Subgroups — #34058870

Order 19072.

1166 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750371	C₂	1	2	yes	maximal, complemented
2	#23750363	C₂	1	2	yes	maximal, complemented
3	#23750318	C₂	1	2	yes	maximal, complemented
4	#23750302	C₂	1	2	yes	maximal, complemented
5	#23750264	C₂	1	2	yes	maximal, complemented
6	#23750263	C₂	1	2	yes	maximal, complemented
7	#23750263	C₂	1	2	yes	maximal, complemented
8	#23750259	C₂	1	2	yes	maximal, complemented
9	#23750225	C₂	1	2	yes	maximal, complemented
10	#23750222	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750221	C₂	1	2	yes	maximal, complemented
12	#23750215	C₂	1	2	yes	maximal, complemented
13	#23750212	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750183	C₂	1	2	yes	maximal, complemented
15	#23750183	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750135	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#18011896	C₂	1	1	yes	maximal, characteristic, complemented
18	#121×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#537×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14558735	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic
22	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
24	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
25	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
26	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
27	#18011907	C₂²	1	2	yes	complemented
28	#18011906	C₂²	1	2	yes	complemented
29	#18011906	C₂²	1	2	yes	complemented
30	#18011906	C₂²	1	2	yes	complemented
31	#18011904	C₂²	1	2	yes	complemented
32	#18011901	C₂²	1	2	yes	complemented
33	#18011901	C₂²	1	2	yes	complemented
34	#18011900	C₂²	1	2	yes	complemented
35	#18011900	C₂²	1	2	yes	complemented
36	#18011897	C₂²	1	2	yes	complemented
37	#18011896	C₂²	1	2	yes	complemented
38	#18011896	C₂²	1	2	yes	complemented
39	#18011896	C₂²	1	2	yes	complemented
40	#18011896	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	#18011894	C₂²	1	2	yes	complemented
46	#18011894	C₂²	1	2	yes	complemented
47	#18011893	C₂²	1	2	yes	complemented
48	#18011893	C₂²	1	2	yes	complemented
49	#18011893	C₂²	1	2	yes	complemented
50	#18011892	C₂²	1	2	yes	complemented
51	#18011891	C₂²	1	1	yes	characteristic, complemented
52	#18011890	C₂²	1	1	yes	characteristic, complemented
53	#18011889	C₂²	1	2	yes	complemented
54	#18011887	C₂²	1	2	yes	complemented
55	#18011887	C₂²	1	2	yes	complemented
56	#18011886	C₂²	1	1	yes	characteristic, complemented
57	#18011886	C₂²	1	2	yes	complemented
58	#18011885	C₂²	1	1	yes	characteristic
59	#18011885	C₂²	1	2	yes	complemented
60	#18011885	C₂²	1	2	yes	complemented
61	#18011884	C₂²	1	2	yes	—
62	#18011884	C₂²	1	2	yes	complemented
63	#18011884	C₂²	1	2	yes	complemented
64	#18011883	C₂²	1	2	yes	complemented
65	#18011883	C₂²	1	2	yes	complemented
66	#18011883	C₂²	1	2	yes	complemented
67	#18011883	C₂²	1	2	yes	complemented
68	#18011883	C₂²	1	2	yes	complemented
69	#18011883	C₂²	1	2	yes	complemented
70	#18011882	C₂²	1	1	yes	characteristic, complemented
71	#18011882	C₂²	1	1	yes	characteristic, complemented
72	#18011881	C₂²	1	2	yes	—
73	#18011881	C₂²	1	2	yes	complemented
74	#18011881	C₂²	1	2	yes	complemented
75	#18011879	C₂²	1	2	yes	complemented
76	#18011879	C₂²	1	2	yes	complemented
77	#18011879	C₂²	1	2	yes	complemented
78	#18011879	C₂²	1	2	yes	complemented
79	#18011879	C₂²	1	2	yes	complemented
80	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
81	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
82	#18011873	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
86	#18011871	C₂²	1	2	yes	complemented
87	#18011871	C₂²	1	2	yes	complemented
88	#18011869	C₂²	1	1	yes	characteristic, complemented
89	#18011867	C₂²	1	2	yes	complemented
90	C₂×#14558715	C₂²	1	1	yes	characteristic, complemented
91	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
92	C₂×#14558713	C₂²	1	1	yes	characteristic, complemented
93	C₂×#14558713	C₂²	1	2	yes	complemented
94	C₂×#14558713	C₂²	1	2	yes	complemented
95	C₂×#14558713	C₂²	1	1	yes	characteristic, complemented
96	C₂×#14558713	C₂²	1	1	yes	characteristic, complemented
97	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
98	C₂×#41×C₁₄₉	C₂²	1	2	yes	complemented
99	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
100	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
101	#121×C₁₄₉	C₂²	1	2	yes	complemented
102	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
103	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
104	#121×C₁₄₉	C₂²	1	2	yes	complemented
105	#121×C₁₄₉	C₂²	1	2	yes	complemented
106	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
108	C₂³×D₁₄₉	C₂³	1	2	yes	—
109	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
110	C₂³×D₁₄₉	C₂³	1	2	yes	—
111	#14558735	—	4	2	no	—
112	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
113	C₂×D₅₉₆	—	4	2	no	—
114	C₂×D₅₉₆	C₂³	1	2	yes	—
115	C₂×D₅₉₆	C₂³	1	2	yes	—
116	C₂×D₅₉₆	C₂³	1	2	yes	—
117	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
118	C₂×D₅₉₆	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	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
128	D₄×D₁₄₉	—	4	4	no	—
129	D₄×D₁₄₉	—	4	4	no	—
130	D₄×D₁₄₉	—	4	2	no	—
131	D₄×D₁₄₉	—	4	4	no	—
132	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
134	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
136	C₂×C₄×D₁₄₉	—	4	2	no	—
137	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
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	2	yes	—
142	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
143	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
144	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
145	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₄₉	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	#14558715	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	#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	#14558713	C₂³	1	2	yes	—
170	#14558713	C₂³	1	2	yes	—
171	#14558713	C₂³	1	2	yes	—
172	#14558713	C₂³	1	2	yes	—
173	#14558713	C₂³	1	2	yes	—
174	#14558713	C₂³	1	2	yes	—
175	#14558713	C₂³	1	2	yes	—
176	#14558713	C₂³	1	2	yes	—
177	C₄×Dic₁₄₉	C₂³	1	2	yes	—
178	C₄×Dic₁₄₉	C₂³	1	2	yes	—
179	C₄×Dic₁₄₉	C₂³	1	2	yes	—
180	#41×C₁₄₉	—	4	4	no	—
181	C₂×Q₈×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	2	yes	—
185	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
186	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
187	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
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	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
192	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
193	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
194	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
195	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
196	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
197	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
198	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
202	C₂²×D₁₄₉	—	2	2	no	—
203	C₂²×D₁₄₉	—	2	2	no	—
204	C₂²×D₁₄₉	—	2	2	no	—
205	C₂²×D₁₄₉	—	2	4	no	—
206	C₂²×D₁₄₉	—	4	1	no	—
207	C₂²×D₁₄₉	—	4	2	no	—
208	C₂²×D₁₄₉	—	4	2	no	—
209	C₂²×D₁₄₉	—	4	2	no	—
210	C₂²×D₁₄₉	—	4	1	no	—
211	C₂²×D₁₄₉	—	4	2	no	—
212	C₂²×D₁₄₉	—	4	1	no	—
213	C₂²×D₁₄₉	—	4	2	no	—
214	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
215	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
216	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
217	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
218	Dic₂₉₈	—	4	1	no	—
219	D₅₉₆	—	2	4	no	—
220	D₅₉₆	—	4	2	no	—
221	D₅₉₆	—	4	2	no	—
222	D₅₉₆	—	4	1	no	—
223	D₅₉₆	—	4	2	no	—
224	C₂²⋊D₁₄₉	—	2	4	no	—
225	C₂²⋊D₁₄₉	—	2	4	no	—
226	C₂²⋊D₁₄₉	—	4	2	no	—
227	C₂²⋊D₁₄₉	—	4	2	no	—
228	C₂²⋊D₁₄₉	—	4	2	no	—
229	C₂²⋊D₁₄₉	—	4	2	no	—
230	C₂²⋊D₁₄₉	—	4	2	no	—
231	C₂²⋊D₁₄₉	—	4	2	no	—
232	C₂²⋊D₁₄₉	—	4	2	no	—
233	C₂×Dic₁₄₉	—	4	1	no	—
234	C₂×Dic₁₄₉	—	4	1	no	—
235	C₂×Dic₁₄₉	—	4	2	no	—
236	C₂×Dic₁₄₉	—	4	2	no	—
237	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
242	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
243	C₄×D₁₄₉	—	2	2	no	—
244	C₄×D₁₄₉	—	2	2	no	—
245	C₄×D₁₄₉	—	4	1	no	—
246	C₄×D₁₄₉	—	4	1	no	—
247	C₄×D₁₄₉	—	4	2	no	—
248	C₄×D₁₄₉	—	4	2	no	—
249	C₄×D₁₄₉	—	4	2	no	—
250	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
251	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
252	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
253	Q₈×C₁₄₉	—	4	2	no	—
254	D₄×C₁₄₉	—	2	4	no	—
255	D₄×C₁₄₉	—	2	4	no	—
256	D₄×C₁₄₉	—	4	1	no	—
257	D₄×C₁₄₉	—	4	2	no	—
258	D₄×C₁₄₉	—	4	1	no	—
259	D₄×C₁₄₉	—	4	2	no	—
260	C₂×C₄×C₁₄₉	—	2	2	no	—
261	C₂×C₄×C₁₄₉	—	4	1	no	—
262	C₂×C₄×C₁₄₉	—	4	1	no	—
263	C₂×C₄×C₁₄₉	—	4	2	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	2	yes	—
270	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
271	C₂²×C₁₄₉	—	2	1	no	—
272	C₂²×C₁₄₉	—	2	1	no	—
273	C₂²×C₁₄₉	—	2	2	no	—
274	C₂²×C₁₄₉	—	2	2	no	—
275	C₂²×C₁₄₉	—	2	2	no	—
276	C₂²×C₁₄₉	—	2	2	no	—
277	C₂²×C₁₄₉	—	2	2	no	—
278	C₂²×C₁₄₉	—	2	2	no	—
279	C₂²×C₁₄₉	H(5,𝔽₂)	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	2	no	—
285	C₂×D₁₄₉	—	2	2	no	—
286	C₂×D₁₄₉	—	2	2	no	—
287	C₂×D₁₄₉	—	2	1	no	—
288	C₂×D₁₄₉	—	2	2	no	—
289	C₂×D₁₄₉	—	2	1	no	—
290	C₂×D₁₄₉	—	2	2	no	—
291	C₂×D₁₄₉	—	2	2	no	—
292	C₂×D₁₄₉	—	4	4	no	—
293	C₂×D₁₄₉	—	8	4	no	—
294	C₂×D₁₄₉	—	8	2	no	—
295	C₂×D₁₄₉	—	8	4	no	—
296	C₂×D₁₄₉	H(5,𝔽₂)	1	2	yes	—
297	C₄×C₁₄₉	—	2	2	no	—
298	C₄×C₁₄₉	—	2	2	no	—
299	C₄×C₁₄₉	—	2	2	no	—
300	C₄×C₁₄₉	—	2	1	no	—
301	C₄×C₁₄₉	—	2	1	no	—
302	C₄×C₁₄₉	—	2	2	no	—
303	Dic₁₄₉	—	2	1	no	—
304	Dic₁₄₉	—	2	1	no	—
305	Dic₁₄₉	—	2	2	no	—
306	Dic₁₄₉	—	2	2	no	—
307	Dic₁₄₉	—	2	2	no	—
308	Dic₁₄₉	—	2	2	no	—
309	C₂×C₁₄₉	—	2	2	no	—
310	C₂×C₁₄₉	—	4	2	no	—
311	C₂×C₁₄₉	—	4	2	no	—
312	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂×C₁₄₉	#585	1	1	yes	characteristic
315	D₁₄₉	—	2	2	no	—
316	D₁₄₉	—	4	1	no	—
317	D₁₄₉	—	4	2	no	—
318	D₁₄₉	—	4	2	no	—
319	C₁₄₉	#3534	1	1	yes	characteristic, complemented, Sylow
320	#3534	—	149	1	no	maximal, Sylow
321	#562	—	149	2	no	—
322	#560	—	149	2	no	—
323	#553	—	149	2	no	—
324	#551	—	149	2	no	—
325	#546	—	149	2	no	—
326	#546	—	149	2	no	—
327	#546	—	149	2	no	—
328	D₄²	—	149	2	no	—
329	#540	—	149	2	no	—
330	#539	—	149	2	no	—
331	#539	—	149	1	no	—
332	#538	—	149	2	no	—
333	#538	—	149	1	no	—
334	#537	D₁₄₉	1	1	yes	characteristic, complemented
335	#534	—	149	1	no	—
336	#534	—	149	2	no	—
337	#525	—	149	1	no	—
338	C₂×#123	—	149	1	no	—
339	C₂×#121	—	149	1	no	—
340	C₂×#41	—	149	1	no	—
341	C₂×#41	C₂×D₁₄₉	1	2	yes	complemented
342	C₂²×D₄	—	149	1	no	—
343	C₂²×D₄	—	149	2	no	—
344	C₂²×D₄	—	149	2	no	—
345	C₂²×D₄	—	149	2	no	—
346	C₂²×D₄	—	149	1	no	—
347	C₂³×C₄	—	149	1	no	—
348	#127	—	149	2	no	—
349	#126	—	149	2	no	—
350	#126	—	149	2	no	—
351	#126	—	149	2	no	—
352	#126	—	149	2	no	—
353	#125	—	149	2	no	—
354	#125	—	149	2	no	—
355	#124	—	149	2	no	—
356	#124	—	149	2	no	—
357	#124	—	149	2	no	—
358	#123	—	149	2	no	—
359	#123	—	149	2	no	—
360	#123	—	149	2	no	—
361	#123	—	149	2	no	—
362	#123	—	149	2	no	—
363	#123	—	149	2	no	—
364	#123	—	149	2	no	—
365	#123	—	149	2	no	—
366	#123	—	149	2	no	—
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	C₂²⋊Q₈	—	149	2	no	—
373	C₂²⋊Q₈	—	149	2	no	—
374	C₂²⋊Q₈	—	149	1	no	—
375	C₂²⋊Q₈	—	149	1	no	—
376	C₂²⋊Q₈	—	149	2	no	—
377	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
378	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
379	#121	—	149	1	no	—
380	#121	—	149	2	no	—
381	#121	—	149	1	no	—
382	#121	—	149	2	no	—
383	#121	—	149	2	no	—
384	#121	—	149	2	no	—
385	#121	—	149	2	no	—
386	#121	—	149	2	no	—
387	#121	—	149	1	no	—
388	#121	—	149	2	no	—
389	#121	—	149	2	no	—
390	#121	—	149	1	no	—
391	#121	—	149	2	no	—
392	#121	—	149	2	no	—
393	#121	—	149	2	no	—
394	#121	—	149	2	no	—
395	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
396	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
397	#121	C₂×D₁₄₉	1	2	yes	complemented
398	#121	C₂×D₁₄₉	1	2	yes	complemented
399	#121	C₂×D₁₄₉	1	2	yes	complemented
400	#120	—	149	2	no	—
401	#120	—	149	2	no	—
402	#120	—	149	2	no	—
403	#120	—	149	2	no	—
404	#120	—	149	2	no	—
405	#120	—	149	2	no	—
406	#120	—	149	2	no	—
407	#120	—	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	2	no	—
412	C₄×D₄	—	149	2	no	—
413	C₄×D₄	—	149	2	no	—
414	C₄×D₄	—	149	2	no	—
415	C₄×D₄	—	149	2	no	—
416	#117	—	149	1	no	—
417	#117	—	149	2	no	—
418	C₂×C₄⋊C₄	—	149	1	no	—
419	C₂×C₄⋊C₄	—	149	1	no	—
420	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
421	C₂×C₂²⋊C₄	—	149	1	no	—
422	C₂×C₂²⋊C₄	—	149	1	no	—
423	C₂×C₂²⋊C₄	—	149	1	no	—
424	C₂×C₂²⋊C₄	—	149	2	no	—
425	C₂×C₂²⋊C₄	—	149	2	no	—
426	C₂×C₂²⋊C₄	—	149	2	no	—
427	C₂⁴	—	149	1	no	—
428	C₂⁴	—	149	2	no	—
429	C₂⁴	—	149	1	no	—
430	C₂⁴	—	149	2	no	—
431	#41	—	4	4	no	—
432	#41	—	596	2	no	—
433	C₂×Q₈	—	149	1	no	—
434	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
435	C₂×D₄	—	596	2	no	—
436	C₂×D₄	—	596	2	no	—
437	C₂×D₄	—	596	4	no	—
438	C₂×D₄	—	596	4	no	—
439	C₂×D₄	—	596	4	no	—
440	C₂×D₄	—	149	2	no	—
441	C₂×D₄	—	149	2	no	—
442	C₂×D₄	—	149	2	no	—
443	C₂×D₄	—	149	2	no	—
444	C₂×D₄	—	149	2	no	—
445	C₂×D₄	—	149	2	no	—
446	C₂×D₄	—	149	2	no	—
447	C₂×D₄	—	149	2	no	—
448	C₂×D₄	—	149	2	no	—
449	C₂×D₄	—	149	2	no	—
450	C₂×D₄	—	149	1	no	—
451	C₂×D₄	—	149	2	no	—
452	C₂×D₄	—	149	2	no	—
453	C₂×D₄	—	149	2	no	—
454	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
455	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
456	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
457	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
458	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
459	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
460	C₂²×C₄	—	596	2	no	—
461	C₂²×C₄	—	149	1	no	—
462	C₂²×C₄	—	149	1	no	—
463	C₂²×C₄	—	149	1	no	—
464	C₂²×C₄	—	149	1	no	—
465	C₂²×C₄	—	149	2	no	—
466	C₂²×C₄	—	149	2	no	—
467	C₂²×C₄	—	149	2	no	—
468	C₂²×C₄	—	149	1	no	—
469	C₂²×C₄	—	149	2	no	—
470	C₂²×C₄	—	149	2	no	—
471	C₂²×C₄	—	149	1	no	—
472	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
476	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
477	C₄⋊C₄	—	149	2	no	—
478	C₄⋊C₄	—	149	2	no	—
479	C₄⋊C₄	—	149	1	no	—
480	C₄⋊C₄	—	149	2	no	—
481	C₄⋊C₄	—	149	2	no	—
482	C₄⋊C₄	—	149	1	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	C₂²×D₁₄₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
491	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
492	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
494	C₂²⋊C₄	—	149	2	no	—
495	C₂²⋊C₄	—	149	2	no	—
496	C₂²⋊C₄	—	149	2	no	—
497	C₂²⋊C₄	—	149	2	no	—
498	C₂²⋊C₄	—	149	2	no	—
499	C₂²⋊C₄	—	149	2	no	—
500	C₂²⋊C₄	—	149	2	no	—
501	C₂²⋊C₄	—	149	2	no	—
502	C₂²⋊C₄	—	149	2	no	—
503	C₂²⋊C₄	—	149	2	no	—
504	C₂²⋊C₄	—	149	2	no	—
505	C₂²⋊C₄	—	149	2	no	—
506	C₂²⋊C₄	—	149	2	no	—
507	C₂²⋊C₄	—	149	2	no	—
508	C₂²⋊C₄	—	149	2	no	—
509	C₂²⋊C₄	—	149	2	no	—
510	C₂²⋊C₄	—	149	2	no	—
511	C₂²⋊C₄	—	149	2	no	—
512	C₂²⋊C₄	—	149	2	no	—
513	C₂²⋊C₄	—	149	2	no	—
514	C₂²⋊C₄	—	149	2	no	—
515	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
518	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
519	C₄²	—	149	2	no	—
520	C₄²	—	149	2	no	—
521	C₄²	—	149	2	no	—
522	C₂³	—	298	2	no	—
523	C₂³	—	298	4	no	—
524	C₂³	—	298	2	no	—
525	C₂³	—	298	2	no	—
526	C₂³	—	596	1	no	—
527	C₂³	—	596	1	no	—
528	C₂³	—	596	2	no	—
529	C₂³	—	596	2	no	—
530	C₂³	—	596	2	no	—
531	C₂³	—	596	1	no	—
532	C₂³	—	596	2	no	—
533	C₂³	—	596	2	no	—
534	C₂³	—	149	2	no	—
535	C₂³	—	149	2	no	—
536	C₂³	—	149	1	no	—
537	C₂³	—	149	1	no	—
538	C₂³	C₂³×D₁₄₉	1	2	yes	—
539	C₂³	C₂³×D₁₄₉	1	2	yes	—
540	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
541	Q₈	—	4	2	no	—
542	Q₈	—	596	1	no	—
543	D₄	—	2	4	no	—
544	D₄	—	2	4	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	1	no	—
549	D₄	—	298	4	no	—
550	D₄	—	298	4	no	—
551	D₄	—	298	4	no	—
552	D₄	—	596	1	no	—
553	D₄	—	596	2	no	—
554	D₄	—	596	2	no	—
555	D₄	—	596	2	no	—
556	D₄	—	596	2	no	—
557	D₄	—	596	2	no	—
558	D₄	—	596	2	no	—
559	D₄	—	596	2	no	—
560	D₄	—	596	2	no	—
561	D₄	—	596	2	no	—
562	D₄	—	596	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	298	2	no	—
569	C₂×C₄	—	298	2	no	—
570	C₂×C₄	—	596	1	no	—
571	C₂×C₄	—	596	1	no	—
572	C₂×C₄	—	596	2	no	—
573	C₂×C₄	—	596	2	no	—
574	C₂×C₄	—	596	2	no	—
575	C₂×C₄	—	596	1	no	—
576	C₂×C₄	—	596	1	no	—
577	C₂×C₄	—	596	2	no	—
578	C₂×C₄	—	596	2	no	—
579	C₂×C₄	—	149	2	no	—
580	C₂×C₄	—	149	1	no	—
581	C₂×C₄	—	149	2	no	—
582	C₂×C₄	—	149	2	no	—
583	C₂×C₄	—	149	2	no	—
584	C₂×C₄	—	149	1	no	—
585	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
586	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
587	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
588	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
589	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	298	1	no	—
600	C₂²	—	298	1	no	—
601	C₂²	—	298	1	no	—
602	C₂²	—	298	2	no	—
603	C₂²	—	298	2	no	—
604	C₂²	—	298	2	no	—
605	C₂²	—	298	2	no	—
606	C₂²	—	298	1	no	—
607	C₂²	—	298	1	no	—
608	C₂²	—	298	2	no	—
609	C₂²	—	298	2	no	—
610	C₂²	—	596	4	no	—
611	C₂²	—	149	2	no	—
612	C₂²	—	1192	2	no	—
613	C₂²	—	1192	4	no	—
614	C₂²	—	1192	4	no	—
615	C₂²	#18011956	1	2	yes	—
616	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	298	1	no	—
624	C₄	—	298	1	no	—
625	C₄	—	298	2	no	—
626	C₄	—	298	2	no	—
627	C₄	—	298	2	no	—
628	C₄	—	298	2	no	—
629	C₂	—	2	2	no	—
630	C₂	—	4	2	no	—
631	C₂	—	4	2	no	—
632	C₂	—	298	2	no	—
633	C₂	—	596	1	no	—
634	C₂	—	596	2	no	—
635	C₂	—	596	2	no	—
636	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic
637	C₂	C₂×#18011956	1	1	yes	characteristic
638	C₂	#23750462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#537×C₁₄₉	C₂
hypercenter	#537	D₁₄₉
hypocenter	C₁₄₉	#3534
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. #23750371	C₂	semidirect
2. #23750363	C₂	semidirect
3. #23750318	C₂	semidirect
4. #23750302	C₂	semidirect
5. #23750264	C₂	semidirect
6. #23750263	C₂	semidirect
7. #23750263	C₂	semidirect
8. #23750259	C₂	semidirect
9. #23750225	C₂	semidirect
10. #23750222	C₂	semidirect
11. #23750221	C₂	semidirect
12. #23750215	C₂	semidirect
13. #23750212	C₂	semidirect
14. #23750183	C₂	semidirect
15. #23750183	C₂	semidirect
16. #23750135	C₂	semidirect
17. C₂×#18011896	C₂	semidirect
18. #121×D₁₄₉	C₂	semidirect
19. #537×C₁₄₉	C₂	semidirect
20. C₂×#14558735	C₂²	semidirect
22. C₂×D₄×D₁₄₉	C₂²	semidirect
23. C₂×D₄×D₁₄₉	C₂²	semidirect
24. C₂×D₄×D₁₄₉	C₂²	semidirect
25. C₂×D₄×D₁₄₉	C₂²	semidirect
26. C₂²×C₄×D₁₄₉	C₂²	semidirect
27. #18011907	C₂²	semidirect
28. #18011906	C₂²	semidirect
29. #18011906	C₂²	semidirect
30. #18011906	C₂²	semidirect
31. #18011904	C₂²	semidirect
32. #18011901	C₂²	semidirect
33. #18011901	C₂²	semidirect
34. #18011900	C₂²	semidirect
35. #18011900	C₂²	semidirect
36. #18011897	C₂²	semidirect
37. #18011896	C₂²	semidirect
38. #18011896	C₂²	semidirect
39. #18011896	C₂²	semidirect
40. #18011896	C₂²	semidirect
41. #18011896	C₂²	semidirect
42. #18011896	C₂²	semidirect
43. #18011895	C₂²	semidirect
44. #18011894	C₂²	semidirect
45. #18011894	C₂²	semidirect
46. #18011894	C₂²	semidirect
47. #18011893	C₂²	semidirect
48. #18011893	C₂²	semidirect
49. #18011893	C₂²	semidirect
50. #18011892	C₂²	semidirect
51. #18011891	C₂²	semidirect
52. #18011890	C₂²	semidirect
53. #18011889	C₂²	semidirect
54. #18011887	C₂²	semidirect
55. #18011887	C₂²	semidirect
56. #18011886	C₂²	semidirect
57. #18011886	C₂²	semidirect
59. #18011885	C₂²	semidirect
60. #18011885	C₂²	semidirect
62. #18011884	C₂²	semidirect
63. #18011884	C₂²	semidirect
64. #18011883	C₂²	semidirect
65. #18011883	C₂²	semidirect
66. #18011883	C₂²	semidirect
67. #18011883	C₂²	semidirect
68. #18011883	C₂²	semidirect
69. #18011883	C₂²	semidirect
70. #18011882	C₂²	semidirect
71. #18011882	C₂²	semidirect
73. #18011881	C₂²	semidirect
74. #18011881	C₂²	semidirect
75. #18011879	C₂²	semidirect
76. #18011879	C₂²	semidirect
77. #18011879	C₂²	semidirect
78. #18011879	C₂²	semidirect
79. #18011879	C₂²	semidirect
80. D₄×Dic₁₄₉	C₂²	semidirect
81. D₄×Dic₁₄₉	C₂²	semidirect
82. #18011873	C₂²	semidirect
83. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
84. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
85. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
86. #18011871	C₂²	semidirect
87. #18011871	C₂²	semidirect
88. #18011869	C₂²	semidirect
89. #18011867	C₂²	semidirect
90. C₂×#14558715	C₂²	semidirect
91. C₄⋊C₄×D₁₄₉	C₂²	semidirect
92. C₂×#14558713	C₂²	semidirect
93. C₂×#14558713	C₂²	semidirect
94. C₂×#14558713	C₂²	semidirect
95. C₂×#14558713	C₂²	semidirect
96. C₂×#14558713	C₂²	semidirect
97. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
98. C₂×#41×C₁₄₉	C₂²	semidirect
99. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
100. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
101. #121×C₁₄₉	C₂²	semidirect
102. #121×C₁₄₉	C₂²	semidirect
103. #121×C₁₄₉	C₂²	semidirect
104. #121×C₁₄₉	C₂²	semidirect
105. #121×C₁₄₉	C₂²	semidirect
106. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
319. C₁₄₉	#3534	semidirect
334. #537	D₁₄₉	semidirect
341. C₂×#41	C₂×D₁₄₉	semidirect
377. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
378. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
395. #121	C₂×D₁₄₉	semidirect
396. #121	C₂×D₁₄₉	semidirect
397. #121	C₂×D₁₄₉	semidirect
398. #121	C₂×D₁₄₉	semidirect
399. #121	C₂×D₁₄₉	semidirect
420. C₂×C₄⋊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
#23750371	2
#23750363	2
#23750318	2
#23750302	2
#23750264	2
#23750263	2
#23750259	2
#23750225	2
#23750222	2
#23750221	2
#23750215	2
#23750212	2
#23750183	2
#23750135	2
C₂×#18011896	2
#121×D₁₄₉	2
#537×C₁₄₉	2
#3534	149