Subgroups — #34058102

Order 19072.

1160 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750250	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750218	C₂	1	2	yes	maximal, complemented
3	#23750217	C₂	1	2	yes	maximal, complemented
4	#23750216	C₂	1	2	yes	maximal, complemented
5	#23750213	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750209	C₂	1	2	yes	maximal, complemented
7	#23750207	C₂	1	2	yes	maximal, complemented
8	#23750185	C₂	1	2	yes	maximal, complemented
9	#23750183	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750161	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750158	C₂	1	2	yes	maximal, complemented
12	#23750156	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750154	C₂	1	2	yes	maximal, complemented
14	#23750135	C₂	1	2	yes	maximal, complemented
15	#23750133	C₂	1	2	yes	maximal, complemented
16	#23750131	C₂	1	2	yes	maximal, complemented
17	C₂×#18011871	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×D₄×D₁₄₉	C₂	1	2	yes	maximal, complemented
19	#538×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14558735	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
22	C₂×D₄×D₁₄₉	C₂²	1	2	yes	—
23	C₂³×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	complemented
26	#18011906	C₂²	1	2	yes	complemented
27	#18011905	C₂²	1	2	yes	complemented
28	#18011904	C₂²	1	2	yes	complemented
29	#18011904	C₂²	1	2	yes	complemented
30	#18011904	C₂²	1	2	yes	complemented
31	#18011903	C₂²	1	2	yes	complemented
32	#18011902	C₂²	1	1	yes	characteristic, complemented
33	#18011902	C₂²	1	1	yes	characteristic, complemented
34	#18011901	C₂²	1	2	yes	complemented
35	#18011900	C₂²	1	1	yes	characteristic, complemented
36	#18011898	C₂²	1	1	yes	characteristic, complemented
37	#18011897	C₂²	1	2	yes	complemented
38	#18011896	C₂²	1	2	yes	complemented
39	#18011895	C₂²	1	2	yes	complemented
40	#18011895	C₂²	1	2	yes	complemented
41	#18011894	C₂²	1	2	yes	complemented
42	#18011893	C₂²	1	2	yes	complemented
43	#18011893	C₂²	1	2	yes	complemented
44	#18011893	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	#18011892	C₂²	1	2	yes	complemented
49	#18011891	C₂²	1	2	yes	complemented
50	#18011890	C₂²	1	1	yes	characteristic, complemented
51	#18011890	C₂²	1	2	yes	complemented
52	#18011889	C₂²	1	2	yes	complemented
53	#18011889	C₂²	1	2	yes	complemented
54	#18011889	C₂²	1	2	yes	complemented
55	#18011888	C₂²	1	2	yes	complemented
56	#18011888	C₂²	1	2	yes	complemented
57	#18011887	C₂²	1	2	yes	complemented
58	#18011885	C₂²	1	1	yes	characteristic
59	#18011884	C₂²	1	2	yes	—
60	#18011884	C₂²	1	2	yes	—
61	#18011884	C₂²	1	2	yes	complemented
62	#18011883	C₂²	1	2	yes	—
63	#18011883	C₂²	1	2	yes	complemented
64	#18011882	C₂²	1	2	yes	—
65	#18011882	C₂²	1	2	yes	—
66	#18011881	C₂²	1	2	yes	complemented
67	#18011880	C₂²	1	2	yes	complemented
68	#18011879	C₂²	1	2	yes	complemented
69	#18011879	C₂²	1	2	yes	complemented
70	#18011879	C₂²	1	2	yes	complemented
71	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
72	#18011876	C₂²	1	1	yes	characteristic, complemented
73	C₄×D₅₉₆	C₂²	1	2	yes	complemented
74	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
75	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
76	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
77	#18011873	C₂²	1	2	yes	complemented
78	#18011873	C₂²	1	1	yes	characteristic, complemented
79	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
81	#18011871	C₂²	1	2	yes	complemented
82	#18011871	C₂²	1	2	yes	complemented
83	#18011871	C₂²	1	2	yes	complemented
84	#18011871	C₂²	1	2	yes	complemented
85	#18011871	C₂²	1	2	yes	complemented
86	#18011871	C₂²	1	2	yes	complemented
87	#18011871	C₂²	1	2	yes	complemented
88	#18011869	C₂²	1	2	yes	complemented
89	#18011867	C₂²	1	2	yes	complemented
90	#18011867	C₂²	1	2	yes	complemented
91	C₂×#14558715	C₂²	1	1	yes	characteristic, complemented
92	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
93	C₂×#14558713	C₂²	1	1	yes	characteristic
94	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
96	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
97	C₄²×D₁₄₉	C₂²	1	2	yes	complemented
98	#126×C₁₄₉	C₂²	1	2	yes	complemented
99	#124×C₁₄₉	C₂²	1	2	yes	complemented
100	#123×C₁₄₉	C₂²	1	2	yes	complemented
101	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
102	#121×C₁₄₉	C₂²	1	1	yes	characteristic
103	#121×C₁₄₉	C₂²	1	2	yes	complemented
104	#120×C₁₄₉	C₂²	1	2	yes	complemented
105	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₄₉	C₂³	1	2	yes	—
108	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
109	#14558735	—	4	4	no	—
110	C₂×Dic₂₉₈	C₂³	1	2	yes	—
111	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
112	C₂×D₅₉₆	C₂³	1	2	yes	—
113	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊D₁₄₉	—	2	4	no	—
115	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
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	D₄×D₁₄₉	—	2	8	no	—
123	C₂²×Dic₁₄₉	—	4	2	no	—
124	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
125	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
126	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
127	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
128	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
129	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
130	C₂×C₄×D₁₄₉	—	4	2	no	—
131	C₂×C₄×D₁₄₉	—	4	4	no	—
132	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
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	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
139	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
141	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
142	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
143	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
144	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
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	#14558715	C₂³	1	2	yes	—
153	#14558715	C₂³	1	2	yes	—
154	#14558715	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	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₄₉	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	#14558713	C₂³	1	2	yes	—
170	#14558713	C₂³	1	2	yes	—
171	#14558713	C₂³	1	2	yes	—
172	C₄×Dic₁₄₉	C₂³	1	2	yes	—
173	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
174	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
175	C₄×Dic₁₄₉	C₂³	1	2	yes	—
176	C₄×Dic₁₄₉	C₂³	1	2	yes	—
177	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
178	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
179	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
180	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
181	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
182	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
183	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
184	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
187	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
190	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
191	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
192	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
194	C₂²⋊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	C₄²×C₁₄₉	C₂³	1	2	yes	—
200	C₂²×D₁₄₉	—	2	4	no	—
201	C₂²×D₁₄₉	—	4	1	no	—
202	C₂²×D₁₄₉	—	4	2	no	—
203	C₂²×D₁₄₉	—	4	1	no	—
204	C₂²×D₁₄₉	—	4	2	no	—
205	C₂²×D₁₄₉	#41	1	4	yes	complemented
206	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
207	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
208	Dic₂₉₈	—	4	1	no	—
209	Dic₂₉₈	—	4	2	no	—
210	D₅₉₆	—	2	4	no	—
211	D₅₉₆	—	4	1	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	C₂×Dic₁₄₉	—	2	2	no	—
220	C₂×Dic₁₄₉	—	2	2	no	—
221	C₂×Dic₁₄₉	—	2	4	no	—
222	C₂×Dic₁₄₉	—	2	4	no	—
223	C₂×Dic₁₄₉	—	4	2	no	—
224	C₂×Dic₁₄₉	—	4	1	no	—
225	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
231	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
232	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
233	C₄×D₁₄₉	—	2	4	no	—
234	C₄×D₁₄₉	—	2	4	no	—
235	C₄×D₁₄₉	—	2	4	no	—
236	C₄×D₁₄₉	—	4	2	no	—
237	C₄×D₁₄₉	—	4	2	no	—
238	C₄×D₁₄₉	—	4	2	no	—
239	C₄×D₁₄₉	—	4	2	no	—
240	C₂³×C₁₄₉	—	2	2	no	—
241	C₂³×C₁₄₉	—	4	1	no	—
242	C₂³×C₁₄₉	—	4	1	no	—
243	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
244	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
245	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
246	Q₈×C₁₄₉	—	4	1	no	—
247	D₄×C₁₄₉	—	2	4	no	—
248	D₄×C₁₄₉	—	4	2	no	—
249	D₄×C₁₄₉	—	4	1	no	—
250	D₄×C₁₄₉	—	4	2	no	—
251	C₂×C₄×C₁₄₉	—	4	1	no	—
252	C₂×C₄×C₁₄₉	—	4	2	no	—
253	C₂×C₄×C₁₄₉	—	4	1	no	—
254	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
258	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
260	C₂²×C₁₄₉	—	2	1	no	—
261	C₂²×C₁₄₉	—	2	1	no	—
262	C₂²×C₁₄₉	—	2	2	no	—
263	C₂²×C₁₄₉	—	2	2	no	—
264	C₂²×C₁₄₉	—	2	2	no	—
265	C₂²×C₁₄₉	—	2	2	no	—
266	C₂²×C₁₄₉	—	2	2	no	—
267	C₂²×C₁₄₉	—	2	2	no	—
268	C₂²×C₁₄₉	—	4	4	no	—
269	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
270	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
271	C₂×D₁₄₉	—	2	2	no	—
272	C₂×D₁₄₉	—	2	2	no	—
273	C₂×D₁₄₉	—	2	2	no	—
274	C₂×D₁₄₉	—	2	2	no	—
275	C₂×D₁₄₉	—	2	2	no	—
276	C₂×D₁₄₉	—	4	4	no	—
277	C₂×D₁₄₉	—	4	8	no	—
278	C₂×D₁₄₉	C₂×#41	1	4	yes	—
279	C₄×C₁₄₉	—	2	2	no	—
280	C₄×C₁₄₉	—	2	2	no	—
281	C₄×C₁₄₉	—	2	2	no	—
282	C₄×C₁₄₉	—	2	1	no	—
283	C₄×C₁₄₉	—	2	1	no	—
284	C₄×C₁₄₉	—	2	2	no	—
285	Dic₁₄₉	—	2	2	no	—
286	Dic₁₄₉	—	2	1	no	—
287	Dic₁₄₉	—	2	1	no	—
288	Dic₁₄₉	—	2	1	no	—
289	Dic₁₄₉	—	2	2	no	—
290	Dic₁₄₉	—	2	2	no	—
291	Dic₁₄₉	—	2	2	no	—
292	Dic₁₄₉	H(5,𝔽₂)	1	2	yes	—
293	C₂×C₁₄₉	—	2	2	no	—
294	C₂×C₁₄₉	—	4	2	no	—
295	C₂×C₁₄₉	—	4	2	no	—
296	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
297	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₁₄₉	#585	1	1	yes	characteristic
299	D₁₄₉	—	2	4	no	—
300	D₁₄₉	—	4	2	no	—
301	C₁₄₉	#3459	1	1	yes	characteristic, complemented, Sylow
302	#3459	—	149	1	no	maximal, Sylow
303	#543	—	149	1	no	—
304	#539	—	149	2	no	—
305	#539	—	149	2	no	—
306	#539	—	149	2	no	—
307	#538	—	149	2	no	—
308	#538	—	149	2	no	—
309	#538	—	149	1	no	—
310	#538	D₁₄₉	1	1	yes	characteristic, complemented
311	#534	—	149	1	no	—
312	#534	—	149	2	no	—
313	#529	—	149	2	no	—
314	#529	—	149	2	no	—
315	#529	—	149	1	no	—
316	#529	—	149	1	no	—
317	#525	—	149	2	no	—
318	#525	—	149	2	no	—
319	#525	—	149	2	no	—
320	C₂×C₄×D₄	—	149	2	no	—
321	C₂×C₄×D₄	—	149	1	no	—
322	C₂×#41	—	149	2	no	—
323	C₂²×D₄	—	149	1	no	—
324	C₂²×D₄	—	149	2	no	—
325	C₂³×C₄	—	149	1	no	—
326	C₂³×C₄	—	149	1	no	—
327	C₂³×C₄	—	149	2	no	—
328	#126	—	149	2	no	—
329	#126	—	149	2	no	—
330	#126	—	149	2	no	—
331	#126	—	149	2	no	—
332	#126	—	149	2	no	—
333	#126	C₂×D₁₄₉	1	2	yes	complemented
334	#125	—	149	2	no	—
335	#125	—	149	1	no	—
336	#125	—	149	1	no	—
337	#125	—	149	2	no	—
338	#124	—	149	1	no	—
339	#124	—	149	1	no	—
340	#124	—	149	2	no	—
341	#124	C₂×D₁₄₉	1	2	yes	complemented
342	#123	—	149	2	no	—
343	#123	—	149	2	no	—
344	#123	—	149	2	no	—
345	#123	—	149	2	no	—
346	#123	—	149	2	no	—
347	#123	—	149	2	no	—
348	#123	—	149	2	no	—
349	#123	—	149	2	no	—
350	#123	—	149	2	no	—
351	#123	—	149	2	no	—
352	#123	—	149	2	no	—
353	#123	C₂×D₁₄₉	1	2	yes	complemented
354	C₂²⋊Q₈	—	149	2	no	—
355	C₂²⋊Q₈	—	149	2	no	—
356	C₂²⋊Q₈	—	149	1	no	—
357	C₂²⋊Q₈	—	149	2	no	—
358	C₂²⋊Q₈	—	149	2	no	—
359	C₂²⋊Q₈	—	149	2	no	—
360	C₂²⋊Q₈	—	149	2	no	—
361	C₂²⋊Q₈	—	149	2	no	—
362	C₂²⋊Q₈	—	149	2	no	—
363	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
364	#121	—	149	2	no	—
365	#121	—	149	2	no	—
366	#121	—	149	2	no	—
367	#121	—	149	2	no	—
368	#121	—	149	1	no	—
369	#121	—	149	2	no	—
370	#121	—	149	2	no	—
371	#121	—	149	2	no	—
372	#121	C₂×D₁₄₉	1	1	yes	characteristic
373	#121	C₂×D₁₄₉	1	2	yes	complemented
374	#120	—	149	2	no	—
375	#120	—	149	2	no	—
376	#120	—	149	2	no	—
377	#120	—	149	2	no	—
378	#120	—	149	2	no	—
379	#120	C₂×D₁₄₉	1	2	yes	complemented
380	C₄×Q₈	—	149	1	no	—
381	C₄×Q₈	—	149	1	no	—
382	C₄×D₄	—	149	2	no	—
383	C₄×D₄	—	149	1	no	—
384	C₄×D₄	—	149	2	no	—
385	C₄×D₄	—	149	2	no	—
386	C₄×D₄	—	149	2	no	—
387	C₄×D₄	—	149	2	no	—
388	C₄×D₄	—	149	1	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	C₂×D₁₄₉	1	2	yes	complemented
398	#117	—	149	2	no	—
399	#117	—	149	2	no	—
400	#117	—	149	2	no	—
401	C₂×C₄⋊C₄	—	149	1	no	—
402	C₂×C₄⋊C₄	—	149	2	no	—
403	C₂×C₂²⋊C₄	—	149	1	no	—
404	C₂×C₂²⋊C₄	—	149	2	no	—
405	C₂×C₂²⋊C₄	—	149	2	no	—
406	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
407	C₂×C₄²	—	149	1	no	—
408	C₂×C₄²	—	149	2	no	—
409	C₂⁴	—	149	2	no	—
410	C₂⁴	—	149	1	no	—
411	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
412	#41	—	596	4	no	—
413	C₂×Q₈	—	149	1	no	—
414	C₂×Q₈	—	149	2	no	—
415	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
416	C₂×D₄	—	298	8	no	—
417	C₂×D₄	—	298	4	no	—
418	C₂×D₄	—	149	2	no	—
419	C₂×D₄	—	149	2	no	—
420	C₂×D₄	—	149	2	no	—
421	C₂×D₄	—	149	2	no	—
422	C₂×D₄	—	149	2	no	—
423	C₂×D₄	—	149	2	no	—
424	C₂×D₄	—	149	2	no	—
425	C₂×D₄	—	149	2	no	—
426	C₂×D₄	—	149	1	no	—
427	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
428	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
430	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
431	C₂²×C₄	—	596	2	no	—
432	C₂²×C₄	—	596	4	no	—
433	C₂²×C₄	—	596	2	no	—
434	C₂²×C₄	—	149	1	no	—
435	C₂²×C₄	—	149	1	no	—
436	C₂²×C₄	—	149	2	no	—
437	C₂²×C₄	—	149	2	no	—
438	C₂²×C₄	—	149	2	no	—
439	C₂²×C₄	—	149	2	no	—
440	C₂²×C₄	—	149	2	no	—
441	C₂²×C₄	—	149	1	no	—
442	C₂²×C₄	—	149	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	C₂²×D₁₄₉	1	1	yes	characteristic
448	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
449	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
450	C₄⋊C₄	—	149	2	no	—
451	C₄⋊C₄	—	149	2	no	—
452	C₄⋊C₄	—	149	2	no	—
453	C₄⋊C₄	—	149	2	no	—
454	C₄⋊C₄	—	149	2	no	—
455	C₄⋊C₄	—	149	2	no	—
456	C₄⋊C₄	—	149	2	no	—
457	C₄⋊C₄	—	149	2	no	—
458	C₄⋊C₄	—	149	2	no	—
459	C₄⋊C₄	—	149	2	no	—
460	C₄⋊C₄	—	149	2	no	—
461	C₄⋊C₄	—	149	1	no	—
462	C₄⋊C₄	—	149	2	no	—
463	C₄⋊C₄	—	149	2	no	—
464	C₄⋊C₄	—	149	1	no	—
465	C₄⋊C₄	—	149	2	no	—
466	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
467	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
468	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
470	C₂²⋊C₄	—	149	2	no	—
471	C₂²⋊C₄	—	149	2	no	—
472	C₂²⋊C₄	—	149	2	no	—
473	C₂²⋊C₄	—	149	2	no	—
474	C₂²⋊C₄	—	149	2	no	—
475	C₂²⋊C₄	—	149	2	no	—
476	C₂²⋊C₄	—	149	2	no	—
477	C₂²⋊C₄	—	149	2	no	—
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	C₂²×D₁₄₉	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
489	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
490	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
491	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
492	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
493	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
494	C₄²	—	149	2	no	—
495	C₄²	—	149	1	no	—
496	C₄²	—	149	1	no	—
497	C₄²	—	149	2	no	—
498	C₄²	—	149	2	no	—
499	C₄²	—	149	1	no	—
500	C₄²	—	149	1	no	—
501	C₄²	C₂²×D₁₄₉	1	2	yes	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	298	4	no	—
506	C₂³	—	596	1	no	—
507	C₂³	—	596	2	no	—
508	C₂³	—	596	1	no	—
509	C₂³	—	596	2	no	—
510	C₂³	—	149	2	no	—
511	C₂³	—	149	2	no	—
512	C₂³	—	149	4	no	—
513	C₂³	C₂³×D₁₄₉	1	2	yes	—
514	C₂³	C₂³×D₁₄₉	1	2	yes	—
515	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
516	Q₈	—	4	1	no	—
517	Q₈	—	596	1	no	—
518	Q₈	—	596	2	no	—
519	D₄	—	2	4	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	298	4	no	—
524	D₄	—	298	4	no	—
525	D₄	—	298	4	no	—
526	D₄	—	298	4	no	—
527	D₄	—	298	4	no	—
528	D₄	—	596	1	no	—
529	D₄	—	596	2	no	—
530	D₄	—	596	2	no	—
531	D₄	—	596	2	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	298	4	no	—
536	C₂×C₄	—	298	4	no	—
537	C₂×C₄	—	298	4	no	—
538	C₂×C₄	—	298	2	no	—
539	C₂×C₄	—	298	2	no	—
540	C₂×C₄	—	298	4	no	—
541	C₂×C₄	—	298	4	no	—
542	C₂×C₄	—	596	2	no	—
543	C₂×C₄	—	596	2	no	—
544	C₂×C₄	—	596	2	no	—
545	C₂×C₄	—	596	2	no	—
546	C₂×C₄	—	596	2	no	—
547	C₂×C₄	—	596	1	no	—
548	C₂×C₄	—	149	2	no	—
549	C₂×C₄	—	149	2	no	—
550	C₂×C₄	—	149	1	no	—
551	C₂×C₄	—	149	1	no	—
552	C₂×C₄	—	149	1	no	—
553	C₂×C₄	—	149	2	no	—
554	C₂×C₄	—	149	2	no	—
555	C₂×C₄	—	149	1	no	—
556	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
559	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
560	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
561	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	298	2	no	—
572	C₂²	—	298	2	no	—
573	C₂²	—	298	2	no	—
574	C₂²	—	298	2	no	—
575	C₂²	—	298	2	no	—
576	C₂²	—	596	4	no	—
577	C₂²	—	596	8	no	—
578	C₂²	—	149	4	no	—
579	C₂²	#41×D₁₄₉	1	2	yes	—
580	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	2	no	—
587	C₄	—	298	2	no	—
588	C₄	—	298	1	no	—
589	C₄	—	298	1	no	—
590	C₄	—	298	1	no	—
591	C₄	—	298	2	no	—
592	C₄	—	298	2	no	—
593	C₄	—	298	2	no	—
594	C₄	—	149	2	no	—
595	C₂	—	2	2	no	—
596	C₂	—	4	2	no	—
597	C₂	—	4	2	no	—
598	C₂	—	298	4	no	—
599	C₂	—	596	2	no	—
600	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
601	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic
602	C₂	#23750460	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#538×C₁₄₉	C₂
hypercenter	#538	D₁₄₉
hypocenter	C₁₄₉	#3459
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #23750250	C₂	semidirect
2. #23750218	C₂	semidirect
3. #23750217	C₂	semidirect
4. #23750216	C₂	semidirect
5. #23750213	C₂	semidirect
6. #23750209	C₂	semidirect
7. #23750207	C₂	semidirect
8. #23750185	C₂	semidirect
9. #23750183	C₂	semidirect
10. #23750161	C₂	semidirect
11. #23750158	C₂	semidirect
12. #23750156	C₂	semidirect
13. #23750154	C₂	semidirect
14. #23750135	C₂	semidirect
15. #23750133	C₂	semidirect
16. #23750131	C₂	semidirect
17. C₂×#18011871	C₂	semidirect
18. C₄×D₄×D₁₄₉	C₂	semidirect
19. #538×C₁₄₉	C₂	semidirect
20. C₂×#14558735	C₂²	semidirect
23. C₂³×Dic₁₄₉	C₂²	semidirect
25. C₂²×C₄×D₁₄₉	C₂²	semidirect
26. #18011906	C₂²	semidirect
27. #18011905	C₂²	semidirect
28. #18011904	C₂²	semidirect
29. #18011904	C₂²	semidirect
30. #18011904	C₂²	semidirect
31. #18011903	C₂²	semidirect
32. #18011902	C₂²	semidirect
33. #18011902	C₂²	semidirect
34. #18011901	C₂²	semidirect
35. #18011900	C₂²	semidirect
36. #18011898	C₂²	semidirect
37. #18011897	C₂²	semidirect
38. #18011896	C₂²	semidirect
39. #18011895	C₂²	semidirect
40. #18011895	C₂²	semidirect
41. #18011894	C₂²	semidirect
42. #18011893	C₂²	semidirect
43. #18011893	C₂²	semidirect
44. #18011893	C₂²	semidirect
45. #18011893	C₂²	semidirect
46. #18011893	C₂²	semidirect
47. #18011892	C₂²	semidirect
48. #18011892	C₂²	semidirect
49. #18011891	C₂²	semidirect
50. #18011890	C₂²	semidirect
51. #18011890	C₂²	semidirect
52. #18011889	C₂²	semidirect
53. #18011889	C₂²	semidirect
54. #18011889	C₂²	semidirect
55. #18011888	C₂²	semidirect
56. #18011888	C₂²	semidirect
57. #18011887	C₂²	semidirect
61. #18011884	C₂²	semidirect
63. #18011883	C₂²	semidirect
66. #18011881	C₂²	semidirect
67. #18011880	C₂²	semidirect
68. #18011879	C₂²	semidirect
69. #18011879	C₂²	semidirect
70. #18011879	C₂²	semidirect
71. Q₈×Dic₁₄₉	C₂²	semidirect
72. #18011876	C₂²	semidirect
73. C₄×D₅₉₆	C₂²	semidirect
74. D₄×Dic₁₄₉	C₂²	semidirect
75. D₄×Dic₁₄₉	C₂²	semidirect
76. D₄×Dic₁₄₉	C₂²	semidirect
77. #18011873	C₂²	semidirect
78. #18011873	C₂²	semidirect
79. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
80. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
81. #18011871	C₂²	semidirect
82. #18011871	C₂²	semidirect
83. #18011871	C₂²	semidirect
84. #18011871	C₂²	semidirect
85. #18011871	C₂²	semidirect
86. #18011871	C₂²	semidirect
87. #18011871	C₂²	semidirect
88. #18011869	C₂²	semidirect
89. #18011867	C₂²	semidirect
90. #18011867	C₂²	semidirect
91. C₂×#14558715	C₂²	semidirect
92. C₄⋊C₄×D₁₄₉	C₂²	semidirect
95. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
96. C₂×C₄×Dic₁₄₉	C₂²	semidirect
97. C₄²×D₁₄₉	C₂²	semidirect
98. #126×C₁₄₉	C₂²	semidirect
99. #124×C₁₄₉	C₂²	semidirect
100. #123×C₁₄₉	C₂²	semidirect
101. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
103. #121×C₁₄₉	C₂²	semidirect
104. #120×C₁₄₉	C₂²	semidirect
105. C₄×D₄×C₁₄₉	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₁₄₉	C₂²	semidirect
205. C₂²×D₁₄₉	#41	semidirect
301. C₁₄₉	#3459	semidirect
310. #538	D₁₄₉	semidirect
333. #126	C₂×D₁₄₉	semidirect
341. #124	C₂×D₁₄₉	semidirect
353. #123	C₂×D₁₄₉	semidirect
363. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
373. #121	C₂×D₁₄₉	semidirect
379. #120	C₂×D₁₄₉	semidirect
397. C₄×D₄	C₂×D₁₄₉	semidirect
406. C₂×C₂²⋊C₄	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750250	2
#23750218	2
#23750217	2
#23750216	2
#23750213	2
#23750209	2
#23750207	2
#23750185	2
#23750183	2
#23750161	2
#23750158	2
#23750156	2
#23750154	2
#23750135	2
#23750133	2
#23750131	2
C₂×#18011871	2
C₄×D₄×D₁₄₉	2
#538×C₁₄₉	2
#3459	149