Subgroups — C₁₄₉×#10719 #49189668

Order 38144.

1974 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	#2280×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#339×C₁₄₉	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₁₄₉	—	2	1	no	—
6	C₂⁴×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
8	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
9	C₂²×C₄²×C₁₄₉	—	2	1	no	—
10	C₂²×C₄²×C₁₄₉	—	2	2	no	—
11	C₂²×C₄²×C₁₄₉	—	2	8	no	—
12	C₂²×C₄²×C₁₄₉	C₄	1	4	yes	complemented
13	C₂²×C₄²×C₁₄₉	C₂²	1	2	yes	—
14	#407×C₁₄₉	—	2	2	no	—
15	#407×C₁₄₉	C₄	1	4	yes	complemented
16	C₂×C₂²⋊C₈×C₁₄₉	—	2	2	no	—
17	#381×C₁₄₉	—	2	1	no	—
18	#380×C₁₄₉	C₄	1	4	yes	complemented
19	#379×C₁₄₉	—	2	1	no	—
20	C₄×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
21	#339×C₁₄₉	—	2	8	no	—
22	C₂⁵×C₁₄₉	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₄₉	—	2	8	no	—
24	C₂³×C₄×C₁₄₉	—	2	16	no	—
25	C₂³×C₄×C₁₄₉	—	2	4	no	—
26	C₂³×C₄×C₁₄₉	—	2	2	no	—
27	C₂³×C₄×C₁₄₉	—	2	4	no	—
28	C₂³×C₄×C₁₄₉	—	2	4	no	—
29	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
34	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
35	C₂³×C₄×C₁₄₉	Q₈	1	2	yes	—
36	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₁₄₉	—	2	2	no	—
38	C₂×M₁₆×C₁₄₉	—	2	4	no	—
39	C₂×M₁₆×C₁₄₉	—	2	4	no	—
40	C₂×M₁₆×C₁₄₉	C₂×C₄	1	4	yes	complemented
41	C₂²×C₈×C₁₄₉	—	2	2	no	—
42	#117×C₁₄₉	—	2	4	no	—
43	#117×C₁₄₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	4	yes	complemented
45	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
46	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
47	C₂×C₄²×C₁₄₉	—	2	8	no	—
48	C₂×C₄²×C₁₄₉	—	2	16	no	—
49	C₂×C₄²×C₁₄₉	—	2	4	no	—
50	C₂×C₄²×C₁₄₉	—	2	4	no	—
51	C₂×C₄²×C₁₄₉	—	2	2	no	—
52	C₂×C₄²×C₁₄₉	—	2	16	no	—
53	C₂×C₄²×C₁₄₉	—	2	2	no	—
54	C₂×C₄²×C₁₄₉	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₁₄₉	D₄	1	8	yes	—
56	C₂²⋊C₈×C₁₄₉	—	2	8	no	—
57	#95×C₁₄₉	—	2	4	no	—
58	C₂⁴×C₁₄₉	—	2	8	no	—
59	C₂⁴×C₁₄₉	—	2	2	no	—
60	C₂⁴×C₁₄₉	—	2	2	no	—
61	C₂⁴×C₁₄₉	C₂²⋊C₄	1	2	yes	—
62	C₂⁴×C₁₄₉	C₂²⋊C₄	1	2	yes	—
63	C₂⁴×C₁₄₉	C₄⋊C₄	1	2	yes	—
64	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₄₉	—	2	16	no	—
66	C₂²×C₄×C₁₄₉	—	2	64	no	—
67	C₂²×C₄×C₁₄₉	—	2	32	no	—
68	C₂²×C₄×C₁₄₉	—	2	16	no	—
69	C₂²×C₄×C₁₄₉	—	2	4	no	—
70	C₂²×C₄×C₁₄₉	—	2	2	no	—
71	C₂²×C₄×C₁₄₉	—	2	8	no	—
72	C₂²×C₄×C₁₄₉	—	2	2	no	—
73	C₂²×C₄×C₁₄₉	—	2	4	no	—
74	C₂²×C₄×C₁₄₉	—	2	4	no	—
75	C₂²×C₄×C₁₄₉	—	2	8	no	—
76	C₂²×C₄×C₁₄₉	—	2	8	no	—
77	C₂²×C₄×C₁₄₉	—	2	4	no	—
78	C₂²×C₄×C₁₄₉	—	2	8	no	—
79	C₂²×C₄×C₁₄₉	—	2	8	no	—
80	C₂²×C₄×C₁₄₉	—	2	4	no	—
81	C₂²×C₄×C₁₄₉	—	2	4	no	—
82	C₂²×C₄×C₁₄₉	C₄²	1	4	yes	—
83	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
84	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
86	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
87	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
88	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
89	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
94	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₄₉	#41	1	4	yes	—
97	M₁₆×C₁₄₉	—	2	8	no	—
98	M₁₆×C₁₄₉	—	4	2	no	—
99	M₁₆×C₁₄₉	—	4	2	no	—
100	C₂×C₈×C₁₄₉	—	2	4	no	—
101	C₂×C₈×C₁₄₉	—	4	4	no	—
102	C₄⋊C₄×C₁₄₉	—	2	8	no	—
103	C₂²⋊C₄×C₁₄₉	—	4	8	no	—
104	C₂²⋊C₄×C₁₄₉	—	4	2	no	—
105	C₂²⋊C₄×C₁₄₉	—	4	2	no	—
106	C₄²×C₁₄₉	—	2	16	no	—
107	C₄²×C₁₄₉	—	2	4	no	—
108	C₄²×C₁₄₉	—	2	8	no	—
109	C₄²×C₁₄₉	—	4	4	no	—
110	C₄²×C₁₄₉	C₂²⋊C₄	1	8	yes	complemented
111	C₂³×C₁₄₉	—	2	16	no	—
112	C₂³×C₁₄₉	—	2	16	no	—
113	C₂³×C₁₄₉	—	2	8	no	—
114	C₂³×C₁₄₉	—	2	8	no	—
115	C₂³×C₁₄₉	—	2	2	no	—
116	C₂³×C₁₄₉	—	2	2	no	—
117	C₂³×C₁₄₉	—	2	4	no	—
118	C₂³×C₁₄₉	—	2	4	no	—
119	C₂³×C₁₄₉	—	2	4	no	—
120	C₂³×C₁₄₉	—	2	4	no	—
121	C₂³×C₁₄₉	#95	1	4	yes	—
122	C₂³×C₁₄₉	#104	1	8	yes	—
123	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂³×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂³×C₁₄₉	#120	1	2	yes	—
127	C₂³×C₁₄₉	#123	1	2	yes	—
128	C₂×C₄×C₁₄₉	—	2	64	no	—
129	C₂×C₄×C₁₄₉	—	2	32	no	—
130	C₂×C₄×C₁₄₉	—	2	16	no	—
131	C₂×C₄×C₁₄₉	—	2	2	no	—
132	C₂×C₄×C₁₄₉	—	2	8	no	—
133	C₂×C₄×C₁₄₉	—	2	2	no	—
134	C₂×C₄×C₁₄₉	—	2	4	no	—
135	C₂×C₄×C₁₄₉	—	2	4	no	—
136	C₂×C₄×C₁₄₉	—	2	8	no	—
137	C₂×C₄×C₁₄₉	—	2	8	no	—
138	C₂×C₄×C₁₄₉	—	2	8	no	—
139	C₂×C₄×C₁₄₉	—	2	8	no	—
140	C₂×C₄×C₁₄₉	—	4	4	no	—
141	C₂×C₄×C₁₄₉	—	4	8	no	—
142	C₂×C₄×C₁₄₉	#95	1	4	yes	—
143	C₂×C₄×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₄₉	#117	1	2	yes	—
149	C₂×C₄×C₁₄₉	C₄×D₄	1	4	yes	—
150	C₂×C₄×C₁₄₉	C₄×D₄	1	4	yes	—
151	C₂×C₄×C₁₄₉	#120	1	2	yes	—
152	C₂×C₄×C₁₄₉	#121	1	4	yes	—
153	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	4	yes	—
154	C₂×C₄×C₁₄₉	#123	1	2	yes	—
155	C₈×C₁₄₉	—	4	4	no	—
156	C₂²×C₁₄₉	—	2	8	no	—
157	C₂²×C₁₄₉	—	2	8	no	—
158	C₂²×C₁₄₉	—	2	16	no	—
159	C₂²×C₁₄₉	—	2	4	no	—
160	C₂²×C₁₄₉	—	2	16	no	—
161	C₂²×C₁₄₉	—	2	4	no	—
162	C₂²×C₁₄₉	—	2	4	no	—
163	C₂²×C₁₄₉	—	2	2	no	—
164	C₂²×C₁₄₉	—	2	4	no	—
165	C₂²×C₁₄₉	—	2	2	no	—
166	C₂²×C₁₄₉	#339	1	8	yes	complemented
167	C₂²×C₁₄₉	C₂×#95	1	1	yes	characteristic
168	C₂²×C₁₄₉	#379	1	1	yes	characteristic
169	C₂²×C₁₄₉	#381	1	1	yes	characteristic
170	C₂²×C₁₄₉	#385	1	2	yes	—
171	C₂²×C₁₄₉	#386	1	2	yes	—
172	C₂²×C₁₄₉	C₂×#104	1	4	yes	—
173	C₄×C₁₄₉	—	2	16	no	—
174	C₄×C₁₄₉	—	2	4	no	—
175	C₄×C₁₄₉	—	8	4	no	—
176	C₄×C₁₄₉	C₄×C₂²⋊C₄	1	2	yes	—
177	C₄×C₁₄₉	#380	1	2	yes	—
178	C₄×C₁₄₉	#385	1	2	yes	—
179	C₄×C₁₄₉	#386	1	2	yes	—
180	C₂×C₁₄₉	—	2	1	no	—
181	C₂×C₁₄₉	—	2	8	no	—
182	C₂×C₁₄₉	—	2	1	no	—
183	C₂×C₁₄₉	—	2	2	no	—
184	C₂×C₁₄₉	C₂²⋊#95	1	1	yes	characteristic
185	C₂×C₁₄₉	C₂×#339	1	2	yes	—
186	C₂×C₁₄₉	#1896	1	4	yes	—
187	#10719	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₁₄₉	#10719	1	1	yes	characteristic, direct product factor, Sylow
189	C₂³×C₄²	C₂×C₁₄₉	1	1	yes	characteristic
190	C₂×#407	C₂×C₁₄₉	1	1	yes	characteristic
191	#2280	C₂×C₁₄₉	1	1	yes	characteristic
192	C₂×#339	C₂×C₁₄₉	1	4	yes	complemented
193	C₂⁴×C₄	—	2	1	no	—
194	C₂⁴×C₄	C₂²×C₁₄₉	1	1	yes	characteristic
195	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
196	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
197	C₂²×C₄²	—	2	1	no	—
198	C₂²×C₄²	—	2	2	no	—
199	C₂²×C₄²	—	2	8	no	—
200	C₂²×C₄²	C₄×C₁₄₉	1	4	yes	complemented
201	C₂²×C₄²	C₂²×C₁₄₉	1	2	yes	—
202	#407	—	2	2	no	—
203	#407	C₄×C₁₄₉	1	4	yes	complemented
204	C₂×C₂²⋊C₈	—	2	2	no	—
205	#381	—	2	1	no	—
206	#380	C₄×C₁₄₉	1	4	yes	complemented
207	#379	—	2	1	no	—
208	C₄×C₂²⋊C₄	—	2	2	no	—
209	#339	—	2	8	no	—
210	C₂⁵	D₄×C₁₄₉	1	1	yes	characteristic
211	C₂³×C₄	—	2	16	no	—
212	C₂³×C₄	—	2	8	no	—
213	C₂³×C₄	—	2	4	no	—
214	C₂³×C₄	—	2	2	no	—
215	C₂³×C₄	—	2	4	no	—
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
218	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
219	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
220	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
221	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
222	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
223	C₂³×C₄	Q₈×C₁₄₉	1	2	yes	—
224	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	2	4	no	—
227	C₂×M₁₆	—	2	4	no	—
228	C₂×M₁₆	C₂×C₄×C₁₄₉	1	4	yes	complemented
229	C₂²×C₈	—	2	2	no	—
230	#117	—	2	4	no	—
231	#117	—	2	4	no	—
232	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	4	yes	complemented
233	C₂×C₂²⋊C₄	—	2	4	no	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₄²	—	2	8	no	—
236	C₂×C₄²	—	2	16	no	—
237	C₂×C₄²	—	2	4	no	—
238	C₂×C₄²	—	2	4	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	16	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	C₂×C₄×C₁₄₉	1	4	yes	—
243	C₂×C₄²	D₄×C₁₄₉	1	8	yes	—
244	C₂²⋊C₈	—	2	8	no	—
245	#95	—	2	4	no	—
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	2	2	no	—
248	C₂⁴	—	2	2	no	—
249	C₂⁴	C₂²⋊C₄×C₁₄₉	1	2	yes	—
250	C₂⁴	C₂²⋊C₄×C₁₄₉	1	2	yes	—
251	C₂⁴	C₄⋊C₄×C₁₄₉	1	2	yes	—
252	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
253	C₂²×C₄	—	2	16	no	—
254	C₂²×C₄	—	2	64	no	—
255	C₂²×C₄	—	2	16	no	—
256	C₂²×C₄	—	2	32	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	8	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	8	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	C₄²×C₁₄₉	1	4	yes	—
271	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
272	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
273	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
274	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
275	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
276	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
277	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
283	C₂²×C₄	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
284	C₂²×C₄	#41×C₁₄₉	1	4	yes	—
285	M₁₆	—	2	8	no	—
286	M₁₆	—	4	2	no	—
287	M₁₆	—	4	2	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	4	4	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₂²⋊C₄	—	4	8	no	—
292	C₂²⋊C₄	—	4	2	no	—
293	C₂²⋊C₄	—	4	2	no	—
294	C₄²	—	2	16	no	—
295	C₄²	—	2	4	no	—
296	C₄²	—	2	8	no	—
297	C₄²	—	4	4	no	—
298	C₄²	C₂²⋊C₄×C₁₄₉	1	8	yes	complemented
299	C₂³	—	2	16	no	—
300	C₂³	—	2	16	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	2	8	no	—
308	C₂³	—	2	8	no	—
309	C₂³	#95×C₁₄₉	1	4	yes	—
310	C₂³	#104×C₁₄₉	1	8	yes	—
311	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
312	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
313	C₂³	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
314	C₂³	#120×C₁₄₉	1	2	yes	—
315	C₂³	#123×C₁₄₉	1	2	yes	—
316	C₂×C₄	—	2	64	no	—
317	C₂×C₄	—	2	16	no	—
318	C₂×C₄	—	2	32	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	8	no	—
330	C₂×C₄	#95×C₁₄₉	1	4	yes	—
331	C₂×C₄	C₂×C₄²×C₁₄₉	1	1	yes	characteristic
332	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
333	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
336	C₂×C₄	#117×C₁₄₉	1	2	yes	—
337	C₂×C₄	C₄×D₄×C₁₄₉	1	4	yes	—
338	C₂×C₄	C₄×D₄×C₁₄₉	1	4	yes	—
339	C₂×C₄	#120×C₁₄₉	1	2	yes	—
340	C₂×C₄	#121×C₁₄₉	1	4	yes	—
341	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	4	yes	—
342	C₂×C₄	#123×C₁₄₉	1	2	yes	—
343	C₈	—	4	4	no	—
344	C₂²	—	2	8	no	—
345	C₂²	—	2	8	no	—
346	C₂²	—	2	16	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	16	no	—
353	C₂²	—	2	4	no	—
354	C₂²	#339×C₁₄₉	1	8	yes	complemented
355	C₂²	C₂×#95×C₁₄₉	1	1	yes	characteristic
356	C₂²	#379×C₁₄₉	1	1	yes	characteristic
357	C₂²	#381×C₁₄₉	1	1	yes	characteristic
358	C₂²	#385×C₁₄₉	1	2	yes	—
359	C₂²	#386×C₁₄₉	1	2	yes	—
360	C₂²	C₂×#104×C₁₄₉	1	4	yes	—
361	C₄	—	2	16	no	—
362	C₄	—	2	4	no	—
363	C₄	—	8	4	no	—
364	C₄	C₄×C₂²⋊C₄×C₁₄₉	1	2	yes	—
365	C₄	#380×C₁₄₉	1	2	yes	—
366	C₄	#385×C₁₄₉	1	2	yes	—
367	C₄	#386×C₁₄₉	1	2	yes	—
368	C₂	—	2	1	no	—
369	C₂	—	2	1	no	—
370	C₂	—	2	2	no	—
371	C₂	—	2	8	no	—
372	C₂	C₂²⋊#95×C₁₄₉	1	1	yes	characteristic
373	C₂	C₂×#339×C₁₄₉	1	2	yes	—
374	C₂	#1896×C₁₄₉	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
socle	C₂³×C₁₄₉	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₁₄₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ C₂⁴×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#339×C₁₄₉	C₂	semidirect
12. C₂²×C₄²×C₁₄₉	C₄	semidirect
15. #407×C₁₄₉	C₄	semidirect
18. #380×C₁₄₉	C₄	semidirect
40. C₂×M₁₆×C₁₄₉	C₂×C₄	semidirect
44. C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	semidirect
110. C₄²×C₁₄₉	C₂²⋊C₄	semidirect
166. C₂²×C₁₄₉	#339	semidirect
187. #10719	C₁₄₉	direct (N × H)
188. C₁₄₉	#10719	direct (N × H)
192. C₂×#339	C₂×C₁₄₉	semidirect
200. C₂²×C₄²	C₄×C₁₄₉	semidirect
203. #407	C₄×C₁₄₉	semidirect
206. #380	C₄×C₁₄₉	semidirect
228. C₂×M₁₆	C₂×C₄×C₁₄₉	semidirect
232. C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	semidirect
298. C₄²	C₂²⋊C₄×C₁₄₉	semidirect
354. C₂²	#339×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄²×C₁₄₉	2
C₂×#407×C₁₄₉	2
#2280×C₁₄₉	2
C₂×#339×C₁₄₉	2
#10719	149

Subgroups — C149×#10719 #49189668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#10719 #49189668