Subgroups — C₁₄₉×#11054 #49190003

Order 38144.

1174 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#418×C₁₄₉	C₂	1	2	yes	maximal
2	#2316×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#390×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#343×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#339×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	C₂³×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
8	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₂²×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
11	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
12	#418×C₁₄₉	—	2	4	no	—
13	#418×C₁₄₉	—	2	4	no	—
14	C₂×#102×C₁₄₉	—	2	4	no	—
15	#390×C₁₄₉	—	2	2	no	—
16	#390×C₁₄₉	C₄	1	4	yes	complemented
17	#389×C₁₄₉	—	2	4	no	—
18	#380×C₁₄₉	—	2	2	no	—
19	#343×C₁₄₉	—	2	2	no	—
20	#339×C₁₄₉	—	2	4	no	—
21	C₂⁵×C₁₄₉	—	2	1	no	—
22	C₂²×D₄×C₁₄₉	—	2	2	no	—
23	C₂²×D₄×C₁₄₉	—	2	2	no	—
24	C₂²×D₄×C₁₄₉	—	2	1	no	—
25	C₂²×D₄×C₁₄₉	—	2	2	no	—
26	C₂²×D₄×C₁₄₉	—	2	2	no	—
27	C₂²×D₄×C₁₄₉	—	2	1	no	—
28	C₂²×D₄×C₁₄₉	—	2	1	no	—
29	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₄₉	D₄	1	2	yes	—
31	C₂²×D₄×C₁₄₉	Q₈	1	2	yes	—
32	C₂³×C₄×C₁₄₉	—	2	1	no	—
33	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
34	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₁₄₉	—	2	2	no	—
36	C₂×M₁₆×C₁₄₉	—	2	2	no	—
37	C₂×M₁₆×C₁₄₉	—	2	2	no	—
38	C₂×M₁₆×C₁₄₉	—	2	2	no	—
39	C₂×M₁₆×C₁₄₉	—	2	2	no	—
40	C₂×M₁₆×C₁₄₉	D₄	1	4	yes	—
41	C₂²×C₈×C₁₄₉	—	2	2	no	—
42	#117×C₁₄₉	—	2	2	no	—
43	#117×C₁₄₉	—	2	2	no	—
44	#117×C₁₄₉	—	2	2	no	—
45	#117×C₁₄₉	—	2	2	no	—
46	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₄₉	—	2	4	no	—
49	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₁₄₉	D₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₁₄₉	D₄	1	2	yes	—
52	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₁₄₉	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₁₄₉	—	4	8	no	—
55	C₂×C₄²×C₁₄₉	—	2	2	no	—
56	C₂×C₄²×C₁₄₉	—	2	2	no	—
57	C₂×C₄²×C₁₄₉	—	2	2	no	—
58	C₂×C₄²×C₁₄₉	—	2	1	no	—
59	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
60	#102×C₁₄₉	—	2	16	no	—
61	#95×C₁₄₉	—	2	4	no	—
62	C₂⁴×C₁₄₉	—	2	2	no	—
63	C₂⁴×C₁₄₉	—	2	2	no	—
64	C₂⁴×C₁₄₉	—	2	2	no	—
65	C₂⁴×C₁₄₉	—	4	4	no	—
66	C₂⁴×C₁₄₉	—	4	4	no	—
67	C₂⁴×C₁₄₉	—	4	1	no	—
68	C₂⁴×C₁₄₉	—	4	1	no	—
69	C₂⁴×C₁₄₉	—	4	1	no	—
70	C₂⁴×C₁₄₉	—	4	1	no	—
71	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
72	C₂×D₄×C₁₄₉	—	2	2	no	—
73	C₂×D₄×C₁₄₉	—	2	4	no	—
74	C₂×D₄×C₁₄₉	—	2	4	no	—
75	C₂×D₄×C₁₄₉	—	2	4	no	—
76	C₂×D₄×C₁₄₉	—	2	2	no	—
77	C₂×D₄×C₁₄₉	—	2	4	no	—
78	C₂×D₄×C₁₄₉	—	2	4	no	—
79	C₂×D₄×C₁₄₉	—	2	2	no	—
80	C₂×D₄×C₁₄₉	—	2	4	no	—
81	C₂×D₄×C₁₄₉	—	4	2	no	—
82	C₂×D₄×C₁₄₉	—	4	2	no	—
83	C₂×D₄×C₁₄₉	—	4	2	no	—
84	C₂×D₄×C₁₄₉	—	4	2	no	—
85	C₂×D₄×C₁₄₉	—	4	2	no	—
86	C₂×D₄×C₁₄₉	—	4	2	no	—
87	C₂×D₄×C₁₄₉	C₄⋊C₄	1	4	yes	complemented
88	C₂²×C₄×C₁₄₉	—	2	4	no	—
89	C₂²×C₄×C₁₄₉	—	2	2	no	—
90	C₂²×C₄×C₁₄₉	—	2	2	no	—
91	C₂²×C₄×C₁₄₉	—	2	2	no	—
92	C₂²×C₄×C₁₄₉	—	2	4	no	—
93	C₂²×C₄×C₁₄₉	—	4	2	no	—
94	C₂²×C₄×C₁₄₉	—	4	1	no	—
95	C₂²×C₄×C₁₄₉	—	4	1	no	—
96	C₂²×C₄×C₁₄₉	—	4	4	no	—
97	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
107	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
108	M₁₆×C₁₄₉	—	2	4	no	—
109	M₁₆×C₁₄₉	—	2	4	no	—
110	M₁₆×C₁₄₉	—	4	2	no	—
111	M₁₆×C₁₄₉	—	4	2	no	—
112	C₂×C₈×C₁₄₉	—	2	4	no	—
113	C₂×C₈×C₁₄₉	—	4	2	no	—
114	C₂×C₈×C₁₄₉	—	4	2	no	—
115	C₄⋊C₄×C₁₄₉	—	2	4	no	—
116	C₄⋊C₄×C₁₄₉	—	2	4	no	—
117	C₄⋊C₄×C₁₄₉	—	2	4	no	—
118	C₄⋊C₄×C₁₄₉	—	2	4	no	—
119	C₄⋊C₄×C₁₄₉	—	8	4	no	—
120	C₂²⋊C₄×C₁₄₉	—	4	16	no	—
121	C₂²⋊C₄×C₁₄₉	—	4	2	no	—
122	C₂²⋊C₄×C₁₄₉	—	4	2	no	—
123	C₄²×C₁₄₉	—	2	4	no	—
124	C₄²×C₁₄₉	—	4	2	no	—
125	C₄²×C₁₄₉	—	4	2	no	—
126	C₄²×C₁₄₉	—	4	2	no	—
127	C₂³×C₁₄₉	—	2	2	no	—
128	C₂³×C₁₄₉	—	2	2	no	—
129	C₂³×C₁₄₉	—	2	4	no	—
130	C₂³×C₁₄₉	—	4	4	no	—
131	C₂³×C₁₄₉	—	4	4	no	—
132	C₂³×C₁₄₉	—	4	8	no	—
133	C₂³×C₁₄₉	—	4	8	no	—
134	C₂³×C₁₄₉	—	4	2	no	—
135	C₂³×C₁₄₉	—	4	2	no	—
136	C₂³×C₁₄₉	—	4	2	no	—
137	C₂³×C₁₄₉	—	4	2	no	—
138	C₂³×C₁₄₉	—	4	2	no	—
139	C₂³×C₁₄₉	—	4	2	no	—
140	C₂³×C₁₄₉	—	8	2	no	—
141	C₂³×C₁₄₉	—	8	2	no	—
142	C₂³×C₁₄₉	—	8	4	no	—
143	C₂³×C₁₄₉	—	8	4	no	—
144	C₂³×C₁₄₉	—	8	2	no	—
145	C₂³×C₁₄₉	—	8	2	no	—
146	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₁₄₉	#120	1	1	yes	characteristic
148	C₂³×C₁₄₉	#121	1	1	yes	characteristic
149	C₂³×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂³×C₁₄₉	#123	1	1	yes	characteristic
151	C₂³×C₁₄₉	#124	1	1	yes	characteristic
152	C₂³×C₁₄₉	#127	1	1	yes	characteristic
153	D₄×C₁₄₉	—	2	8	no	—
154	D₄×C₁₄₉	—	4	4	no	—
155	D₄×C₁₄₉	—	4	4	no	—
156	D₄×C₁₄₉	—	4	4	no	—
157	C₂×C₄×C₁₄₉	—	2	4	no	—
158	C₂×C₄×C₁₄₉	—	2	4	no	—
159	C₂×C₄×C₁₄₉	—	4	2	no	—
160	C₂×C₄×C₁₄₉	—	4	4	no	—
161	C₂×C₄×C₁₄₉	—	4	4	no	—
162	C₂×C₄×C₁₄₉	—	4	2	no	—
163	C₂×C₄×C₁₄₉	—	4	4	no	—
164	C₂×C₄×C₁₄₉	—	4	4	no	—
165	C₂×C₄×C₁₄₉	—	4	4	no	—
166	C₂×C₄×C₁₄₉	—	4	4	no	—
167	C₂×C₄×C₁₄₉	—	4	4	no	—
168	C₂×C₄×C₁₄₉	—	8	2	no	—
169	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₄₉	#117	1	1	yes	characteristic
171	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₁₄₉	#120	1	2	yes	—
174	C₂×C₄×C₁₄₉	#121	1	2	yes	—
175	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₄₉	#121	1	2	yes	—
177	C₂×C₄×C₁₄₉	#121	1	2	yes	—
178	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₄₉	#123	1	2	yes	—
182	C₂×C₄×C₁₄₉	#123	1	2	yes	—
183	C₂×C₄×C₁₄₉	#124	1	2	yes	—
184	C₂×C₄×C₁₄₉	#126	1	2	yes	—
185	C₈×C₁₄₉	—	4	4	no	—
186	C₂²×C₁₄₉	—	2	1	no	—
187	C₂²×C₁₄₉	—	2	1	no	—
188	C₂²×C₁₄₉	—	2	1	no	—
189	C₂²×C₁₄₉	—	2	1	no	—
190	C₂²×C₁₄₉	—	2	2	no	—
191	C₂²×C₁₄₉	—	2	2	no	—
192	C₂²×C₁₄₉	—	2	2	no	—
193	C₂²×C₁₄₉	—	2	2	no	—
194	C₂²×C₁₄₉	—	4	8	no	—
195	C₂²×C₁₄₉	—	4	4	no	—
196	C₂²×C₁₄₉	—	8	4	no	—
197	C₂²×C₁₄₉	—	8	4	no	—
198	C₂²×C₁₄₉	—	8	4	no	—
199	C₂²×C₁₄₉	—	8	2	no	—
200	C₂²×C₁₄₉	—	8	2	no	—
201	C₂²×C₁₄₉	—	8	4	no	—
202	C₂²×C₁₄₉	—	8	4	no	—
203	C₂²×C₁₄₉	#380	1	1	yes	characteristic
204	C₂²×C₁₄₉	#386	1	1	yes	characteristic
205	C₂²×C₁₄₉	#390	1	1	yes	characteristic
206	C₂²×C₁₄₉	#392	1	1	yes	characteristic
207	C₂²×C₁₄₉	#393	1	1	yes	characteristic
208	C₂²×C₁₄₉	#397	1	1	yes	characteristic
209	C₂²×C₁₄₉	#399	1	1	yes	characteristic
210	C₂²×C₁₄₉	#453	1	2	yes	—
211	C₂²×C₁₄₉	#454	1	2	yes	—
212	C₄×C₁₄₉	—	4	4	no	—
213	C₄×C₁₄₉	—	4	4	no	—
214	C₄×C₁₄₉	—	8	4	no	—
215	C₄×C₁₄₉	#385	1	2	yes	—
216	C₄×C₁₄₉	#388	1	2	yes	—
217	C₄×C₁₄₉	#394	1	2	yes	—
218	C₄×C₁₄₉	#396	1	2	yes	—
219	C₂×C₁₄₉	—	2	1	no	—
220	C₂×C₁₄₉	—	2	1	no	—
221	C₂×C₁₄₉	—	2	1	no	—
222	C₂×C₁₄₉	—	2	1	no	—
223	C₂×C₁₄₉	—	8	4	no	—
224	C₂×C₁₄₉	#1439	1	1	yes	characteristic
225	C₂×C₁₄₉	#1887	1	1	yes	characteristic
226	C₂×C₁₄₉	#1888	1	1	yes	characteristic
227	C₂×C₁₄₉	#2006	1	2	yes	—
228	C₂×C₁₄₉	#2027	1	2	yes	—
229	#11054	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₁₄₉	#11054	1	1	yes	characteristic, direct product factor, Sylow
231	C₂×#418	C₂×C₁₄₉	1	2	yes	—
232	#2316	C₂×C₁₄₉	1	1	yes	characteristic, complemented
233	C₂×#390	C₂×C₁₄₉	1	1	yes	characteristic
234	C₂×#343	C₂×C₁₄₉	1	1	yes	characteristic, complemented
235	C₂×#339	C₂×C₁₄₉	1	2	yes	complemented
236	C₂³×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
238	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
239	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
240	C₂²×C₂²⋊C₄	—	2	2	no	—
241	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
242	#418	—	2	4	no	—
243	#418	—	2	4	no	—
244	C₂×#102	—	2	4	no	—
245	#390	—	2	2	no	—
246	#390	C₄×C₁₄₉	1	4	yes	complemented
247	#389	—	2	4	no	—
248	#380	—	2	2	no	—
249	#343	—	2	2	no	—
250	#339	—	2	4	no	—
251	C₂⁵	—	2	1	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
260	C₂²×D₄	D₄×C₁₄₉	1	2	yes	—
261	C₂²×D₄	Q₈×C₁₄₉	1	2	yes	—
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
264	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	D₄×C₁₄₉	1	4	yes	—
271	C₂²×C₈	—	2	2	no	—
272	#117	—	2	2	no	—
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	#117	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
280	C₂×C₄⋊C₄	D₄×C₁₄₉	1	4	yes	—
281	C₂×C₄⋊C₄	D₄×C₁₄₉	1	2	yes	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	8	no	—
284	C₂×C₂²⋊C₄	—	4	8	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
290	#102	—	2	16	no	—
291	#95	—	2	4	no	—
292	C₂⁴	—	2	2	no	—
293	C₂⁴	—	2	2	no	—
294	C₂⁴	—	2	2	no	—
295	C₂⁴	—	4	4	no	—
296	C₂⁴	—	4	4	no	—
297	C₂⁴	—	4	1	no	—
298	C₂⁴	—	4	1	no	—
299	C₂⁴	—	4	1	no	—
300	C₂⁴	—	4	1	no	—
301	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	C₄⋊C₄×C₁₄₉	1	4	yes	complemented
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
328	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
334	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
335	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
336	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
337	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	2	4	no	—
340	M₁₆	—	4	2	no	—
341	M₁₆	—	4	2	no	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	4	2	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	8	4	no	—
350	C₂²⋊C₄	—	4	16	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	4	2	no	—
355	C₄²	—	4	2	no	—
356	C₄²	—	4	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	8	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	8	4	no	—
371	C₂³	—	8	4	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	8	2	no	—
375	C₂³	—	8	2	no	—
376	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
377	C₂³	#120×C₁₄₉	1	1	yes	characteristic
378	C₂³	#121×C₁₄₉	1	1	yes	characteristic
379	C₂³	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
380	C₂³	#123×C₁₄₉	1	1	yes	characteristic
381	C₂³	#124×C₁₄₉	1	1	yes	characteristic
382	C₂³	#127×C₁₄₉	1	1	yes	characteristic
383	D₄	—	2	8	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
400	C₂×C₄	#117×C₁₄₉	1	1	yes	characteristic
401	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
402	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
403	C₂×C₄	#120×C₁₄₉	1	2	yes	—
404	C₂×C₄	#121×C₁₄₉	1	2	yes	—
405	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
406	C₂×C₄	#121×C₁₄₉	1	2	yes	—
407	C₂×C₄	#121×C₁₄₉	1	2	yes	—
408	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
409	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
410	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	1	yes	characteristic
411	C₂×C₄	#123×C₁₄₉	1	2	yes	—
412	C₂×C₄	#123×C₁₄₉	1	2	yes	—
413	C₂×C₄	#124×C₁₄₉	1	2	yes	—
414	C₂×C₄	#126×C₁₄₉	1	2	yes	—
415	C₈	—	4	4	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	4	8	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	4	no	—
427	C₂²	—	8	4	no	—
428	C₂²	—	8	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	8	4	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	#380×C₁₄₉	1	1	yes	characteristic
434	C₂²	#386×C₁₄₉	1	1	yes	characteristic
435	C₂²	#390×C₁₄₉	1	1	yes	characteristic
436	C₂²	#392×C₁₄₉	1	1	yes	characteristic
437	C₂²	#393×C₁₄₉	1	1	yes	characteristic
438	C₂²	#397×C₁₄₉	1	1	yes	characteristic
439	C₂²	#399×C₁₄₉	1	1	yes	characteristic
440	C₂²	#453×C₁₄₉	1	2	yes	—
441	C₂²	#454×C₁₄₉	1	2	yes	—
442	C₄	—	4	4	no	—
443	C₄	—	4	4	no	—
444	C₄	—	8	4	no	—
445	C₄	#385×C₁₄₉	1	2	yes	—
446	C₄	#388×C₁₄₉	1	2	yes	—
447	C₄	#394×C₁₄₉	1	2	yes	—
448	C₄	#396×C₁₄₉	1	2	yes	—
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	8	4	no	—
454	C₂	#1439×C₁₄₉	1	1	yes	characteristic
455	C₂	#1887×C₁₄₉	1	1	yes	characteristic
456	C₂	#1888×C₁₄₉	1	1	yes	characteristic
457	C₂	#2006×C₁₄₉	1	2	yes	—
458	C₂	#2027×C₁₄₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₄₉	#120
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 ◁ C₂³×C₁₄₉ ◁ C₂³×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2316×C₁₄₉	C₂	semidirect
4. C₂×#343×C₁₄₉	C₂	semidirect
5. C₂×#339×C₁₄₉	C₂	semidirect
16. #390×C₁₄₉	C₄	semidirect
87. C₂×D₄×C₁₄₉	C₄⋊C₄	semidirect
229. #11054	C₁₄₉	direct (N × H)
230. C₁₄₉	#11054	direct (N × H)
232. #2316	C₂×C₁₄₉	semidirect
234. C₂×#343	C₂×C₁₄₉	semidirect
235. C₂×#339	C₂×C₁₄₉	semidirect
246. #390	C₄×C₁₄₉	semidirect
317. C₂×D₄	C₄⋊C₄×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#418×C₁₄₉	2
#2316×C₁₄₉	2
C₂×#390×C₁₄₉	2
C₂×#343×C₁₄₉	2
C₂×#339×C₁₄₉	2
#11054	149

Subgroups — C149×#11054 #49190003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#11054 #49190003