Subgroups — C₁₄₉×#10749 #49189698

Order 38144.

1562 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#518×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#100×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#390×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#1736×C₁₄₉	C₂	1	2	yes	maximal, 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	#518×C₁₄₉	—	2	2	no	—
9	#518×C₁₄₉	—	2	4	no	—
10	#518×C₁₄₉	C₄	1	4	yes	complemented
11	C₂×C₄×D₄×C₁₄₉	—	2	4	no	—
12	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
15	C₂²×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
16	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
17	C₂×#100×C₁₄₉	—	2	2	no	—
18	C₂×#100×C₁₄₉	—	2	2	no	—
19	C₂×#100×C₁₄₉	C₄	1	4	yes	complemented
20	#390×C₁₄₉	—	2	2	no	—
21	#390×C₁₄₉	C₄	1	4	yes	complemented
22	#340×C₁₄₉	—	2	4	no	—
23	#339×C₁₄₉	—	2	4	no	—
24	C₂⁵×C₁₄₉	D₄	1	2	yes	—
25	C₂²×D₄×C₁₄₉	—	2	2	no	—
26	C₂²×D₄×C₁₄₉	—	2	2	no	—
27	C₂²×D₄×C₁₄₉	—	2	2	no	—
28	C₂²×D₄×C₁₄₉	—	2	2	no	—
29	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
31	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₄₉	D₄	1	2	yes	—
33	C₂²×D₄×C₁₄₉	D₄	1	2	yes	—
34	C₂²×D₄×C₁₄₉	Q₈	1	2	yes	—
35	C₂³×C₄×C₁₄₉	—	2	1	no	—
36	C₂³×C₄×C₁₄₉	—	2	4	no	—
37	C₂³×C₄×C₁₄₉	—	2	1	no	—
38	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₁₄₉	—	2	2	no	—
40	C₂×M₁₆×C₁₄₉	—	2	2	no	—
41	C₂×M₁₆×C₁₄₉	—	2	2	no	—
42	C₂×M₁₆×C₁₄₉	—	2	2	no	—
43	C₂×M₁₆×C₁₄₉	—	2	2	no	—
44	C₂×M₁₆×C₁₄₉	C₂×C₄	1	4	yes	complemented
45	C₂²×C₈×C₁₄₉	—	2	2	no	—
46	C₄×D₄×C₁₄₉	—	2	16	no	—
47	C₄×D₄×C₁₄₉	—	2	16	no	—
48	#117×C₁₄₉	—	2	2	no	—
49	#117×C₁₄₉	—	2	2	no	—
50	#117×C₁₄₉	C₂×C₄	1	4	yes	—
51	#117×C₁₄₉	D₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	complemented
56	C₂×C₄⋊C₄×C₁₄₉	D₄	1	4	yes	—
57	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₄₉	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₁₄₉	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₄₉	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₁₄₉	—	4	8	no	—
63	C₂×C₄²×C₁₄₉	—	2	2	no	—
64	C₂×C₄²×C₁₄₉	—	2	2	no	—
65	C₂×C₄²×C₁₄₉	—	2	2	no	—
66	C₂×C₄²×C₁₄₉	—	2	1	no	—
67	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	complemented
68	#100×C₁₄₉	—	2	8	no	—
69	C₂⁴×C₁₄₉	—	2	2	no	—
70	C₂⁴×C₁₄₉	—	2	2	no	—
71	C₂⁴×C₁₄₉	—	2	2	no	—
72	C₂⁴×C₁₄₉	—	2	2	no	—
73	C₂⁴×C₁₄₉	—	4	4	no	—
74	C₂⁴×C₁₄₉	—	4	4	no	—
75	C₂⁴×C₁₄₉	C₂²⋊C₄	1	4	yes	—
76	C₂⁴×C₁₄₉	C₂²⋊C₄	1	4	yes	—
77	C₂⁴×C₁₄₉	C₄⋊C₄	1	4	yes	—
78	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₁₄₉	—	2	4	no	—
80	C₂×D₄×C₁₄₉	—	2	4	no	—
81	C₂×D₄×C₁₄₉	—	2	4	no	—
82	C₂×D₄×C₁₄₉	—	2	4	no	—
83	C₂×D₄×C₁₄₉	—	2	4	no	—
84	C₂×D₄×C₁₄₉	—	2	4	no	—
85	C₂×D₄×C₁₄₉	—	2	4	no	—
86	C₂×D₄×C₁₄₉	—	2	4	no	—
87	C₂×D₄×C₁₄₉	—	2	4	no	—
88	C₂×D₄×C₁₄₉	—	2	4	no	—
89	C₂×D₄×C₁₄₉	—	2	4	no	—
90	C₂×D₄×C₁₄₉	—	2	4	no	—
91	C₂×D₄×C₁₄₉	C₄²	1	4	yes	—
92	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
93	C₂×D₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
94	C₂×D₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
95	C₂²×C₄×C₁₄₉	—	2	4	no	—
96	C₂²×C₄×C₁₄₉	—	2	2	no	—
97	C₂²×C₄×C₁₄₉	—	2	4	no	—
98	C₂²×C₄×C₁₄₉	—	2	16	no	—
99	C₂²×C₄×C₁₄₉	—	2	2	no	—
100	C₂²×C₄×C₁₄₉	—	4	2	no	—
101	C₂²×C₄×C₁₄₉	—	4	1	no	—
102	C₂²×C₄×C₁₄₉	—	4	1	no	—
103	C₂²×C₄×C₁₄₉	—	4	4	no	—
104	C₂²×C₄×C₁₄₉	—	4	1	no	—
105	C₂²×C₄×C₁₄₉	—	4	1	no	—
106	C₂²×C₄×C₁₄₉	—	8	4	no	—
107	C₂²×C₄×C₁₄₉	—	8	4	no	—
108	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
116	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
117	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
118	M₁₆×C₁₄₉	—	2	4	no	—
119	M₁₆×C₁₄₉	—	2	4	no	—
120	M₁₆×C₁₄₉	—	4	2	no	—
121	M₁₆×C₁₄₉	—	4	2	no	—
122	C₂×C₈×C₁₄₉	—	2	4	no	—
123	C₂×C₈×C₁₄₉	—	4	2	no	—
124	C₂×C₈×C₁₄₉	—	4	2	no	—
125	C₄⋊C₄×C₁₄₉	—	2	4	no	—
126	C₄⋊C₄×C₁₄₉	—	2	4	no	—
127	C₄⋊C₄×C₁₄₉	—	4	2	no	—
128	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	8	yes	complemented
129	C₂²⋊C₄×C₁₄₉	—	2	16	no	—
130	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
131	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
132	C₂²⋊C₄×C₁₄₉	—	4	16	no	—
133	C₄²×C₁₄₉	—	2	4	no	—
134	C₄²×C₁₄₉	—	2	4	no	—
135	C₄²×C₁₄₉	—	2	4	no	—
136	C₄²×C₁₄₉	—	4	2	no	—
137	C₂³×C₁₄₉	—	2	2	no	—
138	C₂³×C₁₄₉	—	2	2	no	—
139	C₂³×C₁₄₉	—	2	4	no	—
140	C₂³×C₁₄₉	—	2	4	no	—
141	C₂³×C₁₄₉	—	2	4	no	—
142	C₂³×C₁₄₉	—	2	4	no	—
143	C₂³×C₁₄₉	—	2	4	no	—
144	C₂³×C₁₄₉	—	2	4	no	—
145	C₂³×C₁₄₉	—	4	4	no	—
146	C₂³×C₁₄₉	—	4	8	no	—
147	C₂³×C₁₄₉	—	4	4	no	—
148	C₂³×C₁₄₉	—	4	8	no	—
149	C₂³×C₁₄₉	—	4	4	no	—
150	C₂³×C₁₄₉	—	4	4	no	—
151	C₂³×C₁₄₉	—	8	4	no	—
152	C₂³×C₁₄₉	—	8	4	no	—
153	C₂³×C₁₄₉	—	8	2	no	—
154	C₂³×C₁₄₉	—	8	2	no	—
155	C₂³×C₁₄₉	#95	1	8	yes	—
156	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂³×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂³×C₁₄₉	#120	1	1	yes	characteristic
160	C₂³×C₁₄₉	#120	1	1	yes	characteristic
161	C₂³×C₁₄₉	#123	1	1	yes	characteristic
162	C₂³×C₁₄₉	#123	1	1	yes	characteristic
163	D₄×C₁₄₉	—	2	8	no	—
164	D₄×C₁₄₉	—	2	8	no	—
165	D₄×C₁₄₉	—	2	8	no	—
166	D₄×C₁₄₉	—	2	8	no	—
167	C₂×C₄×C₁₄₉	—	2	4	no	—
168	C₂×C₄×C₁₄₉	—	2	8	no	—
169	C₂×C₄×C₁₄₉	—	4	4	no	—
170	C₂×C₄×C₁₄₉	—	4	4	no	—
171	C₂×C₄×C₁₄₉	—	4	2	no	—
172	C₂×C₄×C₁₄₉	—	4	2	no	—
173	C₂×C₄×C₁₄₉	—	4	4	no	—
174	C₂×C₄×C₁₄₉	—	4	4	no	—
175	C₂×C₄×C₁₄₉	—	4	4	no	—
176	C₂×C₄×C₁₄₉	—	4	2	no	—
177	C₂×C₄×C₁₄₉	—	8	16	no	—
178	C₂×C₄×C₁₄₉	—	8	2	no	—
179	C₂×C₄×C₁₄₉	—	8	2	no	—
180	C₂×C₄×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₄₉	#117	1	2	yes	—
186	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₁₄₉	#120	1	2	yes	—
191	C₂×C₄×C₁₄₉	#121	1	2	yes	—
192	C₂×C₄×C₁₄₉	#121	1	2	yes	—
193	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
194	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
195	C₂×C₄×C₁₄₉	#123	1	2	yes	—
196	C₈×C₁₄₉	—	4	4	no	—
197	C₂²×C₁₄₉	—	2	2	no	—
198	C₂²×C₁₄₉	—	2	2	no	—
199	C₂²×C₁₄₉	—	2	2	no	—
200	C₂²×C₁₄₉	—	2	2	no	—
201	C₂²×C₁₄₉	—	2	1	no	—
202	C₂²×C₁₄₉	—	2	1	no	—
203	C₂²×C₁₄₉	—	2	1	no	—
204	C₂²×C₁₄₉	—	2	1	no	—
205	C₂²×C₁₄₉	—	2	8	no	—
206	C₂²×C₁₄₉	—	4	8	no	—
207	C₂²×C₁₄₉	—	4	8	no	—
208	C₂²×C₁₄₉	—	4	8	no	—
209	C₂²×C₁₄₉	—	4	4	no	—
210	C₂²×C₁₄₉	—	4	4	no	—
211	C₂²×C₁₄₉	—	8	4	no	—
212	C₂²×C₁₄₉	—	8	4	no	—
213	C₂²×C₁₄₉	—	8	4	no	—
214	C₂²×C₁₄₉	C₂×#95	1	1	yes	characteristic
215	C₂²×C₁₄₉	#379	1	1	yes	characteristic
216	C₂²×C₁₄₉	#381	1	1	yes	characteristic
217	C₂²×C₁₄₉	#385	1	1	yes	characteristic
218	C₂²×C₁₄₉	#385	1	1	yes	characteristic
219	C₂²×C₁₄₉	#386	1	1	yes	characteristic
220	C₂²×C₁₄₉	#386	1	1	yes	characteristic
221	C₂²×C₁₄₉	#453	1	2	yes	—
222	C₂²×C₁₄₉	#455	1	2	yes	—
223	C₄×C₁₄₉	—	4	4	no	—
224	C₄×C₁₄₉	—	4	8	no	—
225	C₄×C₁₄₉	—	8	2	no	—
226	C₄×C₁₄₉	C₄×C₂²⋊C₄	1	2	yes	—
227	C₄×C₁₄₉	#380	1	2	yes	—
228	C₄×C₁₄₉	#385	1	2	yes	—
229	C₄×C₁₄₉	#386	1	2	yes	—
230	C₂×C₁₄₉	—	2	1	no	—
231	C₂×C₁₄₉	—	2	1	no	—
232	C₂×C₁₄₉	—	2	1	no	—
233	C₂×C₁₄₉	—	2	1	no	—
234	C₂×C₁₄₉	—	4	8	no	—
235	C₂×C₁₄₉	C₂²⋊#95	1	1	yes	characteristic
236	C₂×C₁₄₉	#1792	1	2	yes	—
237	C₂×C₁₄₉	#1856	1	2	yes	—
238	C₂×C₁₄₉	#1885	1	1	yes	characteristic
239	C₂×C₁₄₉	#1887	1	1	yes	characteristic
240	#10749	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₁₄₉	#10749	1	1	yes	characteristic, direct product factor, Sylow
242	C₂×#518	C₂×C₁₄₉	1	1	yes	characteristic
243	C₂²×#100	C₂×C₁₄₉	1	1	yes	characteristic
244	C₂×#390	C₂×C₁₄₉	1	1	yes	characteristic
245	#1736	C₂×C₁₄₉	1	2	yes	complemented
246	C₂×#339	C₂×C₁₄₉	1	2	yes	complemented
247	C₂³×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
249	#518	—	2	2	no	—
250	#518	—	2	4	no	—
251	#518	C₄×C₁₄₉	1	4	yes	complemented
252	C₂×C₄×D₄	—	2	4	no	—
253	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
254	C₂²×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
255	C₂²×C₂²⋊C₄	—	2	2	no	—
256	C₂²×C₂²⋊C₄	—	2	2	no	—
257	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
258	C₂×#100	—	2	2	no	—
259	C₂×#100	—	2	2	no	—
260	C₂×#100	C₄×C₁₄₉	1	4	yes	complemented
261	#390	—	2	2	no	—
262	#390	C₄×C₁₄₉	1	4	yes	complemented
263	#340	—	2	4	no	—
264	#339	—	2	4	no	—
265	C₂⁵	D₄×C₁₄₉	1	2	yes	—
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
271	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
272	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
273	C₂²×D₄	D₄×C₁₄₉	1	2	yes	—
274	C₂²×D₄	D₄×C₁₄₉	1	2	yes	—
275	C₂²×D₄	Q₈×C₁₄₉	1	2	yes	—
276	C₂³×C₄	—	2	1	no	—
277	C₂³×C₄	—	2	4	no	—
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	C₂×C₄×C₁₄₉	1	4	yes	complemented
286	C₂²×C₈	—	2	2	no	—
287	C₄×D₄	—	2	16	no	—
288	C₄×D₄	—	2	16	no	—
289	#117	—	2	2	no	—
290	#117	—	2	2	no	—
291	#117	C₂×C₄×C₁₄₉	1	4	yes	—
292	#117	D₄×C₁₄₉	1	4	yes	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	complemented
297	C₂×C₄⋊C₄	D₄×C₁₄₉	1	4	yes	—
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₂²⋊C₄	—	2	8	no	—
300	C₂×C₂²⋊C₄	—	2	8	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	8	no	—
303	C₂×C₂²⋊C₄	—	4	8	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	complemented
309	#100	—	2	8	no	—
310	C₂⁴	—	2	2	no	—
311	C₂⁴	—	2	2	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	4	4	no	—
315	C₂⁴	—	4	4	no	—
316	C₂⁴	C₂²⋊C₄×C₁₄₉	1	4	yes	—
317	C₂⁴	C₂²⋊C₄×C₁₄₉	1	4	yes	—
318	C₂⁴	C₄⋊C₄×C₁₄₉	1	4	yes	—
319	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	C₄²×C₁₄₉	1	4	yes	—
333	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
334	C₂×D₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
335	C₂×D₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	8	4	no	—
348	C₂²×C₄	—	8	4	no	—
349	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
356	C₂²×C₄	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
357	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
358	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	—	4	2	no	—
362	M₁₆	—	4	2	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	4	2	no	—
365	C₂×C₈	—	4	2	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	8	yes	complemented
370	C₂²⋊C₄	—	2	16	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	4	16	no	—
374	C₄²	—	2	4	no	—
375	C₄²	—	2	4	no	—
376	C₄²	—	2	4	no	—
377	C₄²	—	4	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	8	no	—
388	C₂³	—	4	4	no	—
389	C₂³	—	4	8	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	8	4	no	—
393	C₂³	—	8	4	no	—
394	C₂³	—	8	2	no	—
395	C₂³	—	8	2	no	—
396	C₂³	#95×C₁₄₉	1	8	yes	—
397	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
398	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
399	C₂³	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
400	C₂³	#120×C₁₄₉	1	1	yes	characteristic
401	C₂³	#120×C₁₄₉	1	1	yes	characteristic
402	C₂³	#123×C₁₄₉	1	1	yes	characteristic
403	C₂³	#123×C₁₄₉	1	1	yes	characteristic
404	D₄	—	2	8	no	—
405	D₄	—	2	8	no	—
406	D₄	—	2	8	no	—
407	D₄	—	2	8	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	16	no	—
419	C₂×C₄	—	8	2	no	—
420	C₂×C₄	—	8	2	no	—
421	C₂×C₄	C₂×C₄²×C₁₄₉	1	1	yes	characteristic
422	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
423	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
424	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
426	C₂×C₄	#117×C₁₄₉	1	2	yes	—
427	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
428	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
429	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
430	C₂×C₄	C₄×D₄×C₁₄₉	1	2	yes	—
431	C₂×C₄	#120×C₁₄₉	1	2	yes	—
432	C₂×C₄	#121×C₁₄₉	1	2	yes	—
433	C₂×C₄	#121×C₁₄₉	1	2	yes	—
434	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
435	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
436	C₂×C₄	#123×C₁₄₉	1	2	yes	—
437	C₈	—	4	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	4	8	no	—
448	C₂²	—	4	8	no	—
449	C₂²	—	4	8	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	8	4	no	—
453	C₂²	—	8	4	no	—
454	C₂²	—	8	4	no	—
455	C₂²	C₂×#95×C₁₄₉	1	1	yes	characteristic
456	C₂²	#379×C₁₄₉	1	1	yes	characteristic
457	C₂²	#381×C₁₄₉	1	1	yes	characteristic
458	C₂²	#385×C₁₄₉	1	1	yes	characteristic
459	C₂²	#385×C₁₄₉	1	1	yes	characteristic
460	C₂²	#386×C₁₄₉	1	1	yes	characteristic
461	C₂²	#386×C₁₄₉	1	1	yes	characteristic
462	C₂²	#453×C₁₄₉	1	2	yes	—
463	C₂²	#455×C₁₄₉	1	2	yes	—
464	C₄	—	4	4	no	—
465	C₄	—	4	8	no	—
466	C₄	—	8	2	no	—
467	C₄	C₄×C₂²⋊C₄×C₁₄₉	1	2	yes	—
468	C₄	#380×C₁₄₉	1	2	yes	—
469	C₄	#385×C₁₄₉	1	2	yes	—
470	C₄	#386×C₁₄₉	1	2	yes	—
471	C₂	—	2	1	no	—
472	C₂	—	2	1	no	—
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	4	8	no	—
476	C₂	C₂²⋊#95×C₁₄₉	1	1	yes	characteristic
477	C₂	#1792×C₁₄₉	1	2	yes	—
478	C₂	#1856×C₁₄₉	1	2	yes	—
479	C₂	#1885×C₁₄₉	1	1	yes	characteristic
480	C₂	#1887×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₄₉	#120
commutator	C₂×C₄	C₂×C₄²×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
prime radical	C₂³×D₄×C₁₄₉	C₂²
LCS	G ▷ C₂×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
4. #1736×C₁₄₉	C₂	semidirect
5. C₂×#339×C₁₄₉	C₂	semidirect
10. #518×C₁₄₉	C₄	semidirect
19. C₂×#100×C₁₄₉	C₄	semidirect
21. #390×C₁₄₉	C₄	semidirect
44. C₂×M₁₆×C₁₄₉	C₂×C₄	semidirect
55. C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	semidirect
67. C₂×C₄²×C₁₄₉	C₂×C₄	semidirect
128. C₄⋊C₄×C₁₄₉	C₂²⋊C₄	semidirect
240. #10749	C₁₄₉	direct (N × H)
241. C₁₄₉	#10749	direct (N × H)
245. #1736	C₂×C₁₄₉	semidirect
246. C₂×#339	C₂×C₁₄₉	semidirect
251. #518	C₄×C₁₄₉	semidirect
260. C₂×#100	C₄×C₁₄₉	semidirect
262. #390	C₄×C₁₄₉	semidirect
285. C₂×M₁₆	C₂×C₄×C₁₄₉	semidirect
296. C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	semidirect
308. C₂×C₄²	C₂×C₄×C₁₄₉	semidirect
369. C₄⋊C₄	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
C₂×#518×C₁₄₉	2
C₂²×#100×C₁₄₉	2
C₂×#390×C₁₄₉	2
#1736×C₁₄₉	2
C₂×#339×C₁₄₉	2
#10749	149

Subgroups — C149×#10749 #49189698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#10749 #49189698