Subgroups — C₂×#1480×C₁₄₉ #49196404

Order 38144.

1346 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#431×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄⋊C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1480×C₁₄₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×D₄⋊C₈×C₁₄₉	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₁₄₉	—	2	1	no	—
7	C₂³×C₈×C₁₄₉	—	2	1	no	—
8	#532×C₁₄₉	—	2	2	no	—
9	#532×C₁₄₉	—	2	2	no	—
10	#532×C₁₄₉	C₄	1	4	yes	—
11	#532×C₁₄₉	C₂²	1	4	yes	—
12	C₂×C₄⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
13	C₂×#127×C₁₄₉	C₄	1	1	yes	characteristic
14	C₂×#124×C₁₄₉	—	2	1	no	—
15	C₂×#121×C₁₄₉	—	2	1	no	—
16	C₂×#121×C₁₄₉	C₄	1	2	yes	—
17	C₂×C₄×D₄×C₁₄₉	—	2	1	no	—
18	C₂×C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
20	#431×C₁₄₉	—	2	2	no	—
21	#431×C₁₄₉	C₂²	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₁₄₉	—	2	2	no	—
23	C₂×C₄⋊C₈×C₁₄₉	—	2	1	no	—
24	C₂×C₄⋊C₈×C₁₄₉	—	2	1	no	—
25	C₂×C₄⋊C₈×C₁₄₉	C₂²	1	2	yes	—
26	C₂×C₄⋊C₈×C₁₄₉	C₂²	1	4	yes	complemented
27	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
28	C₂×C₄×C₈×C₁₄₉	C₂²	1	2	yes	—
29	D₄⋊C₈×C₁₄₉	C₂²	1	16	yes	complemented
30	C₂×#41×C₁₄₉	—	2	4	no	—
31	C₂×#41×C₁₄₉	—	2	4	no	—
32	C₂×#41×C₁₄₉	—	4	4	no	—
33	C₂×#41×C₁₄₉	—	4	4	no	—
34	C₂²×Q₈×C₁₄₉	—	2	1	no	—
35	C₂²×D₄×C₁₄₉	—	2	2	no	—
36	C₂²×D₄×C₁₄₉	—	2	1	no	—
37	C₂²×D₄×C₁₄₉	—	2	1	no	—
38	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₁₄₉	—	2	2	no	—
40	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₄₉	—	2	2	no	—
44	C₂²×C₈×C₁₄₉	—	2	4	no	—
45	C₂²×C₈×C₁₄₉	—	2	2	no	—
46	C₂²×C₈×C₁₄₉	—	4	4	no	—
47	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
48	C₄⋊Q₈×C₁₄₉	C₂×C₄	1	4	yes	—
49	#127×C₁₄₉	—	2	2	no	—
50	#127×C₁₄₉	C₂×C₄	1	4	yes	—
51	#124×C₁₄₉	—	2	4	no	—
52	#124×C₁₄₉	—	2	4	no	—
53	#121×C₁₄₉	—	2	4	no	—
54	#121×C₁₄₉	—	2	4	no	—
55	#121×C₁₄₉	—	2	4	no	—
56	#121×C₁₄₉	C₂×C₄	1	8	yes	—
57	C₄×D₄×C₁₄₉	—	2	4	no	—
58	C₄×D₄×C₁₄₉	—	2	4	no	—
59	C₄×D₄×C₁₄₉	—	2	2	no	—
60	C₄×D₄×C₁₄₉	—	2	2	no	—
61	C₄×D₄×C₁₄₉	C₂×C₄	1	4	yes	—
62	C₄×D₄×C₁₄₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
67	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
71	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
72	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₄₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₁₄₉	—	2	2	no	—
76	C₄⋊C₈×C₁₄₉	—	2	4	no	—
77	C₄⋊C₈×C₁₄₉	—	2	4	no	—
78	C₄⋊C₈×C₁₄₉	C₂³	1	4	yes	—
79	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
80	C₄×C₈×C₁₄₉	—	2	2	no	—
81	C₄×C₈×C₁₄₉	C₂³	1	4	yes	—
82	C₂⁴×C₁₄₉	—	2	2	no	—
83	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
84	#41×C₁₄₉	—	4	16	no	—
85	#41×C₁₄₉	—	4	8	no	—
86	#41×C₁₄₉	—	4	8	no	—
87	C₂×Q₈×C₁₄₉	—	2	4	no	—
88	C₂×Q₈×C₁₄₉	—	4	4	no	—
89	C₂×D₄×C₁₄₉	—	2	8	no	—
90	C₂×D₄×C₁₄₉	—	2	2	no	—
91	C₂×D₄×C₁₄₉	—	2	4	no	—
92	C₂×D₄×C₁₄₉	—	2	4	no	—
93	C₂×D₄×C₁₄₉	—	2	8	no	—
94	C₂×D₄×C₁₄₉	—	4	4	no	—
95	C₂×D₄×C₁₄₉	—	4	8	no	—
96	C₂×D₄×C₁₄₉	—	4	4	no	—
97	C₂×D₄×C₁₄₉	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₄₉	—	2	4	no	—
99	C₂²×C₄×C₁₄₉	—	2	2	no	—
100	C₂²×C₄×C₁₄₉	—	2	4	no	—
101	C₂²×C₄×C₁₄₉	—	2	4	no	—
102	C₂²×C₄×C₁₄₉	—	4	2	no	—
103	C₂²×C₄×C₁₄₉	—	4	4	no	—
104	C₂²×C₄×C₁₄₉	—	4	4	no	—
105	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
108	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
109	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₁₄₉	D₈	1	4	yes	—
112	C₂²×C₄×C₁₄₉	SD₁₆	1	4	yes	—
113	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₄₉	—	2	4	no	—
120	C₂×C₈×C₁₄₉	—	2	4	no	—
121	C₂×C₈×C₁₄₉	—	4	4	no	—
122	C₂×C₈×C₁₄₉	—	4	4	no	—
123	C₂×C₈×C₁₄₉	—	4	8	no	—
124	C₄⋊C₄×C₁₄₉	—	2	4	no	—
125	C₄⋊C₄×C₁₄₉	—	2	2	no	—
126	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	4	yes	—
127	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
128	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
129	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
130	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
131	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₄₉	C₂²×C₄	1	2	yes	—
135	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
138	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
139	C₄²×C₁₄₉	C₂⁴	1	1	yes	characteristic
140	C₂³×C₁₄₉	—	2	2	no	—
141	C₂³×C₁₄₉	—	2	2	no	—
142	C₂³×C₁₄₉	—	2	4	no	—
143	C₂³×C₁₄₉	—	4	4	no	—
144	C₂³×C₁₄₉	—	4	4	no	—
145	C₂³×C₁₄₉	—	4	4	no	—
146	C₂³×C₁₄₉	#102	1	4	yes	—
147	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	Q₈×C₁₄₉	—	4	8	no	—
150	D₄×C₁₄₉	—	2	8	no	—
151	D₄×C₁₄₉	—	4	8	no	—
152	D₄×C₁₄₉	—	4	16	no	—
153	D₄×C₁₄₉	—	4	4	no	—
154	D₄×C₁₄₉	—	4	8	no	—
155	C₂×C₄×C₁₄₉	—	2	2	no	—
156	C₂×C₄×C₁₄₉	—	2	2	no	—
157	C₂×C₄×C₁₄₉	—	2	2	no	—
158	C₂×C₄×C₁₄₉	—	2	4	no	—
159	C₂×C₄×C₁₄₉	—	2	4	no	—
160	C₂×C₄×C₁₄₉	—	2	4	no	—
161	C₂×C₄×C₁₄₉	—	4	2	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	8	no	—
167	C₂×C₄×C₁₄₉	#102	1	4	yes	—
168	C₂×C₄×C₁₄₉	#102	1	8	yes	—
169	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₄₉	#131	1	4	yes	—
176	C₂×C₄×C₁₄₉	C₂×D₈	1	2	yes	—
177	C₂×C₄×C₁₄₉	C₂×D₈	1	4	yes	—
178	C₂×C₄×C₁₄₉	C₂×SD₁₆	1	2	yes	—
179	C₂×C₄×C₁₄₉	C₂×SD₁₆	1	4	yes	—
180	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₁₄₉	—	4	4	no	—
184	C₈×C₁₄₉	—	4	4	no	—
185	C₂²×C₁₄₉	—	2	2	no	—
186	C₂²×C₁₄₉	—	2	2	no	—
187	C₂²×C₁₄₉	—	2	8	no	—
188	C₂²×C₁₄₉	—	4	4	no	—
189	C₂²×C₁₄₉	—	4	4	no	—
190	C₂²×C₁₄₉	—	4	4	no	—
191	C₂²×C₁₄₉	—	8	8	no	—
192	C₂²×C₁₄₉	#408	1	2	yes	—
193	C₂²×C₁₄₉	C₂×#102	1	4	yes	—
194	C₂²×C₁₄₉	C₂×#102	1	2	yes	—
195	C₂²×C₁₄₉	#421	1	2	yes	—
196	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
197	C₄×C₁₄₉	—	2	2	no	—
198	C₄×C₁₄₉	—	2	1	no	—
199	C₄×C₁₄₉	—	2	1	no	—
200	C₄×C₁₄₉	—	2	2	no	—
201	C₄×C₁₄₉	—	4	4	no	—
202	C₄×C₁₄₉	#408	1	2	yes	—
203	C₄×C₁₄₉	C₂×#102	1	2	yes	—
204	C₄×C₁₄₉	C₂×#102	1	4	yes	—
205	C₄×C₁₄₉	C₂×#131	1	2	yes	—
206	C₄×C₁₄₉	C₂²×D₈	1	1	yes	characteristic
207	C₄×C₁₄₉	C₂²×SD₁₆	1	1	yes	characteristic
208	C₂×C₁₄₉	—	2	4	no	—
209	C₂×C₁₄₉	—	8	4	no	—
210	C₂×C₁₄₉	#1480	1	4	yes	direct product factor
211	C₂×C₁₄₉	C₂×#408	1	1	yes	characteristic
212	C₂×C₁₄₉	C₂²×#102	1	1	yes	characteristic
213	C₂×C₁₄₉	C₂×#421	1	1	yes	characteristic
214	C₂×#1480	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₁₄₉	C₂×#1480	1	1	yes	characteristic, direct product factor, Sylow
216	C₂×#532	C₂×C₁₄₉	1	1	yes	characteristic
217	C₂×#431	C₂×C₁₄₉	1	1	yes	characteristic, complemented
218	C₂²×C₄⋊C₈	C₂×C₁₄₉	1	1	yes	characteristic, complemented
219	#1480	C₂×C₁₄₉	1	8	yes	direct product factor
220	C₂×D₄⋊C₈	C₂×C₁₄₉	1	4	yes	complemented
221	C₂²×#41	—	2	1	no	—
222	C₂³×C₈	—	2	1	no	—
223	#532	—	2	2	no	—
224	#532	—	2	2	no	—
225	#532	C₄×C₁₄₉	1	4	yes	—
226	#532	C₂²×C₁₄₉	1	4	yes	—
227	C₂×C₄⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
228	C₂×#127	C₄×C₁₄₉	1	1	yes	characteristic
229	C₂×#124	—	2	1	no	—
230	C₂×#121	—	2	1	no	—
231	C₂×#121	C₄×C₁₄₉	1	2	yes	—
232	C₂×C₄×D₄	—	2	1	no	—
233	C₂×C₄×D₄	C₂²×C₁₄₉	1	2	yes	—
234	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
235	#431	—	2	2	no	—
236	#431	C₂²×C₁₄₉	1	4	yes	complemented
237	C₂×C₄⋊C₈	—	2	2	no	—
238	C₂×C₄⋊C₈	—	2	1	no	—
239	C₂×C₄⋊C₈	—	2	1	no	—
240	C₂×C₄⋊C₈	C₂²×C₁₄₉	1	2	yes	—
241	C₂×C₄⋊C₈	C₂²×C₁₄₉	1	4	yes	complemented
242	C₂×C₂²⋊C₈	—	2	1	no	—
243	C₂×C₄×C₈	C₂²×C₁₄₉	1	2	yes	—
244	D₄⋊C₈	C₂²×C₁₄₉	1	16	yes	complemented
245	C₂×#41	—	2	4	no	—
246	C₂×#41	—	2	4	no	—
247	C₂×#41	—	4	4	no	—
248	C₂×#41	—	4	4	no	—
249	C₂²×Q₈	—	2	1	no	—
250	C₂²×D₄	—	2	2	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	1	no	—
253	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
256	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
257	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	—	2	4	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	4	4	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	C₂×C₄×C₁₄₉	1	4	yes	—
264	#127	—	2	2	no	—
265	#127	C₂×C₄×C₁₄₉	1	4	yes	—
266	#124	—	2	4	no	—
267	#124	—	2	4	no	—
268	#121	—	2	4	no	—
269	#121	—	2	4	no	—
270	#121	—	2	4	no	—
271	#121	C₂×C₄×C₁₄₉	1	8	yes	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	C₂×C₄×C₁₄₉	1	4	yes	—
277	C₄×D₄	C₂³×C₁₄₉	1	4	yes	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
283	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
284	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
286	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
287	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
288	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₁₄₉	1	2	yes	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	2	4	no	—
292	C₄⋊C₈	—	2	4	no	—
293	C₄⋊C₈	C₂³×C₁₄₉	1	4	yes	—
294	C₂²⋊C₈	—	2	4	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	C₂³×C₁₄₉	1	4	yes	—
297	C₂⁴	—	2	2	no	—
298	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
299	#41	—	4	16	no	—
300	#41	—	4	8	no	—
301	#41	—	4	8	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	4	4	no	—
304	C₂×D₄	—	2	8	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	8	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	8	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	C₂²×C₄×C₁₄₉	1	4	yes	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
321	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
322	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
323	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
324	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
325	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
326	C₂²×C₄	D₈×C₁₄₉	1	4	yes	—
327	C₂²×C₄	SD₁₆×C₁₄₉	1	4	yes	—
328	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
329	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
334	C₂×C₈	—	2	4	no	—
335	C₂×C₈	—	2	4	no	—
336	C₂×C₈	—	4	4	no	—
337	C₂×C₈	—	4	4	no	—
338	C₂×C₈	—	4	8	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	4	yes	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
346	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
347	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
348	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
349	C₄²	C₂²×C₄×C₁₄₉	1	2	yes	—
350	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
351	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
352	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
353	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
354	C₄²	C₂⁴×C₁₄₉	1	1	yes	characteristic
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	4	4	no	—
359	C₂³	—	4	4	no	—
360	C₂³	—	4	4	no	—
361	C₂³	#102×C₁₄₉	1	4	yes	—
362	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
363	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
364	Q₈	—	4	8	no	—
365	D₄	—	2	8	no	—
366	D₄	—	4	8	no	—
367	D₄	—	4	16	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	8	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	8	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	#102×C₁₄₉	1	4	yes	—
383	C₂×C₄	#102×C₁₄₉	1	8	yes	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
385	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
386	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
388	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
389	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
390	C₂×C₄	#131×C₁₄₉	1	4	yes	—
391	C₂×C₄	C₂×D₈×C₁₄₉	1	2	yes	—
392	C₂×C₄	C₂×D₈×C₁₄₉	1	4	yes	—
393	C₂×C₄	C₂×SD₁₆×C₁₄₉	1	2	yes	—
394	C₂×C₄	C₂×SD₁₆×C₁₄₉	1	4	yes	—
395	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
398	C₈	—	4	4	no	—
399	C₈	—	4	4	no	—
400	C₂²	—	2	8	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	8	8	no	—
407	C₂²	#408×C₁₄₉	1	2	yes	—
408	C₂²	C₂×#102×C₁₄₉	1	4	yes	—
409	C₂²	C₂×#102×C₁₄₉	1	2	yes	—
410	C₂²	#421×C₁₄₉	1	2	yes	—
411	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	4	no	—
417	C₄	#408×C₁₄₉	1	2	yes	—
418	C₄	C₂×#102×C₁₄₉	1	2	yes	—
419	C₄	C₂×#102×C₁₄₉	1	4	yes	—
420	C₄	C₂×#131×C₁₄₉	1	2	yes	—
421	C₄	C₂²×D₈×C₁₄₉	1	1	yes	characteristic
422	C₄	C₂²×SD₁₆×C₁₄₉	1	1	yes	characteristic
423	C₂	—	2	4	no	—
424	C₂	—	8	4	no	—
425	C₂	#1480×C₁₄₉	1	4	yes	direct product factor
426	C₂	C₂×#408×C₁₄₉	1	1	yes	characteristic
427	C₂	C₂²×#102×C₁₄₉	1	1	yes	characteristic
428	C₂	C₂×#421×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₄₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
socle	C₂³×C₁₄₉	C₂×C₂²⋊C₄
prime radical	C₂×#532×C₁₄₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₄₉ ◁ C₂²×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#431×C₁₄₉	C₂	semidirect
3. C₂²×C₄⋊C₈×C₁₄₉	C₂	semidirect
4. #1480×C₁₄₉	C₂	direct (N × H)
5. C₂×D₄⋊C₈×C₁₄₉	C₂	semidirect
21. #431×C₁₄₉	C₂²	semidirect
26. C₂×C₄⋊C₈×C₁₄₉	C₂²	semidirect
29. D₄⋊C₈×C₁₄₉	C₂²	semidirect
210. C₂×C₁₄₉	#1480	direct (N × H)
214. C₂×#1480	C₁₄₉	direct (N × H)
215. C₁₄₉	C₂×#1480	direct (N × H)
217. C₂×#431	C₂×C₁₄₉	semidirect
218. C₂²×C₄⋊C₈	C₂×C₁₄₉	semidirect
219. #1480	C₂×C₁₄₉	direct (N × H)
220. C₂×D₄⋊C₈	C₂×C₁₄₉	semidirect
236. #431	C₂²×C₁₄₉	semidirect
241. C₂×C₄⋊C₈	C₂²×C₁₄₉	semidirect
244. D₄⋊C₈	C₂²×C₁₄₉	semidirect
425. C₂	#1480×C₁₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₄₉	2
C₂×#431×C₁₄₉	2
C₂²×C₄⋊C₈×C₁₄₉	2
#1480×C₁₄₉	2
C₂×D₄⋊C₈×C₁₄₉	2
C₂×#1480	149

Subgroups — C2×#1480×C149 #49196404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1480×C₁₄₉ #49196404