Subgroups — C₁₄₉×#11129 #49190078

Order 38144.

1022 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2911×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#418×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#418×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#2309×C₁₄₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#344×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1740×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1733×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₄₉	C₂²	1	1	yes	characteristic
11	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
12	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
15	#428×C₁₄₉	—	2	2	no	—
16	#428×C₁₄₉	—	2	2	no	—
17	#427×C₁₄₉	—	2	2	no	—
18	#418×C₁₄₉	—	2	2	no	—
19	#418×C₁₄₉	—	2	2	no	—
20	#418×C₁₄₉	—	2	2	no	—
21	#418×C₁₄₉	C₄	1	4	yes	complemented
22	C₂×#102×C₁₄₉	—	2	2	no	—
23	C₂×#102×C₁₄₉	—	2	2	no	—
24	#390×C₁₄₉	—	2	2	no	—
25	#390×C₁₄₉	—	2	2	no	—
26	#379×C₁₄₉	—	2	2	no	—
27	#344×C₁₄₉	—	2	2	no	—
28	#342×C₁₄₉	—	2	2	no	—
29	#339×C₁₄₉	—	2	2	no	—
30	C₂⁵×C₁₄₉	—	2	1	no	—
31	C₂²×D₄×C₁₄₉	—	2	1	no	—
32	C₂²×D₄×C₁₄₉	—	2	1	no	—
33	C₂²×D₄×C₁₄₉	—	2	1	no	—
34	C₂²×D₄×C₁₄₉	—	2	1	no	—
35	C₂²×D₄×C₁₄₉	—	2	1	no	—
36	C₂²×D₄×C₁₄₉	—	2	1	no	—
37	C₂²×D₄×C₁₄₉	—	2	1	no	—
38	C₂²×D₄×C₁₄₉	—	2	1	no	—
39	C₂²×D₄×C₁₄₉	—	2	1	no	—
40	C₂²×D₄×C₁₄₉	—	2	1	no	—
41	C₂²×D₄×C₁₄₉	—	2	1	no	—
42	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₄₉	D₄	1	2	yes	—
44	C₂²×D₄×C₁₄₉	Q₈	1	2	yes	—
45	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₄₉	—	2	1	no	—
47	C₂×M₁₆×C₁₄₉	—	2	1	no	—
48	C₂×M₁₆×C₁₄₉	—	2	1	no	—
49	C₂×M₁₆×C₁₄₉	—	2	1	no	—
50	C₂×M₁₆×C₁₄₉	—	2	1	no	—
51	C₂×M₁₆×C₁₄₉	—	2	1	no	—
52	C₂×M₁₆×C₁₄₉	—	2	1	no	—
53	C₂×M₁₆×C₁₄₉	—	2	1	no	—
54	C₂×M₁₆×C₁₄₉	—	2	1	no	—
55	C₂×M₁₆×C₁₄₉	C₂×C₄	1	2	yes	—
56	C₂×M₁₆×C₁₄₉	D₄	1	2	yes	—
57	C₂×M₁₆×C₁₄₉	D₄	1	2	yes	—
58	C₂²×C₈×C₁₄₉	—	2	1	no	—
59	C₂²×C₈×C₁₄₉	D₄	1	2	yes	—
60	#117×C₁₄₉	—	2	1	no	—
61	#117×C₁₄₉	—	2	1	no	—
62	#117×C₁₄₉	—	2	1	no	—
63	#117×C₁₄₉	—	2	1	no	—
64	#117×C₁₄₉	—	2	1	no	—
65	#117×C₁₄₉	—	2	1	no	—
66	#117×C₁₄₉	—	2	1	no	—
67	#117×C₁₄₉	—	2	1	no	—
68	#117×C₁₄₉	—	2	1	no	—
69	#117×C₁₄₉	—	2	1	no	—
70	#117×C₁₄₉	—	2	1	no	—
71	#117×C₁₄₉	—	2	1	no	—
72	#117×C₁₄₉	—	2	1	no	—
73	#117×C₁₄₉	—	2	1	no	—
74	#117×C₁₄₉	—	2	1	no	—
75	#117×C₁₄₉	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₄₉	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₄₉	D₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₁₄₉	—	2	8	no	—
84	C₂×C₂²⋊C₄×C₁₄₉	D₄	1	2	yes	—
85	C₂×C₄²×C₁₄₉	—	2	1	no	—
86	C₂×C₄²×C₁₄₉	—	2	1	no	—
87	C₂×C₄²×C₁₄₉	—	2	1	no	—
88	C₂×C₄²×C₁₄₉	—	2	1	no	—
89	#107×C₁₄₉	—	2	4	no	—
90	#106×C₁₄₉	—	2	4	no	—
91	#102×C₁₄₉	—	2	8	no	—
92	#102×C₁₄₉	—	2	8	no	—
93	C₂⁴×C₁₄₉	—	2	2	no	—
94	C₂⁴×C₁₄₉	—	2	2	no	—
95	C₂⁴×C₁₄₉	—	2	2	no	—
96	C₂⁴×C₁₄₉	—	4	1	no	—
97	C₂⁴×C₁₄₉	—	4	1	no	—
98	C₂⁴×C₁₄₉	—	4	1	no	—
99	C₂⁴×C₁₄₉	—	4	1	no	—
100	C₂⁴×C₁₄₉	—	8	4	no	—
101	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₁₄₉	—	2	2	no	—
103	C₂×D₄×C₁₄₉	—	2	2	no	—
104	C₂×D₄×C₁₄₉	—	2	2	no	—
105	C₂×D₄×C₁₄₉	—	2	2	no	—
106	C₂×D₄×C₁₄₉	—	2	2	no	—
107	C₂×D₄×C₁₄₉	—	2	2	no	—
108	C₂×D₄×C₁₄₉	—	2	2	no	—
109	C₂×D₄×C₁₄₉	—	2	2	no	—
110	C₂×D₄×C₁₄₉	—	2	2	no	—
111	C₂×D₄×C₁₄₉	—	2	2	no	—
112	C₂×D₄×C₁₄₉	—	2	2	no	—
113	C₂×D₄×C₁₄₉	—	2	2	no	—
114	C₂×D₄×C₁₄₉	—	2	2	no	—
115	C₂×D₄×C₁₄₉	—	2	2	no	—
116	C₂×D₄×C₁₄₉	—	2	2	no	—
117	C₂×D₄×C₁₄₉	—	4	1	no	—
118	C₂×D₄×C₁₄₉	—	4	1	no	—
119	C₂×D₄×C₁₄₉	—	4	1	no	—
120	C₂×D₄×C₁₄₉	—	4	1	no	—
121	C₂×D₄×C₁₄₉	—	4	1	no	—
122	C₂×D₄×C₁₄₉	—	4	1	no	—
123	C₂×D₄×C₁₄₉	—	4	1	no	—
124	C₂×D₄×C₁₄₉	—	4	1	no	—
125	C₂×D₄×C₁₄₉	—	4	1	no	—
126	C₂×D₄×C₁₄₉	—	4	1	no	—
127	C₂×D₄×C₁₄₉	—	4	1	no	—
128	C₂×D₄×C₁₄₉	—	4	1	no	—
129	C₂×D₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
130	C₂²×C₄×C₁₄₉	—	2	2	no	—
131	C₂²×C₄×C₁₄₉	—	2	2	no	—
132	C₂²×C₄×C₁₄₉	—	2	2	no	—
133	C₂²×C₄×C₁₄₉	—	4	1	no	—
134	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
142	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
143	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
144	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
145	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
146	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
147	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
148	M₁₆×C₁₄₉	—	2	2	no	—
149	M₁₆×C₁₄₉	—	2	2	no	—
150	M₁₆×C₁₄₉	—	2	2	no	—
151	M₁₆×C₁₄₉	—	2	2	no	—
152	M₁₆×C₁₄₉	—	2	2	no	—
153	M₁₆×C₁₄₉	—	2	2	no	—
154	M₁₆×C₁₄₉	—	4	1	no	—
155	M₁₆×C₁₄₉	—	4	1	no	—
156	C₂×C₈×C₁₄₉	—	2	2	no	—
157	C₂×C₈×C₁₄₉	—	2	2	no	—
158	C₂×C₈×C₁₄₉	—	2	2	no	—
159	C₂×C₈×C₁₄₉	—	4	1	no	—
160	C₂×C₈×C₁₄₉	—	4	1	no	—
161	C₂×C₈×C₁₄₉	C₂²⋊C₄	1	4	yes	complemented
162	C₄⋊C₄×C₁₄₉	—	2	2	no	—
163	C₄⋊C₄×C₁₄₉	—	2	2	no	—
164	C₄⋊C₄×C₁₄₉	—	2	2	no	—
165	C₄⋊C₄×C₁₄₉	—	2	2	no	—
166	C₄⋊C₄×C₁₄₉	—	2	2	no	—
167	C₄⋊C₄×C₁₄₉	—	4	1	no	—
168	C₄⋊C₄×C₁₄₉	—	4	1	no	—
169	C₄⋊C₄×C₁₄₉	—	4	1	no	—
170	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
174	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
175	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
176	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
177	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
178	C₂²⋊C₄×C₁₄₉	—	8	8	no	—
179	C₄²×C₁₄₉	—	2	2	no	—
180	C₄²×C₁₄₉	—	4	1	no	—
181	C₄²×C₁₄₉	—	4	1	no	—
182	C₄²×C₁₄₉	—	4	1	no	—
183	C₄²×C₁₄₉	—	4	1	no	—
184	C₄²×C₁₄₉	—	4	1	no	—
185	C₄²×C₁₄₉	—	4	1	no	—
186	C₄²×C₁₄₉	—	4	1	no	—
187	C₂³×C₁₄₉	—	2	4	no	—
188	C₂³×C₁₄₉	—	4	2	no	—
189	C₂³×C₁₄₉	—	4	8	no	—
190	C₂³×C₁₄₉	—	4	2	no	—
191	C₂³×C₁₄₉	—	4	2	no	—
192	C₂³×C₁₄₉	—	4	2	no	—
193	C₂³×C₁₄₉	—	4	2	no	—
194	C₂³×C₁₄₉	—	4	2	no	—
195	C₂³×C₁₄₉	—	4	2	no	—
196	C₂³×C₁₄₉	—	8	4	no	—
197	C₂³×C₁₄₉	—	8	4	no	—
198	C₂³×C₁₄₉	—	8	4	no	—
199	C₂³×C₁₄₉	—	8	4	no	—
200	C₂³×C₁₄₉	—	8	4	no	—
201	C₂³×C₁₄₉	—	8	4	no	—
202	C₂³×C₁₄₉	C₄×D₄	1	1	yes	characteristic
203	C₂³×C₁₄₉	#120	1	1	yes	characteristic
204	C₂³×C₁₄₉	#121	1	1	yes	characteristic
205	C₂³×C₁₄₉	#121	1	1	yes	characteristic
206	C₂³×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
207	C₂³×C₁₄₉	#123	1	1	yes	characteristic
208	C₂³×C₁₄₉	#127	1	1	yes	characteristic
209	D₄×C₁₄₉	—	2	4	no	—
210	D₄×C₁₄₉	—	2	4	no	—
211	D₄×C₁₄₉	—	4	2	no	—
212	D₄×C₁₄₉	—	4	2	no	—
213	D₄×C₁₄₉	—	4	2	no	—
214	D₄×C₁₄₉	—	4	2	no	—
215	D₄×C₁₄₉	—	4	2	no	—
216	D₄×C₁₄₉	—	4	2	no	—
217	C₂×C₄×C₁₄₉	—	4	4	no	—
218	C₂×C₄×C₁₄₉	—	4	4	no	—
219	C₂×C₄×C₁₄₉	—	4	2	no	—
220	C₂×C₄×C₁₄₉	—	4	2	no	—
221	C₂×C₄×C₁₄₉	—	4	2	no	—
222	C₂×C₄×C₁₄₉	—	4	2	no	—
223	C₂×C₄×C₁₄₉	—	8	2	no	—
224	C₂×C₄×C₁₄₉	—	8	2	no	—
225	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₁₄₉	#117	1	1	yes	characteristic
228	C₂×C₄×C₁₄₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₄₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₄₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
232	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
234	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
235	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
236	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
237	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
238	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
239	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
242	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
244	C₂×C₄×C₁₄₉	#123	1	1	yes	characteristic
245	C₂×C₄×C₁₄₉	#123	1	1	yes	characteristic
246	C₂×C₄×C₁₄₉	#123	1	1	yes	characteristic
247	C₂×C₄×C₁₄₉	#123	1	1	yes	characteristic
248	C₂×C₄×C₁₄₉	#124	1	1	yes	characteristic
249	C₂×C₄×C₁₄₉	#124	1	1	yes	characteristic
250	C₂×C₄×C₁₄₉	#124	1	1	yes	characteristic
251	C₂×C₄×C₁₄₉	#126	1	1	yes	characteristic
252	C₂×C₄×C₁₄₉	#126	1	1	yes	characteristic
253	C₈×C₁₄₉	—	2	4	no	—
254	C₈×C₁₄₉	—	4	2	no	—
255	C₂²×C₁₄₉	—	2	2	no	—
256	C₂²×C₁₄₉	—	2	2	no	—
257	C₂²×C₁₄₉	—	2	2	no	—
258	C₂²×C₁₄₉	—	4	1	no	—
259	C₂²×C₁₄₉	—	4	1	no	—
260	C₂²×C₁₄₉	—	4	1	no	—
261	C₂²×C₁₄₉	—	4	1	no	—
262	C₂²×C₁₄₉	—	4	8	no	—
263	C₂²×C₁₄₉	—	4	4	no	—
264	C₂²×C₁₄₉	—	8	4	no	—
265	C₂²×C₁₄₉	—	8	4	no	—
266	C₂²×C₁₄₉	—	8	4	no	—
267	C₂²×C₁₄₉	—	8	4	no	—
268	C₂²×C₁₄₉	—	8	4	no	—
269	C₂²×C₁₄₉	—	8	4	no	—
270	C₂²×C₁₄₉	#385	1	1	yes	characteristic
271	C₂²×C₁₄₉	#388	1	1	yes	characteristic
272	C₂²×C₁₄₉	#390	1	1	yes	characteristic
273	C₂²×C₁₄₉	#392	1	1	yes	characteristic
274	C₂²×C₁₄₉	#394	1	1	yes	characteristic
275	C₂²×C₁₄₉	#396	1	1	yes	characteristic
276	C₂²×C₁₄₉	#399	1	1	yes	characteristic
277	C₄×C₁₄₉	—	8	2	no	—
278	C₄×C₁₄₉	—	8	2	no	—
279	C₄×C₁₄₉	—	8	2	no	—
280	C₄×C₁₄₉	—	8	2	no	—
281	C₄×C₁₄₉	#380	1	1	yes	characteristic
282	C₄×C₁₄₉	#385	1	1	yes	characteristic
283	C₄×C₁₄₉	#386	1	1	yes	characteristic
284	C₄×C₁₄₉	#388	1	1	yes	characteristic
285	C₄×C₁₄₉	#393	1	1	yes	characteristic
286	C₄×C₁₄₉	#394	1	1	yes	characteristic
287	C₄×C₁₄₉	#396	1	1	yes	characteristic
288	C₄×C₁₄₉	#397	1	1	yes	characteristic
289	C₂×C₁₄₉	—	2	1	no	—
290	C₂×C₁₄₉	—	2	1	no	—
291	C₂×C₁₄₉	—	2	1	no	—
292	C₂×C₁₄₉	—	2	1	no	—
293	C₂×C₁₄₉	—	2	1	no	—
294	C₂×C₁₄₉	—	2	1	no	—
295	C₂×C₁₄₉	—	8	4	no	—
296	C₂×C₁₄₉	#1439	1	1	yes	characteristic
297	C₂×C₁₄₉	#2008	1	2	yes	—
298	#11129	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₁₄₉	#11129	1	1	yes	characteristic, direct product factor, Sylow
300	#2911	C₂×C₁₄₉	1	1	yes	characteristic, complemented
301	C₂×#418	C₂×C₁₄₉	1	1	yes	characteristic
302	C₂×#418	C₂×C₁₄₉	1	1	yes	characteristic
303	#2309	C₂×C₁₄₉	1	1	yes	characteristic
304	C₂×#344	C₂×C₁₄₉	1	1	yes	characteristic, complemented
305	#1740	C₂×C₁₄₉	1	1	yes	characteristic, complemented
306	#1733	C₂×C₁₄₉	1	1	yes	characteristic, complemented
307	C₂³×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
308	C₂²×M₁₆	C₂²×C₁₄₉	1	1	yes	characteristic
309	C₂²×M₁₆	C₂²×C₁₄₉	1	1	yes	characteristic
310	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
311	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
312	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
313	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
314	#428	—	2	2	no	—
315	#428	—	2	2	no	—
316	#427	—	2	2	no	—
317	#418	—	2	2	no	—
318	#418	—	2	2	no	—
319	#418	—	2	2	no	—
320	#418	C₄×C₁₄₉	1	4	yes	complemented
321	C₂×#102	—	2	2	no	—
322	C₂×#102	—	2	2	no	—
323	#390	—	2	2	no	—
324	#390	—	2	2	no	—
325	#379	—	2	2	no	—
326	#344	—	2	2	no	—
327	#342	—	2	2	no	—
328	#339	—	2	2	no	—
329	C₂⁵	—	2	1	no	—
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
342	C₂²×D₄	D₄×C₁₄₉	1	2	yes	—
343	C₂²×D₄	Q₈×C₁₄₉	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	C₂×C₄×C₁₄₉	1	2	yes	—
355	C₂×M₁₆	D₄×C₁₄₉	1	2	yes	—
356	C₂×M₁₆	D₄×C₁₄₉	1	2	yes	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	D₄×C₁₄₉	1	2	yes	—
359	#117	—	2	1	no	—
360	#117	—	2	1	no	—
361	#117	—	2	1	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	#117	—	2	1	no	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	C₂×C₄×C₁₄₉	1	2	yes	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	D₄×C₁₄₉	1	2	yes	—
378	C₂×C₄⋊C₄	D₄×C₁₄₉	1	2	yes	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	8	no	—
383	C₂×C₂²⋊C₄	D₄×C₁₄₉	1	2	yes	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	#107	—	2	4	no	—
389	#106	—	2	4	no	—
390	#102	—	2	8	no	—
391	#102	—	2	8	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	4	1	no	—
396	C₂⁴	—	4	1	no	—
397	C₂⁴	—	4	1	no	—
398	C₂⁴	—	4	1	no	—
399	C₂⁴	—	8	4	no	—
400	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
441	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
442	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
443	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
444	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
445	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
446	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	4	1	no	—
454	M₁₆	—	4	1	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	4	1	no	—
459	C₂×C₈	—	4	1	no	—
460	C₂×C₈	C₂²⋊C₄×C₁₄₉	1	4	yes	complemented
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	8	8	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	4	1	no	—
480	C₄²	—	4	1	no	—
481	C₄²	—	4	1	no	—
482	C₄²	—	4	1	no	—
483	C₄²	—	4	1	no	—
484	C₄²	—	4	1	no	—
485	C₄²	—	4	1	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	8	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	8	4	no	—
496	C₂³	—	8	4	no	—
497	C₂³	—	8	4	no	—
498	C₂³	—	8	4	no	—
499	C₂³	—	8	4	no	—
500	C₂³	—	8	4	no	—
501	C₂³	C₄×D₄×C₁₄₉	1	1	yes	characteristic
502	C₂³	#120×C₁₄₉	1	1	yes	characteristic
503	C₂³	#121×C₁₄₉	1	1	yes	characteristic
504	C₂³	#121×C₁₄₉	1	1	yes	characteristic
505	C₂³	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
506	C₂³	#123×C₁₄₉	1	1	yes	characteristic
507	C₂³	#127×C₁₄₉	1	1	yes	characteristic
508	D₄	—	2	4	no	—
509	D₄	—	2	4	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	8	2	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
525	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
526	C₂×C₄	#117×C₁₄₉	1	1	yes	characteristic
527	C₂×C₄	C₄×D₄×C₁₄₉	1	1	yes	characteristic
528	C₂×C₄	C₄×D₄×C₁₄₉	1	1	yes	characteristic
529	C₂×C₄	C₄×D₄×C₁₄₉	1	1	yes	characteristic
530	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
531	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
532	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
533	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
534	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
535	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
536	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
537	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
538	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
539	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
540	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
541	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
542	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
543	C₂×C₄	#123×C₁₄₉	1	1	yes	characteristic
544	C₂×C₄	#123×C₁₄₉	1	1	yes	characteristic
545	C₂×C₄	#123×C₁₄₉	1	1	yes	characteristic
546	C₂×C₄	#123×C₁₄₉	1	1	yes	characteristic
547	C₂×C₄	#124×C₁₄₉	1	1	yes	characteristic
548	C₂×C₄	#124×C₁₄₉	1	1	yes	characteristic
549	C₂×C₄	#124×C₁₄₉	1	1	yes	characteristic
550	C₂×C₄	#126×C₁₄₉	1	1	yes	characteristic
551	C₂×C₄	#126×C₁₄₉	1	1	yes	characteristic
552	C₈	—	2	4	no	—
553	C₈	—	4	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	8	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	8	4	no	—
564	C₂²	—	8	4	no	—
565	C₂²	—	8	4	no	—
566	C₂²	—	8	4	no	—
567	C₂²	—	8	4	no	—
568	C₂²	—	8	4	no	—
569	C₂²	#385×C₁₄₉	1	1	yes	characteristic
570	C₂²	#388×C₁₄₉	1	1	yes	characteristic
571	C₂²	#390×C₁₄₉	1	1	yes	characteristic
572	C₂²	#392×C₁₄₉	1	1	yes	characteristic
573	C₂²	#394×C₁₄₉	1	1	yes	characteristic
574	C₂²	#396×C₁₄₉	1	1	yes	characteristic
575	C₂²	#399×C₁₄₉	1	1	yes	characteristic
576	C₄	—	8	2	no	—
577	C₄	—	8	2	no	—
578	C₄	—	8	2	no	—
579	C₄	—	8	2	no	—
580	C₄	#380×C₁₄₉	1	1	yes	characteristic
581	C₄	#385×C₁₄₉	1	1	yes	characteristic
582	C₄	#386×C₁₄₉	1	1	yes	characteristic
583	C₄	#388×C₁₄₉	1	1	yes	characteristic
584	C₄	#393×C₁₄₉	1	1	yes	characteristic
585	C₄	#394×C₁₄₉	1	1	yes	characteristic
586	C₄	#396×C₁₄₉	1	1	yes	characteristic
587	C₄	#397×C₁₄₉	1	1	yes	characteristic
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	1	no	—
592	C₂	—	2	1	no	—
593	C₂	—	2	1	no	—
594	C₂	—	8	4	no	—
595	C₂	#1439×C₁₄₉	1	1	yes	characteristic
596	C₂	#2008×C₁₄₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₄₉	#392
commutator	C₂²×C₄	C₂²×C₄×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
prime radical	C₂³×D₄×C₁₄₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂³×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2911×C₁₄₉	C₂	semidirect
5. C₂×#344×C₁₄₉	C₂	semidirect
6. #1740×C₁₄₉	C₂	semidirect
7. #1733×C₁₄₉	C₂	semidirect
21. #418×C₁₄₉	C₄	semidirect
161. C₂×C₈×C₁₄₉	C₂²⋊C₄	semidirect
298. #11129	C₁₄₉	direct (N × H)
299. C₁₄₉	#11129	direct (N × H)
300. #2911	C₂×C₁₄₉	semidirect
304. C₂×#344	C₂×C₁₄₉	semidirect
305. #1740	C₂×C₁₄₉	semidirect
306. #1733	C₂×C₁₄₉	semidirect
320. #418	C₄×C₁₄₉	semidirect
460. C₂×C₈	C₂²⋊C₄×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#2911×C₁₄₉	2
C₂×#418×C₁₄₉	2
#2309×C₁₄₉	2
C₂×#344×C₁₄₉	2
#1740×C₁₄₉	2
#1733×C₁₄₉	2
#11129	149

Subgroups — C149×#11129 #49190078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#11129 #49190078