Subgroups — C₁₄₉×#17381 #49196330

Order 38144.

1446 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂²⋊C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1472×C₁₄₉	C₂	1	2	yes	maximal, complemented
5	#1471×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	#1468×C₁₄₉	C₂	1	4	yes	maximal, complemented
7	#1459×C₁₄₉	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₄₉	C₄	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₄₉	—	2	1	no	—
11	C₂³×C₈×C₁₄₉	—	2	1	no	—
12	#525×C₁₄₉	—	2	1	no	—
13	#525×C₁₄₉	—	2	1	no	—
14	#525×C₁₄₉	—	2	1	no	—
15	#525×C₁₄₉	—	2	1	no	—
16	#525×C₁₄₉	—	2	1	no	—
17	#525×C₁₄₉	—	2	1	no	—
18	#525×C₁₄₉	—	2	1	no	—
19	#525×C₁₄₉	—	2	1	no	—
20	C₂×#123×C₁₄₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₄₉	C₄	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₁₄₉	C₄	1	1	yes	characteristic
24	C₂×#121×C₁₄₉	C₂²	1	1	yes	characteristic
25	C₂×#120×C₁₄₉	C₄	1	2	yes	—
26	C₂×C₄×D₄×C₁₄₉	C₄	1	2	yes	—
27	C₂×C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
28	C₂×#117×C₁₄₉	C₄	1	1	yes	characteristic
29	#407×C₁₄₉	—	2	1	no	—
30	#407×C₁₄₉	—	2	1	no	—
31	#407×C₁₄₉	C₂²	1	2	yes	—
32	#407×C₁₄₉	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
34	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
35	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
36	C₂×C₂²⋊C₈×C₁₄₉	—	2	1	no	—
37	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	2	yes	—
38	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	2	yes	—
39	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	2	yes	—
40	C₂×C₂²⋊C₈×C₁₄₉	C₂²	1	2	yes	—
41	#324×C₁₄₉	C₂²	1	8	yes	complemented
42	#323×C₁₄₉	C₂²	1	8	yes	complemented
43	C₂⁵×C₁₄₉	C₂×C₄	1	1	yes	characteristic
44	C₂×#41×C₁₄₉	—	2	1	no	—
45	C₂×#41×C₁₄₉	—	2	1	no	—
46	C₂×#41×C₁₄₉	—	2	1	no	—
47	C₂×#41×C₁₄₉	—	2	1	no	—
48	C₂×#41×C₁₄₉	—	4	4	no	—
49	C₂²×Q₈×C₁₄₉	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
51	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
52	C₂²×D₄×C₁₄₉	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₄₉	—	4	4	no	—
55	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
57	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₄₉	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₁₄₉	—	2	2	no	—
71	C₂×M₁₆×C₁₄₉	—	2	2	no	—
72	C₂×M₁₆×C₁₄₉	—	4	4	no	—
73	C₂²×C₈×C₁₄₉	—	2	2	no	—
74	C₂²×C₈×C₁₄₉	—	2	2	no	—
75	C₂²×C₈×C₁₄₉	—	2	2	no	—
76	C₂²×C₈×C₁₄₉	—	2	2	no	—
77	C₂²×C₈×C₁₄₉	—	4	4	no	—
78	#123×C₁₄₉	—	2	2	no	—
79	#123×C₁₄₉	—	2	2	no	—
80	#123×C₁₄₉	—	2	2	no	—
81	#123×C₁₄₉	—	2	2	no	—
82	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
83	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
84	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
85	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
86	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
87	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
88	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
89	C₂²⋊Q₈×C₁₄₉	—	2	1	no	—
90	#121×C₁₄₉	—	2	1	no	—
91	#121×C₁₄₉	—	2	1	no	—
92	#121×C₁₄₉	—	2	1	no	—
93	#121×C₁₄₉	—	2	1	no	—
94	#121×C₁₄₉	—	2	1	no	—
95	#121×C₁₄₉	—	2	1	no	—
96	#121×C₁₄₉	—	2	1	no	—
97	#121×C₁₄₉	—	2	1	no	—
98	#120×C₁₄₉	—	2	2	no	—
99	#120×C₁₄₉	—	2	2	no	—
100	#120×C₁₄₉	—	2	2	no	—
101	#120×C₁₄₉	—	2	2	no	—
102	C₄×D₄×C₁₄₉	—	2	2	no	—
103	C₄×D₄×C₁₄₉	—	2	2	no	—
104	C₄×D₄×C₁₄₉	—	2	2	no	—
105	C₄×D₄×C₁₄₉	—	2	2	no	—
106	C₄×D₄×C₁₄₉	—	2	2	no	—
107	C₄×D₄×C₁₄₉	—	2	2	no	—
108	C₄×D₄×C₁₄₉	—	2	2	no	—
109	C₄×D₄×C₁₄₉	—	2	2	no	—
110	#117×C₁₄₉	—	2	1	no	—
111	#117×C₁₄₉	—	2	1	no	—
112	#117×C₁₄₉	—	2	1	no	—
113	#117×C₁₄₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
120	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
121	C₂×C₂²⋊C₄×C₁₄₉	C₂×C₄	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₄₉	C₂×C₄	1	2	yes	—
124	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
125	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
126	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
127	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
128	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
129	C₂²⋊C₈×C₁₄₉	—	2	2	no	—
130	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
131	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
132	C₂⁴×C₁₄₉	—	2	4	no	—
133	C₂⁴×C₁₄₉	—	4	2	no	—
134	C₂⁴×C₁₄₉	—	4	2	no	—
135	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
136	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
137	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
138	C₂⁴×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
139	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
140	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
141	C₂⁴×C₁₄₉	C₂²×C₄	1	2	yes	—
142	C₂⁴×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
143	#41×C₁₄₉	—	4	4	no	—
144	#41×C₁₄₉	—	4	4	no	—
145	#41×C₁₄₉	—	4	4	no	—
146	#41×C₁₄₉	—	4	4	no	—
147	C₂×Q₈×C₁₄₉	—	2	1	no	—
148	C₂×Q₈×C₁₄₉	—	2	1	no	—
149	C₂×Q₈×C₁₄₉	—	4	2	no	—
150	C₂×D₄×C₁₄₉	—	2	2	no	—
151	C₂×D₄×C₁₄₉	—	2	2	no	—
152	C₂×D₄×C₁₄₉	—	2	2	no	—
153	C₂×D₄×C₁₄₉	—	2	2	no	—
154	C₂×D₄×C₁₄₉	—	2	2	no	—
155	C₂×D₄×C₁₄₉	—	2	2	no	—
156	C₂×D₄×C₁₄₉	—	2	8	no	—
157	C₂×D₄×C₁₄₉	—	2	1	no	—
158	C₂×D₄×C₁₄₉	—	2	1	no	—
159	C₂×D₄×C₁₄₉	—	4	2	no	—
160	C₂×D₄×C₁₄₉	—	4	4	no	—
161	C₂×D₄×C₁₄₉	—	4	4	no	—
162	C₂²×C₄×C₁₄₉	—	2	4	no	—
163	C₂²×C₄×C₁₄₉	—	2	4	no	—
164	C₂²×C₄×C₁₄₉	—	2	4	no	—
165	C₂²×C₄×C₁₄₉	—	2	2	no	—
166	C₂²×C₄×C₁₄₉	—	2	2	no	—
167	C₂²×C₄×C₁₄₉	—	4	2	no	—
168	C₂²×C₄×C₁₄₉	—	4	2	no	—
169	C₂²×C₄×C₁₄₉	—	4	2	no	—
170	C₂²×C₄×C₁₄₉	—	4	2	no	—
171	C₂²×C₄×C₁₄₉	—	4	2	no	—
172	C₂²×C₄×C₁₄₉	—	4	2	no	—
173	C₂²×C₄×C₁₄₉	—	4	2	no	—
174	C₂²×C₄×C₁₄₉	—	4	2	no	—
175	C₂²×C₄×C₁₄₉	—	4	2	no	—
176	C₂²×C₄×C₁₄₉	—	4	2	no	—
177	C₂²×C₄×C₁₄₉	—	4	2	no	—
178	C₂²×C₄×C₁₄₉	—	4	4	no	—
179	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₄₉	C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
192	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
195	C₂²×C₄×C₁₄₉	C₂²×C₄	1	2	yes	—
196	C₂²×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
210	M₁₆×C₁₄₉	—	4	4	no	—
211	M₁₆×C₁₄₉	—	4	4	no	—
212	C₂×C₈×C₁₄₉	—	2	4	no	—
213	C₂×C₈×C₁₄₉	—	2	4	no	—
214	C₂×C₈×C₁₄₉	—	4	4	no	—
215	C₂×C₈×C₁₄₉	—	4	4	no	—
216	C₂×C₈×C₁₄₉	—	4	4	no	—
217	C₂×C₈×C₁₄₉	—	4	4	no	—
218	C₄⋊C₄×C₁₄₉	—	2	1	no	—
219	C₄⋊C₄×C₁₄₉	—	2	1	no	—
220	C₄⋊C₄×C₁₄₉	—	2	1	no	—
221	C₄⋊C₄×C₁₄₉	—	2	1	no	—
222	C₄⋊C₄×C₁₄₉	—	2	2	no	—
223	C₄⋊C₄×C₁₄₉	—	2	2	no	—
224	C₄⋊C₄×C₁₄₉	—	2	2	no	—
225	C₄⋊C₄×C₁₄₉	—	2	2	no	—
226	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
227	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
228	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
229	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
230	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
231	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
232	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
233	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
234	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
235	C₂²⋊C₄×C₁₄₉	—	2	2	no	—
236	C₄²×C₁₄₉	—	2	2	no	—
237	C₄²×C₁₄₉	—	2	2	no	—
238	C₂³×C₁₄₉	—	2	2	no	—
239	C₂³×C₁₄₉	—	2	2	no	—
240	C₂³×C₁₄₉	—	2	2	no	—
241	C₂³×C₁₄₉	—	2	2	no	—
242	C₂³×C₁₄₉	—	2	2	no	—
243	C₂³×C₁₄₉	—	2	2	no	—
244	C₂³×C₁₄₉	—	2	2	no	—
245	C₂³×C₁₄₉	—	2	2	no	—
246	C₂³×C₁₄₉	—	2	2	no	—
247	C₂³×C₁₄₉	—	2	2	no	—
248	C₂³×C₁₄₉	—	2	2	no	—
249	C₂³×C₁₄₉	—	2	2	no	—
250	C₂³×C₁₄₉	—	2	2	no	—
251	C₂³×C₁₄₉	—	2	4	no	—
252	C₂³×C₁₄₉	—	4	1	no	—
253	C₂³×C₁₄₉	—	4	1	no	—
254	C₂³×C₁₄₉	—	4	1	no	—
255	C₂³×C₁₄₉	—	4	1	no	—
256	C₂³×C₁₄₉	—	4	1	no	—
257	C₂³×C₁₄₉	—	4	1	no	—
258	C₂³×C₁₄₉	—	4	1	no	—
259	C₂³×C₁₄₉	—	4	1	no	—
260	C₂³×C₁₄₉	—	4	16	no	—
261	C₂³×C₁₄₉	—	4	2	no	—
262	C₂³×C₁₄₉	—	4	2	no	—
263	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂³×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂³×C₁₄₉	#131	1	4	yes	—
270	C₂³×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
271	Q₈×C₁₄₉	—	4	2	no	—
272	Q₈×C₁₄₉	—	4	2	no	—
273	D₄×C₁₄₉	—	4	2	no	—
274	D₄×C₁₄₉	—	4	4	no	—
275	D₄×C₁₄₉	—	4	4	no	—
276	D₄×C₁₄₉	—	4	4	no	—
277	D₄×C₁₄₉	—	4	4	no	—
278	D₄×C₁₄₉	—	4	4	no	—
279	D₄×C₁₄₉	—	4	4	no	—
280	D₄×C₁₄₉	—	4	2	no	—
281	C₂×C₄×C₁₄₉	—	2	2	no	—
282	C₂×C₄×C₁₄₉	—	2	2	no	—
283	C₂×C₄×C₁₄₉	—	2	2	no	—
284	C₂×C₄×C₁₄₉	—	2	2	no	—
285	C₂×C₄×C₁₄₉	—	2	2	no	—
286	C₂×C₄×C₁₄₉	—	2	2	no	—
287	C₂×C₄×C₁₄₉	—	2	2	no	—
288	C₂×C₄×C₁₄₉	—	2	2	no	—
289	C₂×C₄×C₁₄₉	—	2	2	no	—
290	C₂×C₄×C₁₄₉	—	2	2	no	—
291	C₂×C₄×C₁₄₉	—	2	2	no	—
292	C₂×C₄×C₁₄₉	—	2	2	no	—
293	C₂×C₄×C₁₄₉	—	2	2	no	—
294	C₂×C₄×C₁₄₉	—	2	2	no	—
295	C₂×C₄×C₁₄₉	—	2	2	no	—
296	C₂×C₄×C₁₄₉	—	2	2	no	—
297	C₂×C₄×C₁₄₉	—	2	2	no	—
298	C₂×C₄×C₁₄₉	—	2	2	no	—
299	C₂×C₄×C₁₄₉	—	2	4	no	—
300	C₂×C₄×C₁₄₉	—	4	1	no	—
301	C₂×C₄×C₁₄₉	—	4	1	no	—
302	C₂×C₄×C₁₄₉	—	4	1	no	—
303	C₂×C₄×C₁₄₉	—	4	1	no	—
304	C₂×C₄×C₁₄₉	—	4	1	no	—
305	C₂×C₄×C₁₄₉	—	4	1	no	—
306	C₂×C₄×C₁₄₉	—	4	1	no	—
307	C₂×C₄×C₁₄₉	—	4	1	no	—
308	C₂×C₄×C₁₄₉	—	4	1	no	—
309	C₂×C₄×C₁₄₉	—	4	1	no	—
310	C₂×C₄×C₁₄₉	—	4	1	no	—
311	C₂×C₄×C₁₄₉	—	4	1	no	—
312	C₂×C₄×C₁₄₉	—	4	4	no	—
313	C₂×C₄×C₁₄₉	—	4	4	no	—
314	C₂×C₄×C₁₄₉	—	4	2	no	—
315	C₂×C₄×C₁₄₉	—	4	2	no	—
316	C₂×C₄×C₁₄₉	#99	1	4	yes	—
317	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
319	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
321	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
322	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
325	C₈×C₁₄₉	—	4	4	no	—
326	C₈×C₁₄₉	—	4	4	no	—
327	C₂²×C₁₄₉	—	2	8	no	—
328	C₂²×C₁₄₉	—	2	1	no	—
329	C₂²×C₁₄₉	—	2	1	no	—
330	C₂²×C₁₄₉	—	2	1	no	—
331	C₂²×C₁₄₉	—	2	1	no	—
332	C₂²×C₁₄₉	—	2	1	no	—
333	C₂²×C₁₄₉	—	2	1	no	—
334	C₂²×C₁₄₉	—	2	1	no	—
335	C₂²×C₁₄₉	—	2	1	no	—
336	C₂²×C₁₄₉	—	2	1	no	—
337	C₂²×C₁₄₉	—	2	1	no	—
338	C₂²×C₁₄₉	—	2	1	no	—
339	C₂²×C₁₄₉	—	2	1	no	—
340	C₂²×C₁₄₉	—	2	1	no	—
341	C₂²×C₁₄₉	—	2	1	no	—
342	C₂²×C₁₄₉	—	2	1	no	—
343	C₂²×C₁₄₉	—	2	1	no	—
344	C₂²×C₁₄₉	—	4	4	no	—
345	C₂²×C₁₄₉	—	4	4	no	—
346	C₂²×C₁₄₉	—	4	4	no	—
347	C₂²×C₁₄₉	—	4	4	no	—
348	C₂²×C₁₄₉	—	4	4	no	—
349	C₂²×C₁₄₉	—	4	4	no	—
350	C₂²×C₁₄₉	—	4	2	no	—
351	C₂²×C₁₄₉	—	4	2	no	—
352	C₂²×C₁₄₉	—	4	2	no	—
353	C₂²×C₁₄₉	—	8	4	no	—
354	C₂²×C₁₄₉	#408	1	2	yes	—
355	C₂²×C₁₄₉	#408	1	2	yes	—
356	C₂²×C₁₄₉	C₂×#99	1	2	yes	—
357	C₂²×C₁₄₉	#413	1	2	yes	—
358	C₂²×C₁₄₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
359	C₂²×C₁₄₉	C₂×#131	1	2	yes	—
360	C₄×C₁₄₉	—	2	1	no	—
361	C₄×C₁₄₉	—	2	1	no	—
362	C₄×C₁₄₉	—	2	1	no	—
363	C₄×C₁₄₉	—	2	1	no	—
364	C₄×C₁₄₉	—	2	1	no	—
365	C₄×C₁₄₉	—	2	1	no	—
366	C₄×C₁₄₉	—	4	2	no	—
367	C₄×C₁₄₉	—	4	2	no	—
368	C₄×C₁₄₉	—	4	2	no	—
369	C₄×C₁₄₉	C₂×#99	1	2	yes	—
370	C₄×C₁₄₉	C₂×#99	1	2	yes	—
371	C₂×C₁₄₉	—	2	2	no	—
372	C₂×C₁₄₉	—	2	2	no	—
373	C₂×C₁₄₉	—	2	2	no	—
374	C₂×C₁₄₉	—	2	2	no	—
375	C₂×C₁₄₉	—	2	2	no	—
376	C₂×C₁₄₉	—	4	1	no	—
377	C₂×C₁₄₉	—	4	1	no	—
378	C₂×C₁₄₉	—	8	2	no	—
379	C₂×C₁₄₉	C₂×#408	1	1	yes	characteristic
380	C₂×C₁₄₉	C₂²×#99	1	1	yes	characteristic
381	C₂×C₁₄₉	C₂×#413	1	1	yes	characteristic
382	#17381	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₁₄₉	#17381	1	1	yes	characteristic, direct product factor, Sylow
384	C₂×#525	C₂×C₁₄₉	1	1	yes	characteristic
385	C₂×#407	C₂×C₁₄₉	1	1	yes	characteristic, complemented
386	C₂²×C₂²⋊C₈	C₂×C₁₄₉	1	1	yes	characteristic, complemented
387	#1472	C₂×C₁₄₉	1	2	yes	complemented
388	#1471	C₂×C₁₄₉	1	2	yes	complemented
389	#1468	C₂×C₁₄₉	1	4	yes	complemented
390	#1459	C₂×C₁₄₉	1	4	yes	complemented
391	C₂²×#41	C₄×C₁₄₉	1	1	yes	characteristic
392	C₂⁴×C₄	C₂²×C₁₄₉	1	1	yes	characteristic
393	C₂²×M₁₆	—	2	1	no	—
394	C₂³×C₈	—	2	1	no	—
395	#525	—	2	1	no	—
396	#525	—	2	1	no	—
397	#525	—	2	1	no	—
398	#525	—	2	1	no	—
399	#525	—	2	1	no	—
400	#525	—	2	1	no	—
401	#525	—	2	1	no	—
402	#525	—	2	1	no	—
403	C₂×#123	C₂²×C₁₄₉	1	2	yes	—
404	C₂×C₂²⋊Q₈	C₄×C₁₄₉	1	1	yes	characteristic
405	C₂×C₂²⋊Q₈	C₂²×C₁₄₉	1	1	yes	characteristic
406	C₂×#121	C₄×C₁₄₉	1	1	yes	characteristic
407	C₂×#121	C₂²×C₁₄₉	1	1	yes	characteristic
408	C₂×#120	C₄×C₁₄₉	1	2	yes	—
409	C₂×C₄×D₄	C₄×C₁₄₉	1	2	yes	—
410	C₂×C₄×D₄	C₂²×C₁₄₉	1	2	yes	—
411	C₂×#117	C₄×C₁₄₉	1	1	yes	characteristic
412	#407	—	2	1	no	—
413	#407	—	2	1	no	—
414	#407	C₂²×C₁₄₉	1	2	yes	—
415	#407	C₂²×C₁₄₉	1	2	yes	—
416	C₂×C₂²⋊C₈	—	2	1	no	—
417	C₂×C₂²⋊C₈	—	2	1	no	—
418	C₂×C₂²⋊C₈	—	2	1	no	—
419	C₂×C₂²⋊C₈	—	2	1	no	—
420	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	2	yes	—
421	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	2	yes	—
422	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	2	yes	—
423	C₂×C₂²⋊C₈	C₂²×C₁₄₉	1	2	yes	—
424	#324	C₂²×C₁₄₉	1	8	yes	complemented
425	#323	C₂²×C₁₄₉	1	8	yes	complemented
426	C₂⁵	C₂×C₄×C₁₄₉	1	1	yes	characteristic
427	C₂×#41	—	2	1	no	—
428	C₂×#41	—	2	1	no	—
429	C₂×#41	—	2	1	no	—
430	C₂×#41	—	2	1	no	—
431	C₂×#41	—	4	4	no	—
432	C₂²×Q₈	C₂×C₄×C₁₄₉	1	1	yes	characteristic
433	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
434	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
435	C₂²×D₄	C₂×C₄×C₁₄₉	1	2	yes	—
436	C₂²×D₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
437	C₂³×C₄	—	4	4	no	—
438	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
439	C₂³×C₄	C₂×C₄×C₁₄₉	1	2	yes	—
440	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
441	C₂³×C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
442	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
443	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
444	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
445	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
446	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
447	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
448	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
449	C₂³×C₄	D₄×C₁₄₉	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₁₄₉	1	1	yes	characteristic
453	C₂×M₁₆	—	2	2	no	—
454	C₂×M₁₆	—	2	2	no	—
455	C₂×M₁₆	—	4	4	no	—
456	C₂²×C₈	—	2	2	no	—
457	C₂²×C₈	—	2	2	no	—
458	C₂²×C₈	—	2	2	no	—
459	C₂²×C₈	—	2	2	no	—
460	C₂²×C₈	—	4	4	no	—
461	#123	—	2	2	no	—
462	#123	—	2	2	no	—
463	#123	—	2	2	no	—
464	#123	—	2	2	no	—
465	C₂²⋊Q₈	—	2	1	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	—	2	1	no	—
468	C₂²⋊Q₈	—	2	1	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	#121	—	2	1	no	—
474	#121	—	2	1	no	—
475	#121	—	2	1	no	—
476	#121	—	2	1	no	—
477	#121	—	2	1	no	—
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#120	—	2	2	no	—
482	#120	—	2	2	no	—
483	#120	—	2	2	no	—
484	#120	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	2	no	—
493	#117	—	2	1	no	—
494	#117	—	2	1	no	—
495	#117	—	2	1	no	—
496	#117	—	2	1	no	—
497	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₄₉	1	2	yes	—
501	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂×C₄×C₁₄₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	2	yes	—
506	C₂×C₄²	C₂×C₄×C₁₄₉	1	2	yes	—
507	C₂²⋊C₈	—	2	2	no	—
508	C₂²⋊C₈	—	2	2	no	—
509	C₂²⋊C₈	—	2	2	no	—
510	C₂²⋊C₈	—	2	2	no	—
511	C₂²⋊C₈	—	2	2	no	—
512	C₂²⋊C₈	—	2	2	no	—
513	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
514	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
515	C₂⁴	—	2	4	no	—
516	C₂⁴	—	4	2	no	—
517	C₂⁴	—	4	2	no	—
518	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
519	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
520	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
521	C₂⁴	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
522	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
523	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
524	C₂⁴	C₂²×C₄×C₁₄₉	1	2	yes	—
525	C₂⁴	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
526	#41	—	4	4	no	—
527	#41	—	4	4	no	—
528	#41	—	4	4	no	—
529	#41	—	4	4	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	4	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	8	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	4	2	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	4	2	no	—
551	C₂²×C₄	—	4	2	no	—
552	C₂²×C₄	—	4	2	no	—
553	C₂²×C₄	—	4	2	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	2	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	4	no	—
562	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
563	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
564	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
565	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
566	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
567	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
568	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
569	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
570	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
571	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
572	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
573	C₂²×C₄	C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
574	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
575	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
576	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
577	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
578	C₂²×C₄	C₂²×C₄×C₁₄₉	1	2	yes	—
579	C₂²×C₄	C₂²×C₄×C₁₄₉	1	1	yes	characteristic
580	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
581	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
593	M₁₆	—	4	4	no	—
594	M₁₆	—	4	4	no	—
595	C₂×C₈	—	2	4	no	—
596	C₂×C₈	—	2	4	no	—
597	C₂×C₈	—	4	4	no	—
598	C₂×C₈	—	4	4	no	—
599	C₂×C₈	—	4	4	no	—
600	C₂×C₈	—	4	4	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₄²	—	2	2	no	—
620	C₄²	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	16	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
647	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
648	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
649	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
650	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
651	C₂³	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
652	C₂³	#131×C₁₄₉	1	4	yes	—
653	C₂³	C₂³×C₄×C₁₄₉	1	1	yes	characteristic
654	Q₈	—	4	2	no	—
655	Q₈	—	4	2	no	—
656	D₄	—	4	2	no	—
657	D₄	—	4	4	no	—
658	D₄	—	4	4	no	—
659	D₄	—	4	4	no	—
660	D₄	—	4	4	no	—
661	D₄	—	4	4	no	—
662	D₄	—	4	4	no	—
663	D₄	—	4	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	4	2	no	—
699	C₂×C₄	#99×C₁₄₉	1	4	yes	—
700	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
701	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
702	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
703	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
704	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
705	C₂×C₄	C₂×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
708	C₈	—	4	4	no	—
709	C₈	—	4	4	no	—
710	C₂²	—	2	8	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	8	4	no	—
737	C₂²	#408×C₁₄₉	1	2	yes	—
738	C₂²	#408×C₁₄₉	1	2	yes	—
739	C₂²	C₂×#99×C₁₄₉	1	2	yes	—
740	C₂²	#413×C₁₄₉	1	2	yes	—
741	C₂²	C₂²×C₂²⋊C₄×C₁₄₉	1	1	yes	characteristic
742	C₂²	C₂×#131×C₁₄₉	1	2	yes	—
743	C₄	—	2	1	no	—
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	1	no	—
749	C₄	—	4	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	C₂×#99×C₁₄₉	1	2	yes	—
753	C₄	C₂×#99×C₁₄₉	1	2	yes	—
754	C₂	—	2	2	no	—
755	C₂	—	2	2	no	—
756	C₂	—	2	2	no	—
757	C₂	—	2	2	no	—
758	C₂	—	2	2	no	—
759	C₂	—	4	1	no	—
760	C₂	—	4	1	no	—
761	C₂	—	8	2	no	—
762	C₂	C₂×#408×C₁₄₉	1	1	yes	characteristic
763	C₂	C₂²×#99×C₁₄₉	1	1	yes	characteristic
764	C₂	C₂×#413×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₄₉	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₄₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
socle	C₂²×C₁₄₉	C₂²×C₂²⋊C₄
prime radical	C₂×#525×C₁₄₉	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₄₉ ◁ C₂⁴×C₄×C₁₄₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#407×C₁₄₉	C₂	semidirect
3. C₂²×C₂²⋊C₈×C₁₄₉	C₂	semidirect
4. #1472×C₁₄₉	C₂	semidirect
5. #1471×C₁₄₉	C₂	semidirect
6. #1468×C₁₄₉	C₂	semidirect
7. #1459×C₁₄₉	C₂	semidirect
41. #324×C₁₄₉	C₂²	semidirect
42. #323×C₁₄₉	C₂²	semidirect
382. #17381	C₁₄₉	direct (N × H)
383. C₁₄₉	#17381	direct (N × H)
385. C₂×#407	C₂×C₁₄₉	semidirect
386. C₂²×C₂²⋊C₈	C₂×C₁₄₉	semidirect
387. #1472	C₂×C₁₄₉	semidirect
388. #1471	C₂×C₁₄₉	semidirect
389. #1468	C₂×C₁₄₉	semidirect
390. #1459	C₂×C₁₄₉	semidirect
424. #324	C₂²×C₁₄₉	semidirect
425. #323	C₂²×C₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₁₄₉	2
C₂×#407×C₁₄₉	2
C₂²×C₂²⋊C₈×C₁₄₉	2
#1472×C₁₄₉	2
#1471×C₁₄₉	2
#1468×C₁₄₉	2
#1459×C₁₄₉	2
#17381	149

Subgroups — C149×#17381 #49196330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#17381 #49196330