Subgroups — #34058657

Order 19072.

1014 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750351	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750334	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750333	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750327	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750325	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750317	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750316	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750314	C₂	1	2	yes	maximal, complemented
9	#23750312	C₂	1	2	yes	maximal, complemented
10	#23750308	C₂	1	2	yes	maximal, complemented
11	#23750275	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750273	C₂	1	2	yes	maximal, complemented
13	#23750232	C₂	1	2	yes	maximal, complemented
14	#23750217	C₂	1	2	yes	maximal, complemented
15	#23750216	C₂	1	2	yes	maximal, complemented
16	#23750181	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750154	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750154	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#18011903	C₂	1	1	yes	maximal, characteristic, complemented
20	#125×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750104	C₂	1	2	yes	maximal, complemented
22	C₄×#14558736	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558736	C₂²	1	1	yes	characteristic
25	C₂×#14558735	C₂²	1	2	yes	—
26	#18011910	C₂²	1	1	yes	characteristic
27	#18011910	C₂²	1	1	yes	characteristic
28	#18011910	C₂²	1	2	yes	—
29	#18011906	C₂²	1	2	yes	—
30	#18011905	C₂²	1	2	yes	—
31	#18011904	C₂²	1	2	yes	—
32	#18011904	C₂²	1	2	yes	—
33	#18011904	C₂²	1	2	yes	—
34	#18011904	C₂²	1	2	yes	—
35	#18011903	C₂²	1	1	yes	characteristic
36	#18011903	C₂²	1	1	yes	characteristic
37	#18011903	C₂²	1	2	yes	—
38	#18011903	C₂²	1	2	yes	—
39	#18011903	C₂²	1	1	yes	characteristic
40	#18011903	C₂²	1	1	yes	characteristic
41	#18011903	C₂²	1	2	yes	—
42	#18011902	C₂²	1	1	yes	characteristic
43	#18011902	C₂²	1	1	yes	characteristic
44	#18011902	C₂²	1	2	yes	—
45	#18011902	C₂²	1	2	yes	—
46	#18011901	C₂²	1	2	yes	—
47	#18011901	C₂²	1	2	yes	—
48	#18011901	C₂²	1	2	yes	—
49	#18011901	C₂²	1	2	yes	—
50	#18011896	C₂²	1	2	yes	—
51	#18011895	C₂²	1	2	yes	—
52	#18011895	C₂²	1	2	yes	—
53	#18011894	C₂²	1	2	yes	—
54	#18011893	C₂²	1	2	yes	—
55	#18011893	C₂²	1	2	yes	—
56	#18011893	C₂²	1	2	yes	—
57	#18011892	C₂²	1	2	yes	—
58	#18011891	C₂²	1	2	yes	—
59	#18011890	C₂²	1	2	yes	—
60	#18011889	C₂²	1	2	yes	—
61	#18011889	C₂²	1	2	yes	—
62	#18011888	C₂²	1	2	yes	—
63	#18011888	C₂²	1	2	yes	—
64	#18011888	C₂²	1	2	yes	—
65	#18011888	C₂²	1	2	yes	—
66	#18011887	C₂²	1	1	yes	characteristic
67	#18011887	C₂²	1	1	yes	characteristic
68	#18011884	C₂²	1	2	yes	—
69	#18011883	C₂²	1	2	yes	—
70	#18011882	C₂²	1	1	yes	characteristic
71	#18011882	C₂²	1	1	yes	characteristic
72	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
73	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
74	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
75	C₄×Dic₂₉₈	C₂²	1	2	yes	—
76	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
77	#18011876	C₂²	1	2	yes	—
78	#18011876	C₂²	1	2	yes	—
79	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
80	C₄×D₅₉₆	C₂²	1	1	yes	characteristic
81	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
82	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
83	D₄×Dic₁₄₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
87	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
89	#18011871	C₂²	1	2	yes	—
90	#18011871	C₂²	1	2	yes	—
91	#18011871	C₂²	1	2	yes	—
92	#18011870	C₂²	1	1	yes	characteristic
93	#18011869	C₂²	1	1	yes	characteristic
94	#18011869	C₂²	1	1	yes	characteristic
95	#18011868	C₂²	1	1	yes	characteristic
96	#18011868	C₂²	1	1	yes	characteristic
97	#18011868	C₂²	1	2	yes	—
98	#18011867	C₂²	1	2	yes	—
99	#18011867	C₂²	1	2	yes	—
100	#18011867	C₂²	1	2	yes	—
101	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
102	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
103	C₂×#14558715	C₂²	1	2	yes	—
104	C₂×#14558715	C₂²	1	2	yes	—
105	C₂×#14558715	C₂²	1	2	yes	—
106	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
107	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
108	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
110	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
111	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
112	#126×C₁₄₉	C₂²	1	2	yes	—
113	#125×C₁₄₉	C₂²	1	1	yes	characteristic
114	#124×C₁₄₉	C₂²	1	1	yes	characteristic
115	#123×C₁₄₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
117	#121×C₁₄₉	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
120	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
121	#117×C₁₄₉	C₂²	1	2	yes	—
122	C₂×C₄²×C₁₄₉	C₂²	1	1	yes	characteristic
123	#14558736	—	2	4	no	—
124	#14558735	—	2	8	no	—
125	C₂×Dic₂₉₈	C₂³	1	2	yes	—
126	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₉₈	C₂³	1	2	yes	—
128	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
134	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
135	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
136	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
137	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
138	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
145	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
147	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
148	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
149	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
150	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
155	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
156	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
157	#14558715	C₂³	1	1	yes	characteristic
158	#14558715	C₂³	1	2	yes	—
159	#14558715	C₂³	1	2	yes	—
160	#14558715	C₂³	1	2	yes	—
161	#14558715	C₂³	1	2	yes	—
162	#14558715	C₂³	1	2	yes	—
163	#14558715	C₂³	1	2	yes	—
164	#14558715	C₂³	1	2	yes	—
165	#14558715	C₂³	1	2	yes	—
166	#14558715	C₂³	1	2	yes	—
167	#14558715	C₂³	1	2	yes	—
168	#14558715	C₂³	1	2	yes	—
169	#14558715	C₂³	1	2	yes	—
170	#14558715	C₂³	1	2	yes	—
171	#14558715	C₂³	1	1	yes	characteristic
172	#14558715	C₂³	1	2	yes	—
173	#14558715	C₂³	1	2	yes	—
174	#14558715	C₂³	1	2	yes	—
175	#14558715	C₂³	1	1	yes	characteristic
176	#14558715	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
183	#14558713	C₂³	1	1	yes	characteristic
184	#14558713	C₂³	1	2	yes	—
185	#14558713	C₂³	1	2	yes	—
186	#14558713	C₂³	1	1	yes	characteristic
187	#14558713	C₂³	1	2	yes	—
188	#14558713	C₂³	1	1	yes	characteristic
189	#14558713	C₂³	1	2	yes	—
190	#14558713	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
193	C₄×Dic₁₄₉	C₂³	1	2	yes	—
194	C₄×Dic₁₄₉	C₂³	1	2	yes	—
195	C₄×Dic₁₄₉	C₂³	1	2	yes	—
196	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₁₄₉	C₂³	1	2	yes	—
198	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
201	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
202	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
203	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
208	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
209	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
212	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
214	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
219	C₄²×C₁₄₉	C₂³	1	2	yes	—
220	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
221	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
222	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
223	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
224	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
225	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
226	Dic₂₉₈	—	2	4	no	—
227	Dic₂₉₈	—	2	2	no	—
228	Dic₂₉₈	—	4	2	no	—
229	D₅₉₆	—	2	2	no	—
230	C₂²⋊D₁₄₉	—	2	2	no	—
231	C₂²⋊D₁₄₉	—	2	4	no	—
232	C₂²⋊D₁₄₉	—	4	2	no	—
233	C₂²⋊D₁₄₉	#41	1	4	yes	—
234	C₂×Dic₁₄₉	—	2	4	no	—
235	C₂×Dic₁₄₉	—	2	4	no	—
236	C₂×Dic₁₄₉	—	4	2	no	—
237	C₂×Dic₁₄₉	—	4	2	no	—
238	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
239	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
240	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
241	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
243	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
246	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
247	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
248	C₄×D₁₄₉	—	2	4	no	—
249	C₄×D₁₄₉	—	2	2	no	—
250	C₄×D₁₄₉	—	2	2	no	—
251	C₄×D₁₄₉	—	2	2	no	—
252	C₄×D₁₄₉	—	2	2	no	—
253	C₄×D₁₄₉	—	4	1	no	—
254	C₄×D₁₄₉	—	4	2	no	—
255	C₄×D₁₄₉	—	4	1	no	—
256	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
257	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
258	Q₈×C₁₄₉	—	2	2	no	—
259	D₄×C₁₄₉	—	2	4	no	—
260	D₄×C₁₄₉	—	2	2	no	—
261	C₂×C₄×C₁₄₉	—	2	2	no	—
262	C₂×C₄×C₁₄₉	—	2	2	no	—
263	C₂×C₄×C₁₄₉	—	4	1	no	—
264	C₂×C₄×C₁₄₉	—	4	2	no	—
265	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
268	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
269	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
270	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
273	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
274	C₂²×C₁₄₉	—	2	1	no	—
275	C₂²×C₁₄₉	—	2	1	no	—
276	C₂²×C₁₄₉	—	2	2	no	—
277	C₂²×C₁₄₉	—	2	2	no	—
278	C₂²×C₁₄₉	—	2	2	no	—
279	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
280	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
281	C₂×D₁₄₉	—	2	1	no	—
282	C₂×D₁₄₉	—	2	1	no	—
283	C₂×D₁₄₉	—	2	1	no	—
284	C₂×D₁₄₉	—	2	1	no	—
285	C₂×D₁₄₉	—	2	1	no	—
286	C₂×D₁₄₉	C₂×#41	1	2	yes	—
287	C₄×C₁₄₉	—	2	1	no	—
288	C₄×C₁₄₉	—	2	1	no	—
289	C₄×C₁₄₉	—	2	2	no	—
290	C₄×C₁₄₉	—	2	1	no	—
291	C₄×C₁₄₉	—	2	2	no	—
292	C₄×C₁₄₉	—	2	1	no	—
293	C₄×C₁₄₉	—	2	1	no	—
294	C₄×C₁₄₉	—	2	2	no	—
295	C₄×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
296	Dic₁₄₉	—	2	2	no	—
297	Dic₁₄₉	—	2	1	no	—
298	Dic₁₄₉	—	2	2	no	—
299	Dic₁₄₉	—	2	1	no	—
300	Dic₁₄₉	—	2	1	no	—
301	Dic₁₄₉	—	2	1	no	—
302	Dic₁₄₉	—	2	2	no	—
303	Dic₁₄₉	—	2	1	no	—
304	Dic₁₄₉	—	2	2	no	—
305	Dic₁₄₉	C₂×#41	1	2	yes	—
306	C₂×C₁₄₉	—	2	2	no	—
307	C₂×C₁₄₉	—	4	2	no	—
308	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
309	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	C₂×C₁₄₉	#585	1	1	yes	characteristic
311	D₁₄₉	—	2	2	no	—
312	D₁₄₉	—	4	1	no	—
313	C₁₄₉	#3515	1	1	yes	characteristic, complemented, Sylow
314	#3515	—	149	1	no	maximal, Sylow
315	#557	—	149	1	no	—
316	#554	—	149	1	no	—
317	#554	—	149	1	no	—
318	#553	—	149	1	no	—
319	#553	—	149	1	no	—
320	#552	—	149	2	no	—
321	#552	—	149	1	no	—
322	#552	—	149	1	no	—
323	#552	—	149	2	no	—
324	#552	—	149	2	no	—
325	#547	—	149	2	no	—
326	#547	—	149	1	no	—
327	#541	—	149	2	no	—
328	#539	—	149	2	no	—
329	#539	—	149	2	no	—
330	#533	—	149	1	no	—
331	#529	—	149	1	no	—
332	#529	—	149	1	no	—
333	#529	D₁₄₉	1	1	yes	characteristic, complemented
334	C₂×#125	—	149	1	no	—
335	C₂×#125	—	149	1	no	—
336	#520	—	149	2	no	—
337	C₄×#41	—	149	1	no	—
338	C₂×#41	—	149	2	no	—
339	C₂×#41	—	149	1	no	—
340	C₄⋊Q₈	—	149	1	no	—
341	C₄⋊Q₈	—	149	1	no	—
342	C₄⋊Q₈	—	149	2	no	—
343	#126	—	149	2	no	—
344	#126	—	149	2	no	—
345	#126	—	149	2	no	—
346	#126	—	149	2	no	—
347	#126	—	149	2	no	—
348	#126	—	149	2	no	—
349	#126	C₂×D₁₄₉	1	2	yes	—
350	#125	—	149	2	no	—
351	#125	—	149	2	no	—
352	#125	—	149	1	no	—
353	#125	—	149	1	no	—
354	#125	—	149	2	no	—
355	#125	—	149	2	no	—
356	#125	—	149	2	no	—
357	#125	—	149	2	no	—
358	#125	—	149	1	no	—
359	#125	—	149	1	no	—
360	#125	—	149	2	no	—
361	#125	—	149	2	no	—
362	#125	—	149	1	no	—
363	#125	—	149	1	no	—
364	#125	—	149	2	no	—
365	#125	C₂×D₁₄₉	1	1	yes	characteristic
366	#124	C₂×D₁₄₉	1	1	yes	characteristic
367	#123	—	149	2	no	—
368	#123	—	149	2	no	—
369	#123	—	149	2	no	—
370	#123	—	149	2	no	—
371	#123	—	149	2	no	—
372	#123	—	149	2	no	—
373	#123	—	149	2	no	—
374	#123	—	149	2	no	—
375	#123	C₂×D₁₄₉	1	2	yes	—
376	C₂²⋊Q₈	—	149	1	no	—
377	C₂²⋊Q₈	—	149	1	no	—
378	C₂²⋊Q₈	—	149	2	no	—
379	C₂²⋊Q₈	—	149	2	no	—
380	C₂²⋊Q₈	—	149	2	no	—
381	C₂²⋊Q₈	—	149	2	no	—
382	C₂²⋊Q₈	—	149	2	no	—
383	C₂²⋊Q₈	—	149	2	no	—
384	C₂²⋊Q₈	—	149	2	no	—
385	C₂²⋊Q₈	—	149	2	no	—
386	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
387	#121	—	149	1	no	—
388	#121	—	149	1	no	—
389	#121	—	149	2	no	—
390	#121	—	149	2	no	—
391	#121	C₂×D₁₄₉	1	1	yes	characteristic
392	C₄×Q₈	—	149	1	no	—
393	C₄×Q₈	—	149	1	no	—
394	C₄×Q₈	—	149	2	no	—
395	C₄×Q₈	—	149	2	no	—
396	C₄×Q₈	—	149	1	no	—
397	C₄×Q₈	—	149	1	no	—
398	C₄×Q₈	—	149	2	no	—
399	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
400	C₄×D₄	—	149	2	no	—
401	C₄×D₄	—	149	1	no	—
402	C₄×D₄	—	149	1	no	—
403	C₄×D₄	—	149	1	no	—
404	C₄×D₄	—	149	1	no	—
405	C₄×D₄	—	149	1	no	—
406	C₄×D₄	—	149	1	no	—
407	C₄×D₄	—	149	2	no	—
408	C₄×D₄	—	149	2	no	—
409	C₄×D₄	—	149	2	no	—
410	C₄×D₄	—	149	2	no	—
411	C₄×D₄	—	149	1	no	—
412	C₄×D₄	—	149	1	no	—
413	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
414	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
415	#117	—	149	1	no	—
416	#117	—	149	1	no	—
417	#117	—	149	1	no	—
418	#117	—	149	2	no	—
419	#117	—	149	2	no	—
420	#117	—	149	2	no	—
421	#117	—	149	1	no	—
422	#117	—	149	1	no	—
423	#117	—	149	2	no	—
424	#117	C₂×D₁₄₉	1	2	yes	—
425	C₂×C₄⋊C₄	—	149	2	no	—
426	C₂×C₄⋊C₄	—	149	2	no	—
427	C₂×C₄⋊C₄	—	149	2	no	—
428	C₂×C₄⋊C₄	—	149	1	no	—
429	C₂×C₄⋊C₄	—	149	1	no	—
430	C₂×C₄⋊C₄	—	149	2	no	—
431	C₂×C₄⋊C₄	—	149	1	no	—
432	C₂×C₄⋊C₄	—	149	2	no	—
433	C₂×C₄⋊C₄	—	149	1	no	—
434	C₂×C₄²	—	149	1	no	—
435	C₂×C₄²	—	149	1	no	—
436	C₂×C₄²	C₂×D₁₄₉	1	1	yes	characteristic
437	#41	—	298	4	no	—
438	#41	—	298	8	no	—
439	C₂×Q₈	—	149	2	no	—
440	C₂×Q₈	—	149	1	no	—
441	C₂×Q₈	—	149	2	no	—
442	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
443	C₂×D₄	—	149	2	no	—
444	C₂×D₄	—	149	1	no	—
445	C₂×D₄	—	149	2	no	—
446	C₂×D₄	—	149	1	no	—
447	C₂×D₄	—	149	1	no	—
448	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
449	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
450	C₂²×C₄	—	149	2	no	—
451	C₂²×C₄	—	149	2	no	—
452	C₂²×C₄	—	149	1	no	—
453	C₂²×C₄	—	149	1	no	—
454	C₂²×C₄	—	149	1	no	—
455	C₂²×C₄	—	149	1	no	—
456	C₂²×C₄	—	149	2	no	—
457	C₂²×C₄	—	149	2	no	—
458	C₂²×C₄	—	149	2	no	—
459	C₂²×C₄	—	149	1	no	—
460	C₂²×C₄	—	149	1	no	—
461	C₂²×C₄	—	149	2	no	—
462	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
463	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
464	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
465	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
466	C₄⋊C₄	—	149	1	no	—
467	C₄⋊C₄	—	149	2	no	—
468	C₄⋊C₄	—	149	2	no	—
469	C₄⋊C₄	—	149	2	no	—
470	C₄⋊C₄	—	149	1	no	—
471	C₄⋊C₄	—	149	2	no	—
472	C₄⋊C₄	—	149	1	no	—
473	C₄⋊C₄	—	149	1	no	—
474	C₄⋊C₄	—	149	1	no	—
475	C₄⋊C₄	—	149	2	no	—
476	C₄⋊C₄	—	149	2	no	—
477	C₄⋊C₄	—	149	2	no	—
478	C₄⋊C₄	—	149	2	no	—
479	C₄⋊C₄	—	149	2	no	—
480	C₄⋊C₄	—	149	2	no	—
481	C₄⋊C₄	—	149	2	no	—
482	C₄⋊C₄	—	149	2	no	—
483	C₄⋊C₄	—	149	2	no	—
484	C₄⋊C₄	—	149	2	no	—
485	C₄⋊C₄	—	149	2	no	—
486	C₄⋊C₄	—	149	2	no	—
487	C₄⋊C₄	—	149	2	no	—
488	C₄⋊C₄	—	149	2	no	—
489	C₄⋊C₄	—	149	1	no	—
490	C₄⋊C₄	—	149	1	no	—
491	C₄⋊C₄	—	149	1	no	—
492	C₄⋊C₄	—	149	1	no	—
493	C₄⋊C₄	—	149	1	no	—
494	C₄⋊C₄	—	149	2	no	—
495	C₄⋊C₄	—	149	2	no	—
496	C₄⋊C₄	—	149	2	no	—
497	C₄⋊C₄	—	149	2	no	—
498	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
504	C₂²⋊C₄	—	149	1	no	—
505	C₂²⋊C₄	—	149	2	no	—
506	C₂²⋊C₄	—	149	1	no	—
507	C₂²⋊C₄	—	149	2	no	—
508	C₂²⋊C₄	—	149	2	no	—
509	C₂²⋊C₄	—	149	2	no	—
510	C₂²⋊C₄	—	149	1	no	—
511	C₂²⋊C₄	—	149	1	no	—
512	C₂²⋊C₄	—	149	2	no	—
513	C₂²⋊C₄	—	149	1	no	—
514	C₂²⋊C₄	—	149	1	no	—
515	C₂²⋊C₄	—	149	2	no	—
516	C₂²⋊C₄	—	149	2	no	—
517	C₂²⋊C₄	—	149	2	no	—
518	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
519	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
520	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
523	C₄²	—	149	1	no	—
524	C₄²	—	149	1	no	—
525	C₄²	—	149	1	no	—
526	C₄²	—	149	1	no	—
527	C₄²	—	149	1	no	—
528	C₄²	—	149	1	no	—
529	C₄²	—	149	2	no	—
530	C₄²	—	149	2	no	—
531	C₄²	—	149	2	no	—
532	C₄²	—	149	2	no	—
533	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
534	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
535	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
536	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
537	C₄²	C₂²×D₁₄₉	1	2	yes	—
538	C₂³	—	149	1	no	—
539	C₂³	—	149	1	no	—
540	C₂³	C₂³×D₁₄₉	1	2	yes	—
541	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
542	Q₈	—	2	2	no	—
543	Q₈	—	298	2	no	—
544	Q₈	—	298	4	no	—
545	Q₈	—	596	2	no	—
546	D₄	—	2	4	no	—
547	D₄	—	2	2	no	—
548	D₄	—	298	2	no	—
549	D₄	—	298	4	no	—
550	D₄	—	298	2	no	—
551	D₄	—	596	2	no	—
552	D₄	—	149	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	298	2	no	—
558	C₂×C₄	—	298	4	no	—
559	C₂×C₄	—	298	2	no	—
560	C₂×C₄	—	298	4	no	—
561	C₂×C₄	—	298	4	no	—
562	C₂×C₄	—	298	2	no	—
563	C₂×C₄	—	298	2	no	—
564	C₂×C₄	—	596	1	no	—
565	C₂×C₄	—	596	1	no	—
566	C₂×C₄	—	596	2	no	—
567	C₂×C₄	—	596	2	no	—
568	C₂×C₄	—	596	2	no	—
569	C₂×C₄	—	149	1	no	—
570	C₂×C₄	—	149	1	no	—
571	C₂×C₄	—	149	1	no	—
572	C₂×C₄	—	149	1	no	—
573	C₂×C₄	—	149	1	no	—
574	C₂×C₄	—	149	2	no	—
575	C₂×C₄	—	149	2	no	—
576	C₂×C₄	—	149	2	no	—
577	C₂×C₄	—	149	2	no	—
578	C₂×C₄	—	149	1	no	—
579	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
582	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
583	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
584	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	298	1	no	—
594	C₂²	—	298	1	no	—
595	C₂²	—	298	1	no	—
596	C₂²	—	298	1	no	—
597	C₂²	—	298	1	no	—
598	C₂²	—	149	2	no	—
599	C₂²	#41×D₁₄₉	1	2	yes	—
600	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	298	2	no	—
610	C₄	—	298	1	no	—
611	C₄	—	298	2	no	—
612	C₄	—	298	1	no	—
613	C₄	—	298	1	no	—
614	C₄	—	298	1	no	—
615	C₄	—	298	2	no	—
616	C₄	—	298	2	no	—
617	C₄	—	298	1	no	—
618	C₄	—	149	2	no	—
619	C₄	#18011958	1	2	yes	—
620	C₂	—	2	2	no	—
621	C₂	—	4	2	no	—
622	C₂	—	298	2	no	—
623	C₂	—	596	1	no	—
624	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
625	C₂	C₂×#18011958	1	1	yes	characteristic
626	C₂	#23750461	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#529×C₁₄₉	C₂
hypercenter	#529	D₁₄₉
hypocenter	C₁₄₉	#3515
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #23750351	C₂	semidirect
2. #23750334	C₂	semidirect
3. #23750333	C₂	semidirect
4. #23750327	C₂	semidirect
5. #23750325	C₂	semidirect
6. #23750317	C₂	semidirect
7. #23750316	C₂	semidirect
8. #23750314	C₂	semidirect
9. #23750312	C₂	semidirect
10. #23750308	C₂	semidirect
11. #23750275	C₂	semidirect
12. #23750273	C₂	semidirect
13. #23750232	C₂	semidirect
14. #23750217	C₂	semidirect
15. #23750216	C₂	semidirect
16. #23750181	C₂	semidirect
17. #23750154	C₂	semidirect
18. #23750154	C₂	semidirect
19. C₂×#18011903	C₂	semidirect
20. #125×D₁₄₉	C₂	semidirect
21. #23750104	C₂	semidirect
22. C₄×#14558736	C₂	semidirect
23. #529×C₁₄₉	C₂	semidirect
313. C₁₄₉	#3515	semidirect
333. #529	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750351	2
#23750334	2
#23750333	2
#23750327	2
#23750325	2
#23750317	2
#23750316	2
#23750314	2
#23750312	2
#23750308	2
#23750275	2
#23750273	2
#23750232	2
#23750217	2
#23750216	2
#23750181	2
#23750154	2
C₂×#18011903	2
#125×D₁₄₉	2
#23750104	2
C₄×#14558736	2
#529×C₁₄₉	2
#3515	149