Subgroups — C₁₄₉×#19110 #49198059

Order 38144.

716 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3131×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3101×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#3100×C₁₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1683×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	#1681×C₁₄₉	C₂	1	2	yes	maximal, complemented
7	#1679×C₁₄₉	C₂	1	2	yes	maximal, complemented
8	#1677×C₁₄₉	C₂	1	2	yes	maximal, complemented
9	#1564×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#1542×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#1540×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₄₉	—	2	1	no	—
13	#533×C₁₄₉	C₂²	1	1	yes	characteristic
14	#532×C₁₄₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
16	#488×C₁₄₉	—	2	1	no	—
17	#488×C₁₄₉	—	2	1	no	—
18	#487×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
19	#487×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
20	#486×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
21	#486×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
22	#483×C₁₄₉	—	2	1	no	—
23	#480×C₁₄₉	—	2	1	no	—
24	#476×C₁₄₉	C₂²	1	2	yes	—
25	#474×C₁₄₉	C₂²	1	2	yes	—
26	#461×C₁₄₉	C₂²	1	2	yes	—
27	#459×C₁₄₉	C₂²	1	2	yes	—
28	#450×C₁₄₉	—	2	1	no	—
29	#447×C₁₄₉	—	2	1	no	—
30	C₄×SD₁₆×C₁₄₉	—	2	2	no	—
31	C₄×D₈×C₁₄₉	—	2	2	no	—
32	C₈×D₄×C₁₄₉	—	2	1	no	—
33	C₈×D₄×C₁₄₉	—	2	1	no	—
34	C₈×D₄×C₁₄₉	C₂²	1	2	yes	—
35	C₈×D₄×C₁₄₉	C₂²	1	2	yes	—
36	#431×C₁₄₉	C₂²	1	1	yes	characteristic
37	#431×C₁₄₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₁₄₉	C₂²	1	1	yes	characteristic
39	#416×C₁₄₉	—	2	1	no	—
40	#416×C₁₄₉	—	2	1	no	—
41	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
42	C₂×C₄×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
43	#335×C₁₄₉	C₂²	1	2	yes	complemented
44	#334×C₁₄₉	C₂²	1	2	yes	complemented
45	#333×C₁₄₉	C₂²	1	2	yes	complemented
46	#332×C₁₄₉	C₂²	1	2	yes	complemented
47	#332×C₁₄₉	C₂²	1	2	yes	complemented
48	#331×C₁₄₉	C₂²	1	2	yes	complemented
49	C₂×#41×C₁₄₉	—	2	1	no	—
50	C₂²×D₄×C₁₄₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₄₉	—	2	1	no	—
52	C₂×SD₁₆×C₁₄₉	—	2	2	no	—
53	C₂×D₈×C₁₄₉	—	2	2	no	—
54	C₂²×C₈×C₁₄₉	—	2	1	no	—
55	C₂²×C₈×C₁₄₉	—	2	2	no	—
56	C₂²×C₈×C₁₄₉	—	2	2	no	—
57	C₂²×C₈×C₁₄₉	—	4	4	no	—
58	C₂²×C₈×C₁₄₉	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₁₄₉	D₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
63	#127×C₁₄₉	C₂³	1	1	yes	characteristic
64	#125×C₁₄₉	—	2	1	no	—
65	#124×C₁₄₉	—	2	1	no	—
66	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
67	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
68	#121×C₁₄₉	—	2	1	no	—
69	#121×C₁₄₉	—	2	1	no	—
70	C₄×Q₈×C₁₄₉	—	2	1	no	—
71	C₄×Q₈×C₁₄₉	—	2	1	no	—
72	C₄×D₄×C₁₄₉	—	2	1	no	—
73	C₄×D₄×C₁₄₉	—	2	1	no	—
74	C₄×D₄×C₁₄₉	—	2	1	no	—
75	C₄×D₄×C₁₄₉	—	2	1	no	—
76	C₄×D₄×C₁₄₉	D₄	1	2	yes	—
77	C₄×D₄×C₁₄₉	C₂³	1	2	yes	—
78	#117×C₁₄₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₄₉	D₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₁₄₉	—	2	1	no	—
81	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
82	#107×C₁₄₉	—	2	2	no	—
83	#106×C₁₄₉	—	2	2	no	—
84	C₄⋊C₈×C₁₄₉	—	2	1	no	—
85	C₄⋊C₈×C₁₄₉	C₂³	1	2	yes	—
86	C₄⋊C₈×C₁₄₉	C₂³	1	2	yes	—
87	C₄⋊C₈×C₁₄₉	C₂³	1	2	yes	—
88	#103×C₁₄₉	—	2	1	no	—
89	#103×C₁₄₉	—	2	1	no	—
90	#103×C₁₄₉	—	2	1	no	—
91	#103×C₁₄₉	—	2	1	no	—
92	#103×C₁₄₉	—	2	2	no	—
93	#102×C₁₄₉	—	2	2	no	—
94	#102×C₁₄₉	—	2	2	no	—
95	#102×C₁₄₉	—	2	1	no	—
96	#102×C₁₄₉	—	2	1	no	—
97	#102×C₁₄₉	—	2	1	no	—
98	#102×C₁₄₉	—	2	1	no	—
99	#102×C₁₄₉	—	2	2	no	—
100	C₂²⋊C₈×C₁₄₉	—	2	1	no	—
101	C₂²⋊C₈×C₁₄₉	—	2	1	no	—
102	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
103	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
104	C₄×C₈×C₁₄₉	—	2	1	no	—
105	C₄×C₈×C₁₄₉	—	2	1	no	—
106	C₄×C₈×C₁₄₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₁₄₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₁₄₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₄₉	C₂³	1	1	yes	characteristic
110	C₂⁴×C₁₄₉	—	2	1	no	—
111	#41×C₁₄₉	—	4	2	no	—
112	#41×C₁₄₉	—	4	2	no	—
113	C₂×Q₈×C₁₄₉	—	2	1	no	—
114	C₂×Q₈×C₁₄₉	—	2	1	no	—
115	C₂×Q₈×C₁₄₉	—	2	1	no	—
116	C₂×D₄×C₁₄₉	—	2	4	no	—
117	C₂×D₄×C₁₄₉	—	2	1	no	—
118	C₂×D₄×C₁₄₉	—	2	1	no	—
119	C₂×D₄×C₁₄₉	—	2	1	no	—
120	C₂×D₄×C₁₄₉	—	2	1	no	—
121	C₂×D₄×C₁₄₉	—	4	1	no	—
122	C₂×D₄×C₁₄₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₄₉	—	2	1	no	—
124	C₂²×C₄×C₁₄₉	—	2	2	no	—
125	C₂²×C₄×C₁₄₉	—	2	2	no	—
126	C₂²×C₄×C₁₄₉	—	4	2	no	—
127	C₂²×C₄×C₁₄₉	—	4	2	no	—
128	C₂²×C₄×C₁₄₉	—	4	1	no	—
129	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₄₉	#41	1	1	yes	characteristic
132	SD₁₆×C₁₄₉	—	4	4	no	—
133	D₈×C₁₄₉	—	4	4	no	—
134	C₂×C₈×C₁₄₉	—	2	2	no	—
135	C₂×C₈×C₁₄₉	—	2	2	no	—
136	C₂×C₈×C₁₄₉	—	2	2	no	—
137	C₂×C₈×C₁₄₉	—	2	2	no	—
138	C₂×C₈×C₁₄₉	—	2	2	no	—
139	C₂×C₈×C₁₄₉	—	4	4	no	—
140	C₂×C₈×C₁₄₉	—	4	4	no	—
141	C₂×C₈×C₁₄₉	—	4	2	no	—
142	C₂×C₈×C₁₄₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₄₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₄₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₄₉	C₂×D₄	1	1	yes	characteristic
146	C₄⋊C₄×C₁₄₉	—	2	1	no	—
147	C₄⋊C₄×C₁₄₉	—	2	1	no	—
148	C₄⋊C₄×C₁₄₉	—	2	1	no	—
149	C₄⋊C₄×C₁₄₉	—	2	1	no	—
150	C₄⋊C₄×C₁₄₉	—	2	1	no	—
151	C₄⋊C₄×C₁₄₉	—	2	1	no	—
152	C₄⋊C₄×C₁₄₉	—	2	1	no	—
153	C₄⋊C₄×C₁₄₉	—	4	1	no	—
154	C₄⋊C₄×C₁₄₉	—	4	1	no	—
155	C₄⋊C₄×C₁₄₉	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
157	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
158	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
159	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
160	C₂²⋊C₄×C₁₄₉	—	4	1	no	—
161	C₄²×C₁₄₉	—	4	1	no	—
162	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₄₉	#41	1	1	yes	characteristic
165	C₄²×C₁₄₉	C₂⁴	1	1	yes	characteristic
166	C₂³×C₁₄₉	—	2	4	no	—
167	C₂³×C₁₄₉	—	2	2	no	—
168	C₂³×C₁₄₉	—	4	2	no	—
169	C₂³×C₁₄₉	—	4	2	no	—
170	C₂³×C₁₄₉	—	4	1	no	—
171	C₂³×C₁₄₉	#121	1	1	yes	characteristic
172	Q₈×C₁₄₉	—	4	2	no	—
173	Q₈×C₁₄₉	—	4	1	no	—
174	Q₈×C₁₄₉	—	4	1	no	—
175	Q₈×C₁₄₉	—	8	1	no	—
176	D₄×C₁₄₉	—	2	4	no	—
177	D₄×C₁₄₉	—	2	2	no	—
178	D₄×C₁₄₉	—	4	2	no	—
179	D₄×C₁₄₉	—	4	1	no	—
180	D₄×C₁₄₉	—	4	1	no	—
181	D₄×C₁₄₉	—	8	1	no	—
182	D₄×C₁₄₉	—	8	2	no	—
183	D₄×C₁₄₉	#135	1	4	yes	—
184	C₂×C₄×C₁₄₉	—	2	2	no	—
185	C₂×C₄×C₁₄₉	—	2	2	no	—
186	C₂×C₄×C₁₄₉	—	4	1	no	—
187	C₂×C₄×C₁₄₉	—	4	2	no	—
188	C₂×C₄×C₁₄₉	—	4	2	no	—
189	C₂×C₄×C₁₄₉	—	4	2	no	—
190	C₂×C₄×C₁₄₉	—	4	4	no	—
191	C₂×C₄×C₁₄₉	—	4	1	no	—
192	C₂×C₄×C₁₄₉	—	4	1	no	—
193	C₂×C₄×C₁₄₉	—	4	1	no	—
194	C₂×C₄×C₁₄₉	—	8	2	no	—
195	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₁₄₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₁₄₉	#135	1	2	yes	—
199	C₂×C₄×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₄₉	C₂×#41	1	1	yes	characteristic
203	C₈×C₁₄₉	—	2	1	no	—
204	C₈×C₁₄₉	—	2	1	no	—
205	C₈×C₁₄₉	—	2	1	no	—
206	C₈×C₁₄₉	—	2	1	no	—
207	C₈×C₁₄₉	—	4	2	no	—
208	C₈×C₁₄₉	—	4	2	no	—
209	C₈×C₁₄₉	—	4	2	no	—
210	C₂²×C₁₄₉	—	2	1	no	—
211	C₂²×C₁₄₉	—	2	1	no	—
212	C₂²×C₁₄₉	—	2	4	no	—
213	C₂²×C₁₄₉	—	4	8	no	—
214	C₂²×C₁₄₉	—	4	2	no	—
215	C₂²×C₁₄₉	—	4	2	no	—
216	C₂²×C₁₄₉	—	8	1	no	—
217	C₂²×C₁₄₉	—	8	1	no	—
218	C₂²×C₁₄₉	—	8	1	no	—
219	C₂²×C₁₄₉	#463	1	2	yes	—
220	C₂²×C₁₄₉	C₂×#121	1	1	yes	characteristic
221	C₄×C₁₄₉	—	2	1	no	—
222	C₄×C₁₄₉	—	2	1	no	—
223	C₄×C₁₄₉	—	2	1	no	—
224	C₄×C₁₄₉	—	4	2	no	—
225	C₄×C₁₄₉	—	8	1	no	—
226	C₄×C₁₄₉	—	8	1	no	—
227	C₄×C₁₄₉	—	8	1	no	—
228	C₄×C₁₄₉	#463	1	2	yes	—
229	C₄×C₁₄₉	C₂×#135	1	1	yes	characteristic
230	C₄×C₁₄₉	C₂×#135	1	2	yes	—
231	C₄×C₁₄₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₂×C₁₄₉	—	2	2	no	—
233	C₂×C₁₄₉	—	4	4	no	—
234	C₂×C₁₄₉	—	16	1	no	—
235	C₂×C₁₄₉	C₂×#463	1	1	yes	characteristic
236	C₂×C₁₄₉	#3050	1	1	yes	characteristic
237	C₂×C₁₄₉	#3067	1	1	yes	characteristic
238	#19110	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₁₄₉	#19110	1	1	yes	characteristic, direct product factor, Sylow
240	#3131	C₂×C₁₄₉	1	1	yes	characteristic, complemented
241	#3101	C₂×C₁₄₉	1	1	yes	characteristic, complemented
242	#3100	C₂×C₁₄₉	1	1	yes	characteristic
243	C₂×C₈×D₄	C₂×C₁₄₉	1	1	yes	characteristic, complemented
244	#1683	C₂×C₁₄₉	1	2	yes	complemented
245	#1681	C₂×C₁₄₉	1	2	yes	complemented
246	#1679	C₂×C₁₄₉	1	2	yes	complemented
247	#1677	C₂×C₁₄₉	1	2	yes	complemented
248	#1564	C₂×C₁₄₉	1	1	yes	characteristic, complemented
249	#1542	C₂×C₁₄₉	1	1	yes	characteristic, complemented
250	#1540	C₂×C₁₄₉	1	1	yes	characteristic, complemented
251	C₂³×C₈	—	2	1	no	—
252	#533	C₂²×C₁₄₉	1	1	yes	characteristic
253	#532	C₂²×C₁₄₉	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
255	#488	—	2	1	no	—
256	#488	—	2	1	no	—
257	#487	C₂²×C₁₄₉	1	1	yes	characteristic, complemented
258	#487	C₂²×C₁₄₉	1	1	yes	characteristic, complemented
259	#486	C₂²×C₁₄₉	1	1	yes	characteristic, complemented
260	#486	C₂²×C₁₄₉	1	1	yes	characteristic, complemented
261	#483	—	2	1	no	—
262	#480	—	2	1	no	—
263	#476	C₂²×C₁₄₉	1	2	yes	—
264	#474	C₂²×C₁₄₉	1	2	yes	—
265	#461	C₂²×C₁₄₉	1	2	yes	—
266	#459	C₂²×C₁₄₉	1	2	yes	—
267	#450	—	2	1	no	—
268	#447	—	2	1	no	—
269	C₄×SD₁₆	—	2	2	no	—
270	C₄×D₈	—	2	2	no	—
271	C₈×D₄	—	2	1	no	—
272	C₈×D₄	—	2	1	no	—
273	C₈×D₄	C₂²×C₁₄₉	1	2	yes	—
274	C₈×D₄	C₂²×C₁₄₉	1	2	yes	—
275	#431	C₂²×C₁₄₉	1	1	yes	characteristic
276	#431	C₂²×C₁₄₉	1	1	yes	characteristic
277	C₂×C₄⋊C₈	C₂²×C₁₄₉	1	1	yes	characteristic
278	#416	—	2	1	no	—
279	#416	—	2	1	no	—
280	C₂×C₂²⋊C₈	—	2	1	no	—
281	C₂×C₄×C₈	C₂²×C₁₄₉	1	1	yes	characteristic
282	#335	C₂²×C₁₄₉	1	2	yes	complemented
283	#334	C₂²×C₁₄₉	1	2	yes	complemented
284	#333	C₂²×C₁₄₉	1	2	yes	complemented
285	#332	C₂²×C₁₄₉	1	2	yes	complemented
286	#332	C₂²×C₁₄₉	1	2	yes	complemented
287	#331	C₂²×C₁₄₉	1	2	yes	complemented
288	C₂×#41	—	2	1	no	—
289	C₂²×D₄	D₄×C₁₄₉	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×D₈	—	2	2	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	—	4	4	no	—
297	C₂²×C₈	D₄×C₁₄₉	1	1	yes	characteristic
298	C₂²×C₈	D₄×C₁₄₉	1	1	yes	characteristic
299	C₄⋊Q₈	C₂³×C₁₄₉	1	1	yes	characteristic
300	C₄⋊Q₈	C₂³×C₁₄₉	1	1	yes	characteristic
301	C₄⋊Q₈	C₂³×C₁₄₉	1	1	yes	characteristic
302	#127	C₂³×C₁₄₉	1	1	yes	characteristic
303	#125	—	2	1	no	—
304	#124	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	#121	—	2	1	no	—
308	#121	—	2	1	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	D₄×C₁₄₉	1	2	yes	—
316	C₄×D₄	C₂³×C₁₄₉	1	2	yes	—
317	#117	—	2	1	no	—
318	C₂×C₄⋊C₄	D₄×C₁₄₉	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
321	#107	—	2	2	no	—
322	#106	—	2	2	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	C₂³×C₁₄₉	1	2	yes	—
325	C₄⋊C₈	C₂³×C₁₄₉	1	2	yes	—
326	C₄⋊C₈	C₂³×C₁₄₉	1	2	yes	—
327	#103	—	2	1	no	—
328	#103	—	2	1	no	—
329	#103	—	2	1	no	—
330	#103	—	2	1	no	—
331	#103	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	2	2	no	—
334	#102	—	2	1	no	—
335	#102	—	2	1	no	—
336	#102	—	2	1	no	—
337	#102	—	2	1	no	—
338	#102	—	2	2	no	—
339	C₂²⋊C₈	—	2	1	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	2	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	—	2	1	no	—
345	C₄×C₈	D₄×C₁₄₉	1	1	yes	characteristic
346	C₄×C₈	D₄×C₁₄₉	1	1	yes	characteristic
347	C₄×C₈	C₂³×C₁₄₉	1	1	yes	characteristic
348	C₄×C₈	C₂³×C₁₄₉	1	1	yes	characteristic
349	C₂⁴	—	2	1	no	—
350	#41	—	4	2	no	—
351	#41	—	4	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	C₂×D₄×C₁₄₉	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
370	C₂²×C₄	#41×C₁₄₉	1	1	yes	characteristic
371	SD₁₆	—	4	4	no	—
372	D₈	—	4	4	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	4	4	no	—
379	C₂×C₈	—	4	4	no	—
380	C₂×C₈	—	4	2	no	—
381	C₂×C₈	C₂×D₄×C₁₄₉	1	1	yes	characteristic
382	C₂×C₈	C₂×D₄×C₁₄₉	1	1	yes	characteristic
383	C₂×C₈	C₂×D₄×C₁₄₉	1	1	yes	characteristic
384	C₂×C₈	C₂×D₄×C₁₄₉	1	1	yes	characteristic
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₄⋊C₄	—	4	1	no	—
394	C₄⋊C₄	C₂×D₄×C₁₄₉	1	2	yes	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	—	4	1	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
402	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
403	C₄²	#41×C₁₄₉	1	1	yes	characteristic
404	C₄²	C₂⁴×C₁₄₉	1	1	yes	characteristic
405	C₂³	—	2	4	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	#121×C₁₄₉	1	1	yes	characteristic
411	Q₈	—	4	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	8	1	no	—
415	D₄	—	2	4	no	—
416	D₄	—	2	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	1	no	—
419	D₄	—	4	1	no	—
420	D₄	—	8	1	no	—
421	D₄	—	8	2	no	—
422	D₄	#135×C₁₄₉	1	4	yes	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	8	2	no	—
434	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
435	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
436	C₂×C₄	#121×C₁₄₉	1	1	yes	characteristic
437	C₂×C₄	#135×C₁₄₉	1	2	yes	—
438	C₂×C₄	AGL(1,ℤ/8)×C₁₄₉	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₁₄₉	1	1	yes	characteristic
442	C₈	—	2	1	no	—
443	C₈	—	2	1	no	—
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	2	no	—
448	C₈	—	4	2	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	#463×C₁₄₉	1	2	yes	—
459	C₂²	C₂×#121×C₁₄₉	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	1	no	—
466	C₄	—	8	1	no	—
467	C₄	#463×C₁₄₉	1	2	yes	—
468	C₄	C₂×#135×C₁₄₉	1	1	yes	characteristic
469	C₄	C₂×#135×C₁₄₉	1	2	yes	—
470	C₄	C₂×AGL(1,ℤ/8)×C₁₄₉	1	1	yes	characteristic
471	C₂	—	2	2	no	—
472	C₂	—	4	4	no	—
473	C₂	—	16	1	no	—
474	C₂	C₂×#463×C₁₄₉	1	1	yes	characteristic
475	C₂	#3050×C₁₄₉	1	1	yes	characteristic
476	C₂	#3067×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₄₉	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₄₉
socle	C₂²×C₁₄₉	C₂×#121
prime radical	#3100×C₁₄₉	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3131×C₁₄₉	C₂	semidirect
2. #3101×C₁₄₉	C₂	semidirect
4. C₂×C₈×D₄×C₁₄₉	C₂	semidirect
5. #1683×C₁₄₉	C₂	semidirect
6. #1681×C₁₄₉	C₂	semidirect
7. #1679×C₁₄₉	C₂	semidirect
8. #1677×C₁₄₉	C₂	semidirect
9. #1564×C₁₄₉	C₂	semidirect
10. #1542×C₁₄₉	C₂	semidirect
11. #1540×C₁₄₉	C₂	semidirect
18. #487×C₁₄₉	C₂²	semidirect
19. #487×C₁₄₉	C₂²	semidirect
20. #486×C₁₄₉	C₂²	semidirect
21. #486×C₁₄₉	C₂²	semidirect
43. #335×C₁₄₉	C₂²	semidirect
44. #334×C₁₄₉	C₂²	semidirect
45. #333×C₁₄₉	C₂²	semidirect
46. #332×C₁₄₉	C₂²	semidirect
47. #332×C₁₄₉	C₂²	semidirect
48. #331×C₁₄₉	C₂²	semidirect
238. #19110	C₁₄₉	direct (N × H)
239. C₁₄₉	#19110	direct (N × H)
240. #3131	C₂×C₁₄₉	semidirect
241. #3101	C₂×C₁₄₉	semidirect
243. C₂×C₈×D₄	C₂×C₁₄₉	semidirect
244. #1683	C₂×C₁₄₉	semidirect
245. #1681	C₂×C₁₄₉	semidirect
246. #1679	C₂×C₁₄₉	semidirect
247. #1677	C₂×C₁₄₉	semidirect
248. #1564	C₂×C₁₄₉	semidirect
249. #1542	C₂×C₁₄₉	semidirect
250. #1540	C₂×C₁₄₉	semidirect
257. #487	C₂²×C₁₄₉	semidirect
258. #487	C₂²×C₁₄₉	semidirect
259. #486	C₂²×C₁₄₉	semidirect
260. #486	C₂²×C₁₄₉	semidirect
282. #335	C₂²×C₁₄₉	semidirect
283. #334	C₂²×C₁₄₉	semidirect
284. #333	C₂²×C₁₄₉	semidirect
285. #332	C₂²×C₁₄₉	semidirect
286. #332	C₂²×C₁₄₉	semidirect
287. #331	C₂²×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#3131×C₁₄₉	2
#3101×C₁₄₉	2
#3100×C₁₄₉	2
C₂×C₈×D₄×C₁₄₉	2
#1683×C₁₄₉	2
#1681×C₁₄₉	2
#1679×C₁₄₉	2
#1677×C₁₄₉	2
#1564×C₁₄₉	2
#1542×C₁₄₉	2
#1540×C₁₄₉	2
#19110	149

Subgroups — C149×#19110 #49198059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#19110 #49198059