2	1	no	—
377	C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
378	Dic₁₄₉	—	2	1	no	—
379	Dic₁₄₉	—	2	1	no	—
380	Dic₁₄₉	—	2	2	no	—
381	Dic₁₄₉	—	2	2	no	—
382	Dic₁₄₉	—	2	1	no	—
383	Dic₁₄₉	—	2	1	no	—
384	Dic₁₄₉	C₂²×D₄	1	2	yes	—
385	Dic₁₄₉	C₂²×D₄	1	4	yes	—
386	C₂×C₁₄₉	—	2	2	no	—
387	C₂×C₁₄₉	—	2	4	no	—
388	C₂×C₁₄₉	—	4	2	no	—
389	C₂×C₁₄₉	—	4	2	no	—
390	C₂×C₁₄₉	—	4	1	no	—
391	C₂×C₁₄₉	C₂³×D₄	1	1	yes	characteristic
392	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
393	C₂×C₁₄₉	#585	1	1	yes	characteristic
394	D₁₄₉	—	2	2	no	—
395	D₁₄₉	—	4	1	no	—
396	D₁₄₉	—	4	1	no	—
397	D₁₄₉	—	4	2	no	—
398	C₁₄₉	#3488	1	1	yes	characteristic, complemented, Sylow
399	#3488	—	149	1	no	maximal, Sylow
400	C₂×H(5,𝔽₂)	—	149	1	no	—
401	C₂²×#41	—	149	1	no	—
402	#550	—	149	1	no	—
403	#550	—	149	1	no	—
404	#548	—	149	1	no	—
405	#548	—	149	1	no	—
406	#546	—	149	1	no	—
407	#546	—	149	2	no	—
408	#546	—	149	2	no	—
409	#546	—	149	1	no	—
410	D₄²	—	149	1	no	—
411	D₄²	—	149	2	no	—
412	D₄²	—	149	2	no	—
413	D₄²	D₁₄₉	1	1	yes	characteristic, complemented
414	#537	—	149	2	no	—
415	#537	—	149	1	no	—
416	#535	—	149	1	no	—
417	#535	—	149	2	no	—
418	#525	—	149	2	no	—
419	#525	—	149	1	no	—
420	C₂×#121	—	149	2	no	—
421	C₂×#121	—	149	1	no	—
422	#520	—	149	1	no	—
423	H(5,𝔽₂)	—	298	8	no	—
424	C₂×#41	—	298	8	no	—
425	C₂×#41	—	149	2	no	—
426	C₂×#41	—	149	1	no	—
427	C₂×#41	—	149	2	no	—
428	C₂×#41	—	149	1	no	—
429	C₂×#41	—	149	2	no	—
430	C₂×#41	—	149	1	no	—
431	C₂×#41	—	149	1	no	—
432	C₂×#41	—	149	1	no	—
433	C₂×#41	—	149	1	no	—
434	C₂×#41	—	149	1	no	—
435	C₂²×Q₈	—	149	1	no	—
436	C₂²×D₄	—	149	2	no	—
437	C₂²×D₄	—	149	2	no	—
438	C₂²×D₄	—	149	2	no	—
439	C₂²×D₄	—	149	1	no	—
440	C₂²×D₄	—	149	2	no	—
441	C₂²×D₄	—	149	1	no	—
442	C₂²×D₄	—	149	2	no	—
443	C₂²×D₄	—	149	2	no	—
444	C₂²×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
445	C₂²×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
446	C₂²×D₄	C₂×D₁₄₉	1	2	yes	complemented
447	C₂³×C₄	—	149	2	no	—
448	C₂³×C₄	—	149	1	no	—
449	#127	—	149	2	no	—
450	#127	—	149	2	no	—
451	#127	—	149	1	no	—
452	#127	C₂×D₁₄₉	1	1	yes	characteristic, complemented
453	#124	—	149	1	no	—
454	#124	—	149	2	no	—
455	#124	—	149	2	no	—
456	#124	—	149	1	no	—
457	#123	—	149	2	no	—
458	#123	—	149	1	no	—
459	#123	—	149	1	no	—
460	#123	—	149	2	no	—
461	C₂²⋊Q₈	—	149	1	no	—
462	C₂²⋊Q₈	—	149	1	no	—
463	C₂²⋊Q₈	—	149	2	no	—
464	C₂²⋊Q₈	—	149	1	no	—
465	C₂²⋊Q₈	—	149	1	no	—
466	C₂²⋊Q₈	—	149	2	no	—
467	C₂²⋊Q₈	—	149	2	no	—
468	#121	—	149	2	no	—
469	#121	—	149	1	no	—
470	#121	—	149	2	no	—
471	#121	—	149	2	no	—
472	#121	—	149	2	no	—
473	#121	—	149	2	no	—
474	#121	—	149	1	no	—
475	#121	—	149	2	no	—
476	#121	—	149	2	no	—
477	#121	—	149	2	no	—
478	#121	—	149	2	no	—
479	#121	—	149	2	no	—
480	#121	—	149	2	no	—
481	#121	—	149	1	no	—
482	#121	—	149	2	no	—
483	#121	—	149	1	no	—
484	#121	—	149	2	no	—
485	#121	—	149	1	no	—
486	#121	—	149	2	no	—
487	#121	—	149	1	no	—
488	#121	—	149	2	no	—
489	#121	—	149	2	no	—
490	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
491	#121	C₂×D₁₄₉	1	2	yes	complemented
492	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
493	#120	—	149	2	no	—
494	#120	—	149	2	no	—
495	#120	—	149	1	no	—
496	#120	—	149	2	no	—
497	#120	—	149	2	no	—
498	#120	—	149	2	no	—
499	#120	—	149	1	no	—
500	#120	—	149	2	no	—
501	#120	C₂×D₁₄₉	1	2	yes	complemented
502	#120	C₂×D₁₄₉	1	2	yes	complemented
503	C₄×Q₈	—	149	1	no	—
504	C₄×Q₈	—	149	1	no	—
505	C₄×D₄	—	149	1	no	—
506	C₄×D₄	—	149	2	no	—
507	C₄×D₄	—	149	2	no	—
508	C₄×D₄	—	149	2	no	—
509	C₄×D₄	—	149	1	no	—
510	C₄×D₄	—	149	1	no	—
511	C₄×D₄	—	149	2	no	—
512	C₄×D₄	—	149	2	no	—
513	C₄×D₄	—	149	2	no	—
514	C₄×D₄	—	149	1	no	—
515	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
516	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
517	#117	—	149	2	no	—
518	#117	—	149	1	no	—
519	C₂×C₄⋊C₄	—	149	2	no	—
520	C₂×C₄⋊C₄	—	149	1	no	—
521	C₂×C₂²⋊C₄	—	149	2	no	—
522	C₂×C₂²⋊C₄	—	149	2	no	—
523	C₂×C₂²⋊C₄	—	149	2	no	—
524	C₂⁴	—	149	1	no	—
525	C₂⁴	—	149	2	no	—
526	C₂⁴	—	149	2	no	—
527	C₂⁴	C₂²×D₁₄₉	1	2	yes	—
528	C₂⁴	C₂²×D₁₄₉	1	2	yes	—
529	#41	—	298	4	no	—
530	#41	—	298	4	no	—
531	#41	—	298	4	no	—
532	#41	—	298	4	no	—
533	#41	—	298	8	no	—
534	#41	—	298	4	no	—
535	#41	—	298	8	no	—
536	#41	—	298	4	no	—
537	#41	—	298	8	no	—
538	#41	—	149	8	no	—
539	C₂×Q₈	—	298	4	no	—
540	C₂×Q₈	—	149	1	no	—
541	C₂×Q₈	—	149	1	no	—
542	C₂×Q₈	—	149	2	no	—
543	C₂×Q₈	—	149	1	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂×D₄	—	298	8	no	—
548	C₂×D₄	—	298	8	no	—
549	C₂×D₄	—	298	8	no	—
550	C₂×D₄	—	298	4	no	—
551	C₂×D₄	—	298	4	no	—
552	C₂×D₄	—	298	8	no	—
553	C₂×D₄	—	596	4	no	—
554	C₂×D₄	—	596	4	no	—
555	C₂×D₄	—	149	2	no	—
556	C₂×D₄	—	149	1	no	—
557	C₂×D₄	—	149	2	no	—
558	C₂×D₄	—	149	2	no	—
559	C₂×D₄	—	149	1	no	—
560	C₂×D₄	—	149	2	no	—
561	C₂×D₄	—	149	2	no	—
562	C₂×D₄	—	149	1	no	—
563	C₂×D₄	—	149	2	no	—
564	C₂×D₄	—	149	2	no	—
565	C₂×D₄	—	149	2	no	—
566	C₂×D₄	—	149	2	no	—
567	C₂×D₄	—	149	1	no	—
568	C₂×D₄	—	149	2	no	—
569	C₂×D₄	—	149	2	no	—
570	C₂×D₄	—	149	2	no	—
571	C₂×D₄	—	149	2	no	—
572	C₂×D₄	—	149	1	no	—
573	C₂×D₄	—	149	1	no	—
574	C₂×D₄	—	149	1	no	—
575	C₂×D₄	—	149	2	no	—
576	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
577	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
578	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
579	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
580	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
581	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
582	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
583	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
584	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
585	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
586	C₂²×C₄	—	298	4	no	—
587	C₂²×C₄	—	298	8	no	—
588	C₂²×C₄	—	149	2	no	—
589	C₂²×C₄	—	149	2	no	—
590	C₂²×C₄	—	149	2	no	—
591	C₂²×C₄	—	149	2	no	—
592	C₂²×C₄	—	149	1	no	—
593	C₂²×C₄	—	149	2	no	—
594	C₂²×C₄	—	149	1	no	—
595	C₂²×C₄	—	149	1	no	—
596	C₂²×C₄	—	149	2	no	—
597	C₂²×C₄	—	149	1	no	—
598	C₂²×C₄	—	149	1	no	—
599	C₂²×C₄	—	149	2	no	—
600	C₂²×C₄	—	149	2	no	—
601	C₂²×C₄	—	149	2	no	—
602	C₂²×C₄	—	149	1	no	—
603	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
604	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
605	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
606	C₄⋊C₄	—	149	2	no	—
607	C₄⋊C₄	—	149	1	no	—
608	C₄⋊C₄	—	149	2	no	—
609	C₄⋊C₄	—	149	2	no	—
610	C₄⋊C₄	—	149	1	no	—
611	C₄⋊C₄	—	149	1	no	—
612	C₄⋊C₄	—	149	1	no	—
613	C₄⋊C₄	—	149	1	no	—
614	C₄⋊C₄	—	149	2	no	—
615	C₄⋊C₄	—	149	1	no	—
616	C₄⋊C₄	—	149	2	no	—
617	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
618	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
619	C₂²⋊C₄	—	149	2	no	—
620	C₂²⋊C₄	—	149	1	no	—
621	C₂²⋊C₄	—	149	2	no	—
622	C₂²⋊C₄	—	149	2	no	—
623	C₂²⋊C₄	—	149	2	no	—
624	C₂²⋊C₄	—	149	1	no	—
625	C₂²⋊C₄	—	149	2	no	—
626	C₂²⋊C₄	—	149	2	no	—
627	C₂²⋊C₄	—	149	2	no	—
628	C₂²⋊C₄	—	149	1	no	—
629	C₂²⋊C₄	—	149	2	no	—
630	C₂²⋊C₄	—	149	2	no	—
631	C₂²⋊C₄	—	149	2	no	—
632	C₂²⋊C₄	—	149	1	no	—
633	C₂²⋊C₄	—	149	1	no	—
634	C₂²⋊C₄	—	149	1	no	—
635	C₂²⋊C₄	—	149	2	no	—
636	C₂²⋊C₄	—	149	1	no	—
637	C₂²⋊C₄	—	149	1	no	—
638	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
639	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
640	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
641	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
642	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
643	C₄²	—	149	1	no	—
644	C₄²	—	149	2	no	—
645	C₄²	—	149	2	no	—
646	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
647	C₂³	—	2	4	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	4	no	—
650	C₂³	—	4	2	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	298	2	no	—
654	C₂³	—	298	4	no	—
655	C₂³	—	298	2	no	—
656	C₂³	—	298	4	no	—
657	C₂³	—	596	1	no	—
658	C₂³	—	596	2	no	—
659	C₂³	—	596	2	no	—
660	C₂³	—	596	2	no	—
661	C₂³	—	596	2	no	—
662	C₂³	—	149	2	no	—
663	C₂³	—	149	1	no	—
664	C₂³	—	149	1	no	—
665	C₂³	—	149	1	no	—
666	C₂³	C₂³×D₁₄₉	1	2	yes	—
667	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
668	C₂³	C₂³×D₁₄₉	1	2	yes	—
669	C₂³	C₂³×D₁₄₉	1	2	yes	—
670	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
671	Q₈	—	298	4	no	—
672	Q₈	—	298	2	no	—
673	Q₈	—	298	2	no	—
674	Q₈	—	149	4	no	—
675	D₄	—	2	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	2	no	—
683	D₄	—	4	2	no	—
684	D₄	—	298	2	no	—
685	D₄	—	298	2	no	—
686	D₄	—	298	4	no	—
687	D₄	—	298	4	no	—
688	D₄	—	298	4	no	—
689	D₄	—	298	4	no	—
690	D₄	—	298	2	no	—
691	D₄	—	298	2	no	—
692	D₄	—	298	4	no	—
693	D₄	—	298	4	no	—
694	D₄	—	298	4	no	—
695	D₄	—	298	4	no	—
696	D₄	—	298	2	no	—
697	D₄	—	596	2	no	—
698	D₄	—	596	1	no	—
699	D₄	—	596	2	no	—
700	D₄	—	596	2	no	—
701	D₄	—	596	2	no	—
702	D₄	—	596	2	no	—
703	D₄	—	596	1	no	—
704	D₄	—	149	8	no	—
705	D₄	D₄×D₁₄₉	1	4	yes	complemented
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	298	2	no	—
710	C₂×C₄	—	298	2	no	—
711	C₂×C₄	—	298	4	no	—
712	C₂×C₄	—	298	4	no	—
713	C₂×C₄	—	298	2	no	—
714	C₂×C₄	—	298	4	no	—
715	C₂×C₄	—	298	4	no	—
716	C₂×C₄	—	298	4	no	—
717	C₂×C₄	—	298	4	no	—
718	C₂×C₄	—	298	2	no	—
719	C₂×C₄	—	298	2	no	—
720	C₂×C₄	—	596	2	no	—
721	C₂×C₄	—	596	2	no	—
722	C₂×C₄	—	149	1	no	—
723	C₂×C₄	—	149	2	no	—
724	C₂×C₄	—	149	1	no	—
725	C₂×C₄	—	149	1	no	—
726	C₂×C₄	—	149	2	no	—
727	C₂×C₄	—	149	1	no	—
728	C₂×C₄	—	149	8	no	—
729	C₂×C₄	—	149	2	no	—
730	C₂×C₄	—	149	1	no	—
731	C₂×C₄	—	149	4	no	—
732	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
733	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
734	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
735	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
736	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
737	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
738	C₂²	—	2	1	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	4	8	no	—
752	C₂²	—	8	4	no	—
753	C₂²	—	298	1	no	—
754	C₂²	—	298	1	no	—
755	C₂²	—	298	1	no	—
756	C₂²	—	298	2	no	—
757	C₂²	—	298	1	no	—
758	C₂²	—	298	2	no	—
759	C₂²	—	298	1	no	—
760	C₂²	—	298	1	no	—
761	C₂²	—	298	1	no	—
762	C₂²	—	298	1	no	—
763	C₂²	—	298	2	no	—
764	C₂²	—	596	4	no	—
765	C₂²	—	149	2	no	—
766	C₂²	—	1192	4	no	—
767	C₂²	—	1192	4	no	—
768	C₂²	C₂×D₄×D₁₄₉	1	4	yes	—
769	C₂²	#18011956	1	2	yes	complemented
770	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
771	C₄	—	2	1	no	—
772	C₄	—	2	1	no	—
773	C₄	—	2	1	no	—
774	C₄	—	2	2	no	—
775	C₄	—	2	1	no	—
776	C₄	—	298	1	no	—
777	C₄	—	298	1	no	—
778	C₄	—	298	2	no	—
779	C₄	—	298	2	no	—
780	C₄	—	298	1	no	—
781	C₄	—	298	1	no	—
782	C₄	—	149	2	no	—
783	C₄	—	149	4	no	—
784	C₄	C₂×D₄×D₁₄₉	1	2	yes	—
785	C₂	—	2	2	no	—
786	C₂	—	2	4	no	—
787	C₂	—	4	2	no	—
788	C₂	—	4	1	no	—
789	C₂	—	4	2	no	—
790	C₂	—	298	2	no	—
791	C₂	—	596	1	no	—
792	C₂	—	596	1	no	—
793	C₂	—	596	2	no	—
794	C₂	C₂²×D₄×D₁₄₉	1	1	yes	characteristic
795	C₂	C₂×#18011956	1	1	yes	characteristic
796	C₂	#23750460	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	D₄²×C₁₄₉	C₂
hypercenter	D₄²	D₁₄₉
hypocenter	C₁₄₉	#3488
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₂×#18011956	C₂	semidirect
2. C₂²×#14558735	C₂	semidirect
3. #23750295	C₂	semidirect
4. #23750293	C₂	semidirect
5. #23750284	C₂	semidirect
6. #23750281	C₂	semidirect
7. #23750270	C₂	semidirect
8. #23750269	C₂	semidirect
9. #23750264	C₂	semidirect
10. #23750262	C₂	semidirect
11. D₄×C₂²⋊D₁₄₉	C₂	semidirect
12. D₄×C₂²⋊D₁₄₉	C₂	semidirect
13. #23750257	C₂	semidirect
14. #23750204	C₂	semidirect
15. #23750202	C₂	semidirect
16. #23750190	C₂	semidirect
17. #23750188	C₂	semidirect
18. #23750134	C₂	semidirect
19. #23750131	C₂	semidirect
20. C₂×#18011883	C₂	semidirect
21. #121×D₁₄₉	C₂	semidirect
22. #23750104	C₂	semidirect
23. D₄²×C₁₄₉	C₂	semidirect
25. C₂×#14558736	C₂²	semidirect
26. C₂×#14558736	C₂²	semidirect
29. C₂×#14558735	C₂²	semidirect
30. C₂×#14558735	C₂²	semidirect
31. C₂×#14558735	C₂²	semidirect
32. C₂×#14558735	C₂²	semidirect
33. C₂×#14558735	C₂²	semidirect
34. C₂×#14558735	C₂²	semidirect
35. C₂×#14558735	C₂²	semidirect
36. C₂²×Dic₂₉₈	C₂²	semidirect
37. C₂²×C₂²⋊D₁₄₉	C₂²	semidirect
38. C₂²×C₂²⋊D₁₄₉	C₂²	semidirect
39. C₂²×C₂²⋊D₁₄₉	C₂²	semidirect
40. C₂²×C₂²⋊D₁₄₉	C₂²	semidirect
41. C₂×D₄×D₁₄₉	C₂²	semidirect
42. C₂×D₄×D₁₄₉	C₂²	semidirect
43. C₂×D₄×D₁₄₉	C₂²	semidirect
44. C₂×D₄×D₁₄₉	C₂²	semidirect
45. C₂³×Dic₁₄₉	C₂²	semidirect
46. C₂²×C₄×D₁₄₉	C₂²	semidirect
47. #18011907	C₂²	semidirect
48. #18011907	C₂²	semidirect
49. #18011907	C₂²	semidirect
50. #18011899	C₂²	semidirect
51. #18011898	C₂²	semidirect
52. #18011897	C₂²	semidirect
53. #18011897	C₂²	semidirect
54. #18011896	C₂²	semidirect
55. #18011895	C₂²	semidirect
56. #18011893	C₂²	semidirect
57. #18011892	C₂²	semidirect
58. #18011891	C₂²	semidirect
59. #18011890	C₂²	semidirect
60. #18011889	C₂²	semidirect
61. #18011889	C₂²	semidirect
62. #18011888	C₂²	semidirect
63. #18011888	C₂²	semidirect
64. #18011888	C₂²	semidirect
65. #18011886	C₂²	semidirect
66. #18011885	C₂²	semidirect
67. #18011885	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. #18011883	C₂²	semidirect
75. #18011883	C₂²	semidirect
76. #18011883	C₂²	semidirect
77. #18011883	C₂²	semidirect
78. #18011883	C₂²	semidirect
79. #18011883	C₂²	semidirect
80. #18011883	C₂²	semidirect
81. #18011883	C₂²	semidirect
82. #18011883	C₂²	semidirect
83. #18011883	C₂²	semidirect
84. #18011882	C₂²	semidirect
85. #18011882	C₂²	semidirect
86. #18011882	C₂²	semidirect
87. #18011881	C₂²	semidirect
88. #18011881	C₂²	semidirect
89. #18011880	C₂²	semidirect
90. #18011880	C₂²	semidirect
91. #18011879	C₂²	semidirect
92. #18011879	C₂²	semidirect
93. #18011879	C₂²	semidirect
94. #18011879	C₂²	semidirect
95. C₄×Dic₂₉₈	C₂²	semidirect
96. #18011876	C₂²	semidirect
97. C₄×D₅₉₆	C₂²	semidirect
98. D₄×Dic₁₄₉	C₂²	semidirect
99. D₄×Dic₁₄₉	C₂²	semidirect
100. D₄×Dic₁₄₉	C₂²	semidirect
101. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
102. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
103. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
104. #18011871	C₂²	semidirect
105. #18011871	C₂²	semidirect
106. #18011871	C₂²	semidirect
107. #18011868	C₂²	semidirect
108. #18011867	C₂²	semidirect
109. C₂×#14558715	C₂²	semidirect
110. C₄⋊C₄×D₁₄₉	C₂²	semidirect
111. C₂×C₂²⋊Dic₁₄₉	C₂²	semidirect
112. C₂×#14558713	C₂²	semidirect
113. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
114. C₂²×D₄×C₁₄₉	C₂²	semidirect
115. C₂²×D₄×C₁₄₉	C₂²	semidirect
116. C₂²×D₄×C₁₄₉	C₂²	semidirect
117. #127×C₁₄₉	C₂²	semidirect
118. #121×C₁₄₉	C₂²	semidirect
119. #121×C₁₄₉	C₂²	semidirect
120. #121×C₁₄₉	C₂²	semidirect
121. #120×C₁₄₉	C₂²	semidirect
122. #120×C₁₄₉	C₂²	semidirect
123. C₄×D₄×C₁₄₉	C₂²	semidirect
124. C₄×D₄×C₁₄₉	C₂²	semidirect
137. #14558735	D₄	semidirect
264. Dic₂₉₈	C₂×D₄	semidirect
285. C₂²⋊D₁₄₉	C₂×D₄	semidirect
293. C₂×Dic₁₄₉	C₂×D₄	semidirect
308. C₄×D₁₄₉	C₂×D₄	semidirect
329. D₄×C₁₄₉	C₂×D₄	semidirect
355. C₂²×C₁₄₉	H(5,𝔽₂)	semidirect
398. C₁₄₉	#3488	semidirect
413. D₄²	D₁₄₉	semidirect
444. C₂²×D₄	C₂×D₁₄₉	semidirect
445. C₂²×D₄	C₂×D₁₄₉	semidirect
446. C₂²×D₄	C₂×D₁₄₉	semidirect
452. #127	C₂×D₁₄₉	semidirect
490. #121	C₂×D₁₄₉	semidirect
491. #121	C₂×D₁₄₉	semidirect
492. #121	C₂×D₁₄₉	semidirect
501. #120	C₂×D₁₄₉	semidirect
502. #120	C₂×D₁₄₉	semidirect
515. C₄×D₄	C₂×D₁₄₉	semidirect
516. C₄×D₄	C₂×D₁₄₉	semidirect
705. D₄	D₄×D₁₄₉	semidirect
769. C₂²	#18011956	semidirect

Maximal subgroups

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

subgroup	index
C₂×#18011956	2
C₂²×#14558735	2
#23750295	2
#23750293	2
#23750284	2
#23750281	2
#23750270	2
#23750269	2
#23750264	2
#23750262	2
D₄×C₂²⋊D₁₄₉	2
#23750257	2
#23750204	2
#23750202	2
#23750190	2
#23750188	2
#23750134	2
#23750131	2
C₂×#18011883	2
#121×D₁₄₉	2
#23750104	2
D₄²×C₁₄₉	2
#3488	149