Subgroups — C₁₄₉×#17617 #49196566

Order 38144.

1018 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3506×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#2972×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2357×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1518×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1517×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1516×C₁₄₉	C₂	1	4	yes	maximal, complemented
7	#1503×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1502×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1501×C₁₄₉	C₂	1	4	yes	maximal, complemented
10	#559×C₁₄₉	—	2	2	no	—
11	#556×C₁₄₉	C₄	1	2	yes	complemented
12	#555×C₁₄₉	C₄	1	2	yes	complemented
13	#553×C₁₄₉	—	2	2	no	—
14	#550×C₁₄₉	C₄	1	2	yes	complemented
15	#547×C₁₄₉	C₄	1	2	yes	complemented
16	#538×C₁₄₉	—	2	2	no	—
17	#535×C₁₄₉	—	2	1	no	—
18	#533×C₁₄₉	C₂²	1	1	yes	characteristic
19	#532×C₁₄₉	C₂²	1	1	yes	characteristic
20	#525×C₁₄₉	C₂²	1	4	yes	—
21	#520×C₁₄₉	—	2	1	no	—
22	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
23	C₈×D₄×C₁₄₉	—	2	2	no	—
24	C₈×D₄×C₁₄₉	—	2	2	no	—
25	#431×C₁₄₉	C₂²	1	1	yes	characteristic
26	#431×C₁₄₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	4	yes	—
28	#390×C₁₄₉	—	2	1	no	—
29	#388×C₁₄₉	—	2	2	no	—
30	#382×C₁₄₉	C₂²	1	1	yes	characteristic
31	#381×C₁₄₉	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₁₄₉	—	2	1	no	—
33	C₄×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	—
35	#328×C₁₄₉	C₂²	1	2	yes	—
36	#328×C₁₄₉	C₂²	1	4	yes	—
37	#328×C₁₄₉	C₂²	1	2	yes	—
38	#327×C₁₄₉	C₂²	1	2	yes	—
39	#327×C₁₄₉	C₂²	1	4	yes	—
40	#327×C₁₄₉	C₂²	1	2	yes	—
41	C₂×#41×C₁₄₉	—	2	1	no	—
42	C₂×#41×C₁₄₉	C₂×C₄	1	4	yes	—
43	C₂²×D₄×C₁₄₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₄₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₄₉	—	2	4	no	—
46	C₄⋊Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
47	C₄⋊Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
48	C₄⋊Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
49	#127×C₁₄₉	—	2	2	no	—
50	#127×C₁₄₉	C₂×C₄	1	1	yes	characteristic
51	#126×C₁₄₉	—	2	4	no	—
52	#125×C₁₄₉	—	2	1	no	—
53	#124×C₁₄₉	—	2	2	no	—
54	#124×C₁₄₉	—	2	4	no	—
55	#124×C₁₄₉	—	2	1	no	—
56	#123×C₁₄₉	—	2	4	no	—
57	#123×C₁₄₉	—	2	4	no	—
58	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
59	C₂²⋊Q₈×C₁₄₉	C₂×C₄	1	4	yes	—
60	C₂²⋊Q₈×C₁₄₉	C₂³	1	2	yes	—
61	#121×C₁₄₉	—	2	2	no	—
62	#121×C₁₄₉	—	2	2	no	—
63	#121×C₁₄₉	—	2	1	no	—
64	#121×C₁₄₉	—	2	4	no	—
65	#121×C₁₄₉	C₂×C₄	1	4	yes	—
66	#121×C₁₄₉	C₂³	1	2	yes	—
67	#120×C₁₄₉	—	2	4	no	—
68	C₄×Q₈×C₁₄₉	—	2	2	no	—
69	C₄×Q₈×C₁₄₉	—	2	1	no	—
70	C₄×Q₈×C₁₄₉	C₂×C₄	1	2	yes	—
71	C₄×D₄×C₁₄₉	—	2	4	no	—
72	C₄×D₄×C₁₄₉	—	2	4	no	—
73	C₄×D₄×C₁₄₉	—	2	2	no	—
74	C₄×D₄×C₁₄₉	—	2	1	no	—
75	C₄×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
76	C₄×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
77	C₄×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
78	C₄×D₄×C₁₄₉	D₄	1	2	yes	—
79	C₄×D₄×C₁₄₉	D₄	1	2	yes	—
80	#117×C₁₄₉	—	2	1	no	—
81	#117×C₁₄₉	—	2	2	no	—
82	#117×C₁₄₉	C₂×C₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₄₉	D₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₄₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₄₉	D₄	1	2	yes	—
90	C₂×C₄²×C₁₄₉	—	2	1	no	—
91	C₂×C₄²×C₁₄₉	—	2	2	no	—
92	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₁₄₉	—	2	1	no	—
94	C₄⋊C₈×C₁₄₉	—	2	1	no	—
95	C₂²⋊C₈×C₁₄₉	—	2	4	no	—
96	C₂²⋊C₈×C₁₄₉	C₂³	1	2	yes	—
97	C₂²⋊C₈×C₁₄₉	C₂³	1	2	yes	—
98	C₄×C₈×C₁₄₉	—	2	1	no	—
99	C₄×C₈×C₁₄₉	—	2	1	no	—
100	#95×C₁₄₉	—	2	2	no	—
101	#95×C₁₄₉	—	2	1	no	—
102	#95×C₁₄₉	C₂³	1	1	yes	characteristic
103	#95×C₁₄₉	C₂³	1	2	yes	—
104	#95×C₁₄₉	C₂³	1	1	yes	characteristic
105	C₂⁴×C₁₄₉	C₂×D₄	1	2	yes	—
106	#41×C₁₄₉	—	4	2	no	—
107	#41×C₁₄₉	—	4	2	no	—
108	#41×C₁₄₉	—	8	4	no	—
109	C₂×Q₈×C₁₄₉	—	2	1	no	—
110	C₂×Q₈×C₁₄₉	—	2	1	no	—
111	C₂×Q₈×C₁₄₉	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₄₉	—	2	2	no	—
113	C₂×D₄×C₁₄₉	—	2	4	no	—
114	C₂×D₄×C₁₄₉	—	2	4	no	—
115	C₂×D₄×C₁₄₉	—	2	1	no	—
116	C₂×D₄×C₁₄₉	—	2	1	no	—
117	C₂×D₄×C₁₄₉	—	2	2	no	—
118	C₂×D₄×C₁₄₉	—	2	2	no	—
119	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
120	C₂×D₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
121	C₂×D₄×C₁₄₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₄₉	—	2	1	no	—
123	C₂²×C₄×C₁₄₉	—	2	2	no	—
124	C₂²×C₄×C₁₄₉	—	2	4	no	—
125	C₂²×C₄×C₁₄₉	—	2	2	no	—
126	C₂²×C₄×C₁₄₉	—	2	1	no	—
127	C₂²×C₄×C₁₄₉	—	8	2	no	—
128	C₂²×C₄×C₁₄₉	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₁₄₉	—	2	2	no	—
135	C₂×C₈×C₁₄₉	—	2	2	no	—
136	C₂×C₈×C₁₄₉	—	8	4	no	—
137	C₄⋊C₄×C₁₄₉	—	2	1	no	—
138	C₄⋊C₄×C₁₄₉	—	2	4	no	—
139	C₄⋊C₄×C₁₄₉	—	2	1	no	—
140	C₄⋊C₄×C₁₄₉	—	2	1	no	—
141	C₄⋊C₄×C₁₄₉	—	2	1	no	—
142	C₄⋊C₄×C₁₄₉	—	2	2	no	—
143	C₄⋊C₄×C₁₄₉	—	2	2	no	—
144	C₄⋊C₄×C₁₄₉	—	4	2	no	—
145	C₄⋊C₄×C₁₄₉	—	4	2	no	—
146	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
147	C₄⋊C₄×C₁₄₉	C₂²⋊C₄	1	2	yes	—
148	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
149	C₄⋊C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
150	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₄₉	—	4	4	no	—
157	C₂²⋊C₄×C₁₄₉	—	8	2	no	—
158	C₂²⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
159	C₂²⋊C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	—
160	C₄²×C₁₄₉	—	2	4	no	—
161	C₄²×C₁₄₉	—	2	2	no	—
162	C₄²×C₁₄₉	—	4	2	no	—
163	C₄²×C₁₄₉	—	8	2	no	—
164	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
168	C₂³×C₁₄₉	—	2	2	no	—
169	C₂³×C₁₄₉	—	2	2	no	—
170	C₂³×C₁₄₉	—	2	2	no	—
171	C₂³×C₁₄₉	—	4	2	no	—
172	C₂³×C₁₄₉	—	4	2	no	—
173	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
174	C₂³×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₄₉	—	4	2	no	—
176	Q₈×C₁₄₉	—	4	2	no	—
177	Q₈×C₁₄₉	—	8	1	no	—
178	D₄×C₁₄₉	—	2	4	no	—
179	D₄×C₁₄₉	—	2	4	no	—
180	D₄×C₁₄₉	—	4	2	no	—
181	D₄×C₁₄₉	—	4	2	no	—
182	D₄×C₁₄₉	—	4	2	no	—
183	D₄×C₁₄₉	—	4	2	no	—
184	D₄×C₁₄₉	—	8	1	no	—
185	D₄×C₁₄₉	—	8	4	no	—
186	D₄×C₁₄₉	—	8	4	no	—
187	C₂×C₄×C₁₄₉	—	2	2	no	—
188	C₂×C₄×C₁₄₉	—	2	2	no	—
189	C₂×C₄×C₁₄₉	—	2	2	no	—
190	C₂×C₄×C₁₄₉	—	2	2	no	—
191	C₂×C₄×C₁₄₉	—	4	2	no	—
192	C₂×C₄×C₁₄₉	—	4	1	no	—
193	C₂×C₄×C₁₄₉	—	4	4	no	—
194	C₂×C₄×C₁₄₉	—	4	1	no	—
195	C₂×C₄×C₁₄₉	—	4	4	no	—
196	C₂×C₄×C₁₄₉	—	4	1	no	—
197	C₂×C₄×C₁₄₉	—	4	1	no	—
198	C₂×C₄×C₁₄₉	—	4	4	no	—
199	C₂×C₄×C₁₄₉	—	4	2	no	—
200	C₂×C₄×C₁₄₉	—	4	2	no	—
201	C₂×C₄×C₁₄₉	—	4	1	no	—
202	C₂×C₄×C₁₄₉	—	4	1	no	—
203	C₂×C₄×C₁₄₉	—	4	1	no	—
204	C₂×C₄×C₁₄₉	—	4	2	no	—
205	C₂×C₄×C₁₄₉	—	8	4	no	—
206	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	4	yes	—
207	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₄₉	#135	1	2	yes	—
212	C₂×C₄×C₁₄₉	#135	1	2	yes	—
213	C₂×C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
215	C₈×C₁₄₉	—	4	2	no	—
216	C₈×C₁₄₉	—	4	2	no	—
217	C₂²×C₁₄₉	—	2	1	no	—
218	C₂²×C₁₄₉	—	2	1	no	—
219	C₂²×C₁₄₉	—	2	4	no	—
220	C₂²×C₁₄₉	—	2	4	no	—
221	C₂²×C₁₄₉	—	2	4	no	—
222	C₂²×C₁₄₉	—	4	2	no	—
223	C₂²×C₁₄₉	—	4	2	no	—
224	C₂²×C₁₄₉	—	4	2	no	—
225	C₂²×C₁₄₉	—	8	2	no	—
226	C₂²×C₁₄₉	—	8	2	no	—
227	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₁₄₉	C₂×#135	1	1	yes	characteristic
229	C₂²×C₁₄₉	C₂×#135	1	1	yes	characteristic
230	C₄×C₁₄₉	—	2	1	no	—
231	C₄×C₁₄₉	—	2	1	no	—
232	C₄×C₁₄₉	—	2	4	no	—
233	C₄×C₁₄₉	—	2	1	no	—
234	C₄×C₁₄₉	—	2	1	no	—
235	C₄×C₁₄₉	—	4	2	no	—
236	C₄×C₁₄₉	—	4	2	no	—
237	C₄×C₁₄₉	—	4	2	no	—
238	C₄×C₁₄₉	—	4	2	no	—
239	C₄×C₁₄₉	—	8	1	no	—
240	C₄×C₁₄₉	—	8	2	no	—
241	C₄×C₁₄₉	#416	1	2	yes	—
242	C₄×C₁₄₉	#416	1	2	yes	—
243	C₂×C₁₄₉	—	2	1	no	—
244	C₂×C₁₄₉	—	2	1	no	—
245	C₂×C₁₄₉	—	4	4	no	—
246	C₂×C₁₄₉	—	8	2	no	—
247	C₂×C₁₄₉	#2883	1	1	yes	characteristic
248	C₂×C₁₄₉	C₂×#416	1	1	yes	characteristic
249	C₂×C₁₄₉	#2901	1	1	yes	characteristic
250	#17617	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₁₄₉	#17617	1	1	yes	characteristic, direct product factor, Sylow
252	#3506	C₂×C₁₄₉	1	1	yes	characteristic
253	#2972	C₂×C₁₄₉	1	1	yes	characteristic, complemented
254	#2357	C₂×C₁₄₉	1	1	yes	characteristic, complemented
255	#1518	C₂×C₁₄₉	1	1	yes	characteristic, complemented
256	#1517	C₂×C₁₄₉	1	1	yes	characteristic, complemented
257	#1516	C₂×C₁₄₉	1	4	yes	complemented
258	#1503	C₂×C₁₄₉	1	1	yes	characteristic, complemented
259	#1502	C₂×C₁₄₉	1	1	yes	characteristic, complemented
260	#1501	C₂×C₁₄₉	1	4	yes	complemented
261	#559	—	2	2	no	—
262	#556	C₄×C₁₄₉	1	2	yes	complemented
263	#555	C₄×C₁₄₉	1	2	yes	complemented
264	#553	—	2	2	no	—
265	#550	C₄×C₁₄₉	1	2	yes	complemented
266	#547	C₄×C₁₄₉	1	2	yes	complemented
267	#538	—	2	2	no	—
268	#535	—	2	1	no	—
269	#533	C₂²×C₁₄₉	1	1	yes	characteristic
270	#532	C₂²×C₁₄₉	1	1	yes	characteristic
271	#525	C₂²×C₁₄₉	1	4	yes	—
272	#520	—	2	1	no	—
273	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
274	C₈×D₄	—	2	2	no	—
275	C₈×D₄	—	2	2	no	—
276	#431	C₂²×C₁₄₉	1	1	yes	characteristic
277	#431	C₂²×C₁₄₉	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	4	yes	—
279	#390	—	2	1	no	—
280	#388	—	2	2	no	—
281	#382	C₂²×C₁₄₉	1	1	yes	characteristic
282	#381	C₂²×C₁₄₉	1	2	yes	—
283	C₄×C₄⋊C₄	—	2	1	no	—
284	C₄×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic
285	C₄×C₂²⋊C₄	C₂²×C₁₄₉	1	2	yes	—
286	#328	C₂²×C₁₄₉	1	2	yes	—
287	#328	C₂²×C₁₄₉	1	4	yes	—
288	#328	C₂²×C₁₄₉	1	2	yes	—
289	#327	C₂²×C₁₄₉	1	2	yes	—
290	#327	C₂²×C₁₄₉	1	4	yes	—
291	#327	C₂²×C₁₄₉	1	2	yes	—
292	C₂×#41	—	2	1	no	—
293	C₂×#41	C₂×C₄×C₁₄₉	1	4	yes	—
294	C₂²×D₄	D₄×C₁₄₉	1	1	yes	characteristic
295	C₂³×C₄	C₂³×C₁₄₉	1	2	yes	—
296	C₂²×C₈	—	2	4	no	—
297	C₄⋊Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
298	C₄⋊Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
299	C₄⋊Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
300	#127	—	2	2	no	—
301	#127	C₂×C₄×C₁₄₉	1	1	yes	characteristic
302	#126	—	2	4	no	—
303	#125	—	2	1	no	—
304	#124	—	2	2	no	—
305	#124	—	2	4	no	—
306	#124	—	2	1	no	—
307	#123	—	2	4	no	—
308	#123	—	2	4	no	—
309	C₂²⋊Q₈	—	2	1	no	—
310	C₂²⋊Q₈	C₂×C₄×C₁₄₉	1	4	yes	—
311	C₂²⋊Q₈	C₂³×C₁₄₉	1	2	yes	—
312	#121	—	2	2	no	—
313	#121	—	2	2	no	—
314	#121	—	2	1	no	—
315	#121	—	2	4	no	—
316	#121	C₂×C₄×C₁₄₉	1	4	yes	—
317	#121	C₂³×C₁₄₉	1	2	yes	—
318	#120	—	2	4	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	C₂×C₄×C₁₄₉	1	2	yes	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	4	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	1	no	—
326	C₄×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
327	C₄×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
328	C₄×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
329	C₄×D₄	D₄×C₁₄₉	1	2	yes	—
330	C₄×D₄	D₄×C₁₄₉	1	2	yes	—
331	#117	—	2	1	no	—
332	#117	—	2	2	no	—
333	#117	C₂×C₄×C₁₄₉	1	4	yes	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	D₄×C₁₄₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	D₄×C₁₄₉	1	2	yes	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
344	C₄⋊C₈	—	2	1	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₂²⋊C₈	—	2	4	no	—
347	C₂²⋊C₈	C₂³×C₁₄₉	1	2	yes	—
348	C₂²⋊C₈	C₂³×C₁₄₉	1	2	yes	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	#95	—	2	2	no	—
352	#95	—	2	1	no	—
353	#95	C₂³×C₁₄₉	1	1	yes	characteristic
354	#95	C₂³×C₁₄₉	1	2	yes	—
355	#95	C₂³×C₁₄₉	1	1	yes	characteristic
356	C₂⁴	C₂×D₄×C₁₄₉	1	2	yes	—
357	#41	—	4	2	no	—
358	#41	—	4	2	no	—
359	#41	—	8	4	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	C₂²×C₄×C₁₄₉	1	2	yes	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
371	C₂×D₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
372	C₂×D₄	C₂²×C₄×C₁₄₉	1	2	yes	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	8	2	no	—
379	C₂²×C₄	C₂²×C₄×C₁₄₉	1	4	yes	—
380	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₄₉	1	4	yes	—
383	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	8	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
398	C₄⋊C₄	C₂²⋊C₄×C₁₄₉	1	2	yes	—
399	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
400	C₄⋊C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	8	2	no	—
409	C₂²⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
410	C₂²⋊C₄	C₂²⋊C₄×C₁₄₉	1	4	yes	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	4	2	no	—
414	C₄²	—	8	2	no	—
415	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
416	C₄²	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
417	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₁₄₉	1	1	yes	characteristic
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
425	C₂³	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	8	1	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	8	1	no	—
436	D₄	—	8	4	no	—
437	D₄	—	8	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	8	4	no	—
457	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	4	yes	—
458	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
459	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
460	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
461	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
462	C₂×C₄	#135×C₁₄₉	1	2	yes	—
463	C₂×C₄	#135×C₁₄₉	1	2	yes	—
464	C₂×C₄	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
479	C₂²	C₂×#135×C₁₄₉	1	1	yes	characteristic
480	C₂²	C₂×#135×C₁₄₉	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	4	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	2	no	—
492	C₄	#416×C₁₄₉	1	2	yes	—
493	C₄	#416×C₁₄₉	1	2	yes	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	4	4	no	—
497	C₂	—	8	2	no	—
498	C₂	#2883×C₁₄₉	1	1	yes	characteristic
499	C₂	C₂×#416×C₁₄₉	1	1	yes	characteristic
500	C₂	#2901×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
prime radical	#3506×C₁₄₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×C₄×D₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2972×C₁₄₉	C₂	semidirect
3. #2357×C₁₄₉	C₂	semidirect
4. #1518×C₁₄₉	C₂	semidirect
5. #1517×C₁₄₉	C₂	semidirect
6. #1516×C₁₄₉	C₂	semidirect
7. #1503×C₁₄₉	C₂	semidirect
8. #1502×C₁₄₉	C₂	semidirect
9. #1501×C₁₄₉	C₂	semidirect
11. #556×C₁₄₉	C₄	semidirect
12. #555×C₁₄₉	C₄	semidirect
14. #550×C₁₄₉	C₄	semidirect
15. #547×C₁₄₉	C₄	semidirect
250. #17617	C₁₄₉	direct (N × H)
251. C₁₄₉	#17617	direct (N × H)
253. #2972	C₂×C₁₄₉	semidirect
254. #2357	C₂×C₁₄₉	semidirect
255. #1518	C₂×C₁₄₉	semidirect
256. #1517	C₂×C₁₄₉	semidirect
257. #1516	C₂×C₁₄₉	semidirect
258. #1503	C₂×C₁₄₉	semidirect
259. #1502	C₂×C₁₄₉	semidirect
260. #1501	C₂×C₁₄₉	semidirect
262. #556	C₄×C₁₄₉	semidirect
263. #555	C₄×C₁₄₉	semidirect
265. #550	C₄×C₁₄₉	semidirect
266. #547	C₄×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#3506×C₁₄₉	2
#2972×C₁₄₉	2
#2357×C₁₄₉	2
#1518×C₁₄₉	2
#1517×C₁₄₉	2
#1516×C₁₄₉	2
#1503×C₁₄₉	2
#1502×C₁₄₉	2
#1501×C₁₄₉	2
#17617	149

Subgroups — C149×#17617 #49196566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17617 #49196566