Subgroups — #34058769

Order 19072.

1104 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750359	C₂	1	2	yes	maximal, complemented
2	#23750358	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750355	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750330	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750329	C₂	1	2	yes	maximal, complemented
6	#23750293	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750284	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750281	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750276	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750274	C₂	1	2	yes	maximal, complemented
11	#23750273	C₂	1	2	yes	maximal, complemented
12	#23750249	C₂	1	1	yes	maximal, characteristic, complemented
13	#23750245	C₂	1	2	yes	maximal, complemented
14	#23750243	C₂	1	2	yes	maximal, complemented
15	#23750242	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750171	C₂	1	2	yes	maximal, complemented
17	#23750170	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750155	C₂	1	1	yes	maximal, characteristic, complemented
19	#23750152	C₂	1	2	yes	maximal, complemented
20	#23750106	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750104	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#18011876	C₂	1	1	yes	maximal, characteristic, complemented
23	#547×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558736	C₂²	1	1	yes	characteristic
25	C₂×#14558736	C₂²	1	2	yes	—
26	C₂×#14558735	C₂²	1	1	yes	characteristic
27	C₂×#14558735	C₂²	1	2	yes	—
28	C₂²×Dic₂₉₈	C₂²	1	1	yes	characteristic
29	#18011910	C₂²	1	1	yes	characteristic
30	#18011910	C₂²	1	1	yes	characteristic
31	#18011910	C₂²	1	2	yes	—
32	#18011909	C₂²	1	2	yes	—
33	#18011909	C₂²	1	2	yes	—
34	#18011907	C₂²	1	1	yes	characteristic
35	#18011907	C₂²	1	2	yes	—
36	#18011906	C₂²	1	2	yes	—
37	#18011906	C₂²	1	1	yes	characteristic
38	#18011904	C₂²	1	2	yes	—
39	#18011904	C₂²	1	1	yes	characteristic
40	#18011901	C₂²	1	2	yes	—
41	#18011901	C₂²	1	1	yes	characteristic
42	#18011900	C₂²	1	2	yes	—
43	#18011899	C₂²	1	1	yes	characteristic
44	#18011898	C₂²	1	2	yes	—
45	#18011898	C₂²	1	1	yes	characteristic
46	#18011897	C₂²	1	2	yes	—
47	#18011897	C₂²	1	1	yes	characteristic
48	#18011897	C₂²	1	2	yes	—
49	#18011897	C₂²	1	2	yes	—
50	#18011897	C₂²	1	2	yes	—
51	#18011896	C₂²	1	2	yes	—
52	#18011896	C₂²	1	2	yes	—
53	#18011895	C₂²	1	1	yes	characteristic
54	#18011894	C₂²	1	2	yes	—
55	#18011894	C₂²	1	2	yes	—
56	#18011893	C₂²	1	2	yes	—
57	#18011892	C₂²	1	1	yes	characteristic
58	#18011892	C₂²	1	2	yes	—
59	#18011891	C₂²	1	1	yes	characteristic
60	#18011890	C₂²	1	1	yes	characteristic
61	#18011890	C₂²	1	2	yes	—
62	#18011889	C₂²	1	2	yes	—
63	#18011889	C₂²	1	2	yes	—
64	#18011889	C₂²	1	2	yes	—
65	#18011888	C₂²	1	1	yes	characteristic
66	#18011888	C₂²	1	2	yes	—
67	#18011888	C₂²	1	2	yes	—
68	#18011887	C₂²	1	2	yes	—
69	#18011886	C₂²	1	1	yes	characteristic
70	#18011885	C₂²	1	1	yes	characteristic
71	#18011884	C₂²	1	2	yes	—
72	#18011883	C₂²	1	2	yes	—
73	#18011883	C₂²	1	1	yes	characteristic
74	#18011883	C₂²	1	2	yes	—
75	#18011883	C₂²	1	2	yes	—
76	#18011883	C₂²	1	2	yes	—
77	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
78	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
79	#18011876	C₂²	1	2	yes	—
80	#18011876	C₂²	1	1	yes	characteristic
81	#18011876	C₂²	1	2	yes	—
82	#18011876	C₂²	1	1	yes	characteristic
83	#18011876	C₂²	1	1	yes	characteristic
84	#18011876	C₂²	1	2	yes	—
85	#18011876	C₂²	1	1	yes	characteristic
86	#18011876	C₂²	1	1	yes	characteristic
87	D₄×Dic₁₄₉	C₂²	1	2	yes	—
88	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
89	#18011873	C₂²	1	1	yes	characteristic
90	#18011873	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
93	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
94	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
95	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
96	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
98	#18011871	C₂²	1	2	yes	—
99	#18011871	C₂²	1	2	yes	—
100	#18011871	C₂²	1	2	yes	—
101	#18011871	C₂²	1	2	yes	—
102	#18011870	C₂²	1	1	yes	characteristic
103	#18011869	C₂²	1	2	yes	—
104	#18011868	C₂²	1	1	yes	characteristic
105	#18011867	C₂²	1	2	yes	—
106	C₂×#14558715	C₂²	1	2	yes	—
107	C₂×#14558715	C₂²	1	2	yes	—
108	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	—
109	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic
110	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	—
111	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
112	C₂×#41×C₁₄₉	C₂²	1	2	yes	—
113	C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
114	#123×C₁₄₉	C₂²	1	2	yes	—
115	#123×C₁₄₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	—
117	#121×C₁₄₉	C₂²	1	1	yes	characteristic
118	#121×C₁₄₉	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
123	#14558736	—	2	4	no	—
124	#14558736	—	4	4	no	—
125	#14558735	—	2	4	no	—
126	#14558735	—	4	4	no	—
127	C₂×Dic₂₉₈	—	2	4	no	—
128	C₂×Dic₂₉₈	C₂³	1	2	yes	—
129	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
131	C₂×Dic₂₉₈	C₂³	1	2	yes	—
132	C₂×Dic₂₉₈	C₂³	1	2	yes	—
133	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
134	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
135	C₂×D₅₉₆	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
143	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
144	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
145	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
146	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
148	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
150	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
151	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
152	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
153	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
156	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
158	#14558715	C₂³	1	1	yes	characteristic
159	#14558715	C₂³	1	2	yes	—
160	#14558715	C₂³	1	2	yes	—
161	#14558715	C₂³	1	1	yes	characteristic
162	#14558715	C₂³	1	1	yes	characteristic
163	#14558715	C₂³	1	2	yes	—
164	#14558715	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
171	#14558715	C₂³	1	2	yes	—
172	#14558715	C₂³	1	2	yes	—
173	#14558715	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
182	#14558713	C₂³	1	1	yes	characteristic
183	#14558713	C₂³	1	2	yes	—
184	#14558713	C₂³	1	2	yes	—
185	#14558713	C₂³	1	2	yes	—
186	#14558713	C₂³	1	1	yes	characteristic
187	#14558713	C₂³	1	1	yes	characteristic
188	#14558713	C₂³	1	1	yes	characteristic
189	#14558713	C₂³	1	2	yes	—
190	#14558713	C₂³	1	2	yes	—
191	#14558713	C₂³	1	2	yes	—
192	#14558713	C₂³	1	2	yes	—
193	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
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	2	yes	—
199	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₄₉	C₂³	1	2	yes	—
201	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₄₉	C₂³	1	2	yes	—
204	#41×C₁₄₉	—	4	4	no	—
205	C₂×Q₈×C₁₄₉	C₂³	1	2	yes	—
206	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
208	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
210	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
213	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
214	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
226	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
227	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
228	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
230	Dic₂₉₈	—	2	2	no	—
231	Dic₂₉₈	—	2	4	no	—
232	Dic₂₉₈	—	2	2	no	—
233	Dic₂₉₈	—	4	2	no	—
234	Dic₂₉₈	—	4	2	no	—
235	Dic₂₉₈	#41	1	4	yes	complemented
236	D₅₉₆	—	2	2	no	—
237	D₅₉₆	—	4	2	no	—
238	C₂²⋊D₁₄₉	—	2	4	no	—
239	C₂²⋊D₁₄₉	—	2	2	no	—
240	C₂²⋊D₁₄₉	—	2	4	no	—
241	C₂²⋊D₁₄₉	—	2	4	no	—
242	C₂²⋊D₁₄₉	—	2	4	no	—
243	C₂²⋊D₁₄₉	—	2	2	no	—
244	C₂²⋊D₁₄₉	—	4	2	no	—
245	C₂×Dic₁₄₉	—	2	2	no	—
246	C₂×Dic₁₄₉	—	2	4	no	—
247	C₂×Dic₁₄₉	—	2	4	no	—
248	C₂×Dic₁₄₉	—	2	2	no	—
249	C₂×Dic₁₄₉	—	4	2	no	—
250	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
254	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
256	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
259	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
260	C₄×D₁₄₉	—	2	2	no	—
261	C₄×D₁₄₉	—	2	4	no	—
262	C₄×D₁₄₉	—	4	2	no	—
263	C₄×D₁₄₉	—	4	2	no	—
264	C₄×D₁₄₉	—	4	2	no	—
265	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
266	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
267	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
268	Q₈×C₁₄₉	—	4	2	no	—
269	D₄×C₁₄₉	—	2	4	no	—
270	D₄×C₁₄₉	—	2	2	no	—
271	D₄×C₁₄₉	—	2	2	no	—
272	D₄×C₁₄₉	—	4	2	no	—
273	C₂×C₄×C₁₄₉	—	2	4	no	—
274	C₂×C₄×C₁₄₉	—	2	2	no	—
275	C₂×C₄×C₁₄₉	—	2	2	no	—
276	C₂×C₄×C₁₄₉	—	4	2	no	—
277	C₂×C₄×C₁₄₉	—	4	2	no	—
278	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
280	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
281	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
282	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₁₄₉	—	2	1	no	—
287	C₂²×C₁₄₉	—	2	1	no	—
288	C₂²×C₁₄₉	—	2	1	no	—
289	C₂²×C₁₄₉	—	2	2	no	—
290	C₂²×C₁₄₉	—	2	1	no	—
291	C₂²×C₁₄₉	—	2	2	no	—
292	C₂²×C₁₄₉	—	2	2	no	—
293	C₂²×C₁₄₉	—	2	1	no	—
294	C₂²×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
295	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
296	C₂×D₁₄₉	—	2	1	no	—
297	C₂×D₁₄₉	—	2	2	no	—
298	C₂×D₁₄₉	—	2	2	no	—
299	C₂×D₁₄₉	—	2	1	no	—
300	C₂×D₁₄₉	—	2	1	no	—
301	C₂×D₁₄₉	—	2	2	no	—
302	C₄×C₁₄₉	—	2	1	no	—
303	C₄×C₁₄₉	—	2	1	no	—
304	C₄×C₁₄₉	—	2	2	no	—
305	C₄×C₁₄₉	—	2	2	no	—
306	C₄×C₁₄₉	—	2	1	no	—
307	C₄×C₁₄₉	—	2	2	no	—
308	C₄×C₁₄₉	—	2	1	no	—
309	C₄×C₁₄₉	C₂×#41	1	2	yes	—
310	Dic₁₄₉	—	2	1	no	—
311	Dic₁₄₉	—	2	2	no	—
312	Dic₁₄₉	—	2	1	no	—
313	Dic₁₄₉	—	2	1	no	—
314	Dic₁₄₉	—	2	2	no	—
315	Dic₁₄₉	—	2	1	no	—
316	Dic₁₄₉	—	2	1	no	—
317	Dic₁₄₉	—	2	1	no	—
318	Dic₁₄₉	C₂×#41	1	4	yes	—
319	Dic₁₄₉	2₋¹⁺⁴	1	2	yes	—
320	C₂×C₁₄₉	—	2	2	no	—
321	C₂×C₁₄₉	—	4	1	no	—
322	C₂×C₁₄₉	—	4	2	no	—
323	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
324	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
326	D₁₄₉	—	4	1	no	—
327	D₁₄₉	—	4	2	no	—
328	C₁₄₉	#3522	1	1	yes	characteristic, complemented, Sylow
329	#3522	—	149	1	no	maximal, Sylow
330	#559	—	149	2	no	—
331	#559	—	149	1	no	—
332	Q₈²	—	149	1	no	—
333	#554	—	149	2	no	—
334	#554	—	149	1	no	—
335	#550	—	149	1	no	—
336	#548	—	149	1	no	—
337	#548	—	149	1	no	—
338	#547	—	149	2	no	—
339	#547	—	149	2	no	—
340	#547	—	149	1	no	—
341	#547	D₁₄₉	1	1	yes	characteristic, complemented
342	#542	—	149	1	no	—
343	#542	—	149	2	no	—
344	#542	—	149	2	no	—
345	#542	—	149	1	no	—
346	#532	—	149	2	no	—
347	#532	—	149	1	no	—
348	#529	—	149	2	no	—
349	#529	—	149	1	no	—
350	#520	—	149	1	no	—
351	#520	—	149	1	no	—
352	C₂×C₄×Q₈	—	149	1	no	—
353	C₂×#41	—	149	1	no	—
354	C₂×#41	—	149	2	no	—
355	C₂×#41	—	149	1	no	—
356	C₂×#41	—	149	2	no	—
357	C₂×#41	C₂×D₁₄₉	1	2	yes	—
358	C₂²×Q₈	—	149	1	no	—
359	C₄⋊Q₈	—	149	2	no	—
360	C₄⋊Q₈	—	149	2	no	—
361	C₄⋊Q₈	—	149	1	no	—
362	C₄⋊Q₈	—	149	2	no	—
363	C₄⋊Q₈	—	149	1	no	—
364	C₄⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
365	#127	—	149	2	no	—
366	#127	—	149	1	no	—
367	#126	—	149	2	no	—
368	#126	—	149	1	no	—
369	#126	—	149	1	no	—
370	#126	—	149	2	no	—
371	#125	—	149	1	no	—
372	#125	—	149	2	no	—
373	#124	—	149	2	no	—
374	#124	—	149	2	no	—
375	#124	—	149	1	no	—
376	#124	—	149	1	no	—
377	#124	—	149	2	no	—
378	#124	—	149	2	no	—
379	#124	—	149	2	no	—
380	#124	—	149	2	no	—
381	#124	—	149	1	no	—
382	#123	—	149	1	no	—
383	#123	—	149	2	no	—
384	#123	—	149	2	no	—
385	#123	—	149	2	no	—
386	#123	—	149	2	no	—
387	#123	—	149	2	no	—
388	#123	—	149	1	no	—
389	#123	—	149	2	no	—
390	#123	C₂×D₁₄₉	1	2	yes	—
391	#123	C₂×D₁₄₉	1	2	yes	—
392	C₂²⋊Q₈	—	149	2	no	—
393	C₂²⋊Q₈	—	149	2	no	—
394	C₂²⋊Q₈	—	149	1	no	—
395	C₂²⋊Q₈	—	149	2	no	—
396	C₂²⋊Q₈	—	149	2	no	—
397	C₂²⋊Q₈	—	149	2	no	—
398	C₂²⋊Q₈	—	149	1	no	—
399	C₂²⋊Q₈	—	149	1	no	—
400	C₂²⋊Q₈	—	149	2	no	—
401	C₂²⋊Q₈	—	149	2	no	—
402	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	—
403	#121	—	149	2	no	—
404	#121	—	149	1	no	—
405	#121	—	149	2	no	—
406	#121	—	149	2	no	—
407	#121	—	149	2	no	—
408	#121	—	149	1	no	—
409	#121	—	149	1	no	—
410	#121	—	149	2	no	—
411	#121	C₂×D₁₄₉	1	1	yes	characteristic
412	#121	C₂×D₁₄₉	1	1	yes	characteristic
413	C₄×Q₈	—	149	1	no	—
414	C₄×Q₈	—	149	2	no	—
415	C₄×Q₈	—	149	1	no	—
416	C₄×Q₈	—	149	1	no	—
417	C₄×Q₈	—	149	2	no	—
418	C₄×Q₈	—	149	1	no	—
419	C₄×Q₈	—	149	1	no	—
420	C₄×Q₈	—	149	2	no	—
421	C₄×Q₈	—	149	1	no	—
422	C₄×Q₈	—	149	1	no	—
423	C₄×D₄	—	149	1	no	—
424	C₄×D₄	—	149	2	no	—
425	C₄×D₄	—	149	2	no	—
426	C₄×D₄	—	149	2	no	—
427	C₄×D₄	—	149	2	no	—
428	C₄×D₄	—	149	1	no	—
429	C₄×D₄	—	149	1	no	—
430	C₄×D₄	—	149	2	no	—
431	C₄×D₄	—	149	2	no	—
432	C₄×D₄	—	149	1	no	—
433	C₄×D₄	—	149	1	no	—
434	C₄×D₄	—	149	2	no	—
435	C₄×D₄	—	149	2	no	—
436	C₄×D₄	—	149	2	no	—
437	C₄×D₄	—	149	2	no	—
438	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
439	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
440	#117	—	149	1	no	—
441	#117	—	149	2	no	—
442	#117	—	149	2	no	—
443	#117	—	149	1	no	—
444	C₂×C₄⋊C₄	—	149	2	no	—
445	C₂×C₄⋊C₄	—	149	2	no	—
446	C₂×C₄⋊C₄	—	149	2	no	—
447	C₂×C₄⋊C₄	—	149	1	no	—
448	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
450	C₂×C₄²	—	149	1	no	—
451	C₂×C₄²	—	149	2	no	—
452	#41	—	4	4	no	—
453	#41	—	298	4	no	—
454	#41	—	298	4	no	—
455	#41	—	596	4	no	—
456	#41	—	596	4	no	—
457	C₂×Q₈	—	298	4	no	—
458	C₂×Q₈	—	149	1	no	—
459	C₂×Q₈	—	149	1	no	—
460	C₂×Q₈	—	149	2	no	—
461	C₂×Q₈	—	149	2	no	—
462	C₂×Q₈	—	149	2	no	—
463	C₂×Q₈	—	149	1	no	—
464	C₂×Q₈	C₂²×D₁₄₉	1	2	yes	—
465	C₂×D₄	—	149	1	no	—
466	C₂×D₄	—	149	2	no	—
467	C₂×D₄	—	149	2	no	—
468	C₂×D₄	—	149	2	no	—
469	C₂×D₄	—	149	2	no	—
470	C₂×D₄	—	149	1	no	—
471	C₂×D₄	—	149	2	no	—
472	C₂×D₄	—	149	1	no	—
473	C₂×D₄	—	149	2	no	—
474	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
476	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
477	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
478	C₂²×C₄	—	149	1	no	—
479	C₂²×C₄	—	149	1	no	—
480	C₂²×C₄	—	149	2	no	—
481	C₂²×C₄	—	149	2	no	—
482	C₂²×C₄	—	149	2	no	—
483	C₂²×C₄	—	149	1	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	C₂²×D₁₄₉	1	2	yes	—
489	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
491	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
492	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
493	C₄⋊C₄	—	149	2	no	—
494	C₄⋊C₄	—	149	1	no	—
495	C₄⋊C₄	—	149	2	no	—
496	C₄⋊C₄	—	149	1	no	—
497	C₄⋊C₄	—	149	2	no	—
498	C₄⋊C₄	—	149	2	no	—
499	C₄⋊C₄	—	149	1	no	—
500	C₄⋊C₄	—	149	2	no	—
501	C₄⋊C₄	—	149	2	no	—
502	C₄⋊C₄	—	149	2	no	—
503	C₄⋊C₄	—	149	1	no	—
504	C₄⋊C₄	—	149	1	no	—
505	C₄⋊C₄	—	149	1	no	—
506	C₄⋊C₄	—	149	2	no	—
507	C₄⋊C₄	—	149	1	no	—
508	C₄⋊C₄	—	149	2	no	—
509	C₄⋊C₄	—	149	1	no	—
510	C₄⋊C₄	—	149	2	no	—
511	C₄⋊C₄	—	149	1	no	—
512	C₄⋊C₄	—	149	2	no	—
513	C₄⋊C₄	—	149	1	no	—
514	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
516	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
521	C₂²⋊C₄	—	149	1	no	—
522	C₂²⋊C₄	—	149	2	no	—
523	C₂²⋊C₄	—	149	1	no	—
524	C₂²⋊C₄	—	149	1	no	—
525	C₂²⋊C₄	—	149	1	no	—
526	C₂²⋊C₄	—	149	2	no	—
527	C₂²⋊C₄	—	149	2	no	—
528	C₂²⋊C₄	—	149	2	no	—
529	C₂²⋊C₄	—	149	2	no	—
530	C₂²⋊C₄	—	149	1	no	—
531	C₂²⋊C₄	—	149	2	no	—
532	C₂²⋊C₄	—	149	1	no	—
533	C₂²⋊C₄	—	149	1	no	—
534	C₂²⋊C₄	—	149	2	no	—
535	C₂²⋊C₄	—	149	2	no	—
536	C₂²⋊C₄	—	149	2	no	—
537	C₂²⋊C₄	—	149	2	no	—
538	C₂²⋊C₄	—	149	1	no	—
539	C₂²⋊C₄	—	149	2	no	—
540	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
542	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
545	C₄²	—	149	1	no	—
546	C₄²	—	149	2	no	—
547	C₄²	—	149	2	no	—
548	C₄²	—	149	1	no	—
549	C₄²	—	149	1	no	—
550	C₄²	—	149	2	no	—
551	C₄²	—	149	2	no	—
552	C₄²	—	149	1	no	—
553	C₄²	—	149	1	no	—
554	C₄²	—	149	2	no	—
555	C₄²	—	149	2	no	—
556	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
557	C₂³	—	149	1	no	—
558	C₂³	—	149	2	no	—
559	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
560	C₂³	C₂³×D₁₄₉	1	2	yes	—
561	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
562	Q₈	—	4	2	no	—
563	Q₈	—	298	4	no	—
564	Q₈	—	298	2	no	—
565	Q₈	—	298	2	no	—
566	Q₈	—	596	2	no	—
567	Q₈	—	596	2	no	—
568	Q₈	—	149	4	no	—
569	D₄	—	2	2	no	—
570	D₄	—	2	4	no	—
571	D₄	—	2	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	298	4	no	—
574	D₄	—	298	2	no	—
575	D₄	—	298	2	no	—
576	D₄	—	298	4	no	—
577	D₄	—	298	4	no	—
578	D₄	—	298	4	no	—
579	D₄	—	298	2	no	—
580	D₄	—	596	2	no	—
581	D₄	—	596	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	298	4	no	—
588	C₂×C₄	—	298	2	no	—
589	C₂×C₄	—	298	2	no	—
590	C₂×C₄	—	298	4	no	—
591	C₂×C₄	—	298	4	no	—
592	C₂×C₄	—	298	2	no	—
593	C₂×C₄	—	596	2	no	—
594	C₂×C₄	—	596	2	no	—
595	C₂×C₄	—	596	2	no	—
596	C₂×C₄	—	596	2	no	—
597	C₂×C₄	—	149	1	no	—
598	C₂×C₄	—	149	1	no	—
599	C₂×C₄	—	149	2	no	—
600	C₂×C₄	—	149	1	no	—
601	C₂×C₄	—	149	1	no	—
602	C₂×C₄	—	149	1	no	—
603	C₂×C₄	—	149	2	no	—
604	C₂×C₄	—	149	1	no	—
605	C₂×C₄	—	149	1	no	—
606	C₂×C₄	—	149	2	no	—
607	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
610	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
611	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
612	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	298	2	no	—
624	C₂²	—	298	1	no	—
625	C₂²	—	298	1	no	—
626	C₂²	—	298	2	no	—
627	C₂²	—	298	1	no	—
628	C₂²	—	298	2	no	—
629	C₂²	#18011956	1	2	yes	—
630	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	298	1	no	—
639	C₄	—	298	2	no	—
640	C₄	—	298	1	no	—
641	C₄	—	298	1	no	—
642	C₄	—	298	1	no	—
643	C₄	—	298	2	no	—
644	C₄	—	298	1	no	—
645	C₄	—	298	1	no	—
646	C₄	—	149	4	no	—
647	C₄	—	149	2	no	—
648	C₄	#41×D₁₄₉	1	2	yes	—
649	C₂	—	2	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	4	2	no	—
652	C₂	—	596	2	no	—
653	C₂	—	596	1	no	—
654	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
655	C₂	C₂×#18011956	1	1	yes	characteristic
656	C₂	2₋¹⁺⁴×D₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#547×C₁₄₉	C₂
hypercenter	#547	D₁₄₉
hypocenter	C₁₄₉	#3522
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #23750359	C₂	semidirect
2. #23750358	C₂	semidirect
3. #23750355	C₂	semidirect
4. #23750330	C₂	semidirect
5. #23750329	C₂	semidirect
6. #23750293	C₂	semidirect
7. #23750284	C₂	semidirect
8. #23750281	C₂	semidirect
9. #23750276	C₂	semidirect
10. #23750274	C₂	semidirect
11. #23750273	C₂	semidirect
12. #23750249	C₂	semidirect
13. #23750245	C₂	semidirect
14. #23750243	C₂	semidirect
15. #23750242	C₂	semidirect
16. #23750171	C₂	semidirect
17. #23750170	C₂	semidirect
18. #23750155	C₂	semidirect
19. #23750152	C₂	semidirect
20. #23750106	C₂	semidirect
21. #23750104	C₂	semidirect
22. C₂×#18011876	C₂	semidirect
23. #547×C₁₄₉	C₂	semidirect
235. Dic₂₉₈	#41	semidirect
328. C₁₄₉	#3522	semidirect
341. #547	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750359	2
#23750358	2
#23750355	2
#23750330	2
#23750329	2
#23750293	2
#23750284	2
#23750281	2
#23750276	2
#23750274	2
#23750273	2
#23750249	2
#23750245	2
#23750243	2
#23750242	2
#23750171	2
#23750170	2
#23750155	2
#23750152	2
#23750106	2
#23750104	2
C₂×#18011876	2
#547×C₁₄₉	2
#3522	149