Subgroups — #34058363

Order 19072.

1522 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18011958	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14558736	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₂₉₈	C₂	1	2	yes	maximal, complemented
4	#23750284	C₂	1	2	yes	maximal, complemented
5	#23750280	C₂	1	2	yes	maximal, complemented
6	#23750273	C₂	1	4	yes	maximal, complemented
7	#23750271	C₂	1	2	yes	maximal, complemented
8	#23750262	C₂	1	4	yes	maximal, complemented
9	#23750204	C₂	1	2	yes	maximal, complemented
10	#23750203	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750201	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750198	C₂	1	2	yes	maximal, complemented
13	#23750135	C₂	1	2	yes	maximal, complemented
14	C₂×#18011890	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²⋊Q₈×D₁₄₉	C₂	1	2	yes	maximal, complemented
16	#23750105	C₂	1	1	yes	maximal, characteristic, complemented
17	#525×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#18011958	—	2	8	no	—
19	C₂×#14558736	—	2	8	no	—
20	C₂×#14558736	C₂²	1	2	yes	—
21	C₂×#14558736	C₂²	1	1	yes	characteristic
22	C₂×#14558736	C₂²	1	2	yes	—
23	C₂×#14558736	C₂²	1	1	yes	characteristic
24	C₂×#14558736	C₂²	1	1	yes	characteristic
25	C₂×#14558736	C₂²	1	1	yes	characteristic
26	C₂×#14558736	C₂²	1	2	yes	complemented
27	C₂×#14558735	C₂²	1	2	yes	complemented
28	C₂×#14558735	C₂²	1	4	yes	complemented
29	C₂²×Dic₂₉₈	C₂²	1	1	yes	characteristic
30	C₂²×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
31	C₂²×Dic₂₉₈	C₂²	1	2	yes	complemented
32	C₂×Q₈×D₁₄₉	C₂²	1	2	yes	complemented
33	C₂²×D₅₉₆	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊D₁₄₉	C₂²	1	2	yes	—
35	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	—
36	#18011911	C₂²	1	2	yes	complemented
37	#18011910	C₂²	1	4	yes	complemented
38	#18011899	C₂²	1	2	yes	complemented
39	#18011897	C₂²	1	4	yes	complemented
40	#18011896	C₂²	1	4	yes	complemented
41	#18011895	C₂²	1	4	yes	complemented
42	#18011893	C₂²	1	4	yes	complemented
43	#18011893	C₂²	1	4	yes	complemented
44	#18011891	C₂²	1	2	yes	complemented
45	#18011891	C₂²	1	2	yes	complemented
46	#18011890	C₂²	1	2	yes	—
47	#18011890	C₂²	1	2	yes	—
48	#18011890	C₂²	1	2	yes	complemented
49	#18011890	C₂²	1	2	yes	complemented
50	#18011890	C₂²	1	2	yes	complemented
51	#18011889	C₂²	1	4	yes	complemented
52	#18011888	C₂²	1	4	yes	—
53	#18011888	C₂²	1	4	yes	complemented
54	#18011887	C₂²	1	2	yes	complemented
55	#18011885	C₂²	1	2	yes	complemented
56	#18011884	C₂²	1	4	yes	complemented
57	#18011883	C₂²	1	4	yes	complemented
58	#18011883	C₂²	1	4	yes	complemented
59	#18011882	C₂²	1	2	yes	complemented
60	#18011882	C₂²	1	4	yes	complemented
61	#18011879	C₂²	1	4	yes	—
62	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
63	C₄×D₅₉₆	C₂²	1	2	yes	complemented
64	D₄×Dic₁₄₉	C₂²	1	4	yes	—
65	#18011871	C₂²	1	4	yes	complemented
66	#18011871	C₂²	1	4	yes	complemented
67	#18011869	C₂²	1	2	yes	complemented
68	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
69	C₂×#14558715	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₁₄₉	C₂²	1	2	yes	complemented
71	C₄⋊C₄×D₁₄₉	C₂²	1	4	yes	complemented
72	C₂×C₂²⋊Dic₁₄₉	C₂²	1	2	yes	—
73	C₂²⋊C₄×D₁₄₉	C₂²	1	4	yes	—
74	C₂×#41×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
75	C₂³×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
76	#123×C₁₄₉	C₂²	1	2	yes	complemented
77	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
78	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
79	#121×C₁₄₉	C₂²	1	1	yes	characteristic
80	#121×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
81	#120×C₁₄₉	C₂²	1	2	yes	—
82	C₄×D₄×C₁₄₉	C₂²	1	2	yes	—
83	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
84	#117×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
85	C₂³×D₁₄₉	C₂³	1	2	yes	—
86	#14558736	—	2	4	no	—
87	#14558736	—	2	4	no	—
88	#14558736	—	2	8	no	—
89	#14558736	—	2	8	no	—
90	#14558736	—	2	8	no	—
91	#14558736	—	2	4	no	—
92	#14558736	D₄	1	8	yes	complemented
93	#14558735	—	2	16	no	—
94	#14558735	—	2	8	no	—
95	C₂×Dic₂₉₈	—	2	4	no	—
96	C₂×Dic₂₉₈	—	2	8	no	—
97	C₂×Dic₂₉₈	—	2	4	no	—
98	C₂×Dic₂₉₈	C₂³	1	2	yes	—
99	C₂×Dic₂₉₈	C₂³	1	4	yes	—
100	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
101	C₂×Dic₂₉₈	C₂³	1	2	yes	—
102	C₂×Dic₂₉₈	C₂³	1	2	yes	—
103	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
104	Q₈×D₁₄₉	—	2	8	no	—
105	C₂×D₅₉₆	—	2	4	no	—
106	C₂×D₅₉₆	C₂³	1	2	yes	—
107	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
108	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊D₁₄₉	—	2	8	no	—
110	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
111	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
112	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
115	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
116	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
117	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
118	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
119	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
120	C₂×C₄×D₁₄₉	—	2	8	no	—
121	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
122	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
123	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
124	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
125	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
126	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
127	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
128	C₄⋊Dic₁₄₉	C₂³	1	4	yes	—
129	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
130	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
131	#14558715	C₂³	1	4	yes	—
132	#14558715	C₂³	1	4	yes	—
133	#14558715	C₂³	1	4	yes	—
134	#14558715	C₂³	1	4	yes	—
135	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
136	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
137	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
138	#14558713	C₂³	1	4	yes	—
139	#14558713	C₂³	1	4	yes	—
140	#14558713	C₂³	1	4	yes	—
141	#14558713	C₂³	1	4	yes	—
142	C₄×Dic₁₄₉	C₂³	1	4	yes	—
143	C₂⁴×C₁₄₉	C₂³	1	1	yes	characteristic
144	#41×C₁₄₉	—	2	4	no	—
145	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
146	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
147	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
148	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
149	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
150	C₂²×C₄×C₁₄₉	—	2	4	no	—
151	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
152	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
153	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
154	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
155	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
156	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
157	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
159	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
167	C₄²×C₁₄₉	C₂³	1	2	yes	—
168	C₂²×D₁₄₉	—	2	4	no	—
169	C₂²×D₁₄₉	—	2	4	no	—
170	C₂²×D₁₄₉	—	4	2	no	—
171	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
172	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
173	Dic₂₉₈	—	2	4	no	—
174	Dic₂₉₈	—	2	4	no	—
175	Dic₂₉₈	—	2	2	no	—
176	Dic₂₉₈	—	2	8	no	—
177	Dic₂₉₈	—	2	4	no	—
178	Dic₂₉₈	C₂×D₄	1	4	yes	—
179	D₅₉₆	—	2	4	no	—
180	D₅₉₆	—	2	2	no	—
181	D₅₉₆	C₂×D₄	1	4	yes	—
182	C₂²⋊D₁₄₉	—	2	4	no	—
183	C₂²⋊D₁₄₉	—	2	4	no	—
184	C₂²⋊D₁₄₉	—	2	8	no	—
185	C₂²⋊D₁₄₉	—	2	4	no	—
186	C₂²⋊D₁₄₉	—	4	4	no	—
187	C₂²⋊D₁₄₉	C₂×D₄	1	8	yes	—
188	C₂×Dic₁₄₉	—	2	4	no	—
189	C₂×Dic₁₄₉	—	2	4	no	—
190	C₂×Dic₁₄₉	—	2	8	no	—
191	C₂×Dic₁₄₉	—	4	2	no	—
192	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
193	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
194	C₂×Dic₁₄₉	C₂⁴	1	4	yes	—
195	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
196	C₄×D₁₄₉	—	2	4	no	—
197	C₄×D₁₄₉	—	2	8	no	—
198	C₄×D₁₄₉	—	2	4	no	—
199	C₄×D₁₄₉	—	2	4	no	—
200	C₄×D₁₄₉	—	4	4	no	—
201	C₄×D₁₄₉	C₂×D₄	1	8	yes	—
202	C₂³×C₁₄₉	—	2	2	no	—
203	C₂³×C₁₄₉	—	2	2	no	—
204	C₂³×C₁₄₉	—	4	1	no	—
205	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
206	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
207	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
208	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
209	Q₈×C₁₄₉	—	2	2	no	—
210	D₄×C₁₄₉	—	2	4	no	—
211	D₄×C₁₄₉	—	2	4	no	—
212	D₄×C₁₄₉	—	2	2	no	—
213	D₄×C₁₄₉	—	4	2	no	—
214	C₂×C₄×C₁₄₉	—	2	2	no	—
215	C₂×C₄×C₁₄₉	—	2	2	no	—
216	C₂×C₄×C₁₄₉	—	2	2	no	—
217	C₂×C₄×C₁₄₉	—	2	4	no	—
218	C₂×C₄×C₁₄₉	—	2	2	no	—
219	C₂×C₄×C₁₄₉	—	2	2	no	—
220	C₂×C₄×C₁₄₉	C₂×D₄	1	4	yes	—
221	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
222	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
223	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
224	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
225	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
226	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
227	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
228	C₂²×C₁₄₉	—	2	1	no	—
229	C₂²×C₁₄₉	—	2	1	no	—
230	C₂²×C₁₄₉	—	2	1	no	—
231	C₂²×C₁₄₉	—	2	1	no	—
232	C₂²×C₁₄₉	—	2	1	no	—
233	C₂²×C₁₄₉	—	2	2	no	—
234	C₂²×C₁₄₉	—	2	2	no	—
235	C₂²×C₁₄₉	—	2	1	no	—
236	C₂²×C₁₄₉	—	2	1	no	—
237	C₂²×C₁₄₉	—	2	2	no	—
238	C₂²×C₁₄₉	—	4	4	no	—
239	C₂²×C₁₄₉	C₂²×D₄	1	2	yes	—
240	C₂²×C₁₄₉	2₋¹⁺⁴	1	2	yes	complemented
241	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
242	C₂×D₁₄₉	—	2	2	no	—
243	C₂×D₁₄₉	—	2	2	no	—
244	C₂×D₁₄₉	—	2	2	no	—
245	C₂×D₁₄₉	—	2	2	no	—
246	C₂×D₁₄₉	—	2	2	no	—
247	C₂×D₁₄₉	—	4	8	no	—
248	C₂×D₁₄₉	C₂²×D₄	1	4	yes	—
249	C₄×C₁₄₉	—	2	1	no	—
250	C₄×C₁₄₉	—	2	1	no	—
251	C₄×C₁₄₉	—	2	2	no	—
252	C₄×C₁₄₉	—	2	2	no	—
253	C₄×C₁₄₉	—	2	2	no	—
254	C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
255	C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
256	Dic₁₄₉	—	2	2	no	—
257	Dic₁₄₉	—	2	4	no	—
258	Dic₁₄₉	—	2	4	no	—
259	Dic₁₄₉	C₂²×D₄	1	4	yes	—
260	C₂×C₁₄₉	—	2	2	no	—
261	C₂×C₁₄₉	—	2	2	no	—
262	C₂×C₁₄₉	—	4	2	no	—
263	C₂×C₁₄₉	—	4	1	no	—
264	C₂×C₁₄₉	C₂³×D₄	1	1	yes	characteristic
265	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
266	C₂×C₁₄₉	#585	1	1	yes	characteristic
267	D₁₄₉	—	2	4	no	—
268	D₁₄₉	—	4	2	no	—
269	C₁₄₉	#3489	1	1	yes	characteristic, complemented, Sylow
270	#3489	—	149	1	no	maximal, Sylow
271	C₂×2₋¹⁺⁴	—	149	1	no	—
272	C₂²×#41	—	149	1	no	—
273	D₄×Q₈	—	149	2	no	—
274	#548	—	149	2	no	—
275	#547	—	149	4	no	—
276	#547	—	149	2	no	—
277	#546	—	149	4	no	—
278	#546	—	149	2	no	—
279	#537	—	149	1	no	—
280	#537	—	149	2	no	—
281	#536	—	149	2	no	—
282	#536	—	149	1	no	—
283	#525	—	149	2	no	—
284	#525	D₁₄₉	1	1	yes	characteristic, complemented
285	C₂×C₂²⋊Q₈	—	149	1	no	—
286	C₂×C₂²⋊Q₈	—	149	2	no	—
287	#520	—	149	1	no	—
288	2₋¹⁺⁴	—	298	8	no	—
289	C₂×#41	—	298	8	no	—
290	C₂×#41	—	149	2	no	—
291	C₂×#41	—	149	4	no	—
292	C₂×#41	—	149	1	no	—
293	C₂×#41	—	149	2	no	—
294	C₂×#41	—	149	2	no	—
295	C₂×#41	—	149	1	no	—
296	C₂×#41	—	149	2	no	—
297	C₂×#41	—	149	1	no	—
298	C₂×#41	—	149	1	no	—
299	C₂×#41	C₂×D₁₄₉	1	1	yes	characteristic, complemented
300	C₂²×Q₈	—	149	2	no	—
301	C₂²×Q₈	—	149	1	no	—
302	C₂²×Q₈	—	149	2	no	—
303	C₂²×Q₈	—	149	1	no	—
304	C₂²×D₄	—	149	2	no	—
305	C₂²×D₄	—	149	1	no	—
306	C₂³×C₄	—	149	2	no	—
307	C₂³×C₄	C₂×D₁₄₉	1	1	yes	characteristic
308	C₄⋊Q₈	—	149	4	no	—
309	C₄⋊Q₈	—	149	2	no	—
310	#124	—	149	4	no	—
311	#124	—	149	2	no	—
312	#123	—	149	4	no	—
313	#123	—	149	4	no	—
314	#123	—	149	4	no	—
315	#123	—	149	4	no	—
316	#123	C₂×D₁₄₉	1	2	yes	complemented
317	C₂²⋊Q₈	—	149	2	no	—
318	C₂²⋊Q₈	—	149	2	no	—
319	C₂²⋊Q₈	—	149	2	no	—
320	C₂²⋊Q₈	—	149	2	no	—
321	C₂²⋊Q₈	—	149	2	no	—
322	C₂²⋊Q₈	—	149	2	no	—
323	C₂²⋊Q₈	—	149	2	no	—
324	C₂²⋊Q₈	—	149	4	no	—
325	C₂²⋊Q₈	—	149	2	no	—
326	C₂²⋊Q₈	—	149	4	no	—
327	C₂²⋊Q₈	—	149	4	no	—
328	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
329	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
330	#121	—	149	2	no	—
331	#121	—	149	4	no	—
332	#121	—	149	4	no	—
333	#121	—	149	4	no	—
334	#121	—	149	2	no	—
335	#121	—	149	4	no	—
336	#121	C₂×D₁₄₉	1	1	yes	characteristic
337	#121	C₂×D₁₄₉	1	1	yes	characteristic, complemented
338	#120	—	149	4	no	—
339	#120	C₂×D₁₄₉	1	2	yes	—
340	C₄×Q₈	—	149	2	no	—
341	C₄×D₄	—	149	4	no	—
342	C₄×D₄	—	149	4	no	—
343	C₄×D₄	—	149	4	no	—
344	C₄×D₄	—	149	2	no	—
345	C₄×D₄	C₂×D₁₄₉	1	2	yes	—
346	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
347	#117	—	149	2	no	—
348	#117	C₂×D₁₄₉	1	1	yes	characteristic, complemented
349	C₂×C₄⋊C₄	—	149	1	no	—
350	C₂×C₄⋊C₄	—	149	2	no	—
351	C₂×C₄⋊C₄	—	149	2	no	—
352	C₂×C₄⋊C₄	—	149	4	no	—
353	C₂×C₂²⋊C₄	—	149	2	no	—
354	C₂×C₂²⋊C₄	—	149	4	no	—
355	C₂⁴	—	149	2	no	—
356	C₂⁴	C₂²×D₁₄₉	1	1	yes	characteristic
357	#41	—	2	4	no	—
358	#41	—	298	4	no	—
359	#41	—	298	8	no	—
360	#41	—	298	4	no	—
361	#41	—	298	8	no	—
362	#41	—	298	8	no	—
363	#41	—	298	16	no	—
364	#41	—	298	8	no	—
365	#41	—	298	4	no	—
366	#41	—	149	8	no	—
367	C₂×Q₈	—	298	4	no	—
368	C₂×Q₈	—	298	8	no	—
369	C₂×Q₈	—	298	8	no	—
370	C₂×Q₈	—	298	4	no	—
371	C₂×Q₈	—	149	2	no	—
372	C₂×Q₈	—	149	2	no	—
373	C₂×Q₈	—	149	4	no	—
374	C₂×Q₈	—	149	1	no	—
375	C₂×Q₈	—	149	2	no	—
376	C₂×Q₈	—	149	1	no	—
377	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
378	C₂×D₄	—	298	4	no	—
379	C₂×D₄	—	298	8	no	—
380	C₂×D₄	—	149	4	no	—
381	C₂×D₄	—	149	2	no	—
382	C₂×D₄	—	149	2	no	—
383	C₂×D₄	—	149	2	no	—
384	C₂×D₄	—	149	4	no	—
385	C₂×D₄	—	149	2	no	—
386	C₂×D₄	—	149	2	no	—
387	C₂×D₄	—	149	1	no	—
388	C₂×D₄	—	149	1	no	—
389	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
390	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
391	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
392	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	298	8	no	—
395	C₂²×C₄	—	149	2	no	—
396	C₂²×C₄	—	149	4	no	—
397	C₂²×C₄	—	149	2	no	—
398	C₂²×C₄	—	149	4	no	—
399	C₂²×C₄	—	149	2	no	—
400	C₂²×C₄	—	149	2	no	—
401	C₂²×C₄	—	149	2	no	—
402	C₂²×C₄	—	149	2	no	—
403	C₂²×C₄	—	149	4	no	—
404	C₂²×C₄	—	149	2	no	—
405	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
406	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
407	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
408	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
409	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
410	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
411	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
412	C₄⋊C₄	—	149	2	no	—
413	C₄⋊C₄	—	149	4	no	—
414	C₄⋊C₄	—	149	4	no	—
415	C₄⋊C₄	—	149	2	no	—
416	C₄⋊C₄	—	149	4	no	—
417	C₄⋊C₄	—	149	4	no	—
418	C₄⋊C₄	—	149	4	no	—
419	C₄⋊C₄	—	149	4	no	—
420	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
421	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
422	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
423	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
424	C₂²⋊C₄	—	149	4	no	—
425	C₂²⋊C₄	—	149	4	no	—
426	C₂²⋊C₄	—	149	4	no	—
427	C₂²⋊C₄	—	149	4	no	—
428	C₂²⋊C₄	—	149	4	no	—
429	C₂²⋊C₄	—	149	4	no	—
430	C₂²⋊C₄	—	149	4	no	—
431	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
432	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
433	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
434	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
435	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
436	C₄²	—	149	4	no	—
437	C₄²	C₂²×D₁₄₉	1	2	yes	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	298	4	no	—
442	C₂³	—	298	4	no	—
443	C₂³	—	596	2	no	—
444	C₂³	—	149	2	no	—
445	C₂³	—	149	2	no	—
446	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
447	C₂³	C₂³×D₁₄₉	1	2	yes	—
448	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
449	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
450	Q₈	—	2	2	no	—
451	Q₈	—	298	8	no	—
452	Q₈	—	298	4	no	—
453	Q₈	—	298	4	no	—
454	Q₈	—	298	4	no	—
455	Q₈	—	298	2	no	—
456	Q₈	—	149	4	no	—
457	D₄	—	2	4	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	298	4	no	—
462	D₄	—	298	4	no	—
463	D₄	—	298	8	no	—
464	D₄	—	298	4	no	—
465	D₄	—	298	4	no	—
466	D₄	—	298	2	no	—
467	D₄	—	596	4	no	—
468	D₄	—	149	8	no	—
469	D₄	—	149	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	298	4	no	—
477	C₂×C₄	—	298	8	no	—
478	C₂×C₄	—	298	4	no	—
479	C₂×C₄	—	298	4	no	—
480	C₂×C₄	—	298	4	no	—
481	C₂×C₄	—	298	8	no	—
482	C₂×C₄	—	298	4	no	—
483	C₂×C₄	—	596	4	no	—
484	C₂×C₄	—	596	2	no	—
485	C₂×C₄	—	149	4	no	—
486	C₂×C₄	—	149	4	no	—
487	C₂×C₄	—	149	2	no	—
488	C₂×C₄	—	149	2	no	—
489	C₂×C₄	—	149	8	no	—
490	C₂×C₄	D₄×D₁₄₉	1	4	yes	—
491	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
492	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
493	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
494	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
495	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
496	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
497	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	298	2	no	—
510	C₂²	—	298	2	no	—
511	C₂²	—	298	2	no	—
512	C₂²	—	298	2	no	—
513	C₂²	—	298	2	no	—
514	C₂²	—	596	8	no	—
515	C₂²	—	149	4	no	—
516	C₂²	C₂×D₄×D₁₄₉	1	2	yes	—
517	C₂²	#18011958	1	2	yes	complemented
518	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	298	2	no	—
525	C₄	—	298	4	no	—
526	C₄	—	298	4	no	—
527	C₄	—	149	4	no	—
528	C₄	C₂×D₄×D₁₄₉	1	2	yes	—
529	C₄	C₂×D₄×D₁₄₉	1	2	yes	—
530	C₂	—	2	2	no	—
531	C₂	—	2	2	no	—
532	C₂	—	4	1	no	—
533	C₂	—	4	2	no	—
534	C₂	—	298	4	no	—
535	C₂	—	596	2	no	—
536	C₂	C₂²×D₄×D₁₄₉	1	1	yes	characteristic
537	C₂	C₂×#18011958	1	1	yes	characteristic
538	C₂	#23750461	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#525×C₁₄₉	C₂
hypercenter	#525	D₁₄₉
hypocenter	C₁₄₉	#3489
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₂×#18011958	C₂	semidirect
2. C₂²×#14558736	C₂	semidirect
3. D₄×Dic₂₉₈	C₂	semidirect
4. #23750284	C₂	semidirect
5. #23750280	C₂	semidirect
6. #23750273	C₂	semidirect
7. #23750271	C₂	semidirect
8. #23750262	C₂	semidirect
9. #23750204	C₂	semidirect
10. #23750203	C₂	semidirect
11. #23750201	C₂	semidirect
12. #23750198	C₂	semidirect
13. #23750135	C₂	semidirect
14. C₂×#18011890	C₂	semidirect
15. C₂²⋊Q₈×D₁₄₉	C₂	semidirect
16. #23750105	C₂	semidirect
17. #525×C₁₄₉	C₂	semidirect
26. C₂×#14558736	C₂²	semidirect
27. C₂×#14558735	C₂²	semidirect
28. C₂×#14558735	C₂²	semidirect
30. C₂²×Dic₂₉₈	C₂²	semidirect
31. C₂²×Dic₂₉₈	C₂²	semidirect
32. C₂×Q₈×D₁₄₉	C₂²	semidirect
36. #18011911	C₂²	semidirect
37. #18011910	C₂²	semidirect
38. #18011899	C₂²	semidirect
39. #18011897	C₂²	semidirect
40. #18011896	C₂²	semidirect
41. #18011895	C₂²	semidirect
42. #18011893	C₂²	semidirect
43. #18011893	C₂²	semidirect
44. #18011891	C₂²	semidirect
45. #18011891	C₂²	semidirect
48. #18011890	C₂²	semidirect
49. #18011890	C₂²	semidirect
50. #18011890	C₂²	semidirect
51. #18011889	C₂²	semidirect
53. #18011888	C₂²	semidirect
54. #18011887	C₂²	semidirect
55. #18011885	C₂²	semidirect
56. #18011884	C₂²	semidirect
57. #18011883	C₂²	semidirect
58. #18011883	C₂²	semidirect
59. #18011882	C₂²	semidirect
60. #18011882	C₂²	semidirect
62. C₄×Dic₂₉₈	C₂²	semidirect
63. C₄×D₅₉₆	C₂²	semidirect
65. #18011871	C₂²	semidirect
66. #18011871	C₂²	semidirect
67. #18011869	C₂²	semidirect
68. C₂×C₄⋊Dic₁₄₉	C₂²	semidirect
69. C₂×#14558715	C₂²	semidirect
70. C₄⋊C₄×D₁₄₉	C₂²	semidirect
71. C₄⋊C₄×D₁₄₉	C₂²	semidirect
74. C₂×#41×C₁₄₉	C₂²	semidirect
76. #123×C₁₄₉	C₂²	semidirect
78. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
80. #121×C₁₄₉	C₂²	semidirect
83. C₄×D₄×C₁₄₉	C₂²	semidirect
84. #117×C₁₄₉	C₂²	semidirect
92. #14558736	D₄	semidirect
240. C₂²×C₁₄₉	2₋¹⁺⁴	semidirect
269. C₁₄₉	#3489	semidirect
284. #525	D₁₄₉	semidirect
299. C₂×#41	C₂×D₁₄₉	semidirect
316. #123	C₂×D₁₄₉	semidirect
329. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
337. #121	C₂×D₁₄₉	semidirect
346. C₄×D₄	C₂×D₁₄₉	semidirect
348. #117	C₂×D₁₄₉	semidirect
517. C₂²	#18011958	semidirect

Maximal subgroups

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

subgroup	index
C₂×#18011958	2
C₂²×#14558736	2
D₄×Dic₂₉₈	2
#23750284	2
#23750280	2
#23750273	2
#23750271	2
#23750262	2
#23750204	2
#23750203	2
#23750201	2
#23750198	2
#23750135	2
C₂×#18011890	2
C₂²⋊Q₈×D₁₄₉	2
#23750105	2
#525×C₁₄₉	2
#3489	149