Subgroups — C₂×#1505×C₁₄₉ #49196488

Order 38144.

1410 conjugacy classes of subgroups.

The subgroup lattice has 436 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×#432×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#376×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1505×C₁₄₉	C₂	1	8	yes	maximal, direct product factor
5	C₂×#327×C₁₄₉	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₁₄₉	—	2	1	no	—
7	#532×C₁₄₉	—	2	2	no	—
8	#532×C₁₄₉	—	2	2	no	—
9	#532×C₁₄₉	C₄	1	4	yes	complemented
10	#532×C₁₄₉	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic, complemented
12	C₂×#127×C₁₄₉	C₄	1	1	yes	characteristic, complemented
13	C₂×#124×C₁₄₉	—	2	1	no	—
14	C₂×#121×C₁₄₉	—	2	1	no	—
15	C₂×#121×C₁₄₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₄₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₄₉	C₄	1	2	yes	complemented
18	C₂²×C₄²×C₁₄₉	—	2	1	no	—
19	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
20	#432×C₁₄₉	—	2	2	no	—
21	#432×C₁₄₉	C₂²	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₁₄₉	—	2	1	no	—
23	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	2	yes	—
24	C₂×#97×C₁₄₉	—	2	1	no	—
25	#376×C₁₄₉	—	2	2	no	—
26	#376×C₁₄₉	C₂²	1	4	yes	complemented
27	C₂×#95×C₁₄₉	—	2	1	no	—
28	C₂×#95×C₁₄₉	C₂²	1	2	yes	—
29	#327×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	8	no	—
33	C₂²×Q₈×C₁₄₉	—	2	1	no	—
34	C₂²×D₄×C₁₄₉	—	2	2	no	—
35	C₂²×D₄×C₁₄₉	—	2	1	no	—
36	C₂²×D₄×C₁₄₉	—	2	1	no	—
37	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₁₄₉	—	2	2	no	—
39	C₂³×C₄×C₁₄₉	—	2	2	no	—
40	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₁₄₉	—	2	2	no	—
44	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
45	C₄⋊Q₈×C₁₄₉	C₂×C₄	1	4	yes	complemented
46	#127×C₁₄₉	—	2	2	no	—
47	#127×C₁₄₉	C₂×C₄	1	4	yes	complemented
48	#124×C₁₄₉	—	2	4	no	—
49	#124×C₁₄₉	—	2	4	no	—
50	#121×C₁₄₉	—	2	4	no	—
51	#121×C₁₄₉	—	2	4	no	—
52	#121×C₁₄₉	—	2	2	no	—
53	#121×C₁₄₉	—	2	2	no	—
54	#121×C₁₄₉	C₂×C₄	1	4	yes	—
55	#121×C₁₄₉	C₂³	1	4	yes	—
56	C₄×D₄×C₁₄₉	—	2	4	no	—
57	C₄×D₄×C₁₄₉	—	2	4	no	—
58	C₄×D₄×C₁₄₉	—	2	4	no	—
59	C₄×D₄×C₁₄₉	C₂×C₄	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
64	C₂×C₄²×C₁₄₉	—	2	8	no	—
65	C₂×C₄²×C₁₄₉	—	2	4	no	—
66	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
70	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₄₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₄₉	D₄	1	2	yes	—
73	C₂×C₄²×C₁₄₉	C₂³	1	2	yes	—
74	C₄⋊C₈×C₁₄₉	—	2	4	no	—
75	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
76	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
77	#97×C₁₄₉	—	2	4	no	—
78	#95×C₁₄₉	—	2	4	no	—
79	#95×C₁₄₉	—	2	2	no	—
80	#95×C₁₄₉	C₂³	1	4	yes	—
81	C₂⁴×C₁₄₉	—	2	2	no	—
82	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
83	#41×C₁₄₉	—	4	16	no	—
84	#41×C₁₄₉	—	4	16	no	—
85	C₂×Q₈×C₁₄₉	—	2	4	no	—
86	C₂×Q₈×C₁₄₉	—	4	4	no	—
87	C₂×D₄×C₁₄₉	—	2	4	no	—
88	C₂×D₄×C₁₄₉	—	2	4	no	—
89	C₂×D₄×C₁₄₉	—	2	2	no	—
90	C₂×D₄×C₁₄₉	—	2	4	no	—
91	C₂×D₄×C₁₄₉	—	2	4	no	—
92	C₂×D₄×C₁₄₉	—	4	4	no	—
93	C₂×D₄×C₁₄₉	—	4	4	no	—
94	C₂×D₄×C₁₄₉	—	4	8	no	—
95	C₂×D₄×C₁₄₉	—	4	4	no	—
96	C₂×D₄×C₁₄₉	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₄₉	—	2	4	no	—
98	C₂²×C₄×C₁₄₉	—	2	4	no	—
99	C₂²×C₄×C₁₄₉	—	2	8	no	—
100	C₂²×C₄×C₁₄₉	—	2	2	no	—
101	C₂²×C₄×C₁₄₉	—	2	4	no	—
102	C₂²×C₄×C₁₄₉	—	2	8	no	—
103	C₂²×C₄×C₁₄₉	—	4	2	no	—
104	C₂²×C₄×C₁₄₉	—	4	8	no	—
105	C₂²×C₄×C₁₄₉	—	4	4	no	—
106	C₂²×C₄×C₁₄₉	—	4	4	no	—
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	1	yes	characteristic
111	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₁₄₉	—	2	4	no	—
122	C₂×C₈×C₁₄₉	—	4	4	no	—
123	C₄⋊C₄×C₁₄₉	—	2	4	no	—
124	C₄⋊C₄×C₁₄₉	—	2	2	no	—
125	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	4	yes	—
126	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
127	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
128	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
129	C₄²×C₁₄₉	—	2	16	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	2	yes	—
134	C₄²×C₁₄₉	C₂²×C₄	1	2	yes	—
135	C₄²×C₁₄₉	C₂²×C₄	1	2	yes	—
136	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
137	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
138	C₂³×C₁₄₉	—	2	2	no	—
139	C₂³×C₁₄₉	—	2	2	no	—
140	C₂³×C₁₄₉	—	2	4	no	—
141	C₂³×C₁₄₉	—	4	4	no	—
142	C₂³×C₁₄₉	—	4	4	no	—
143	C₂³×C₁₄₉	—	4	4	no	—
144	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₁₄₉	AGL(1,ℤ/8)	1	4	yes	—
147	C₂³×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₁₄₉	—	4	8	no	—
149	D₄×C₁₄₉	—	4	4	no	—
150	D₄×C₁₄₉	—	4	4	no	—
151	D₄×C₁₄₉	—	4	8	no	—
152	D₄×C₁₄₉	—	4	8	no	—
153	D₄×C₁₄₉	—	4	8	no	—
154	D₄×C₁₄₉	—	4	8	no	—
155	C₂×C₄×C₁₄₉	—	2	4	no	—
156	C₂×C₄×C₁₄₉	—	2	2	no	—
157	C₂×C₄×C₁₄₉	—	2	2	no	—
158	C₂×C₄×C₁₄₉	—	2	2	no	—
159	C₂×C₄×C₁₄₉	—	2	2	no	—
160	C₂×C₄×C₁₄₉	—	2	4	no	—
161	C₂×C₄×C₁₄₉	—	2	2	no	—
162	C₂×C₄×C₁₄₉	—	2	4	no	—
163	C₂×C₄×C₁₄₉	—	2	4	no	—
164	C₂×C₄×C₁₄₉	—	2	8	no	—
165	C₂×C₄×C₁₄₉	—	2	4	no	—
166	C₂×C₄×C₁₄₉	—	4	1	no	—
167	C₂×C₄×C₁₄₉	—	4	1	no	—
168	C₂×C₄×C₁₄₉	—	4	1	no	—
169	C₂×C₄×C₁₄₉	—	4	1	no	—
170	C₂×C₄×C₁₄₉	—	4	16	no	—
171	C₂×C₄×C₁₄₉	—	4	4	no	—
172	C₂×C₄×C₁₄₉	—	4	16	no	—
173	C₂×C₄×C₁₄₉	—	4	4	no	—
174	C₂×C₄×C₁₄₉	—	4	4	no	—
175	C₂×C₄×C₁₄₉	#104	1	4	yes	—
176	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
184	C₈×C₁₄₉	—	4	4	no	—
185	C₂²×C₁₄₉	—	2	1	no	—
186	C₂²×C₁₄₉	—	2	1	no	—
187	C₂²×C₁₄₉	—	2	1	no	—
188	C₂²×C₁₄₉	—	2	1	no	—
189	C₂²×C₁₄₉	—	2	8	no	—
190	C₂²×C₁₄₉	—	4	4	no	—
191	C₂²×C₁₄₉	—	4	4	no	—
192	C₂²×C₁₄₉	—	4	4	no	—
193	C₂²×C₁₄₉	—	8	8	no	—
194	C₂²×C₁₄₉	#410	1	2	yes	—
195	C₂²×C₁₄₉	#418	1	2	yes	—
196	C₂²×C₁₄₉	#418	1	2	yes	—
197	C₂²×C₁₄₉	C₂×#104	1	2	yes	—
198	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₁₄₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
200	C₄×C₁₄₉	—	2	1	no	—
201	C₄×C₁₄₉	—	2	1	no	—
202	C₄×C₁₄₉	—	2	1	no	—
203	C₄×C₁₄₉	—	2	1	no	—
204	C₄×C₁₄₉	—	2	2	no	—
205	C₄×C₁₄₉	—	2	2	no	—
206	C₄×C₁₄₉	—	2	2	no	—
207	C₄×C₁₄₉	—	4	8	no	—
208	C₄×C₁₄₉	—	4	4	no	—
209	C₄×C₁₄₉	C₂×#104	1	4	yes	—
210	C₂×C₁₄₉	—	2	2	no	—
211	C₂×C₁₄₉	—	2	2	no	—
212	C₂×C₁₄₉	—	8	4	no	—
213	C₂×C₁₄₉	#1505	1	4	yes	direct product factor
214	C₂×C₁₄₉	C₂×#410	1	1	yes	characteristic
215	C₂×C₁₄₉	C₂×#418	1	1	yes	characteristic
216	C₂×C₁₄₉	C₂²×#104	1	1	yes	characteristic
217	C₂×#1505	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₁₄₉	C₂×#1505	1	1	yes	characteristic, direct product factor, Sylow
219	C₂×#532	C₂×C₁₄₉	1	1	yes	characteristic
220	C₂×#432	C₂×C₁₄₉	1	1	yes	characteristic, complemented
221	C₂×#376	C₂×C₁₄₉	1	1	yes	characteristic, complemented
222	#1505	C₂×C₁₄₉	1	8	yes	direct product factor
223	C₂×#327	C₂×C₁₄₉	1	4	yes	complemented
224	C₂²×#41	—	2	1	no	—
225	#532	—	2	2	no	—
226	#532	—	2	2	no	—
227	#532	C₄×C₁₄₉	1	4	yes	complemented
228	#532	C₂²×C₁₄₉	1	4	yes	—
229	C₂×C₄⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic, complemented
230	C₂×#127	C₄×C₁₄₉	1	1	yes	characteristic, complemented
231	C₂×#124	—	2	1	no	—
232	C₂×#121	—	2	1	no	—
233	C₂×#121	C₂²×C₁₄₉	1	2	yes	—
234	C₂×C₄×D₄	—	2	1	no	—
235	C₂×C₄×D₄	C₄×C₁₄₉	1	2	yes	complemented
236	C₂²×C₄²	—	2	1	no	—
237	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
238	#432	—	2	2	no	—
239	#432	C₂²×C₁₄₉	1	4	yes	complemented
240	C₂×C₄⋊C₈	—	2	1	no	—
241	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	2	yes	—
242	C₂×#97	—	2	1	no	—
243	#376	—	2	2	no	—
244	#376	C₂²×C₁₄₉	1	4	yes	complemented
245	C₂×#95	—	2	1	no	—
246	C₂×#95	C₂²×C₁₄₉	1	2	yes	—
247	#327	C₂²×C₁₄₉	1	16	yes	complemented
248	C₂×#41	—	2	4	no	—
249	C₂×#41	—	2	4	no	—
250	C₂×#41	—	4	8	no	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	—	2	2	no	—
258	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
259	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
261	C₂²×C₈	—	2	2	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	C₂×C₄×C₁₄₉	1	4	yes	complemented
264	#127	—	2	2	no	—
265	#127	C₂×C₄×C₁₄₉	1	4	yes	complemented
266	#124	—	2	4	no	—
267	#124	—	2	4	no	—
268	#121	—	2	4	no	—
269	#121	—	2	4	no	—
270	#121	—	2	2	no	—
271	#121	—	2	2	no	—
272	#121	C₂×C₄×C₁₄₉	1	4	yes	—
273	#121	C₂³×C₁₄₉	1	4	yes	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	4	no	—
276	C₄×D₄	—	2	4	no	—
277	C₄×D₄	C₂×C₄×C₁₄₉	1	8	yes	complemented
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	—	2	8	no	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
285	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
286	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
287	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
288	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
289	C₂×C₄²	D₄×C₁₄₉	1	1	yes	characteristic
290	C₂×C₄²	D₄×C₁₄₉	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₄₉	1	2	yes	—
292	C₄⋊C₈	—	2	4	no	—
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
295	#97	—	2	4	no	—
296	#95	—	2	4	no	—
297	#95	—	2	2	no	—
298	#95	C₂³×C₁₄₉	1	4	yes	—
299	C₂⁴	—	2	2	no	—
300	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
301	#41	—	4	16	no	—
302	#41	—	4	16	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	4	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	—	4	8	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	C₂²×C₄×C₁₄₉	1	4	yes	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	8	no	—
323	C₂²×C₄	—	4	4	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
326	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
327	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
328	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
329	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
330	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	4	4	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	4	yes	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	2	4	no	—
347	C₄²	—	2	16	no	—
348	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
349	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
350	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
351	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
352	C₄²	C₂²×C₄×C₁₄₉	1	2	yes	—
353	C₄²	C₂²×C₄×C₁₄₉	1	2	yes	—
354	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
355	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	4	4	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	4	no	—
362	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
363	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
364	C₂³	AGL(1,ℤ/8)×C₁₄₉	1	4	yes	—
365	C₂³	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
366	Q₈	—	4	8	no	—
367	D₄	—	4	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	8	no	—
370	D₄	—	4	8	no	—
371	D₄	—	4	8	no	—
372	D₄	—	4	8	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	16	no	—
389	C₂×C₄	—	4	16	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	#104×C₁₄₉	1	4	yes	—
394	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
395	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
396	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
397	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
398	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
399	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	2	yes	—
400	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
402	C₈	—	4	4	no	—
403	C₂²	—	2	8	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	8	8	no	—
412	C₂²	#410×C₁₄₉	1	2	yes	—
413	C₂²	#418×C₁₄₉	1	2	yes	—
414	C₂²	#418×C₁₄₉	1	2	yes	—
415	C₂²	C₂×#104×C₁₄₉	1	2	yes	—
416	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
417	C₂²	C₂×AGL(1,ℤ/8)×C₁₄₉	1	2	yes	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	8	no	—
426	C₄	—	4	4	no	—
427	C₄	C₂×#104×C₁₄₉	1	4	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	2	2	no	—
430	C₂	—	8	4	no	—
431	C₂	#1505×C₁₄₉	1	4	yes	direct product factor
432	C₂	C₂×#410×C₁₄₉	1	1	yes	characteristic
433	C₂	C₂×#418×C₁₄₉	1	1	yes	characteristic
434	C₂	C₂²×#104×C₁₄₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×#432×C₁₄₉	C₂	semidirect
3. C₂×#376×C₁₄₉	C₂	semidirect
4. #1505×C₁₄₉	C₂	direct (N × H)
5. C₂×#327×C₁₄₉	C₂	semidirect
9. #532×C₁₄₉	C₄	semidirect
11. C₂×C₄⋊Q₈×C₁₄₉	C₄	semidirect
12. C₂×#127×C₁₄₉	C₄	semidirect
17. C₂×C₄×D₄×C₁₄₉	C₄	semidirect
21. #432×C₁₄₉	C₂²	semidirect
26. #376×C₁₄₉	C₂²	semidirect
29. #327×C₁₄₉	C₂²	semidirect
45. C₄⋊Q₈×C₁₄₉	C₂×C₄	semidirect
47. #127×C₁₄₉	C₂×C₄	semidirect
59. C₄×D₄×C₁₄₉	C₂×C₄	semidirect
213. C₂×C₁₄₉	#1505	direct (N × H)
217. C₂×#1505	C₁₄₉	direct (N × H)
218. C₁₄₉	C₂×#1505	direct (N × H)
220. C₂×#432	C₂×C₁₄₉	semidirect
221. C₂×#376	C₂×C₁₄₉	semidirect
222. #1505	C₂×C₁₄₉	direct (N × H)
223. C₂×#327	C₂×C₁₄₉	semidirect
227. #532	C₄×C₁₄₉	semidirect
229. C₂×C₄⋊Q₈	C₄×C₁₄₉	semidirect
230. C₂×#127	C₄×C₁₄₉	semidirect
235. C₂×C₄×D₄	C₄×C₁₄₉	semidirect
239. #432	C₂²×C₁₄₉	semidirect
244. #376	C₂²×C₁₄₉	semidirect
247. #327	C₂²×C₁₄₉	semidirect
263. C₄⋊Q₈	C₂×C₄×C₁₄₉	semidirect
265. #127	C₂×C₄×C₁₄₉	semidirect
277. C₄×D₄	C₂×C₄×C₁₄₉	semidirect
431. C₂	#1505×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×#432×C₁₄₉	2
C₂×#376×C₁₄₉	2
#1505×C₁₄₉	2
C₂×#327×C₁₄₉	2
C₂×#1505	149

Subgroups — C2×#1505×C149 #49196488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1505×C₁₄₉ #49196488