Subgroups — C₁₄₉×#10758 #49189707

Order 38144.

1298 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#413×C₁₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#410×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#339×C₁₄₉	C₂	1	2	yes	maximal, complemented
5	C₂×H(3,ℤ/4)×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₁₄₉	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₁₄₉	C₂²	1	2	yes	—
8	C₄×#41×C₁₄₉	—	2	4	no	—
9	C₄×#41×C₁₄₉	—	2	4	no	—
10	C₂×C₄×Q₈×C₁₄₉	—	2	1	no	—
11	C₂×C₄×D₄×C₁₄₉	—	2	2	no	—
12	C₂×C₄×D₄×C₁₄₉	—	2	1	no	—
13	C₂×#117×C₁₄₉	C₄	1	2	yes	complemented
14	C₂×#117×C₁₄₉	C₂²	1	2	yes	—
15	C₂×#117×C₁₄₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₄₉	C₄	1	2	yes	complemented
17	C₂²×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
18	#413×C₁₄₉	—	2	2	no	—
19	#413×C₁₄₉	C₄	1	4	yes	complemented
20	C₂×#101×C₁₄₉	—	2	1	no	—
21	C₂×#100×C₁₄₉	—	2	1	no	—
22	#410×C₁₄₉	—	2	2	no	—
23	#410×C₁₄₉	C₄	1	4	yes	complemented
24	C₂×#99×C₁₄₉	—	2	2	no	—
25	#339×C₁₄₉	—	2	4	no	—
26	H(3,ℤ/4)×C₁₄₉	—	2	4	no	—
27	C₂×#41×C₁₄₉	—	2	2	no	—
28	C₂×#41×C₁₄₉	—	2	2	no	—
29	C₂×#41×C₁₄₉	—	2	2	no	—
30	C₂×#41×C₁₄₉	—	2	2	no	—
31	C₂×#41×C₁₄₉	C₂×C₄	1	2	yes	—
32	C₂×#41×C₁₄₉	C₂×C₄	1	2	yes	—
33	C₂×#41×C₁₄₉	D₄	1	2	yes	—
34	C₂×#41×C₁₄₉	Q₈	1	2	yes	—
35	C₂²×Q₈×C₁₄₉	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₁₄₉	D₄	1	2	yes	—
37	C₂²×D₄×C₁₄₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₄₉	—	2	2	no	—
39	C₂³×C₄×C₁₄₉	—	2	1	no	—
40	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₁₄₉	—	2	2	no	—
43	C₂×M₁₆×C₁₄₉	—	2	2	no	—
44	C₂×M₁₆×C₁₄₉	—	2	2	no	—
45	C₂×M₁₆×C₁₄₉	—	2	2	no	—
46	C₂×M₁₆×C₁₄₉	—	2	2	no	—
47	C₂×M₁₆×C₁₄₉	C₂×C₄	1	4	yes	complemented
48	C₂²×C₈×C₁₄₉	—	2	2	no	—
49	C₄×Q₈×C₁₄₉	—	2	8	no	—
50	C₄×D₄×C₁₄₉	—	2	16	no	—
51	C₄×D₄×C₁₄₉	—	2	8	no	—
52	#117×C₁₄₉	—	2	2	no	—
53	#117×C₁₄₉	—	2	2	no	—
54	#117×C₁₄₉	—	2	4	no	—
55	#117×C₁₄₉	—	2	4	no	—
56	#117×C₁₄₉	—	2	2	no	—
57	#117×C₁₄₉	—	2	2	no	—
58	#117×C₁₄₉	C₂×C₄	1	4	yes	complemented
59	#117×C₁₄₉	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
66	C₂×C₄²×C₁₄₉	—	2	2	no	—
67	C₂×C₄²×C₁₄₉	—	2	1	no	—
68	C₂×C₄²×C₁₄₉	—	2	2	no	—
69	C₂×C₄²×C₁₄₉	—	2	4	no	—
70	C₂×C₄²×C₁₄₉	—	2	4	no	—
71	C₂×C₄²×C₁₄₉	—	2	2	no	—
72	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₁₄₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₄₉	D₄	1	4	yes	—
76	#101×C₁₄₉	—	2	4	no	—
77	#100×C₁₄₉	—	2	4	no	—
78	#99×C₁₄₉	—	2	8	no	—
79	C₂⁴×C₁₄₉	C₂²⋊C₄	1	2	yes	—
80	C₂⁴×C₁₄₉	C₂×D₄	1	1	yes	characteristic
81	#41×C₁₄₉	—	2	4	no	—
82	#41×C₁₄₉	—	2	4	no	—
83	#41×C₁₄₉	—	2	4	no	—
84	#41×C₁₄₉	—	2	4	no	—
85	#41×C₁₄₉	—	2	4	no	—
86	#41×C₁₄₉	—	2	4	no	—
87	#41×C₁₄₉	—	2	4	no	—
88	#41×C₁₄₉	—	2	4	no	—
89	C₂×Q₈×C₁₄₉	—	2	2	no	—
90	C₂×Q₈×C₁₄₉	—	2	2	no	—
91	C₂×Q₈×C₁₄₉	C₂²⋊C₄	1	2	yes	—
92	C₂×Q₈×C₁₄₉	C₄⋊C₄	1	2	yes	—
93	C₂×D₄×C₁₄₉	—	2	4	no	—
94	C₂×D₄×C₁₄₉	—	2	4	no	—
95	C₂×D₄×C₁₄₉	—	2	2	no	—
96	C₂×D₄×C₁₄₉	—	2	2	no	—
97	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
98	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
99	C₂×D₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
100	C₂×D₄×C₁₄₉	C₄⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₄₉	—	2	1	no	—
102	C₂²×C₄×C₁₄₉	—	2	2	no	—
103	C₂²×C₄×C₁₄₉	—	2	2	no	—
104	C₂²×C₄×C₁₄₉	—	2	2	no	—
105	C₂²×C₄×C₁₄₉	—	2	2	no	—
106	C₂²×C₄×C₁₄₉	—	2	8	no	—
107	C₂²×C₄×C₁₄₉	—	2	2	no	—
108	C₂²×C₄×C₁₄₉	—	2	1	no	—
109	C₂²×C₄×C₁₄₉	—	2	4	no	—
110	C₂²×C₄×C₁₄₉	—	4	4	no	—
111	C₂²×C₄×C₁₄₉	—	4	8	no	—
112	C₂²×C₄×C₁₄₉	—	4	2	no	—
113	C₂²×C₄×C₁₄₉	C₄²	1	4	yes	—
114	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₁₄₉	C₄⋊C₄	1	4	yes	—
116	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
124	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
125	C₂²×C₄×C₁₄₉	#41	1	2	yes	—
126	M₁₆×C₁₄₉	—	2	4	no	—
127	M₁₆×C₁₄₉	—	2	4	no	—
128	M₁₆×C₁₄₉	—	4	2	no	—
129	M₁₆×C₁₄₉	—	4	2	no	—
130	C₂×C₈×C₁₄₉	—	2	4	no	—
131	C₂×C₈×C₁₄₉	—	4	2	no	—
132	C₂×C₈×C₁₄₉	—	4	2	no	—
133	C₄⋊C₄×C₁₄₉	—	2	8	no	—
134	C₄⋊C₄×C₁₄₉	—	2	4	no	—
135	C₄⋊C₄×C₁₄₉	—	2	4	no	—
136	C₄⋊C₄×C₁₄₉	—	4	2	no	—
137	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
138	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
139	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
140	C₂²⋊C₄×C₁₄₉	—	4	2	no	—
141	C₄²×C₁₄₉	—	2	8	no	—
142	C₄²×C₁₄₉	—	2	1	no	—
143	C₄²×C₁₄₉	—	2	1	no	—
144	C₄²×C₁₄₉	—	2	2	no	—
145	C₄²×C₁₄₉	—	2	4	no	—
146	C₄²×C₁₄₉	—	2	4	no	—
147	C₄²×C₁₄₉	—	4	2	no	—
148	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
149	C₄²×C₁₄₉	C₂²⋊C₄	1	4	yes	—
150	C₄²×C₁₄₉	C₂²⋊C₄	1	2	yes	—
151	C₂³×C₁₄₉	—	2	2	no	—
152	C₂³×C₁₄₉	—	2	2	no	—
153	C₂³×C₁₄₉	—	4	2	no	—
154	C₂³×C₁₄₉	—	4	4	no	—
155	C₂³×C₁₄₉	#95	1	4	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	2	yes	—
160	C₂³×C₁₄₉	#123	1	2	yes	—
161	Q₈×C₁₄₉	—	2	4	no	—
162	Q₈×C₁₄₉	—	2	4	no	—
163	D₄×C₁₄₉	—	2	8	no	—
164	D₄×C₁₄₉	—	2	8	no	—
165	D₄×C₁₄₉	—	2	4	no	—
166	D₄×C₁₄₉	—	2	4	no	—
167	C₂×C₄×C₁₄₉	—	2	4	no	—
168	C₂×C₄×C₁₄₉	—	2	2	no	—
169	C₂×C₄×C₁₄₉	—	2	2	no	—
170	C₂×C₄×C₁₄₉	—	2	2	no	—
171	C₂×C₄×C₁₄₉	—	2	4	no	—
172	C₂×C₄×C₁₄₉	—	2	4	no	—
173	C₂×C₄×C₁₄₉	—	2	4	no	—
174	C₂×C₄×C₁₄₉	—	2	4	no	—
175	C₂×C₄×C₁₄₉	—	2	4	no	—
176	C₂×C₄×C₁₄₉	—	2	2	no	—
177	C₂×C₄×C₁₄₉	—	4	8	no	—
178	C₂×C₄×C₁₄₉	—	4	16	no	—
179	C₂×C₄×C₁₄₉	—	4	4	no	—
180	C₂×C₄×C₁₄₉	—	4	2	no	—
181	C₂×C₄×C₁₄₉	—	4	4	no	—
182	C₂×C₄×C₁₄₉	—	8	4	no	—
183	C₂×C₄×C₁₄₉	#95	1	4	yes	—
184	C₂×C₄×C₁₄₉	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₁₄₉	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₄₉	#117	1	1	yes	characteristic
191	C₂×C₄×C₁₄₉	#117	1	1	yes	characteristic
192	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₄₉	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₄₉	#120	1	2	yes	—
197	C₂×C₄×C₁₄₉	#121	1	2	yes	—
198	C₂×C₄×C₁₄₉	#121	1	2	yes	—
199	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
200	C₂×C₄×C₁₄₉	C₂²⋊Q₈	1	2	yes	—
201	C₂×C₄×C₁₄₉	#123	1	2	yes	—
202	C₈×C₁₄₉	—	4	4	no	—
203	C₂²×C₁₄₉	—	2	2	no	—
204	C₂²×C₁₄₉	—	2	4	no	—
205	C₂²×C₁₄₉	—	2	4	no	—
206	C₂²×C₁₄₉	—	4	2	no	—
207	C₂²×C₁₄₉	—	4	1	no	—
208	C₂²×C₁₄₉	—	4	1	no	—
209	C₂²×C₁₄₉	—	4	4	no	—
210	C₂²×C₁₄₉	—	4	4	no	—
211	C₂²×C₁₄₉	—	4	4	no	—
212	C₂²×C₁₄₉	C₂×#95	1	1	yes	characteristic
213	C₂²×C₁₄₉	#379	1	1	yes	characteristic
214	C₂²×C₁₄₉	#381	1	1	yes	characteristic
215	C₂²×C₁₄₉	#385	1	2	yes	—
216	C₂²×C₁₄₉	#386	1	2	yes	—
217	C₄×C₁₄₉	—	2	4	no	—
218	C₄×C₁₄₉	—	2	4	no	—
219	C₄×C₁₄₉	—	4	4	no	—
220	C₄×C₁₄₉	—	4	2	no	—
221	C₄×C₁₄₉	—	8	4	no	—
222	C₄×C₁₄₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
223	C₄×C₁₄₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
224	C₄×C₁₄₉	#380	1	1	yes	characteristic
225	C₄×C₁₄₉	#380	1	1	yes	characteristic
226	C₄×C₁₄₉	#385	1	2	yes	—
227	C₄×C₁₄₉	#386	1	2	yes	—
228	C₂×C₁₄₉	—	2	1	no	—
229	C₂×C₁₄₉	—	2	2	no	—
230	C₂×C₁₄₉	—	2	1	no	—
231	C₂×C₁₄₉	—	2	2	no	—
232	C₂×C₁₄₉	—	4	4	no	—
233	C₂×C₁₄₉	C₂²⋊#95	1	1	yes	characteristic
234	C₂×C₁₄₉	#1827	1	2	yes	—
235	#10758	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₁₄₉	#10758	1	1	yes	characteristic, direct product factor, Sylow
237	C₂×C₄×#41	C₂×C₁₄₉	1	1	yes	characteristic
238	C₂×#413	C₂×C₁₄₉	1	1	yes	characteristic
239	C₂×#410	C₂×C₁₄₉	1	1	yes	characteristic
240	C₂×#339	C₂×C₁₄₉	1	2	yes	complemented
241	C₂×H(3,ℤ/4)	C₂×C₁₄₉	1	2	yes	complemented
242	C₂²×#41	C₂²×C₁₄₉	1	1	yes	characteristic
243	C₂²×M₁₆	C₂²×C₁₄₉	1	2	yes	—
244	C₄×#41	—	2	4	no	—
245	C₄×#41	—	2	4	no	—
246	C₂×C₄×Q₈	—	2	1	no	—
247	C₂×C₄×D₄	—	2	2	no	—
248	C₂×C₄×D₄	—	2	1	no	—
249	C₂×#117	C₄×C₁₄₉	1	2	yes	complemented
250	C₂×#117	C₂²×C₁₄₉	1	2	yes	—
251	C₂×#117	C₂²×C₁₄₉	1	1	yes	characteristic
252	C₂²×C₄²	C₄×C₁₄₉	1	2	yes	complemented
253	C₂²×C₄²	C₂²×C₁₄₉	1	1	yes	characteristic
254	#413	—	2	2	no	—
255	#413	C₄×C₁₄₉	1	4	yes	complemented
256	C₂×#101	—	2	1	no	—
257	C₂×#100	—	2	1	no	—
258	#410	—	2	2	no	—
259	#410	C₄×C₁₄₉	1	4	yes	complemented
260	C₂×#99	—	2	2	no	—
261	#339	—	2	4	no	—
262	H(3,ℤ/4)	—	2	4	no	—
263	C₂×#41	—	2	2	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	2	2	no	—
267	C₂×#41	C₂×C₄×C₁₄₉	1	2	yes	—
268	C₂×#41	C₂×C₄×C₁₄₉	1	2	yes	—
269	C₂×#41	D₄×C₁₄₉	1	2	yes	—
270	C₂×#41	Q₈×C₁₄₉	1	2	yes	—
271	C₂²×Q₈	D₄×C₁₄₉	1	1	yes	characteristic
272	C₂²×D₄	D₄×C₁₄₉	1	2	yes	—
273	C₂²×D₄	D₄×C₁₄₉	1	1	yes	characteristic
274	C₂³×C₄	—	2	2	no	—
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
277	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	C₂×C₄×C₁₄₉	1	4	yes	complemented
284	C₂²×C₈	—	2	2	no	—
285	C₄×Q₈	—	2	8	no	—
286	C₄×D₄	—	2	16	no	—
287	C₄×D₄	—	2	8	no	—
288	#117	—	2	2	no	—
289	#117	—	2	2	no	—
290	#117	—	2	4	no	—
291	#117	—	2	4	no	—
292	#117	—	2	2	no	—
293	#117	—	2	2	no	—
294	#117	C₂×C₄×C₁₄₉	1	4	yes	complemented
295	#117	D₄×C₁₄₉	1	4	yes	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₄²	—	2	2	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	4	no	—
306	C₂×C₄²	—	2	4	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
309	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
310	C₂×C₄²	C₂×C₄×C₁₄₉	1	1	yes	characteristic
311	C₂×C₄²	D₄×C₁₄₉	1	4	yes	—
312	#101	—	2	4	no	—
313	#100	—	2	4	no	—
314	#99	—	2	8	no	—
315	C₂⁴	C₂²⋊C₄×C₁₄₉	1	2	yes	—
316	C₂⁴	C₂×D₄×C₁₄₉	1	1	yes	characteristic
317	#41	—	2	4	no	—
318	#41	—	2	4	no	—
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	C₂²⋊C₄×C₁₄₉	1	2	yes	—
328	C₂×Q₈	C₄⋊C₄×C₁₄₉	1	2	yes	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
334	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
335	C₂×D₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
336	C₂×D₄	C₄⋊C₄×C₁₄₉	1	2	yes	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	8	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₄²×C₁₄₉	1	4	yes	—
350	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
351	C₂²×C₄	C₄⋊C₄×C₁₄₉	1	4	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
359	C₂²×C₄	C₂×Q₈×C₁₄₉	1	1	yes	characteristic
360	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
361	C₂²×C₄	#41×C₁₄₉	1	2	yes	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	4	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	—	4	2	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	4	2	no	—
368	C₂×C₈	—	4	2	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₄²	—	2	8	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	2	4	no	—
383	C₄²	—	4	2	no	—
384	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
385	C₄²	C₂²⋊C₄×C₁₄₉	1	4	yes	—
386	C₄²	C₂²⋊C₄×C₁₄₉	1	2	yes	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	4	no	—
391	C₂³	#95×C₁₄₉	1	4	yes	—
392	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
393	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
394	C₂³	C₂×C₄⋊C₄×C₁₄₉	1	1	yes	characteristic
395	C₂³	#120×C₁₄₉	1	2	yes	—
396	C₂³	#123×C₁₄₉	1	2	yes	—
397	Q₈	—	2	4	no	—
398	Q₈	—	2	4	no	—
399	D₄	—	2	8	no	—
400	D₄	—	2	8	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	16	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	8	4	no	—
419	C₂×C₄	#95×C₁₄₉	1	4	yes	—
420	C₂×C₄	C₂×C₄²×C₁₄₉	1	1	yes	characteristic
421	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
422	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
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	1	yes	characteristic
427	C₂×C₄	#117×C₁₄₉	1	1	yes	characteristic
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	C₄×D₄×C₁₄₉	1	2	yes	—
432	C₂×C₄	#120×C₁₄₉	1	2	yes	—
433	C₂×C₄	#121×C₁₄₉	1	2	yes	—
434	C₂×C₄	#121×C₁₄₉	1	2	yes	—
435	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
436	C₂×C₄	C₂²⋊Q₈×C₁₄₉	1	2	yes	—
437	C₂×C₄	#123×C₁₄₉	1	2	yes	—
438	C₈	—	4	4	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	C₂×#95×C₁₄₉	1	1	yes	characteristic
449	C₂²	#379×C₁₄₉	1	1	yes	characteristic
450	C₂²	#381×C₁₄₉	1	1	yes	characteristic
451	C₂²	#385×C₁₄₉	1	2	yes	—
452	C₂²	#386×C₁₄₉	1	2	yes	—
453	C₄	—	2	4	no	—
454	C₄	—	2	4	no	—
455	C₄	—	4	4	no	—
456	C₄	—	4	2	no	—
457	C₄	—	8	4	no	—
458	C₄	C₄×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
459	C₄	C₄×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
460	C₄	#380×C₁₄₉	1	1	yes	characteristic
461	C₄	#380×C₁₄₉	1	1	yes	characteristic
462	C₄	#385×C₁₄₉	1	2	yes	—
463	C₄	#386×C₁₄₉	1	2	yes	—
464	C₂	—	2	1	no	—
465	C₂	—	2	2	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	2	no	—
468	C₂	—	4	4	no	—
469	C₂	C₂²⋊#95×C₁₄₉	1	1	yes	characteristic
470	C₂	#1827×C₁₄₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₄₉	#117
commutator	C₂×C₄	C₂×C₄²×C₁₄₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₄₉
socle	C₂²×C₁₄₉	#381
prime radical	C₂²×#41×C₁₄₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₂×#117×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×#339×C₁₄₉	C₂	semidirect
5. C₂×H(3,ℤ/4)×C₁₄₉	C₂	semidirect
13. C₂×#117×C₁₄₉	C₄	semidirect
16. C₂²×C₄²×C₁₄₉	C₄	semidirect
19. #413×C₁₄₉	C₄	semidirect
23. #410×C₁₄₉	C₄	semidirect
47. C₂×M₁₆×C₁₄₉	C₂×C₄	semidirect
58. #117×C₁₄₉	C₂×C₄	semidirect
235. #10758	C₁₄₉	direct (N × H)
236. C₁₄₉	#10758	direct (N × H)
240. C₂×#339	C₂×C₁₄₉	semidirect
241. C₂×H(3,ℤ/4)	C₂×C₁₄₉	semidirect
249. C₂×#117	C₄×C₁₄₉	semidirect
252. C₂²×C₄²	C₄×C₁₄₉	semidirect
255. #413	C₄×C₁₄₉	semidirect
259. #410	C₄×C₁₄₉	semidirect
283. C₂×M₁₆	C₂×C₄×C₁₄₉	semidirect
294. #117	C₂×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×C₄×#41×C₁₄₉	2
C₂×#413×C₁₄₉	2
C₂×#410×C₁₄₉	2
C₂×#339×C₁₄₉	2
C₂×H(3,ℤ/4)×C₁₄₉	2
#10758	149

Subgroups — C149×#10758 #49189707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#10758 #49189707