Subgroups — #34058882

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	#23750369	C₂	1	2	yes	maximal, complemented
2	#23750365	C₂	1	2	yes	maximal, complemented
3	#23750321	C₂	1	2	yes	maximal, complemented
4	#23750298	C₂	1	2	yes	maximal, complemented
5	#23750270	C₂	1	2	yes	maximal, complemented
6	#23750268	C₂	1	2	yes	maximal, complemented
7	#23750262	C₂	1	2	yes	maximal, complemented
8	#23750257	C₂	1	2	yes	maximal, complemented
9	#23750228	C₂	1	2	yes	maximal, complemented
10	#23750224	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750216	C₂	1	2	yes	maximal, complemented
12	#23750214	C₂	1	2	yes	maximal, complemented
13	#23750202	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750187	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750183	C₂	1	2	yes	maximal, complemented
16	#23750138	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#18011893	C₂	1	1	yes	maximal, characteristic, complemented
18	#121×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#538×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14558737	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14558735	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
24	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
26	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
27	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
28	#18011907	C₂²	1	2	yes	complemented
29	#18011906	C₂²	1	2	yes	complemented
30	#18011906	C₂²	1	2	yes	complemented
31	#18011906	C₂²	1	2	yes	complemented
32	#18011903	C₂²	1	2	yes	complemented
33	#18011902	C₂²	1	2	yes	complemented
34	#18011899	C₂²	1	2	yes	complemented
35	#18011897	C₂²	1	2	yes	complemented
36	#18011896	C₂²	1	2	yes	complemented
37	#18011896	C₂²	1	2	yes	complemented
38	#18011895	C₂²	1	2	yes	complemented
39	#18011895	C₂²	1	2	yes	complemented
40	#18011895	C₂²	1	2	yes	complemented
41	#18011895	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	#18011893	C₂²	1	2	yes	complemented
48	#18011893	C₂²	1	2	yes	complemented
49	#18011891	C₂²	1	2	yes	complemented
50	#18011889	C₂²	1	2	yes	complemented
51	#18011888	C₂²	1	2	yes	complemented
52	#18011888	C₂²	1	2	yes	complemented
53	#18011887	C₂²	1	2	yes	complemented
54	#18011887	C₂²	1	1	yes	characteristic, complemented
55	#18011886	C₂²	1	1	yes	characteristic, complemented
56	#18011886	C₂²	1	2	yes	complemented
57	#18011886	C₂²	1	1	yes	characteristic, complemented
58	#18011885	C₂²	1	1	yes	characteristic
59	#18011885	C₂²	1	2	yes	complemented
60	#18011885	C₂²	1	1	yes	characteristic, complemented
61	#18011885	C₂²	1	2	yes	complemented
62	#18011885	C₂²	1	2	yes	complemented
63	#18011884	C₂²	1	2	yes	—
64	#18011884	C₂²	1	2	yes	complemented
65	#18011884	C₂²	1	2	yes	complemented
66	#18011884	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	#18011883	C₂²	1	2	yes	complemented
71	#18011883	C₂²	1	2	yes	complemented
72	#18011882	C₂²	1	1	yes	characteristic, complemented
73	#18011882	C₂²	1	2	yes	complemented
74	#18011881	C₂²	1	2	yes	complemented
75	#18011881	C₂²	1	2	yes	complemented
76	#18011881	C₂²	1	2	yes	complemented
77	#18011881	C₂²	1	2	yes	complemented
78	#18011881	C₂²	1	2	yes	complemented
79	#18011879	C₂²	1	2	yes	—
80	#18011879	C₂²	1	2	yes	complemented
81	C₄×D₅₉₆	C₂²	1	2	yes	complemented
82	C₄×D₅₉₆	C₂²	1	2	yes	complemented
83	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
84	#18011873	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	#18011870	C₂²	1	2	yes	complemented
89	#18011869	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
91	C₂×#14558715	C₂²	1	1	yes	characteristic, complemented
92	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₂²⋊Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
94	C₂×#14558713	C₂²	1	2	yes	complemented
95	C₂×#14558713	C₂²	1	1	yes	characteristic, complemented
96	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×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	2	yes	complemented
103	#121×C₁₄₉	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic
108	C₂³×D₁₄₉	C₂³	1	2	yes	—
109	C₂³×D₁₄₉	C₂³	1	2	yes	—
110	#14558737	—	4	2	no	—
111	#14558735	—	4	4	no	—
112	C₂×Dic₂₉₈	C₂³	1	2	yes	—
113	C₂×D₅₉₆	C₂³	1	2	yes	—
114	C₂×D₅₉₆	C₂³	1	2	yes	—
115	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
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	—	4	4	no	—
120	C₂×C₂²⋊D₁₄₉	—	4	2	no	—
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	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
131	D₄×D₁₄₉	—	4	4	no	—
132	D₄×D₁₄₉	—	4	2	no	—
133	D₄×D₁₄₉	—	4	4	no	—
134	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
138	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
139	C₂×C₄×D₁₄₉	—	4	2	no	—
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	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
146	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
147	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
148	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
149	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
150	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
151	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
154	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
155	#14558715	C₂³	1	2	yes	—
156	#14558715	C₂³	1	2	yes	—
157	#14558715	C₂³	1	2	yes	—
158	#14558715	C₂³	1	2	yes	—
159	#14558715	C₂³	1	2	yes	—
160	#14558715	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
162	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
163	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
164	C₂²⋊Dic₁₄₉	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	#14558713	C₂³	1	2	yes	—
178	#14558713	C₂³	1	2	yes	—
179	C₄×Dic₁₄₉	C₂³	1	2	yes	—
180	C₄×Dic₁₄₉	C₂³	1	2	yes	—
181	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
182	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
183	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
184	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
185	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
186	C₂×D₄×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	2	yes	—
190	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
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	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	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
201	C₄²×C₁₄₉	C₂³	1	2	yes	—
202	C₂²×D₁₄₉	—	2	2	no	—
203	C₂²×D₁₄₉	—	2	2	no	—
204	C₂²×D₁₄₉	—	2	4	no	—
205	C₂²×D₁₄₉	—	4	1	no	—
206	C₂²×D₁₄₉	—	4	2	no	—
207	C₂²×D₁₄₉	—	4	2	no	—
208	C₂²×D₁₄₉	—	4	2	no	—
209	C₂²×D₁₄₉	—	4	2	no	—
210	C₂²×D₁₄₉	—	4	2	no	—
211	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
212	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
213	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
214	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
215	Dic₂₉₈	—	4	2	no	—
216	D₅₉₆	—	2	4	no	—
217	D₅₉₆	—	4	1	no	—
218	D₅₉₆	—	4	2	no	—
219	D₅₉₆	—	4	2	no	—
220	D₅₉₆	—	4	2	no	—
221	D₅₉₆	—	4	1	no	—
222	C₂²⋊D₁₄₉	—	2	4	no	—
223	C₂²⋊D₁₄₉	—	2	4	no	—
224	C₂²⋊D₁₄₉	—	2	4	no	—
225	C₂²⋊D₁₄₉	—	4	2	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	C₂×Dic₁₄₉	—	2	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	C₄×D₁₄₉	—	4	2	no	—
251	C₂³×C₁₄₉	—	2	2	no	—
252	C₂³×C₁₄₉	—	4	1	no	—
253	C₂³×C₁₄₉	—	4	1	no	—
254	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
255	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
256	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
257	Q₈×C₁₄₉	—	4	1	no	—
258	D₄×C₁₄₉	—	2	4	no	—
259	D₄×C₁₄₉	—	4	1	no	—
260	D₄×C₁₄₉	—	4	2	no	—
261	D₄×C₁₄₉	—	4	2	no	—
262	C₂×C₄×C₁₄₉	—	4	1	no	—
263	C₂×C₄×C₁₄₉	—	4	1	no	—
264	C₂×C₄×C₁₄₉	—	4	2	no	—
265	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
266	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
267	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
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	—	8	2	no	—
280	C₂²×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
281	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
282	C₂×D₁₄₉	—	2	1	no	—
283	C₂×D₁₄₉	—	2	1	no	—
284	C₂×D₁₄₉	—	2	1	no	—
285	C₂×D₁₄₉	—	2	2	no	—
286	C₂×D₁₄₉	—	2	2	no	—
287	C₂×D₁₄₉	—	2	2	no	—
288	C₂×D₁₄₉	—	2	2	no	—
289	C₂×D₁₄₉	—	2	1	no	—
290	C₂×D₁₄₉	—	2	1	no	—
291	C₂×D₁₄₉	—	2	2	no	—
292	C₂×D₁₄₉	—	2	2	no	—
293	C₂×D₁₄₉	—	4	4	no	—
294	C₂×D₁₄₉	—	8	4	no	—
295	C₂×D₁₄₉	—	8	4	no	—
296	C₂×D₁₄₉	H(5,𝔽₂)	1	2	yes	—
297	C₄×C₁₄₉	—	2	1	no	—
298	C₄×C₁₄₉	—	2	1	no	—
299	C₄×C₁₄₉	—	2	2	no	—
300	C₄×C₁₄₉	—	2	2	no	—
301	C₄×C₁₄₉	—	2	2	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	D₁₄₉	1	1	yes	characteristic, complemented
334	#537	—	149	1	no	—
335	#534	—	149	2	no	—
336	#534	—	149	1	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	—	149	2	no	—
342	C₂²×D₄	—	149	1	no	—
343	C₂²×D₄	—	149	2	no	—
344	C₂²×D₄	—	149	1	no	—
345	C₂²×D₄	—	149	2	no	—
346	C₂²×D₄	—	149	2	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	C₂×D₁₄₉	1	2	yes	complemented
353	#125	—	149	2	no	—
354	#125	—	149	2	no	—
355	#124	—	149	2	no	—
356	#124	—	149	2	no	—
357	#124	C₂×D₁₄₉	1	2	yes	complemented
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	C₂×D₁₄₉	1	2	yes	complemented
372	C₂²⋊Q₈	—	149	1	no	—
373	C₂²⋊Q₈	—	149	2	no	—
374	C₂²⋊Q₈	—	149	2	no	—
375	C₂²⋊Q₈	—	149	2	no	—
376	C₂²⋊Q₈	—	149	2	no	—
377	C₂²⋊Q₈	—	149	2	no	—
378	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
379	#121	—	149	1	no	—
380	#121	—	149	2	no	—
381	#121	—	149	2	no	—
382	#121	—	149	2	no	—
383	#121	—	149	2	no	—
384	#121	—	149	2	no	—
385	#121	—	149	2	no	—
386	#121	—	149	1	no	—
387	#121	—	149	1	no	—
388	#121	—	149	2	no	—
389	#121	—	149	2	no	—
390	#121	—	149	2	no	—
391	#121	—	149	1	no	—
392	#121	—	149	1	no	—
393	#121	—	149	2	no	—
394	#121	—	149	2	no	—
395	#121	—	149	2	no	—
396	#121	—	149	2	no	—
397	#121	—	149	2	no	—
398	#121	C₂×D₁₄₉	1	1	yes	characteristic, 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	C₂×D₁₄₉	1	2	yes	complemented
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	C₂×D₁₄₉	1	2	yes	complemented
416	#117	—	149	2	no	—
417	#117	—	149	1	no	—
418	C₂×C₄⋊C₄	—	149	1	no	—
419	C₂×C₄⋊C₄	—	149	1	no	—
420	C₂×C₄⋊C₄	—	149	1	no	—
421	C₂×C₂²⋊C₄	—	149	1	no	—
422	C₂×C₂²⋊C₄	—	149	1	no	—
423	C₂×C₂²⋊C₄	—	149	2	no	—
424	C₂×C₂²⋊C₄	—	149	2	no	—
425	C₂×C₂²⋊C₄	—	149	2	no	—
426	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
427	C₂⁴	—	149	1	no	—
428	C₂⁴	—	149	2	no	—
429	C₂⁴	—	149	2	no	—
430	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
431	#41	—	596	4	no	—
432	#41	—	596	2	no	—
433	C₂×Q₈	—	149	2	no	—
434	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
435	C₂×D₄	—	596	2	no	—
436	C₂×D₄	—	596	4	no	—
437	C₂×D₄	—	596	4	no	—
438	C₂×D₄	—	596	4	no	—
439	C₂×D₄	—	596	2	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	2	no	—
451	C₂×D₄	—	149	2	no	—
452	C₂×D₄	—	149	2	no	—
453	C₂×D₄	—	149	1	no	—
454	C₂×D₄	—	149	1	no	—
455	C₂×D₄	—	149	2	no	—
456	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
457	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
458	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
459	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
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	1	no	—
467	C₂²×C₄	—	149	2	no	—
468	C₂²×C₄	—	149	2	no	—
469	C₂²×C₄	—	149	2	no	—
470	C₂²×C₄	—	149	2	no	—
471	C₂²×C₄	—	149	1	no	—
472	C₂²×C₄	—	149	2	no	—
473	C₂²×C₄	—	149	1	no	—
474	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
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	2	no	—
483	C₄⋊C₄	—	149	1	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	2	no	—
490	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
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	C₂²×D₁₄₉	1	2	yes	—
513	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
514	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
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	C₂²×D₁₄₉	1	2	yes	—
522	C₂³	—	2	2	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	298	2	no	—
526	C₂³	—	298	4	no	—
527	C₂³	—	298	2	no	—
528	C₂³	—	596	1	no	—
529	C₂³	—	596	2	no	—
530	C₂³	—	596	2	no	—
531	C₂³	—	596	2	no	—
532	C₂³	—	596	2	no	—
533	C₂³	—	596	2	no	—
534	C₂³	—	149	2	no	—
535	C₂³	—	149	1	no	—
536	C₂³	—	149	2	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	1	no	—
542	Q₈	—	596	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	2	no	—
547	D₄	—	298	4	no	—
548	D₄	—	298	4	no	—
549	D₄	—	298	4	no	—
550	D₄	—	298	4	no	—
551	D₄	—	596	1	no	—
552	D₄	—	596	2	no	—
553	D₄	—	596	2	no	—
554	D₄	—	596	2	no	—
555	D₄	—	596	1	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	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	298	2	no	—
567	C₂×C₄	—	298	2	no	—
568	C₂×C₄	—	298	2	no	—
569	C₂×C₄	—	596	1	no	—
570	C₂×C₄	—	596	1	no	—
571	C₂×C₄	—	596	2	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	1	no	—
580	C₂×C₄	—	149	2	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	—	8	2	no	—
600	C₂²	—	298	1	no	—
601	C₂²	—	298	1	no	—
602	C₂²	—	298	1	no	—
603	C₂²	—	298	2	no	—
604	C₂²	—	298	2	no	—
605	C₂²	—	298	2	no	—
606	C₂²	—	298	2	no	—
607	C₂²	—	298	1	no	—
608	C₂²	—	298	1	no	—
609	C₂²	—	298	2	no	—
610	C₂²	—	298	2	no	—
611	C₂²	—	596	4	no	—
612	C₂²	—	149	2	no	—
613	C₂²	—	1192	4	no	—
614	C₂²	—	1192	4	no	—
615	C₂²	#18011957	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×#18011957	1	1	yes	characteristic
638	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	#3534
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. #23750369	C₂	semidirect
2. #23750365	C₂	semidirect
3. #23750321	C₂	semidirect
4. #23750298	C₂	semidirect
5. #23750270	C₂	semidirect
6. #23750268	C₂	semidirect
7. #23750262	C₂	semidirect
8. #23750257	C₂	semidirect
9. #23750228	C₂	semidirect
10. #23750224	C₂	semidirect
11. #23750216	C₂	semidirect
12. #23750214	C₂	semidirect
13. #23750202	C₂	semidirect
14. #23750187	C₂	semidirect
15. #23750183	C₂	semidirect
16. #23750138	C₂	semidirect
17. C₂×#18011893	C₂	semidirect
18. #121×D₁₄₉	C₂	semidirect
19. #538×C₁₄₉	C₂	semidirect
20. C₂×#14558737	C₂²	semidirect
21. C₂×#14558735	C₂²	semidirect
23. C₂²×C₂²⋊D₁₄₉	C₂²	semidirect
24. C₂×D₄×D₁₄₉	C₂²	semidirect
25. C₂×D₄×D₁₄₉	C₂²	semidirect
26. C₂×D₄×D₁₄₉	C₂²	semidirect
27. C₂²×C₄×D₁₄₉	C₂²	semidirect
28. #18011907	C₂²	semidirect
29. #18011906	C₂²	semidirect
30. #18011906	C₂²	semidirect
31. #18011906	C₂²	semidirect
32. #18011903	C₂²	semidirect
33. #18011902	C₂²	semidirect
34. #18011899	C₂²	semidirect
35. #18011897	C₂²	semidirect
36. #18011896	C₂²	semidirect
37. #18011896	C₂²	semidirect
38. #18011895	C₂²	semidirect
39. #18011895	C₂²	semidirect
40. #18011895	C₂²	semidirect
41. #18011895	C₂²	semidirect
42. #18011893	C₂²	semidirect
43. #18011893	C₂²	semidirect
44. #18011893	C₂²	semidirect
45. #18011893	C₂²	semidirect
46. #18011893	C₂²	semidirect
47. #18011893	C₂²	semidirect
48. #18011893	C₂²	semidirect
49. #18011891	C₂²	semidirect
50. #18011889	C₂²	semidirect
51. #18011888	C₂²	semidirect
52. #18011888	C₂²	semidirect
53. #18011887	C₂²	semidirect
54. #18011887	C₂²	semidirect
55. #18011886	C₂²	semidirect
56. #18011886	C₂²	semidirect
57. #18011886	C₂²	semidirect
59. #18011885	C₂²	semidirect
60. #18011885	C₂²	semidirect
61. #18011885	C₂²	semidirect
62. #18011885	C₂²	semidirect
64. #18011884	C₂²	semidirect
65. #18011884	C₂²	semidirect
66. #18011884	C₂²	semidirect
67. #18011883	C₂²	semidirect
68. #18011883	C₂²	semidirect
69. #18011883	C₂²	semidirect
70. #18011883	C₂²	semidirect
71. #18011883	C₂²	semidirect
72. #18011882	C₂²	semidirect
73. #18011882	C₂²	semidirect
74. #18011881	C₂²	semidirect
75. #18011881	C₂²	semidirect
76. #18011881	C₂²	semidirect
77. #18011881	C₂²	semidirect
78. #18011881	C₂²	semidirect
80. #18011879	C₂²	semidirect
81. C₄×D₅₉₆	C₂²	semidirect
82. C₄×D₅₉₆	C₂²	semidirect
83. D₄×Dic₁₄₉	C₂²	semidirect
84. #18011873	C₂²	semidirect
85. #18011871	C₂²	semidirect
86. #18011871	C₂²	semidirect
87. #18011871	C₂²	semidirect
88. #18011870	C₂²	semidirect
89. #18011869	C₂²	semidirect
90. C₂×C₄⋊Dic₁₄₉	C₂²	semidirect
91. C₂×#14558715	C₂²	semidirect
92. C₄⋊C₄×D₁₄₉	C₂²	semidirect
93. C₂×C₂²⋊Dic₁₄₉	C₂²	semidirect
94. C₂×#14558713	C₂²	semidirect
95. C₂×#14558713	C₂²	semidirect
96. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
97. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
98. #126×C₁₄₉	C₂²	semidirect
99. #124×C₁₄₉	C₂²	semidirect
100. #123×C₁₄₉	C₂²	semidirect
101. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
102. #121×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
319. C₁₄₉	#3534	semidirect
333. #538	D₁₄₉	semidirect
352. #126	C₂×D₁₄₉	semidirect
357. #124	C₂×D₁₄₉	semidirect
371. #123	C₂×D₁₄₉	semidirect
378. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
398. #121	C₂×D₁₄₉	semidirect
399. #121	C₂×D₁₄₉	semidirect
407. #120	C₂×D₁₄₉	semidirect
415. C₄×D₄	C₂×D₁₄₉	semidirect
426. 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
#23750369	2
#23750365	2
#23750321	2
#23750298	2
#23750270	2
#23750268	2
#23750262	2
#23750257	2
#23750228	2
#23750224	2
#23750216	2
#23750214	2
#23750202	2
#23750187	2
#23750183	2
#23750138	2
C₂×#18011893	2
#121×D₁₄₉	2
#538×C₁₄₉	2
#3534	149