Subgroups — #34058523

Order 19072.

1152 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750328	C₂	1	2	yes	maximal, complemented
2	#23750326	C₂	1	2	yes	maximal, complemented
3	#23750320	C₂	1	2	yes	maximal, complemented
4	#23750307	C₂	1	2	yes	maximal, complemented
5	#23750302	C₂	1	2	yes	maximal, complemented
6	#23750300	C₂	1	2	yes	maximal, complemented
7	#23750285	C₂	1	2	yes	maximal, complemented
8	#23750267	C₂	1	2	yes	maximal, complemented
9	#23750222	C₂	1	1	yes	maximal, characteristic, complemented
10	#23750215	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750212	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750186	C₂	1	2	yes	maximal, complemented
13	#23750152	C₂	1	2	yes	maximal, complemented
14	#23750134	C₂	1	2	yes	maximal, complemented
15	C₂²⋊Q₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#121×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750097	C₂	1	2	yes	maximal, complemented
18	C₂×#18011873	C₂	1	1	yes	maximal, characteristic, complemented
19	#539×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14558736	C₂²	1	2	yes	complemented
21	C₂×Q₈×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₁₄₉	C₂²	1	2	yes	—
24	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
27	#18011906	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	#18011897	C₂²	1	2	yes	complemented
36	#18011897	C₂²	1	2	yes	complemented
37	#18011896	C₂²	1	2	yes	—
38	#18011896	C₂²	1	2	yes	—
39	#18011896	C₂²	1	2	yes	complemented
40	#18011896	C₂²	1	2	yes	complemented
41	#18011896	C₂²	1	2	yes	complemented
42	#18011895	C₂²	1	2	yes	complemented
43	#18011894	C₂²	1	2	yes	complemented
44	#18011893	C₂²	1	2	yes	complemented
45	#18011891	C₂²	1	1	yes	characteristic, complemented
46	#18011890	C₂²	1	1	yes	characteristic, complemented
47	#18011889	C₂²	1	2	yes	complemented
48	#18011889	C₂²	1	2	yes	complemented
49	#18011889	C₂²	1	2	yes	complemented
50	#18011888	C₂²	1	2	yes	complemented
51	#18011887	C₂²	1	1	yes	characteristic, complemented
52	#18011886	C₂²	1	2	yes	complemented
53	#18011886	C₂²	1	2	yes	complemented
54	#18011886	C₂²	1	2	yes	complemented
55	#18011886	C₂²	1	1	yes	characteristic, complemented
56	#18011885	C₂²	1	1	yes	characteristic
57	#18011884	C₂²	1	2	yes	complemented
58	#18011884	C₂²	1	2	yes	complemented
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	complemented
63	#18011882	C₂²	1	1	yes	characteristic, complemented
64	#18011881	C₂²	1	2	yes	—
65	#18011881	C₂²	1	2	yes	—
66	#18011881	C₂²	1	2	yes	complemented
67	#18011879	C₂²	1	2	yes	complemented
68	#18011876	C₂²	1	2	yes	complemented
69	C₄×D₅₉₆	C₂²	1	2	yes	complemented
70	C₄×D₅₉₆	C₂²	1	2	yes	complemented
71	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
72	#18011873	C₂²	1	2	yes	—
73	#18011873	C₂²	1	2	yes	—
74	#18011873	C₂²	1	2	yes	complemented
75	#18011873	C₂²	1	2	yes	complemented
76	#18011873	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
79	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
80	#18011871	C₂²	1	2	yes	complemented
81	#18011871	C₂²	1	2	yes	complemented
82	#18011871	C₂²	1	2	yes	complemented
83	#18011869	C₂²	1	2	yes	complemented
84	#18011869	C₂²	1	2	yes	complemented
85	#18011868	C₂²	1	2	yes	complemented
86	#18011868	C₂²	1	2	yes	complemented
87	#18011867	C₂²	1	2	yes	complemented
88	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
90	C₄⋊C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
91	C₂×#14558713	C₂²	1	1	yes	characteristic
92	C₂×#14558713	C₂²	1	1	yes	characteristic, complemented
93	C₂×#14558713	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
97	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
98	#126×C₁₄₉	C₂²	1	2	yes	complemented
99	#125×C₁₄₉	C₂²	1	2	yes	complemented
100	#123×C₁₄₉	C₂²	1	2	yes	complemented
101	#123×C₁₄₉	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
103	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
104	#121×C₁₄₉	C₂²	1	1	yes	characteristic
105	C₄×D₄×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	#14558736	—	4	4	no	—
111	C₂×Dic₂₉₈	C₂³	1	2	yes	—
112	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
113	Q₈×D₁₄₉	—	4	2	no	—
114	C₂×D₅₉₆	—	2	4	no	—
115	C₂×D₅₉₆	C₂³	1	2	yes	—
116	C₂×D₅₉₆	C₂³	1	2	yes	—
117	C₂×D₅₉₆	C₂³	1	2	yes	—
118	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
119	C₂×D₅₉₆	C₂³	1	2	yes	—
120	C₂×D₅₉₆	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	D₄×D₁₄₉	—	2	8	no	—
127	D₄×D₁₄₉	—	4	2	no	—
128	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
129	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
130	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
131	C₂×C₄×D₁₄₉	—	4	2	no	—
132	C₂×C₄×D₁₄₉	—	4	2	no	—
133	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
136	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
137	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
140	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
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	#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	#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	C₄×Dic₁₄₉	C₂³	1	2	yes	—
176	C₄×Dic₁₄₉	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	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
181	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
182	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
184	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
187	C₄⋊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	2	yes	—
191	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
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	—	2	4	no	—
203	C₂²×D₁₄₉	—	4	1	no	—
204	C₂²×D₁₄₉	—	4	1	no	—
205	C₂²×D₁₄₉	—	4	1	no	—
206	C₂²×D₁₄₉	—	4	1	no	—
207	C₂²×D₁₄₉	—	4	2	no	—
208	C₂²×D₁₄₉	—	4	2	no	—
209	C₂²×D₁₄₉	#41	1	4	yes	complemented
210	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
211	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
212	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
213	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
214	Dic₂₉₈	—	2	4	no	—
215	Dic₂₉₈	—	4	1	no	—
216	D₅₉₆	—	2	4	no	—
217	D₅₉₆	—	2	4	no	—
218	D₅₉₆	—	2	4	no	—
219	D₅₉₆	—	4	1	no	—
220	D₅₉₆	—	4	2	no	—
221	D₅₉₆	—	4	2	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	C₂×Dic₁₄₉	—	2	2	no	—
228	C₂×Dic₁₄₉	—	4	1	no	—
229	C₂×Dic₁₄₉	—	4	2	no	—
230	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
231	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
232	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
233	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
234	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
235	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
236	C₄×D₁₄₉	—	2	4	no	—
237	C₄×D₁₄₉	—	2	2	no	—
238	C₄×D₁₄₉	—	2	2	no	—
239	C₄×D₁₄₉	—	2	4	no	—
240	C₄×D₁₄₉	—	4	2	no	—
241	C₄×D₁₄₉	—	4	1	no	—
242	C₄×D₁₄₉	—	4	1	no	—
243	C₄×D₁₄₉	—	4	2	no	—
244	C₄×D₁₄₉	—	4	2	no	—
245	C₄×D₁₄₉	—	4	2	no	—
246	C₄×D₁₄₉	—	4	2	no	—
247	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
248	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
249	Q₈×C₁₄₉	—	4	1	no	—
250	D₄×C₁₄₉	—	2	4	no	—
251	D₄×C₁₄₉	—	4	1	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	2	no	—
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	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
262	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
263	C₂²×C₁₄₉	—	2	1	no	—
264	C₂²×C₁₄₉	—	2	1	no	—
265	C₂²×C₁₄₉	—	2	2	no	—
266	C₂²×C₁₄₉	—	2	2	no	—
267	C₂²×C₁₄₉	—	2	2	no	—
268	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
269	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
270	C₂×D₁₄₉	—	2	1	no	—
271	C₂×D₁₄₉	—	2	1	no	—
272	C₂×D₁₄₉	—	2	1	no	—
273	C₂×D₁₄₉	—	2	1	no	—
274	C₂×D₁₄₉	—	2	2	no	—
275	C₂×D₁₄₉	—	2	2	no	—
276	C₂×D₁₄₉	—	2	2	no	—
277	C₂×D₁₄₉	—	2	2	no	—
278	C₂×D₁₄₉	—	2	2	no	—
279	C₂×D₁₄₉	—	2	2	no	—
280	C₂×D₁₄₉	—	4	4	no	—
281	C₂×D₁₄₉	—	4	4	no	—
282	C₂×D₁₄₉	—	8	4	no	—
283	C₂×D₁₄₉	C₂×#41	1	2	yes	—
284	C₂×D₁₄₉	C₂×#41	1	2	yes	—
285	C₄×C₁₄₉	—	2	2	no	—
286	C₄×C₁₄₉	—	2	2	no	—
287	C₄×C₁₄₉	—	2	2	no	—
288	C₄×C₁₄₉	—	2	1	no	—
289	C₄×C₁₄₉	—	2	1	no	—
290	C₄×C₁₄₉	—	2	2	no	—
291	C₄×C₁₄₉	—	2	2	no	—
292	Dic₁₄₉	—	2	2	no	—
293	Dic₁₄₉	—	2	1	no	—
294	Dic₁₄₉	—	2	2	no	—
295	Dic₁₄₉	—	2	2	no	—
296	Dic₁₄₉	—	2	2	no	—
297	Dic₁₄₉	H(5,𝔽₂)	1	2	yes	—
298	C₂×C₁₄₉	—	2	2	no	—
299	C₂×C₁₄₉	—	4	2	no	—
300	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
301	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
302	C₂×C₁₄₉	#585	1	1	yes	characteristic
303	D₁₄₉	—	2	2	no	—
304	D₁₄₉	—	2	2	no	—
305	D₁₄₉	—	4	2	no	—
306	D₁₄₉	—	4	2	no	—
307	C₁₄₉	#3505	1	1	yes	characteristic, complemented, Sylow
308	#3505	—	149	1	no	maximal, Sylow
309	#553	—	149	2	no	—
310	#553	—	149	2	no	—
311	#553	—	149	2	no	—
312	#552	—	149	2	no	—
313	#551	—	149	2	no	—
314	#551	—	149	2	no	—
315	#548	—	149	2	no	—
316	#546	—	149	2	no	—
317	#539	—	149	1	no	—
318	#539	D₁₄₉	1	1	yes	characteristic, complemented
319	#538	—	149	1	no	—
320	#538	—	149	1	no	—
321	#534	—	149	2	no	—
322	#529	—	149	2	no	—
323	#525	—	149	2	no	—
324	C₂×C₂²⋊Q₈	—	149	1	no	—
325	C₂×#121	—	149	1	no	—
326	#518	—	149	2	no	—
327	C₂×C₄×D₄	—	149	1	no	—
328	C₂×#41	—	149	2	no	—
329	C₂²×Q₈	—	149	1	no	—
330	C₂²×D₄	—	149	2	no	—
331	C₂²×D₄	—	149	1	no	—
332	C₂²×D₄	—	149	1	no	—
333	C₂³×C₄	—	149	1	no	—
334	C₂³×C₄	—	149	1	no	—
335	#126	—	149	2	no	—
336	#126	—	149	2	no	—
337	#126	—	149	2	no	—
338	#126	—	149	2	no	—
339	#126	—	149	2	no	—
340	#126	C₂×D₁₄₉	1	2	yes	complemented
341	#125	—	149	2	no	—
342	#125	—	149	2	no	—
343	#125	C₂×D₁₄₉	1	2	yes	complemented
344	#124	—	149	2	no	—
345	#124	—	149	2	no	—
346	#124	—	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	—	149	2	no	—
354	#123	—	149	2	no	—
355	#123	C₂×D₁₄₉	1	2	yes	complemented
356	#123	C₂×D₁₄₉	1	2	yes	complemented
357	C₂²⋊Q₈	—	149	1	no	—
358	C₂²⋊Q₈	—	149	1	no	—
359	C₂²⋊Q₈	—	149	2	no	—
360	C₂²⋊Q₈	—	149	1	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, complemented
365	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
366	#121	—	149	2	no	—
367	#121	—	149	1	no	—
368	#121	—	149	2	no	—
369	#121	—	149	1	no	—
370	#121	—	149	1	no	—
371	#121	—	149	2	no	—
372	#121	—	149	2	no	—
373	#121	—	149	2	no	—
374	#121	—	149	2	no	—
375	#121	—	149	2	no	—
376	#121	—	149	2	no	—
377	#121	—	149	2	no	—
378	#121	C₂×D₁₄₉	1	1	yes	characteristic
379	#120	—	149	2	no	—
380	#120	—	149	2	no	—
381	#120	—	149	2	no	—
382	#120	—	149	2	no	—
383	C₄×Q₈	—	149	2	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	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	C₂×D₁₄₉	1	2	yes	complemented
399	#117	—	149	2	no	—
400	#117	—	149	2	no	—
401	#117	—	149	2	no	—
402	#117	—	149	2	no	—
403	#117	—	149	2	no	—
404	C₂×C₄⋊C₄	—	149	1	no	—
405	C₂×C₄⋊C₄	—	149	1	no	—
406	C₂×C₄⋊C₄	—	149	2	no	—
407	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
408	C₂×C₂²⋊C₄	—	149	1	no	—
409	C₂×C₂²⋊C₄	—	149	1	no	—
410	C₂×C₂²⋊C₄	—	149	2	no	—
411	C₂×C₂²⋊C₄	—	149	2	no	—
412	C₂×C₂²⋊C₄	—	149	2	no	—
413	C₂×C₂²⋊C₄	—	149	2	no	—
414	C₂×C₄²	—	149	1	no	—
415	C₂⁴	—	149	2	no	—
416	C₂⁴	—	149	1	no	—
417	C₂⁴	—	149	1	no	—
418	#41	—	596	4	no	—
419	C₂×Q₈	—	596	2	no	—
420	C₂×Q₈	—	149	2	no	—
421	C₂×Q₈	—	149	1	no	—
422	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
423	C₂×D₄	—	298	4	no	—
424	C₂×D₄	—	298	8	no	—
425	C₂×D₄	—	596	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	1	yes	characteristic
439	C₂²×C₄	—	596	2	no	—
440	C₂²×C₄	—	596	2	no	—
441	C₂²×C₄	—	149	1	no	—
442	C₂²×C₄	—	149	2	no	—
443	C₂²×C₄	—	149	1	no	—
444	C₂²×C₄	—	149	1	no	—
445	C₂²×C₄	—	149	2	no	—
446	C₂²×C₄	—	149	1	no	—
447	C₂²×C₄	—	149	2	no	—
448	C₂²×C₄	—	149	1	no	—
449	C₂²×C₄	—	149	2	no	—
450	C₂²×C₄	—	149	2	no	—
451	C₂²×C₄	—	149	2	no	—
452	C₂²×C₄	—	149	2	no	—
453	C₂²×C₄	—	149	1	no	—
454	C₂²×C₄	—	149	2	no	—
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	2	yes	—
459	C₄⋊C₄	—	149	2	no	—
460	C₄⋊C₄	—	149	2	no	—
461	C₄⋊C₄	—	149	2	no	—
462	C₄⋊C₄	—	149	2	no	—
463	C₄⋊C₄	—	149	1	no	—
464	C₄⋊C₄	—	149	2	no	—
465	C₄⋊C₄	—	149	1	no	—
466	C₄⋊C₄	—	149	2	no	—
467	C₄⋊C₄	—	149	2	no	—
468	C₄⋊C₄	—	149	2	no	—
469	C₄⋊C₄	—	149	2	no	—
470	C₄⋊C₄	—	149	2	no	—
471	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
473	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
474	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
475	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
476	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
477	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
478	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
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	—	149	2	no	—
496	C₂²⋊C₄	—	149	2	no	—
497	C₂²⋊C₄	—	149	2	no	—
498	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
503	C₄²	—	149	2	no	—
504	C₄²	—	149	2	no	—
505	C₄²	—	149	2	no	—
506	C₄²	—	149	2	no	—
507	C₄²	—	149	2	no	—
508	C₄²	C₂²×D₁₄₉	1	2	yes	—
509	C₂³	—	298	4	no	—
510	C₂³	—	298	2	no	—
511	C₂³	—	596	1	no	—
512	C₂³	—	596	1	no	—
513	C₂³	—	596	1	no	—
514	C₂³	—	596	1	no	—
515	C₂³	—	596	2	no	—
516	C₂³	—	596	2	no	—
517	C₂³	—	149	2	no	—
518	C₂³	—	149	2	no	—
519	C₂³	—	149	1	no	—
520	C₂³	—	149	1	no	—
521	C₂³	—	149	4	no	—
522	C₂³	C₂³×D₁₄₉	1	2	yes	—
523	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
524	Q₈	—	4	1	no	—
525	Q₈	—	298	4	no	—
526	Q₈	—	596	1	no	—
527	D₄	—	2	4	no	—
528	D₄	—	4	1	no	—
529	D₄	—	298	4	no	—
530	D₄	—	298	4	no	—
531	D₄	—	298	4	no	—
532	D₄	—	298	4	no	—
533	D₄	—	298	4	no	—
534	D₄	—	298	4	no	—
535	D₄	—	596	1	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	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	298	4	no	—
545	C₂×C₄	—	298	2	no	—
546	C₂×C₄	—	298	2	no	—
547	C₂×C₄	—	298	4	no	—
548	C₂×C₄	—	298	2	no	—
549	C₂×C₄	—	596	2	no	—
550	C₂×C₄	—	596	1	no	—
551	C₂×C₄	—	596	1	no	—
552	C₂×C₄	—	596	2	no	—
553	C₂×C₄	—	596	2	no	—
554	C₂×C₄	—	596	2	no	—
555	C₂×C₄	—	596	2	no	—
556	C₂×C₄	—	596	1	no	—
557	C₂×C₄	—	596	2	no	—
558	C₂×C₄	—	149	2	no	—
559	C₂×C₄	—	149	2	no	—
560	C₂×C₄	—	149	1	no	—
561	C₂×C₄	—	149	2	no	—
562	C₂×C₄	—	149	2	no	—
563	C₂×C₄	—	149	1	no	—
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	2	yes	—
568	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
569	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	298	1	no	—
577	C₂²	—	298	1	no	—
578	C₂²	—	298	1	no	—
579	C₂²	—	298	1	no	—
580	C₂²	—	298	2	no	—
581	C₂²	—	298	2	no	—
582	C₂²	—	298	2	no	—
583	C₂²	—	298	2	no	—
584	C₂²	—	298	2	no	—
585	C₂²	—	298	2	no	—
586	C₂²	—	596	4	no	—
587	C₂²	—	596	4	no	—
588	C₂²	—	149	2	no	—
589	C₂²	—	149	2	no	—
590	C₂²	—	1192	4	no	—
591	C₂²	#41×D₁₄₉	1	2	yes	—
592	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	298	2	no	—
601	C₄	—	298	1	no	—
602	C₄	—	298	2	no	—
603	C₄	—	298	2	no	—
604	C₄	—	298	2	no	—
605	C₄	—	149	2	no	—
606	C₂	—	2	2	no	—
607	C₂	—	4	2	no	—
608	C₂	—	298	2	no	—
609	C₂	—	298	2	no	—
610	C₂	—	596	2	no	—
611	C₂	—	596	2	no	—
612	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
613	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic
614	C₂	#23750462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#539×C₁₄₉	C₂
hypercenter	#539	D₁₄₉
hypocenter	C₁₄₉	#3505
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #23750328	C₂	semidirect
2. #23750326	C₂	semidirect
3. #23750320	C₂	semidirect
4. #23750307	C₂	semidirect
5. #23750302	C₂	semidirect
6. #23750300	C₂	semidirect
7. #23750285	C₂	semidirect
8. #23750267	C₂	semidirect
9. #23750222	C₂	semidirect
10. #23750215	C₂	semidirect
11. #23750212	C₂	semidirect
12. #23750186	C₂	semidirect
13. #23750152	C₂	semidirect
14. #23750134	C₂	semidirect
15. C₂²⋊Q₈×D₁₄₉	C₂	semidirect
16. #121×D₁₄₉	C₂	semidirect
17. #23750097	C₂	semidirect
18. C₂×#18011873	C₂	semidirect
19. #539×C₁₄₉	C₂	semidirect
20. C₂×#14558736	C₂²	semidirect
21. C₂×Q₈×D₁₄₉	C₂²	semidirect
24. C₂×D₄×D₁₄₉	C₂²	semidirect
26. C₂²×C₄×D₁₄₉	C₂²	semidirect
27. #18011906	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. #18011897	C₂²	semidirect
36. #18011897	C₂²	semidirect
39. #18011896	C₂²	semidirect
40. #18011896	C₂²	semidirect
41. #18011896	C₂²	semidirect
42. #18011895	C₂²	semidirect
43. #18011894	C₂²	semidirect
44. #18011893	C₂²	semidirect
45. #18011891	C₂²	semidirect
46. #18011890	C₂²	semidirect
47. #18011889	C₂²	semidirect
48. #18011889	C₂²	semidirect
49. #18011889	C₂²	semidirect
50. #18011888	C₂²	semidirect
51. #18011887	C₂²	semidirect
52. #18011886	C₂²	semidirect
53. #18011886	C₂²	semidirect
54. #18011886	C₂²	semidirect
55. #18011886	C₂²	semidirect
57. #18011884	C₂²	semidirect
58. #18011884	C₂²	semidirect
59. #18011884	C₂²	semidirect
60. #18011884	C₂²	semidirect
62. #18011883	C₂²	semidirect
63. #18011882	C₂²	semidirect
66. #18011881	C₂²	semidirect
67. #18011879	C₂²	semidirect
68. #18011876	C₂²	semidirect
69. C₄×D₅₉₆	C₂²	semidirect
70. C₄×D₅₉₆	C₂²	semidirect
71. D₄×Dic₁₄₉	C₂²	semidirect
74. #18011873	C₂²	semidirect
75. #18011873	C₂²	semidirect
76. #18011873	C₂²	semidirect
77. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
78. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
79. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
80. #18011871	C₂²	semidirect
81. #18011871	C₂²	semidirect
82. #18011871	C₂²	semidirect
83. #18011869	C₂²	semidirect
84. #18011869	C₂²	semidirect
85. #18011868	C₂²	semidirect
86. #18011868	C₂²	semidirect
87. #18011867	C₂²	semidirect
88. C₄⋊C₄×D₁₄₉	C₂²	semidirect
89. C₄⋊C₄×D₁₄₉	C₂²	semidirect
90. C₄⋊C₄×D₁₄₉	C₂²	semidirect
92. C₂×#14558713	C₂²	semidirect
93. C₂×#14558713	C₂²	semidirect
95. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
96. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
97. C₂×C₄×Dic₁₄₉	C₂²	semidirect
98. #126×C₁₄₉	C₂²	semidirect
99. #125×C₁₄₉	C₂²	semidirect
100. #123×C₁₄₉	C₂²	semidirect
101. #123×C₁₄₉	C₂²	semidirect
102. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
103. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
105. C₄×D₄×C₁₄₉	C₂²	semidirect
106. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
209. C₂²×D₁₄₉	#41	semidirect
307. C₁₄₉	#3505	semidirect
318. #539	D₁₄₉	semidirect
340. #126	C₂×D₁₄₉	semidirect
343. #125	C₂×D₁₄₉	semidirect
355. #123	C₂×D₁₄₉	semidirect
356. #123	C₂×D₁₄₉	semidirect
364. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
365. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
398. C₄×D₄	C₂×D₁₄₉	semidirect
407. 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
#23750328	2
#23750326	2
#23750320	2
#23750307	2
#23750302	2
#23750300	2
#23750285	2
#23750267	2
#23750222	2
#23750215	2
#23750212	2
#23750186	2
#23750152	2
#23750134	2
C₂²⋊Q₈×D₁₄₉	2
#121×D₁₄₉	2
#23750097	2
C₂×#18011873	2
#539×C₁₄₉	2
#3505	149