Subgroups — C₁₄₉×#17429 #49196378

Order 38144.

1016 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2974×C₁₄₉	C₂	1	2	yes	maximal, complemented
3	#1469×C₁₄₉	C₂	1	2	yes	maximal, complemented
4	#1468×C₁₄₉	C₂	1	4	yes	maximal, complemented
5	#1467×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1465×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	#1461×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1459×C₁₄₉	C₂	1	2	yes	maximal, complemented
9	#559×C₁₄₉	—	2	2	no	—
10	#559×C₁₄₉	—	2	4	no	—
11	#559×C₁₄₉	—	2	2	no	—
12	C₂×#127×C₁₄₉	C₄	1	1	yes	characteristic
13	C₂×#124×C₁₄₉	C₄	1	1	yes	characteristic
14	C₂×#124×C₁₄₉	C₄	1	2	yes	—
15	C₂×#124×C₁₄₉	C₂²	1	1	yes	characteristic
16	C₂×#123×C₁₄₉	C₄	1	2	yes	—
17	C₂×#123×C₁₄₉	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₄₉	C₄	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₄₉	C₄	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
23	#436×C₁₄₉	—	2	2	no	—
24	#435×C₁₄₉	—	2	4	no	—
25	C₈×D₄×C₁₄₉	—	2	2	no	—
26	#432×C₁₄₉	C₂²	1	2	yes	—
27	#431×C₁₄₉	C₂²	1	2	yes	—
28	#407×C₁₄₉	C₂²	1	4	yes	—
29	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	4	yes	—
30	#324×C₁₄₉	C₂²	1	1	yes	characteristic
31	#324×C₁₄₉	C₂²	1	2	yes	—
32	#324×C₁₄₉	C₂²	1	1	yes	characteristic
33	#324×C₁₄₉	C₂²	1	2	yes	—
34	#324×C₁₄₉	C₂²	1	2	yes	—
35	#323×C₁₄₉	C₂²	1	4	yes	—
36	#323×C₁₄₉	C₂²	1	4	yes	—
37	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
40	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
42	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
45	C₂×M₁₆×C₁₄₉	—	2	4	no	—
46	C₂²×C₈×C₁₄₉	—	2	4	no	—
47	#127×C₁₄₉	—	2	2	no	—
48	#127×C₁₄₉	—	2	2	no	—
49	#124×C₁₄₉	—	2	2	no	—
50	#124×C₁₄₉	—	2	2	no	—
51	#124×C₁₄₉	—	2	4	no	—
52	#124×C₁₄₉	—	2	4	no	—
53	#124×C₁₄₉	—	2	2	no	—
54	#124×C₁₄₉	—	2	2	no	—
55	#123×C₁₄₉	—	2	4	no	—
56	#123×C₁₄₉	—	2	4	no	—
57	#123×C₁₄₉	—	2	4	no	—
58	#123×C₁₄₉	—	2	4	no	—
59	C₄×Q₈×C₁₄₉	—	2	2	no	—
60	C₄×Q₈×C₁₄₉	—	2	1	no	—
61	C₄×Q₈×C₁₄₉	—	2	1	no	—
62	C₄×Q₈×C₁₄₉	—	2	2	no	—
63	C₄×Q₈×C₁₄₉	—	2	2	no	—
64	C₄×D₄×C₁₄₉	—	2	4	no	—
65	C₄×D₄×C₁₄₉	—	2	4	no	—
66	C₄×D₄×C₁₄₉	—	2	2	no	—
67	C₄×D₄×C₁₄₉	—	2	1	no	—
68	C₄×D₄×C₁₄₉	—	2	1	no	—
69	C₄×D₄×C₁₄₉	D₄	1	2	yes	—
70	C₄×D₄×C₁₄₉	D₄	1	4	yes	—
71	C₄×D₄×C₁₄₉	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
79	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₁₄₉	—	2	2	no	—
88	C₄⋊C₈×C₁₄₉	—	2	2	no	—
89	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
90	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
91	C₂²⋊C₈×C₁₄₉	C₂³	1	2	yes	—
92	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
93	C₂²⋊C₈×C₁₄₉	C₂³	1	2	yes	—
94	#97×C₁₄₉	—	2	2	no	—
95	C₄×C₈×C₁₄₉	—	2	2	no	—
96	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
97	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₁₄₉	—	2	2	no	—
99	C₂×Q₈×C₁₄₉	—	2	1	no	—
100	C₂×Q₈×C₁₄₉	—	2	1	no	—
101	C₂×Q₈×C₁₄₉	—	2	2	no	—
102	C₂×Q₈×C₁₄₉	—	4	1	no	—
103	C₂×Q₈×C₁₄₉	—	4	2	no	—
104	C₂×D₄×C₁₄₉	—	2	4	no	—
105	C₂×D₄×C₁₄₉	—	2	4	no	—
106	C₂×D₄×C₁₄₉	—	2	1	no	—
107	C₂×D₄×C₁₄₉	—	2	1	no	—
108	C₂×D₄×C₁₄₉	—	2	4	no	—
109	C₂×D₄×C₁₄₉	—	4	2	no	—
110	C₂×D₄×C₁₄₉	—	4	2	no	—
111	C₂×D₄×C₁₄₉	—	4	2	no	—
112	C₂×D₄×C₁₄₉	—	8	2	no	—
113	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
114	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₁₄₉	—	2	2	no	—
116	C₂²×C₄×C₁₄₉	—	2	2	no	—
117	C₂²×C₄×C₁₄₉	—	8	2	no	—
118	C₂²×C₄×C₁₄₉	—	8	2	no	—
119	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₁₄₉	—	8	4	no	—
131	C₂×C₈×C₁₄₉	—	2	2	no	—
132	C₂×C₈×C₁₄₉	—	2	2	no	—
133	C₂×C₈×C₁₄₉	—	2	4	no	—
134	C₂×C₈×C₁₄₉	—	8	4	no	—
135	C₄⋊C₄×C₁₄₉	—	2	2	no	—
136	C₄⋊C₄×C₁₄₉	—	2	2	no	—
137	C₄⋊C₄×C₁₄₉	—	2	2	no	—
138	C₄⋊C₄×C₁₄₉	—	2	2	no	—
139	C₄⋊C₄×C₁₄₉	—	2	2	no	—
140	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
141	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
142	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
144	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
145	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
146	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
147	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
148	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
149	C₂²⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
150	C₂²⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
151	C₄²×C₁₄₉	—	2	2	no	—
152	C₄²×C₁₄₉	—	2	2	no	—
153	C₄²×C₁₄₉	—	2	1	no	—
154	C₄²×C₁₄₉	—	2	1	no	—
155	C₄²×C₁₄₉	—	2	1	no	—
156	C₄²×C₁₄₉	—	2	1	no	—
157	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
158	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
159	C₂³×C₁₄₉	—	2	2	no	—
160	C₂³×C₁₄₉	—	2	2	no	—
161	C₂³×C₁₄₉	—	2	2	no	—
162	C₂³×C₁₄₉	—	2	2	no	—
163	C₂³×C₁₄₉	—	2	2	no	—
164	C₂³×C₁₄₉	—	4	2	no	—
165	C₂³×C₁₄₉	—	4	2	no	—
166	C₂³×C₁₄₉	—	4	2	no	—
167	C₂³×C₁₄₉	—	4	2	no	—
168	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
169	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
170	Q₈×C₁₄₉	—	4	4	no	—
171	Q₈×C₁₄₉	—	4	2	no	—
172	Q₈×C₁₄₉	—	4	2	no	—
173	D₄×C₁₄₉	—	2	4	no	—
174	D₄×C₁₄₉	—	4	2	no	—
175	D₄×C₁₄₉	—	4	8	no	—
176	D₄×C₁₄₉	—	4	2	no	—
177	D₄×C₁₄₉	—	4	2	no	—
178	D₄×C₁₄₉	—	8	4	no	—
179	C₂×C₄×C₁₄₉	—	2	1	no	—
180	C₂×C₄×C₁₄₉	—	2	1	no	—
181	C₂×C₄×C₁₄₉	—	2	1	no	—
182	C₂×C₄×C₁₄₉	—	2	1	no	—
183	C₂×C₄×C₁₄₉	—	2	2	no	—
184	C₂×C₄×C₁₄₉	—	2	1	no	—
185	C₂×C₄×C₁₄₉	—	2	2	no	—
186	C₂×C₄×C₁₄₉	—	2	1	no	—
187	C₂×C₄×C₁₄₉	—	2	1	no	—
188	C₂×C₄×C₁₄₉	—	2	1	no	—
189	C₂×C₄×C₁₄₉	—	2	1	no	—
190	C₂×C₄×C₁₄₉	—	4	4	no	—
191	C₂×C₄×C₁₄₉	—	4	4	no	—
192	C₂×C₄×C₁₄₉	—	4	2	no	—
193	C₂×C₄×C₁₄₉	—	4	1	no	—
194	C₂×C₄×C₁₄₉	—	4	1	no	—
195	C₂×C₄×C₁₄₉	—	4	1	no	—
196	C₂×C₄×C₁₄₉	—	4	2	no	—
197	C₂×C₄×C₁₄₉	—	8	2	no	—
198	C₂×C₄×C₁₄₉	—	8	2	no	—
199	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₄₉	#131	1	2	yes	—
205	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
206	C₈×C₁₄₉	—	4	2	no	—
207	C₈×C₁₄₉	—	4	4	no	—
208	C₈×C₁₄₉	—	4	2	no	—
209	C₂²×C₁₄₉	—	2	1	no	—
210	C₂²×C₁₄₉	—	2	1	no	—
211	C₂²×C₁₄₉	—	2	4	no	—
212	C₂²×C₁₄₉	—	2	4	no	—
213	C₂²×C₁₄₉	—	2	4	no	—
214	C₂²×C₁₄₉	—	4	2	no	—
215	C₂²×C₁₄₉	—	4	2	no	—
216	C₂²×C₁₄₉	—	4	2	no	—
217	C₂²×C₁₄₉	—	8	2	no	—
218	C₂²×C₁₄₉	—	8	2	no	—
219	C₂²×C₁₄₉	—	8	2	no	—
220	C₂²×C₁₄₉	—	8	2	no	—
221	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
222	C₂²×C₁₄₉	C₂×#131	1	1	yes	characteristic
223	C₂²×C₁₄₉	#568	1	1	yes	characteristic
224	C₄×C₁₄₉	—	2	2	no	—
225	C₄×C₁₄₉	—	2	2	no	—
226	C₄×C₁₄₉	—	2	2	no	—
227	C₄×C₁₄₉	—	2	2	no	—
228	C₄×C₁₄₉	—	2	2	no	—
229	C₄×C₁₄₉	—	2	1	no	—
230	C₄×C₁₄₉	—	4	1	no	—
231	C₄×C₁₄₉	—	4	1	no	—
232	C₄×C₁₄₉	—	4	1	no	—
233	C₄×C₁₄₉	—	4	2	no	—
234	C₄×C₁₄₉	#413	1	2	yes	—
235	C₂×C₁₄₉	—	2	1	no	—
236	C₂×C₁₄₉	—	2	1	no	—
237	C₂×C₁₄₉	—	4	4	no	—
238	C₂×C₁₄₉	—	8	2	no	—
239	C₂×C₁₄₉	#2880	1	1	yes	characteristic
240	C₂×C₁₄₉	#2883	1	1	yes	characteristic
241	C₂×C₁₄₉	C₂×#413	1	1	yes	characteristic
242	#17429	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₁₄₉	#17429	1	1	yes	characteristic, direct product factor, Sylow
244	C₂×#559	C₂×C₁₄₉	1	1	yes	characteristic
245	#2974	C₂×C₁₄₉	1	2	yes	complemented
246	#1469	C₂×C₁₄₉	1	2	yes	complemented
247	#1468	C₂×C₁₄₉	1	4	yes	complemented
248	#1467	C₂×C₁₄₉	1	1	yes	characteristic, complemented
249	#1465	C₂×C₁₄₉	1	2	yes	complemented
250	#1461	C₂×C₁₄₉	1	1	yes	characteristic, complemented
251	#1459	C₂×C₁₄₉	1	2	yes	complemented
252	#559	—	2	2	no	—
253	#559	—	2	4	no	—
254	#559	—	2	2	no	—
255	C₂×#127	C₄×C₁₄₉	1	1	yes	characteristic
256	C₂×#124	C₄×C₁₄₉	1	1	yes	characteristic
257	C₂×#124	C₄×C₁₄₉	1	2	yes	—
258	C₂×#124	C₂²×C₁₄₉	1	1	yes	characteristic
259	C₂×#123	C₄×C₁₄₉	1	2	yes	—
260	C₂×#123	C₂²×C₁₄₉	1	2	yes	—
261	C₂×C₄×Q₈	C₄×C₁₄₉	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
263	C₂×C₄×D₄	C₄×C₁₄₉	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₁₄₉	1	2	yes	—
265	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
266	#436	—	2	2	no	—
267	#435	—	2	4	no	—
268	C₈×D₄	—	2	2	no	—
269	#432	C₂²×C₁₄₉	1	2	yes	—
270	#431	C₂²×C₁₄₉	1	2	yes	—
271	#407	C₂²×C₁₄₉	1	4	yes	—
272	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	4	yes	—
273	#324	C₂²×C₁₄₉	1	1	yes	characteristic
274	#324	C₂²×C₁₄₉	1	2	yes	—
275	#324	C₂²×C₁₄₉	1	1	yes	characteristic
276	#324	C₂²×C₁₄₉	1	2	yes	—
277	#324	C₂²×C₁₄₉	1	2	yes	—
278	#323	C₂²×C₁₄₉	1	4	yes	—
279	#323	C₂²×C₁₄₉	1	4	yes	—
280	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
281	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
282	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
283	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
284	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
285	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
286	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
287	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
288	C₂×M₁₆	—	2	4	no	—
289	C₂²×C₈	—	2	4	no	—
290	#127	—	2	2	no	—
291	#127	—	2	2	no	—
292	#124	—	2	2	no	—
293	#124	—	2	2	no	—
294	#124	—	2	4	no	—
295	#124	—	2	4	no	—
296	#124	—	2	2	no	—
297	#124	—	2	2	no	—
298	#123	—	2	4	no	—
299	#123	—	2	4	no	—
300	#123	—	2	4	no	—
301	#123	—	2	4	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	D₄×C₁₄₉	1	2	yes	—
313	C₄×D₄	D₄×C₁₄₉	1	4	yes	—
314	C₄×D₄	D₄×C₁₄₉	1	2	yes	—
315	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
321	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
322	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
323	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	2	yes	—
326	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
327	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
328	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	2	no	—
332	C₂²⋊C₈	—	2	4	no	—
333	C₂²⋊C₈	—	2	4	no	—
334	C₂²⋊C₈	C₂³×C₁₄₉	1	2	yes	—
335	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
336	C₂²⋊C₈	C₂³×C₁₄₉	1	2	yes	—
337	#97	—	2	2	no	—
338	C₄×C₈	—	2	2	no	—
339	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
340	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	4	1	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	2	no	—
355	C₂×D₄	—	8	2	no	—
356	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
357	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	8	2	no	—
361	C₂²×C₄	—	8	2	no	—
362	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
365	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
367	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
369	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
372	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
373	M₁₆	—	8	4	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	4	no	—
377	C₂×C₈	—	8	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
384	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
385	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
393	C₂²⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
401	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
412	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
413	Q₈	—	4	4	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	D₄	—	2	4	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	8	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	8	4	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	8	2	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
443	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
444	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
445	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
446	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
447	C₂×C₄	#131×C₁₄₉	1	2	yes	—
448	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
449	C₈	—	4	2	no	—
450	C₈	—	4	4	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
465	C₂²	C₂×#131×C₁₄₉	1	1	yes	characteristic
466	C₂²	#568×C₁₄₉	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	#413×C₁₄₉	1	2	yes	—
478	C₂	—	2	1	no	—
479	C₂	—	2	1	no	—
480	C₂	—	4	4	no	—
481	C₂	—	8	2	no	—
482	C₂	#2880×C₁₄₉	1	1	yes	characteristic
483	C₂	#2883×C₁₄₉	1	1	yes	characteristic
484	C₂	C₂×#413×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
prime radical	C₂×#127×C₁₄₉	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×C₄×D₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2974×C₁₄₉	C₂	semidirect
3. #1469×C₁₄₉	C₂	semidirect
4. #1468×C₁₄₉	C₂	semidirect
5. #1467×C₁₄₉	C₂	semidirect
6. #1465×C₁₄₉	C₂	semidirect
7. #1461×C₁₄₉	C₂	semidirect
8. #1459×C₁₄₉	C₂	semidirect
242. #17429	C₁₄₉	direct (N × H)
243. C₁₄₉	#17429	direct (N × H)
245. #2974	C₂×C₁₄₉	semidirect
246. #1469	C₂×C₁₄₉	semidirect
247. #1468	C₂×C₁₄₉	semidirect
248. #1467	C₂×C₁₄₉	semidirect
249. #1465	C₂×C₁₄₉	semidirect
250. #1461	C₂×C₁₄₉	semidirect
251. #1459	C₂×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₁₄₉	2
#2974×C₁₄₉	2
#1469×C₁₄₉	2
#1468×C₁₄₉	2
#1467×C₁₄₉	2
#1465×C₁₄₉	2
#1461×C₁₄₉	2
#1459×C₁₄₉	2
#17429	149

Subgroups — C149×#17429 #49196378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17429 #49196378