Subgroups — #34058109

Order 19072.

1140 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750254	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750245	C₂	1	2	yes	maximal, complemented
3	#23750243	C₂	1	2	yes	maximal, complemented
4	#23750227	C₂	1	2	yes	maximal, complemented
5	#23750225	C₂	1	2	yes	maximal, complemented
6	#23750215	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750212	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750210	C₂	1	2	yes	maximal, complemented
9	#23750202	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750190	C₂	1	2	yes	maximal, complemented
11	#23750172	C₂	1	2	yes	maximal, complemented
12	#23750171	C₂	1	2	yes	maximal, complemented
13	#23750155	C₂	1	2	yes	maximal, complemented
14	#23750153	C₂	1	2	yes	maximal, complemented
15	#23750136	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750134	C₂	1	2	yes	maximal, complemented
17	C₄×#14558735	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×C₂²⋊D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#525×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14558736	C₂²	1	2	yes	complemented
21	C₂×#14558736	C₂²	1	1	yes	characteristic, complemented
22	C₂×#14558735	C₂²	1	2	yes	—
23	C₂²×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
25	#18011910	C₂²	1	2	yes	complemented
26	#18011909	C₂²	1	2	yes	complemented
27	#18011907	C₂²	1	2	yes	—
28	#18011907	C₂²	1	2	yes	—
29	#18011906	C₂²	1	2	yes	complemented
30	#18011906	C₂²	1	2	yes	complemented
31	#18011904	C₂²	1	2	yes	complemented
32	#18011904	C₂²	1	2	yes	complemented
33	#18011901	C₂²	1	2	yes	complemented
34	#18011901	C₂²	1	2	yes	complemented
35	#18011900	C₂²	1	2	yes	complemented
36	#18011898	C₂²	1	2	yes	complemented
37	#18011897	C₂²	1	2	yes	—
38	#18011897	C₂²	1	2	yes	—
39	#18011897	C₂²	1	2	yes	complemented
40	#18011897	C₂²	1	2	yes	complemented
41	#18011896	C₂²	1	2	yes	complemented
42	#18011896	C₂²	1	2	yes	complemented
43	#18011895	C₂²	1	2	yes	complemented
44	#18011894	C₂²	1	2	yes	complemented
45	#18011893	C₂²	1	2	yes	complemented
46	#18011893	C₂²	1	2	yes	complemented
47	#18011892	C₂²	1	2	yes	complemented
48	#18011890	C₂²	1	1	yes	characteristic
49	#18011890	C₂²	1	1	yes	characteristic, complemented
50	#18011889	C₂²	1	2	yes	complemented
51	#18011889	C₂²	1	2	yes	complemented
52	#18011888	C₂²	1	2	yes	—
53	#18011888	C₂²	1	2	yes	complemented
54	#18011886	C₂²	1	2	yes	complemented
55	#18011885	C₂²	1	1	yes	characteristic
56	#18011885	C₂²	1	1	yes	characteristic, complemented
57	#18011884	C₂²	1	2	yes	—
58	#18011884	C₂²	1	2	yes	—
59	#18011884	C₂²	1	2	yes	complemented
60	#18011884	C₂²	1	2	yes	complemented
61	#18011883	C₂²	1	2	yes	—
62	#18011883	C₂²	1	2	yes	—
63	#18011883	C₂²	1	2	yes	—
64	#18011883	C₂²	1	2	yes	complemented
65	#18011883	C₂²	1	2	yes	complemented
66	#18011883	C₂²	1	2	yes	complemented
67	#18011882	C₂²	1	2	yes	complemented
68	#18011881	C₂²	1	2	yes	—
69	#18011880	C₂²	1	2	yes	—
70	#18011879	C₂²	1	2	yes	—
71	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
72	#18011876	C₂²	1	2	yes	complemented
73	C₄×D₅₉₆	C₂²	1	2	yes	complemented
74	D₄×Dic₁₄₉	C₂²	1	2	yes	—
75	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
76	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
77	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
78	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
79	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
80	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
82	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
83	#18011871	C₂²	1	2	yes	—
84	#18011871	C₂²	1	2	yes	complemented
85	#18011870	C₂²	1	1	yes	characteristic, complemented
86	#18011869	C₂²	1	2	yes	complemented
87	#18011868	C₂²	1	2	yes	complemented
88	#18011867	C₂²	1	2	yes	—
89	#18011867	C₂²	1	2	yes	complemented
90	C₂×#14558715	C₂²	1	1	yes	characteristic
91	C₂×C₂²⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
92	C₂×#14558713	C₂²	1	1	yes	characteristic
93	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
94	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	complemented
95	C₄²×D₁₄₉	C₂²	1	2	yes	complemented
96	C₂×#41×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
98	#123×C₁₄₉	C₂²	1	2	yes	complemented
99	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
100	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
101	#121×C₁₄₉	C₂²	1	1	yes	characteristic
102	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
103	#120×C₁₄₉	C₂²	1	2	yes	—
104	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
105	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
106	#117×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
108	#14558736	—	4	2	no	—
109	#14558736	—	4	4	no	—
110	#14558735	—	2	8	no	—
111	C₂×Dic₂₉₈	C₂³	1	2	yes	—
112	C₂×Dic₂₉₈	C₂³	1	2	yes	—
113	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
114	C₂×D₅₉₆	C₂³	1	2	yes	—
115	C₂×D₅₉₆	C₂³	1	2	yes	—
116	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊D₁₄₉	—	2	4	no	—
118	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
127	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
128	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
129	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
130	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
131	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₁₄₉	—	4	2	no	—
133	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
134	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
135	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
136	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
137	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
138	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
139	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
140	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
142	#14558715	C₂³	1	2	yes	—
143	#14558715	C₂³	1	2	yes	—
144	#14558715	C₂³	1	2	yes	—
145	#14558715	C₂³	1	2	yes	—
146	#14558715	C₂³	1	2	yes	—
147	#14558715	C₂³	1	2	yes	—
148	#14558715	C₂³	1	2	yes	—
149	#14558715	C₂³	1	2	yes	—
150	#14558715	C₂³	1	2	yes	—
151	#14558715	C₂³	1	2	yes	—
152	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
153	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
154	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
159	#14558713	C₂³	1	2	yes	—
160	#14558713	C₂³	1	2	yes	—
161	#14558713	C₂³	1	2	yes	—
162	#14558713	C₂³	1	2	yes	—
163	#14558713	C₂³	1	2	yes	—
164	#14558713	C₂³	1	2	yes	—
165	#14558713	C₂³	1	2	yes	—
166	#14558713	C₂³	1	2	yes	—
167	#14558713	C₂³	1	2	yes	—
168	#14558713	C₂³	1	2	yes	—
169	C₄×Dic₁₄₉	C₂³	1	2	yes	—
170	C₄×Dic₁₄₉	C₂³	1	2	yes	—
171	C₄×Dic₁₄₉	C₂³	1	2	yes	—
172	C₄×Dic₁₄₉	C₂³	1	2	yes	—
173	C₄×Dic₁₄₉	C₂³	1	2	yes	—
174	C₄×Dic₁₄₉	C₂³	1	2	yes	—
175	C₄×Dic₁₄₉	C₂³	1	2	yes	—
176	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
177	#41×C₁₄₉	—	4	2	no	—
178	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
180	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
181	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
182	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₁₄₉	—	4	2	no	—
184	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
186	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
188	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
191	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
192	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
193	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
194	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
198	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
200	C₄²×C₁₄₉	C₂³	1	2	yes	—
201	C₂²×D₁₄₉	—	2	2	no	—
202	C₂²×D₁₄₉	—	4	1	no	—
203	C₂²×D₁₄₉	—	4	1	no	—
204	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
205	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
206	Dic₂₉₈	—	2	4	no	—
207	Dic₂₉₈	—	4	2	no	—
208	Dic₂₉₈	—	4	1	no	—
209	D₅₉₆	—	4	2	no	—
210	D₅₉₆	—	4	1	no	—
211	D₅₉₆	—	4	2	no	—
212	C₂²⋊D₁₄₉	—	2	4	no	—
213	C₂²⋊D₁₄₉	—	2	4	no	—
214	C₂²⋊D₁₄₉	—	2	4	no	—
215	C₂²⋊D₁₄₉	—	2	4	no	—
216	C₂²⋊D₁₄₉	—	4	2	no	—
217	C₂²⋊D₁₄₉	—	4	2	no	—
218	C₂²⋊D₁₄₉	—	4	2	no	—
219	C₂²⋊D₁₄₉	—	4	2	no	—
220	C₂²⋊D₁₄₉	—	4	2	no	—
221	C₂×Dic₁₄₉	—	2	4	no	—
222	C₂×Dic₁₄₉	—	4	1	no	—
223	C₂×Dic₁₄₉	—	4	1	no	—
224	C₂×Dic₁₄₉	—	4	2	no	—
225	C₂×Dic₁₄₉	#41	1	4	yes	complemented
226	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
227	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
228	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
229	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
230	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
231	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
232	C₄×D₁₄₉	—	2	4	no	—
233	C₄×D₁₄₉	—	2	4	no	—
234	C₄×D₁₄₉	—	2	4	no	—
235	C₄×D₁₄₉	—	4	2	no	—
236	C₄×D₁₄₉	—	4	2	no	—
237	C₂³×C₁₄₉	—	2	2	no	—
238	C₂³×C₁₄₉	—	4	1	no	—
239	C₂³×C₁₄₉	—	4	1	no	—
240	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
241	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
242	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
243	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
244	Q₈×C₁₄₉	—	4	1	no	—
245	D₄×C₁₄₉	—	2	4	no	—
246	D₄×C₁₄₉	—	4	2	no	—
247	D₄×C₁₄₉	—	4	1	no	—
248	D₄×C₁₄₉	—	4	2	no	—
249	C₂×C₄×C₁₄₉	—	2	2	no	—
250	C₂×C₄×C₁₄₉	—	2	2	no	—
251	C₂×C₄×C₁₄₉	—	2	4	no	—
252	C₂×C₄×C₁₄₉	—	2	2	no	—
253	C₂×C₄×C₁₄₉	—	4	1	no	—
254	C₂×C₄×C₁₄₉	—	4	1	no	—
255	C₂×C₄×C₁₄₉	—	4	1	no	—
256	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
259	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
260	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
263	C₂²×C₁₄₉	—	2	1	no	—
264	C₂²×C₁₄₉	—	2	1	no	—
265	C₂²×C₁₄₉	—	2	2	no	—
266	C₂²×C₁₄₉	—	2	1	no	—
267	C₂²×C₁₄₉	—	2	1	no	—
268	C₂²×C₁₄₉	—	2	1	no	—
269	C₂²×C₁₄₉	—	2	1	no	—
270	C₂²×C₁₄₉	—	2	2	no	—
271	C₂²×C₁₄₉	—	2	1	no	—
272	C₂²×C₁₄₉	—	2	2	no	—
273	C₂²×C₁₄₉	—	2	1	no	—
274	C₂²×C₁₄₉	—	4	4	no	—
275	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
276	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
277	C₂×D₁₄₉	—	2	2	no	—
278	C₂×D₁₄₉	—	2	2	no	—
279	C₂×D₁₄₉	—	2	2	no	—
280	C₂×D₁₄₉	—	2	2	no	—
281	C₂×D₁₄₉	—	2	2	no	—
282	C₂×D₁₄₉	—	2	2	no	—
283	C₂×D₁₄₉	—	4	4	no	—
284	C₄×C₁₄₉	—	2	2	no	—
285	C₄×C₁₄₉	—	2	1	no	—
286	C₄×C₁₄₉	—	2	1	no	—
287	C₄×C₁₄₉	—	2	1	no	—
288	C₄×C₁₄₉	—	2	2	no	—
289	C₄×C₁₄₉	—	2	2	no	—
290	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
291	Dic₁₄₉	—	2	2	no	—
292	Dic₁₄₉	—	2	2	no	—
293	Dic₁₄₉	—	2	2	no	—
294	Dic₁₄₉	—	2	2	no	—
295	Dic₁₄₉	—	2	2	no	—
296	Dic₁₄₉	C₂×#41	1	4	yes	—
297	C₂×C₁₄₉	—	2	2	no	—
298	C₂×C₁₄₉	—	4	2	no	—
299	C₂×C₁₄₉	—	4	1	no	—
300	C₂×C₁₄₉	—	4	1	no	—
301	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
302	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
303	C₂×C₁₄₉	#585	1	1	yes	characteristic
304	D₁₄₉	—	4	2	no	—
305	D₁₄₉	—	4	2	no	—
306	C₁₄₉	#3460	1	1	yes	characteristic, complemented, Sylow
307	#3460	—	149	1	no	maximal, Sylow
308	#544	—	149	1	no	—
309	#542	—	149	2	no	—
310	#542	—	149	2	no	—
311	#540	—	149	2	no	—
312	#540	—	149	2	no	—
313	#538	—	149	1	no	—
314	#538	—	149	1	no	—
315	#538	—	149	2	no	—
316	#537	—	149	1	no	—
317	#535	—	149	2	no	—
318	#532	—	149	2	no	—
319	#532	—	149	2	no	—
320	#529	—	149	2	no	—
321	#529	—	149	2	no	—
322	#525	—	149	1	no	—
323	#525	—	149	2	no	—
324	#525	D₁₄₉	1	1	yes	characteristic, complemented
325	C₄×#41	—	149	2	no	—
326	C₂×C₄×D₄	—	149	1	no	—
327	C₂×#41	—	149	2	no	—
328	C₂×#41	—	149	1	no	—
329	C₂×#41	—	149	2	no	—
330	C₂×#41	C₂×D₁₄₉	1	1	yes	characteristic, complemented
331	C₂²×D₄	—	149	1	no	—
332	C₂³×C₄	—	149	1	no	—
333	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic
334	C₄⋊Q₈	—	149	2	no	—
335	C₄⋊Q₈	—	149	2	no	—
336	#127	—	149	2	no	—
337	#127	—	149	2	no	—
338	#126	—	149	2	no	—
339	#126	—	149	2	no	—
340	#126	—	149	2	no	—
341	#126	—	149	2	no	—
342	#125	—	149	2	no	—
343	#125	—	149	2	no	—
344	#124	—	149	2	no	—
345	#124	—	149	2	no	—
346	#124	—	149	2	no	—
347	#124	—	149	2	no	—
348	#124	—	149	2	no	—
349	#124	—	149	2	no	—
350	#123	—	149	2	no	—
351	#123	—	149	2	no	—
352	#123	—	149	2	no	—
353	#123	—	149	2	no	—
354	#123	—	149	2	no	—
355	#123	—	149	2	no	—
356	#123	—	149	2	no	—
357	#123	C₂×D₁₄₉	1	2	yes	complemented
358	C₂²⋊Q₈	—	149	1	no	—
359	C₂²⋊Q₈	—	149	1	no	—
360	C₂²⋊Q₈	—	149	2	no	—
361	C₂²⋊Q₈	—	149	2	no	—
362	C₂²⋊Q₈	—	149	2	no	—
363	C₂²⋊Q₈	—	149	2	no	—
364	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
365	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
366	#121	—	149	2	no	—
367	#121	—	149	2	no	—
368	#121	—	149	2	no	—
369	#121	—	149	2	no	—
370	#121	—	149	2	no	—
371	#121	—	149	2	no	—
372	#121	—	149	2	no	—
373	#121	—	149	1	no	—
374	#121	—	149	1	no	—
375	#121	—	149	2	no	—
376	#121	—	149	2	no	—
377	#121	—	149	2	no	—
378	#121	—	149	2	no	—
379	#121	—	149	2	no	—
380	#121	C₂×D₁₄₉	1	1	yes	characteristic
381	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
382	#120	—	149	2	no	—
383	#120	—	149	2	no	—
384	#120	—	149	2	no	—
385	#120	C₂×D₁₄₉	1	2	yes	—
386	C₄×Q₈	—	149	2	no	—
387	C₄×Q₈	—	149	2	no	—
388	C₄×D₄	—	149	2	no	—
389	C₄×D₄	—	149	2	no	—
390	C₄×D₄	—	149	2	no	—
391	C₄×D₄	—	149	2	no	—
392	C₄×D₄	—	149	2	no	—
393	C₄×D₄	—	149	2	no	—
394	C₄×D₄	—	149	2	no	—
395	C₄×D₄	—	149	2	no	—
396	C₄×D₄	—	149	2	no	—
397	C₄×D₄	—	149	2	no	—
398	C₄×D₄	—	149	2	no	—
399	C₄×D₄	—	149	2	no	—
400	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
401	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
402	#117	—	149	1	no	—
403	#117	—	149	2	no	—
404	#117	—	149	2	no	—
405	#117	—	149	2	no	—
406	#117	—	149	2	no	—
407	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
408	C₂×C₄⋊C₄	—	149	1	no	—
409	C₂×C₂²⋊C₄	—	149	1	no	—
410	C₂×C₂²⋊C₄	—	149	1	no	—
411	C₂×C₄²	—	149	1	no	—
412	C₂×C₄²	—	149	2	no	—
413	C₂×C₄²	—	149	2	no	—
414	C₂⁴	—	149	1	no	—
415	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
416	#41	—	4	2	no	—
417	#41	—	298	8	no	—
418	#41	—	596	2	no	—
419	#41	—	596	4	no	—
420	C₂×Q₈	—	149	2	no	—
421	C₂×Q₈	—	149	1	no	—
422	C₂×Q₈	—	149	2	no	—
423	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
424	C₂×D₄	—	298	4	no	—
425	C₂×D₄	—	149	2	no	—
426	C₂×D₄	—	149	2	no	—
427	C₂×D₄	—	149	2	no	—
428	C₂×D₄	—	149	2	no	—
429	C₂×D₄	—	149	2	no	—
430	C₂×D₄	—	149	2	no	—
431	C₂×D₄	—	149	2	no	—
432	C₂×D₄	—	149	2	no	—
433	C₂×D₄	—	149	2	no	—
434	C₂×D₄	—	149	2	no	—
435	C₂×D₄	—	149	2	no	—
436	C₂×D₄	—	149	1	no	—
437	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
438	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
439	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
440	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	596	2	no	—
443	C₂²×C₄	—	149	2	no	—
444	C₂²×C₄	—	149	2	no	—
445	C₂²×C₄	—	149	2	no	—
446	C₂²×C₄	—	149	2	no	—
447	C₂²×C₄	—	149	1	no	—
448	C₂²×C₄	—	149	2	no	—
449	C₂²×C₄	—	149	1	no	—
450	C₂²×C₄	—	149	2	no	—
451	C₂²×C₄	—	149	2	no	—
452	C₂²×C₄	—	149	1	no	—
453	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
454	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
455	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
456	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
457	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
458	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
459	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
460	C₄⋊C₄	—	149	2	no	—
461	C₄⋊C₄	—	149	2	no	—
462	C₄⋊C₄	—	149	2	no	—
463	C₄⋊C₄	—	149	2	no	—
464	C₄⋊C₄	—	149	2	no	—
465	C₄⋊C₄	—	149	2	no	—
466	C₄⋊C₄	—	149	2	no	—
467	C₄⋊C₄	—	149	2	no	—
468	C₄⋊C₄	—	149	1	no	—
469	C₄⋊C₄	—	149	2	no	—
470	C₄⋊C₄	—	149	1	no	—
471	C₄⋊C₄	—	149	2	no	—
472	C₄⋊C₄	—	149	2	no	—
473	C₄⋊C₄	—	149	2	no	—
474	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
475	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
476	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
478	C₂²⋊C₄	—	149	2	no	—
479	C₂²⋊C₄	—	149	2	no	—
480	C₂²⋊C₄	—	149	2	no	—
481	C₂²⋊C₄	—	149	2	no	—
482	C₂²⋊C₄	—	149	2	no	—
483	C₂²⋊C₄	—	149	2	no	—
484	C₂²⋊C₄	—	149	2	no	—
485	C₂²⋊C₄	—	149	2	no	—
486	C₂²⋊C₄	—	149	2	no	—
487	C₂²⋊C₄	—	149	2	no	—
488	C₂²⋊C₄	—	149	2	no	—
489	C₂²⋊C₄	—	149	2	no	—
490	C₂²⋊C₄	—	149	2	no	—
491	C₂²⋊C₄	—	149	2	no	—
492	C₂²⋊C₄	—	149	2	no	—
493	C₂²⋊C₄	—	149	2	no	—
494	C₂²⋊C₄	—	149	2	no	—
495	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
496	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
497	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
500	C₄²	—	149	2	no	—
501	C₄²	—	149	2	no	—
502	C₄²	—	149	2	no	—
503	C₄²	—	149	2	no	—
504	C₄²	—	149	2	no	—
505	C₄²	—	149	2	no	—
506	C₄²	—	149	2	no	—
507	C₄²	C₂²×D₁₄₉	1	2	yes	—
508	C₂³	—	2	2	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	298	2	no	—
512	C₂³	—	596	1	no	—
513	C₂³	—	596	1	no	—
514	C₂³	—	149	2	no	—
515	C₂³	—	149	2	no	—
516	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
517	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
518	C₂³	C₂³×D₁₄₉	1	2	yes	—
519	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
520	Q₈	—	4	1	no	—
521	Q₈	—	298	4	no	—
522	Q₈	—	596	1	no	—
523	Q₈	—	596	2	no	—
524	D₄	—	2	4	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	2	no	—
528	D₄	—	298	4	no	—
529	D₄	—	298	4	no	—
530	D₄	—	298	4	no	—
531	D₄	—	298	4	no	—
532	D₄	—	596	2	no	—
533	D₄	—	596	1	no	—
534	D₄	—	596	2	no	—
535	D₄	—	596	2	no	—
536	D₄	—	596	2	no	—
537	D₄	—	596	2	no	—
538	D₄	—	596	2	no	—
539	D₄	—	596	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	298	4	no	—
548	C₂×C₄	—	298	4	no	—
549	C₂×C₄	—	298	4	no	—
550	C₂×C₄	—	298	4	no	—
551	C₂×C₄	—	596	2	no	—
552	C₂×C₄	—	596	2	no	—
553	C₂×C₄	—	596	1	no	—
554	C₂×C₄	—	596	1	no	—
555	C₂×C₄	—	596	2	no	—
556	C₂×C₄	—	149	2	no	—
557	C₂×C₄	—	149	2	no	—
558	C₂×C₄	—	149	2	no	—
559	C₂×C₄	—	149	2	no	—
560	C₂×C₄	—	149	2	no	—
561	C₂×C₄	—	149	4	no	—
562	C₂×C₄	—	149	2	no	—
563	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
565	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
566	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
567	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	298	2	no	—
583	C₂²	—	298	2	no	—
584	C₂²	—	298	2	no	—
585	C₂²	—	298	2	no	—
586	C₂²	—	298	2	no	—
587	C₂²	—	298	2	no	—
588	C₂²	—	596	4	no	—
589	C₂²	#41×D₁₄₉	1	2	yes	—
590	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	298	2	no	—
598	C₄	—	298	2	no	—
599	C₄	—	298	2	no	—
600	C₄	—	298	2	no	—
601	C₄	—	298	2	no	—
602	C₄	—	149	4	no	—
603	C₄	#18011956	1	2	yes	—
604	C₂	—	2	2	no	—
605	C₂	—	4	1	no	—
606	C₂	—	4	1	no	—
607	C₂	—	4	2	no	—
608	C₂	—	596	2	no	—
609	C₂	—	596	2	no	—
610	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
611	C₂	C₂×#18011956	1	1	yes	characteristic
612	C₂	#23750461	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₄₉
Fitting	#525×C₁₄₉	C₂
hypercenter	#525	D₁₄₉
hypocenter	C₁₄₉	#3460
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. #23750254	C₂	semidirect
2. #23750245	C₂	semidirect
3. #23750243	C₂	semidirect
4. #23750227	C₂	semidirect
5. #23750225	C₂	semidirect
6. #23750215	C₂	semidirect
7. #23750212	C₂	semidirect
8. #23750210	C₂	semidirect
9. #23750202	C₂	semidirect
10. #23750190	C₂	semidirect
11. #23750172	C₂	semidirect
12. #23750171	C₂	semidirect
13. #23750155	C₂	semidirect
14. #23750153	C₂	semidirect
15. #23750136	C₂	semidirect
16. #23750134	C₂	semidirect
17. C₄×#14558735	C₂	semidirect
18. C₂×C₄×C₂²⋊D₁₄₉	C₂	semidirect
19. #525×C₁₄₉	C₂	semidirect
20. C₂×#14558736	C₂²	semidirect
21. C₂×#14558736	C₂²	semidirect
25. #18011910	C₂²	semidirect
26. #18011909	C₂²	semidirect
29. #18011906	C₂²	semidirect
30. #18011906	C₂²	semidirect
31. #18011904	C₂²	semidirect
32. #18011904	C₂²	semidirect
33. #18011901	C₂²	semidirect
34. #18011901	C₂²	semidirect
35. #18011900	C₂²	semidirect
36. #18011898	C₂²	semidirect
39. #18011897	C₂²	semidirect
40. #18011897	C₂²	semidirect
41. #18011896	C₂²	semidirect
42. #18011896	C₂²	semidirect
43. #18011895	C₂²	semidirect
44. #18011894	C₂²	semidirect
45. #18011893	C₂²	semidirect
46. #18011893	C₂²	semidirect
47. #18011892	C₂²	semidirect
49. #18011890	C₂²	semidirect
50. #18011889	C₂²	semidirect
51. #18011889	C₂²	semidirect
53. #18011888	C₂²	semidirect
54. #18011886	C₂²	semidirect
56. #18011885	C₂²	semidirect
59. #18011884	C₂²	semidirect
60. #18011884	C₂²	semidirect
64. #18011883	C₂²	semidirect
65. #18011883	C₂²	semidirect
66. #18011883	C₂²	semidirect
67. #18011882	C₂²	semidirect
71. C₄×Dic₂₉₈	C₂²	semidirect
72. #18011876	C₂²	semidirect
73. C₄×D₅₉₆	C₂²	semidirect
80. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
81. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
82. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
84. #18011871	C₂²	semidirect
85. #18011870	C₂²	semidirect
86. #18011869	C₂²	semidirect
87. #18011868	C₂²	semidirect
89. #18011867	C₂²	semidirect
94. C₂×C₄×Dic₁₄₉	C₂²	semidirect
95. C₄²×D₁₄₉	C₂²	semidirect
96. C₂×#41×C₁₄₉	C₂²	semidirect
98. #123×C₁₄₉	C₂²	semidirect
100. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
102. #121×C₁₄₉	C₂²	semidirect
105. C₄×D₄×C₁₄₉	C₂²	semidirect
106. #117×C₁₄₉	C₂²	semidirect
225. C₂×Dic₁₄₉	#41	semidirect
306. C₁₄₉	#3460	semidirect
324. #525	D₁₄₉	semidirect
330. C₂×#41	C₂×D₁₄₉	semidirect
357. #123	C₂×D₁₄₉	semidirect
365. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
381. #121	C₂×D₁₄₉	semidirect
401. C₄×D₄	C₂×D₁₄₉	semidirect
407. #117	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750254	2
#23750245	2
#23750243	2
#23750227	2
#23750225	2
#23750215	2
#23750212	2
#23750210	2
#23750202	2
#23750190	2
#23750172	2
#23750171	2
#23750155	2
#23750153	2
#23750136	2
#23750134	2
C₄×#14558735	2
C₂×C₄×C₂²⋊D₁₄₉	2
#525×C₁₄₉	2
#3460	149