Subgroups — #34058448

Order 19072.

1660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18011956	C₂	1	2	yes	maximal, complemented
2	#23750276	C₂	1	2	yes	maximal, complemented
3	#23750275	C₂	1	2	yes	maximal, complemented
4	#23750265	C₂	1	4	yes	maximal, complemented
5	#23750264	C₂	1	4	yes	maximal, complemented
6	#23750259	C₂	1	2	yes	maximal, complemented
7	D₄×C₂²⋊D₁₄₉	C₂	1	2	yes	maximal, complemented
8	#23750202	C₂	1	2	yes	maximal, complemented
9	#23750184	C₂	1	2	yes	maximal, complemented
10	#23750183	C₂	1	2	yes	maximal, complemented
11	#23750170	C₂	1	2	yes	maximal, complemented
12	C₂×#18011885	C₂	1	1	yes	maximal, characteristic, complemented
13	#121×D₁₄₉	C₂	1	2	yes	maximal, complemented
14	C₂×C₄×C₂²⋊D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#121×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#18011956	—	2	16	no	—
17	C₂×#14558736	C₂²	1	4	yes	complemented
18	C₂×#14558735	C₂²	1	4	yes	complemented
19	C₂×#14558735	C₂²	1	4	yes	complemented
20	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
24	C₂×D₄×D₁₄₉	C₂²	1	4	yes	complemented
25	C₂×D₄×D₁₄₉	C₂²	1	4	yes	complemented
26	C₂×D₄×D₁₄₉	C₂²	1	2	yes	complemented
27	C₂²×C₄×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
28	#18011910	C₂²	1	2	yes	complemented
29	#18011907	C₂²	1	2	yes	complemented
30	#18011897	C₂²	1	4	yes	complemented
31	#18011896	C₂²	1	4	yes	complemented
32	#18011894	C₂²	1	4	yes	complemented
33	#18011893	C₂²	1	4	yes	complemented
34	#18011892	C₂²	1	4	yes	complemented
35	#18011889	C₂²	1	4	yes	complemented
36	#18011888	C₂²	1	4	yes	complemented
37	#18011886	C₂²	1	2	yes	complemented
38	#18011885	C₂²	1	2	yes	complemented
39	#18011885	C₂²	1	2	yes	complemented
40	#18011885	C₂²	1	2	yes	complemented
41	#18011885	C₂²	1	2	yes	complemented
42	#18011884	C₂²	1	4	yes	complemented
43	#18011884	C₂²	1	4	yes	complemented
44	#18011883	C₂²	1	4	yes	complemented
45	#18011883	C₂²	1	4	yes	complemented
46	#18011883	C₂²	1	4	yes	complemented
47	#18011882	C₂²	1	2	yes	complemented
48	#18011881	C₂²	1	4	yes	complemented
49	#18011880	C₂²	1	4	yes	complemented
50	#18011879	C₂²	1	4	yes	complemented
51	#18011879	C₂²	1	4	yes	complemented
52	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
53	#18011873	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
55	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
57	C₄×C₂²⋊D₁₄₉	C₂²	1	2	yes	complemented
58	#18011871	C₂²	1	4	yes	complemented
59	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×#14558715	C₂²	1	1	yes	characteristic, complemented
61	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
62	C₂×C₂²⋊Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
63	C₂×#14558713	C₂²	1	1	yes	characteristic, complemented
64	C₂×#14558713	C₂²	1	2	yes	complemented
65	C₂²⋊C₄×D₁₄₉	C₂²	1	4	yes	complemented
66	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
67	C₂²×D₄×C₁₄₉	C₂²	1	2	yes	complemented
68	C₂²×D₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
69	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
70	#121×C₁₄₉	C₂²	1	2	yes	complemented
71	#121×C₁₄₉	C₂²	1	2	yes	complemented
72	#121×C₁₄₉	C₂²	1	2	yes	complemented
73	#121×C₁₄₉	C₂²	1	2	yes	complemented
74	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₂²⋊C₄×C₁₄₉	C₂²	1	2	yes	complemented
76	C₂³×D₁₄₉	C₂³	1	4	yes	—
77	C₂³×D₁₄₉	C₂³	1	2	yes	—
78	C₂³×D₁₄₉	C₂³	1	1	yes	characteristic
79	#14558736	—	2	16	no	—
80	#14558735	—	2	16	no	—
81	#14558735	—	2	16	no	—
82	C₂×Dic₂₉₈	C₂³	1	4	yes	—
83	C₂×D₅₉₆	—	4	2	no	—
84	C₂×D₅₉₆	C₂³	1	2	yes	—
85	C₂×D₅₉₆	C₂³	1	4	yes	—
86	C₂×D₅₉₆	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₁₄₉	—	2	16	no	—
88	C₂×C₂²⋊D₁₄₉	—	2	8	no	—
89	C₂×C₂²⋊D₁₄₉	D₄	1	8	yes	complemented
90	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
98	D₄×D₁₄₉	—	2	16	no	—
99	D₄×D₁₄₉	—	2	16	no	—
100	D₄×D₁₄₉	—	4	4	no	—
101	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
102	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
103	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
104	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
105	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₄₉	—	4	2	no	—
107	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
108	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
109	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
110	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
111	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
112	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
113	#14558715	C₂³	1	4	yes	—
114	#14558715	C₂³	1	4	yes	—
115	#14558715	C₂³	1	2	yes	—
116	#14558715	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
119	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
120	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
121	#14558713	C₂³	1	4	yes	—
122	#14558713	C₂³	1	4	yes	—
123	#14558713	C₂³	1	2	yes	—
124	#14558713	C₂³	1	2	yes	—
125	#14558713	C₂³	1	4	yes	—
126	#14558713	C₂³	1	4	yes	—
127	C₄×Dic₁₄₉	C₂³	1	2	yes	—
128	C₄×Dic₁₄₉	C₂³	1	2	yes	—
129	C₂⁴×C₁₄₉	C₂³	1	2	yes	—
130	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₄₉	—	2	8	no	—
132	C₂×D₄×C₁₄₉	—	4	2	no	—
133	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
134	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
135	C₂×D₄×C₁₄₉	C₂³	1	4	yes	—
136	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₄₉	—	4	2	no	—
138	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
141	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
144	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
148	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
149	C₂²×D₁₄₉	—	2	4	no	—
150	C₂²×D₁₄₉	—	2	8	no	—
151	C₂²×D₁₄₉	—	4	1	no	—
152	C₂²×D₁₄₉	—	4	1	no	—
153	C₂²×D₁₄₉	—	4	4	no	—
154	C₂²×D₁₄₉	—	4	2	no	—
155	C₂²×D₁₄₉	—	4	4	no	—
156	C₂²×D₁₄₉	—	4	2	no	—
157	C₂²×D₁₄₉	C₂×D₄	1	4	yes	complemented
158	C₂²×D₁₄₉	C₂⁴	1	4	yes	—
159	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
160	Dic₂₉₈	—	2	8	no	—
161	D₅₉₆	—	2	8	no	—
162	D₅₉₆	—	2	4	no	—
163	D₅₉₆	—	4	2	no	—
164	C₂²⋊D₁₄₉	—	2	8	no	—
165	C₂²⋊D₁₄₉	—	2	8	no	—
166	C₂²⋊D₁₄₉	—	2	8	no	—
167	C₂²⋊D₁₄₉	—	2	8	no	—
168	C₂²⋊D₁₄₉	—	4	4	no	—
169	C₂²⋊D₁₄₉	—	4	4	no	—
170	C₂²⋊D₁₄₉	C₂×D₄	1	8	yes	complemented
171	C₂²⋊D₁₄₉	C₂×D₄	1	8	yes	complemented
172	C₂×Dic₁₄₉	—	2	4	no	—
173	C₂×Dic₁₄₉	—	2	8	no	—
174	C₂×Dic₁₄₉	—	4	1	no	—
175	C₂×Dic₁₄₉	—	4	1	no	—
176	C₂×Dic₁₄₉	C₂×D₄	1	4	yes	complemented
177	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
178	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
179	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
180	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
181	C₄×D₁₄₉	—	2	8	no	—
182	C₄×D₁₄₉	—	2	4	no	—
183	C₄×D₁₄₉	—	2	8	no	—
184	C₄×D₁₄₉	—	4	2	no	—
185	C₂³×C₁₄₉	—	2	4	no	—
186	C₂³×C₁₄₉	—	4	1	no	—
187	C₂³×C₁₄₉	—	4	1	no	—
188	C₂³×C₁₄₉	—	4	2	no	—
189	C₂³×C₁₄₉	—	4	2	no	—
190	C₂³×C₁₄₉	C₂×D₄	1	4	yes	complemented
191	C₂³×C₁₄₉	C₂⁴	1	4	yes	—
192	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
193	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
194	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
195	D₄×C₁₄₉	—	2	8	no	—
196	D₄×C₁₄₉	—	2	8	no	—
197	D₄×C₁₄₉	—	2	4	no	—
198	D₄×C₁₄₉	—	4	2	no	—
199	C₂×C₄×C₁₄₉	—	2	4	no	—
200	C₂×C₄×C₁₄₉	—	2	2	no	—
201	C₂×C₄×C₁₄₉	—	2	2	no	—
202	C₂×C₄×C₁₄₉	—	2	2	no	—
203	C₂×C₄×C₁₄₉	—	4	1	no	—
204	C₂×C₄×C₁₄₉	—	4	1	no	—
205	C₂×C₄×C₁₄₉	—	4	1	no	—
206	C₂×C₄×C₁₄₉	C₂⁴	1	4	yes	—
207	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
208	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
209	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
210	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₁₄₉	—	2	1	no	—
212	C₂²×C₁₄₉	—	2	1	no	—
213	C₂²×C₁₄₉	—	2	1	no	—
214	C₂²×C₁₄₉	—	2	1	no	—
215	C₂²×C₁₄₉	—	2	1	no	—
216	C₂²×C₁₄₉	—	2	1	no	—
217	C₂²×C₁₄₉	—	2	4	no	—
218	C₂²×C₁₄₉	—	2	4	no	—
219	C₂²×C₁₄₉	—	2	4	no	—
220	C₂²×C₁₄₉	—	4	4	no	—
221	C₂²×C₁₄₉	—	8	4	no	—
222	C₂²×C₁₄₉	C₂²×D₄	1	2	yes	—
223	C₂²×C₁₄₉	C₂²×D₄	1	2	yes	—
224	C₂²×C₁₄₉	C₂²×D₄	1	2	yes	—
225	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
226	C₂×D₁₄₉	—	2	2	no	—
227	C₂×D₁₄₉	—	2	2	no	—
228	C₂×D₁₄₉	—	2	4	no	—
229	C₂×D₁₄₉	—	2	4	no	—
230	C₂×D₁₄₉	—	2	4	no	—
231	C₂×D₁₄₉	—	4	4	no	—
232	C₂×D₁₄₉	—	8	8	no	—
233	C₂×D₁₄₉	—	8	4	no	—
234	C₂×D₁₄₉	C₂²×D₄	1	4	yes	—
235	C₄×C₁₄₉	—	2	4	no	—
236	C₄×C₁₄₉	—	2	1	no	—
237	C₄×C₁₄₉	—	2	1	no	—
238	C₄×C₁₄₉	—	2	1	no	—
239	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	complemented
240	Dic₁₄₉	—	2	4	no	—
241	Dic₁₄₉	—	2	2	no	—
242	Dic₁₄₉	—	2	2	no	—
243	Dic₁₄₉	C₂²×D₄	1	4	yes	—
244	C₂×C₁₄₉	—	2	2	no	—
245	C₂×C₁₄₉	—	2	2	no	—
246	C₂×C₁₄₉	—	2	2	no	—
247	C₂×C₁₄₉	—	4	4	no	—
248	C₂×C₁₄₉	C₂³×D₄	1	1	yes	characteristic
249	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₁₄₉	#585	1	1	yes	characteristic
251	D₁₄₉	—	2	4	no	—
252	D₁₄₉	—	4	4	no	—
253	C₁₄₉	#3496	1	1	yes	characteristic, complemented, Sylow
254	#3496	—	149	1	no	maximal, Sylow
255	C₂×H(5,𝔽₂)	—	149	2	no	—
256	#547	—	149	2	no	—
257	#547	—	149	2	no	—
258	#546	—	149	4	no	—
259	#546	—	149	4	no	—
260	D₄²	—	149	2	no	—
261	D₄²	—	149	2	no	—
262	#537	—	149	2	no	—
263	#534	—	149	2	no	—
264	#534	—	149	2	no	—
265	#532	—	149	2	no	—
266	C₂×#121	—	149	1	no	—
267	C₂×#121	—	149	2	no	—
268	C₂×#121	D₁₄₉	1	1	yes	characteristic, complemented
269	C₂×C₄×D₄	—	149	1	no	—
270	H(5,𝔽₂)	—	298	16	no	—
271	C₂×#41	—	149	4	no	—
272	C₂×#41	—	149	4	no	—
273	C₂×#41	—	149	4	no	—
274	C₂²×D₄	—	149	2	no	—
275	C₂²×D₄	—	149	4	no	—
276	C₂²×D₄	—	149	4	no	—
277	C₂²×D₄	—	149	4	no	—
278	C₂²×D₄	—	149	2	no	—
279	C₂²×D₄	—	149	1	no	—
280	C₂²×D₄	—	149	1	no	—
281	C₂²×D₄	C₂×D₁₄₉	1	2	yes	complemented
282	C₂²×D₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
283	C₂³×C₄	—	149	1	no	—
284	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
285	C₄⋊Q₈	—	149	2	no	—
286	#127	—	149	2	no	—
287	#124	—	149	4	no	—
288	#123	—	149	4	no	—
289	#123	—	149	4	no	—
290	#123	—	149	4	no	—
291	#123	—	149	4	no	—
292	C₂²⋊Q₈	—	149	4	no	—
293	C₂²⋊Q₈	—	149	4	no	—
294	#121	—	149	4	no	—
295	#121	—	149	2	no	—
296	#121	—	149	4	no	—
297	#121	—	149	4	no	—
298	#121	—	149	2	no	—
299	#121	—	149	2	no	—
300	#121	—	149	2	no	—
301	#121	—	149	2	no	—
302	#121	—	149	2	no	—
303	#121	—	149	4	no	—
304	#121	—	149	4	no	—
305	#121	C₂×D₁₄₉	1	2	yes	complemented
306	#121	C₂×D₁₄₉	1	2	yes	complemented
307	#121	C₂×D₁₄₉	1	2	yes	complemented
308	#121	C₂×D₁₄₉	1	2	yes	complemented
309	#120	—	149	4	no	—
310	#120	—	149	4	no	—
311	#120	—	149	4	no	—
312	#120	—	149	4	no	—
313	C₄×D₄	—	149	2	no	—
314	C₄×D₄	—	149	2	no	—
315	C₄×D₄	—	149	2	no	—
316	C₄×D₄	—	149	2	no	—
317	C₄×D₄	—	149	2	no	—
318	C₄×D₄	—	149	2	no	—
319	C₄×D₄	—	149	4	no	—
320	C₂×C₄⋊C₄	—	149	1	no	—
321	C₂×C₄⋊C₄	—	149	1	no	—
322	C₂×C₄⋊C₄	—	149	2	no	—
323	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic, complemented
324	C₂×C₂²⋊C₄	—	149	1	no	—
325	C₂×C₂²⋊C₄	—	149	1	no	—
326	C₂×C₂²⋊C₄	—	149	2	no	—
327	C₂×C₂²⋊C₄	—	149	4	no	—
328	C₂×C₂²⋊C₄	C₂×D₁₄₉	1	2	yes	complemented
329	C₂×C₄²	—	149	1	no	—
330	C₂⁴	—	149	4	no	—
331	C₂⁴	—	149	2	no	—
332	C₂⁴	—	149	1	no	—
333	C₂⁴	C₂²×D₁₄₉	1	2	yes	—
334	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
335	#41	—	298	16	no	—
336	#41	—	298	16	no	—
337	#41	—	298	16	no	—
338	C₂×Q₈	—	149	4	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	298	16	no	—
342	C₂×D₄	—	298	16	no	—
343	C₂×D₄	—	298	8	no	—
344	C₂×D₄	—	298	16	no	—
345	C₂×D₄	—	596	2	no	—
346	C₂×D₄	—	596	4	no	—
347	C₂×D₄	—	149	4	no	—
348	C₂×D₄	—	149	4	no	—
349	C₂×D₄	—	149	4	no	—
350	C₂×D₄	—	149	4	no	—
351	C₂×D₄	—	149	4	no	—
352	C₂×D₄	—	149	4	no	—
353	C₂×D₄	—	149	8	no	—
354	C₂×D₄	—	149	2	no	—
355	C₂×D₄	—	149	2	no	—
356	C₂×D₄	—	149	2	no	—
357	C₂×D₄	—	149	4	no	—
358	C₂×D₄	—	149	2	no	—
359	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
360	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
361	C₂×D₄	C₂²×D₁₄₉	1	4	yes	—
362	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	596	2	no	—
365	C₂²×C₄	—	149	2	no	—
366	C₂²×C₄	—	149	4	no	—
367	C₂²×C₄	—	149	4	no	—
368	C₂²×C₄	—	149	2	no	—
369	C₂²×C₄	—	149	4	no	—
370	C₂²×C₄	—	149	1	no	—
371	C₂²×C₄	—	149	1	no	—
372	C₂²×C₄	—	149	2	no	—
373	C₂²×C₄	—	149	1	no	—
374	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
375	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
376	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
377	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
378	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
379	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
380	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
381	C₄⋊C₄	—	149	2	no	—
382	C₄⋊C₄	—	149	2	no	—
383	C₄⋊C₄	—	149	2	no	—
384	C₄⋊C₄	—	149	4	no	—
385	C₄⋊C₄	—	149	2	no	—
386	C₄⋊C₄	—	149	4	no	—
387	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
388	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
389	C₂²⋊C₄	—	149	2	no	—
390	C₂²⋊C₄	—	149	2	no	—
391	C₂²⋊C₄	—	149	4	no	—
392	C₂²⋊C₄	—	149	4	no	—
393	C₂²⋊C₄	—	149	4	no	—
394	C₂²⋊C₄	—	149	2	no	—
395	C₂²⋊C₄	—	149	2	no	—
396	C₂²⋊C₄	—	149	4	no	—
397	C₂²⋊C₄	—	149	4	no	—
398	C₂²⋊C₄	—	149	4	no	—
399	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
400	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
401	C₄²	—	149	2	no	—
402	C₄²	—	149	2	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	298	8	no	—
409	C₂³	—	298	4	no	—
410	C₂³	—	596	1	no	—
411	C₂³	—	596	1	no	—
412	C₂³	—	596	2	no	—
413	C₂³	—	596	4	no	—
414	C₂³	—	596	2	no	—
415	C₂³	—	596	4	no	—
416	C₂³	—	149	4	no	—
417	C₂³	—	149	2	no	—
418	C₂³	—	149	4	no	—
419	C₂³	D₄×D₁₄₉	1	4	yes	complemented
420	C₂³	C₂³×D₁₄₉	1	4	yes	—
421	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
422	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
423	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
424	Q₈	—	298	8	no	—
425	D₄	—	2	8	no	—
426	D₄	—	2	8	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	2	no	—
429	D₄	—	298	8	no	—
430	D₄	—	298	8	no	—
431	D₄	—	298	8	no	—
432	D₄	—	298	8	no	—
433	D₄	—	298	8	no	—
434	D₄	—	298	4	no	—
435	D₄	—	596	2	no	—
436	D₄	—	596	4	no	—
437	D₄	—	596	4	no	—
438	D₄	—	149	8	no	—
439	D₄	—	149	8	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	298	8	no	—
448	C₂×C₄	—	298	8	no	—
449	C₂×C₄	—	298	4	no	—
450	C₂×C₄	—	298	8	no	—
451	C₂×C₄	—	298	4	no	—
452	C₂×C₄	—	596	2	no	—
453	C₂×C₄	—	596	1	no	—
454	C₂×C₄	—	596	1	no	—
455	C₂×C₄	—	149	2	no	—
456	C₂×C₄	—	149	2	no	—
457	C₂×C₄	—	149	4	no	—
458	C₂×C₄	—	149	4	no	—
459	C₂×C₄	—	149	2	no	—
460	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
461	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
462	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
463	C₂×C₄	C₂³×D₁₄₉	1	4	yes	—
464	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	8	4	no	—
476	C₂²	—	298	2	no	—
477	C₂²	—	298	2	no	—
478	C₂²	—	298	4	no	—
479	C₂²	—	298	4	no	—
480	C₂²	—	298	4	no	—
481	C₂²	—	596	4	no	—
482	C₂²	—	149	4	no	—
483	C₂²	—	1192	4	no	—
484	C₂²	—	1192	8	no	—
485	C₂²	C₂×D₄×D₁₄₉	1	2	yes	—
486	C₂²	C₂×D₄×D₁₄₉	1	2	yes	—
487	C₂²	C₂×D₄×D₁₄₉	1	2	yes	—
488	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
489	C₄	—	2	4	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	298	4	no	—
494	C₄	—	298	2	no	—
495	C₄	—	298	2	no	—
496	C₄	—	149	4	no	—
497	C₄	#18011956	1	2	yes	complemented
498	C₂	—	2	2	no	—
499	C₂	—	2	2	no	—
500	C₂	—	2	2	no	—
501	C₂	—	4	4	no	—
502	C₂	—	298	4	no	—
503	C₂	—	596	4	no	—
504	C₂	C₂²×D₄×D₁₄₉	1	1	yes	characteristic
505	C₂	C₂×#18011956	1	1	yes	characteristic
506	C₂	#23750461	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	C₂×#121×C₁₄₉	C₂
hypercenter	C₂×#121	D₁₄₉
hypocenter	C₁₄₉	#3496
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂×#18011956	C₂	semidirect
2. #23750276	C₂	semidirect
3. #23750275	C₂	semidirect
4. #23750265	C₂	semidirect
5. #23750264	C₂	semidirect
6. #23750259	C₂	semidirect
7. D₄×C₂²⋊D₁₄₉	C₂	semidirect
8. #23750202	C₂	semidirect
9. #23750184	C₂	semidirect
10. #23750183	C₂	semidirect
11. #23750170	C₂	semidirect
12. C₂×#18011885	C₂	semidirect
13. #121×D₁₄₉	C₂	semidirect
14. C₂×C₄×C₂²⋊D₁₄₉	C₂	semidirect
15. C₂×#121×C₁₄₉	C₂	semidirect
17. C₂×#14558736	C₂²	semidirect
18. C₂×#14558735	C₂²	semidirect
19. C₂×#14558735	C₂²	semidirect
20. C₂²×D₅₉₆	C₂²	semidirect
22. C₂²×C₂²⋊D₁₄₉	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. #18011910	C₂²	semidirect
29. #18011907	C₂²	semidirect
30. #18011897	C₂²	semidirect
31. #18011896	C₂²	semidirect
32. #18011894	C₂²	semidirect
33. #18011893	C₂²	semidirect
34. #18011892	C₂²	semidirect
35. #18011889	C₂²	semidirect
36. #18011888	C₂²	semidirect
37. #18011886	C₂²	semidirect
38. #18011885	C₂²	semidirect
39. #18011885	C₂²	semidirect
40. #18011885	C₂²	semidirect
41. #18011885	C₂²	semidirect
42. #18011884	C₂²	semidirect
43. #18011884	C₂²	semidirect
44. #18011883	C₂²	semidirect
45. #18011883	C₂²	semidirect
46. #18011883	C₂²	semidirect
47. #18011882	C₂²	semidirect
48. #18011881	C₂²	semidirect
49. #18011880	C₂²	semidirect
50. #18011879	C₂²	semidirect
51. #18011879	C₂²	semidirect
52. D₄×Dic₁₄₉	C₂²	semidirect
53. #18011873	C₂²	semidirect
54. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
55. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
56. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
57. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
58. #18011871	C₂²	semidirect
59. C₂×C₄⋊Dic₁₄₉	C₂²	semidirect
60. C₂×#14558715	C₂²	semidirect
61. C₄⋊C₄×D₁₄₉	C₂²	semidirect
62. C₂×C₂²⋊Dic₁₄₉	C₂²	semidirect
63. C₂×#14558713	C₂²	semidirect
64. C₂×#14558713	C₂²	semidirect
65. C₂²⋊C₄×D₁₄₉	C₂²	semidirect
66. C₂×C₄×Dic₁₄₉	C₂²	semidirect
67. C₂²×D₄×C₁₄₉	C₂²	semidirect
68. C₂²×D₄×C₁₄₉	C₂²	semidirect
69. C₂³×C₄×C₁₄₉	C₂²	semidirect
70. #121×C₁₄₉	C₂²	semidirect
71. #121×C₁₄₉	C₂²	semidirect
72. #121×C₁₄₉	C₂²	semidirect
73. #121×C₁₄₉	C₂²	semidirect
74. C₂×C₄⋊C₄×C₁₄₉	C₂²	semidirect
75. C₂×C₂²⋊C₄×C₁₄₉	C₂²	semidirect
89. C₂×C₂²⋊D₁₄₉	D₄	semidirect
157. C₂²×D₁₄₉	C₂×D₄	semidirect
170. C₂²⋊D₁₄₉	C₂×D₄	semidirect
171. C₂²⋊D₁₄₉	C₂×D₄	semidirect
176. C₂×Dic₁₄₉	C₂×D₄	semidirect
190. C₂³×C₁₄₉	C₂×D₄	semidirect
239. C₄×C₁₄₉	H(5,𝔽₂)	semidirect
253. C₁₄₉	#3496	semidirect
268. C₂×#121	D₁₄₉	semidirect
281. C₂²×D₄	C₂×D₁₄₉	semidirect
282. C₂²×D₄	C₂×D₁₄₉	semidirect
284. C₂³×C₄	C₂×D₁₄₉	semidirect
305. #121	C₂×D₁₄₉	semidirect
306. #121	C₂×D₁₄₉	semidirect
307. #121	C₂×D₁₄₉	semidirect
308. #121	C₂×D₁₄₉	semidirect
323. C₂×C₄⋊C₄	C₂×D₁₄₉	semidirect
328. C₂×C₂²⋊C₄	C₂×D₁₄₉	semidirect
419. C₂³	D₄×D₁₄₉	semidirect
497. C₄	#18011956	semidirect

Maximal subgroups

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

subgroup	index
C₂×#18011956	2
#23750276	2
#23750275	2
#23750265	2
#23750264	2
#23750259	2
D₄×C₂²⋊D₁₄₉	2
#23750202	2
#23750184	2
#23750183	2
#23750170	2
C₂×#18011885	2
#121×D₁₄₉	2
C₂×C₄×C₂²⋊D₁₄₉	2
C₂×#121×C₁₄₉	2
#3496	149