Subgroups — #34058564

Order 19072.

1232 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750360	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750357	C₂	1	2	yes	maximal, complemented
3	#23750297	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750296	C₂	1	2	yes	maximal, complemented
5	#23750295	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750270	C₂	1	2	yes	maximal, complemented
7	#23750268	C₂	1	2	yes	maximal, complemented
8	#23750267	C₂	1	4	yes	maximal, complemented
9	#23750227	C₂	1	4	yes	maximal, complemented
10	#23750193	C₂	1	2	yes	maximal, complemented
11	#23750179	C₂	1	1	yes	maximal, characteristic, complemented
12	#23750174	C₂	1	2	yes	maximal, complemented
13	#23750172	C₂	1	2	yes	maximal, complemented
14	#127×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750097	C₂	1	2	yes	maximal, complemented
16	C₄×#14558737	C₂	1	1	yes	maximal, characteristic, complemented
17	#559×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14558737	C₂²	1	1	yes	characteristic
19	C₂×#14558737	C₂²	1	2	yes	complemented
20	C₂×#14558736	C₂²	1	4	yes	complemented
21	C₂×#14558735	C₂²	1	2	yes	complemented
22	C₂×D₄×D₁₄₉	C₂²	1	2	yes	—
23	C₂×D₄×D₁₄₉	C₂²	1	2	yes	—
24	C₂×D₄×D₁₄₉	C₂²	1	2	yes	—
25	#18011910	C₂²	1	1	yes	characteristic, complemented
26	#18011909	C₂²	1	1	yes	characteristic, complemented
27	#18011908	C₂²	1	1	yes	characteristic
28	#18011908	C₂²	1	2	yes	complemented
29	#18011907	C₂²	1	2	yes	—
30	#18011907	C₂²	1	2	yes	—
31	#18011907	C₂²	1	2	yes	—
32	#18011907	C₂²	1	2	yes	complemented
33	#18011901	C₂²	1	2	yes	complemented
34	#18011900	C₂²	1	2	yes	complemented
35	#18011899	C₂²	1	2	yes	complemented
36	#18011897	C₂²	1	4	yes	complemented
37	#18011896	C₂²	1	4	yes	complemented
38	#18011895	C₂²	1	4	yes	complemented
39	#18011893	C₂²	1	4	yes	complemented
40	#18011891	C₂²	1	1	yes	characteristic
41	#18011889	C₂²	1	2	yes	—
42	#18011887	C₂²	1	1	yes	characteristic
43	#18011886	C₂²	1	2	yes	complemented
44	#18011886	C₂²	1	4	yes	complemented
45	#18011885	C₂²	1	4	yes	complemented
46	#18011884	C₂²	1	4	yes	complemented
47	#18011884	C₂²	1	4	yes	complemented
48	#18011884	C₂²	1	4	yes	complemented
49	#18011884	C₂²	1	4	yes	complemented
50	#18011883	C₂²	1	4	yes	complemented
51	#18011882	C₂²	1	2	yes	complemented
52	#18011881	C₂²	1	4	yes	—
53	#18011881	C₂²	1	4	yes	—
54	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
55	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic, complemented
56	C₄×Dic₂₉₈	C₂²	1	2	yes	complemented
57	C₄×D₅₉₆	C₂²	1	2	yes	—
58	C₄×D₅₉₆	C₂²	1	2	yes	complemented
59	C₄×D₅₉₆	C₂²	1	1	yes	characteristic, complemented
60	C₄×D₅₉₆	C₂²	1	2	yes	complemented
61	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
62	#18011873	C₂²	1	2	yes	—
63	#18011873	C₂²	1	1	yes	characteristic, complemented
64	#18011873	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₄₉	C₂²	1	4	yes	complemented
66	#18011871	C₂²	1	4	yes	complemented
67	#18011871	C₂²	1	4	yes	complemented
68	#18011869	C₂²	1	1	yes	characteristic
69	#18011869	C₂²	1	2	yes	complemented
70	#18011868	C₂²	1	2	yes	—
71	C₂×#14558713	C₂²	1	4	yes	—
72	C₂²⋊C₄×D₁₄₉	C₂²	1	4	yes	—
73	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
74	C₄²×D₁₄₉	C₂²	1	2	yes	complemented
75	#127×C₁₄₉	C₂²	1	1	yes	characteristic
76	#124×C₁₄₉	C₂²	1	2	yes	complemented
77	#124×C₁₄₉	C₂²	1	2	yes	complemented
78	#123×C₁₄₉	C₂²	1	4	yes	complemented
79	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
80	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
82	C₄×D₄×C₁₄₉	C₂²	1	2	yes	complemented
83	C₂³×D₁₄₉	C₂³	1	4	yes	—
84	#14558737	—	2	4	no	—
85	#14558737	—	4	4	no	—
86	#14558736	—	4	8	no	—
87	#14558735	—	4	4	no	—
88	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
89	C₂×Dic₂₉₈	C₂³	1	2	yes	—
90	C₂×D₅₉₆	C₂³	1	2	yes	—
91	C₂×D₅₉₆	C₂³	1	2	yes	—
92	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
93	C₂×D₅₉₆	C₂³	1	2	yes	—
94	C₂×D₅₉₆	C₂³	1	2	yes	—
95	C₂×D₅₉₆	C₂³	1	4	yes	—
96	C₂×D₅₉₆	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₁₄₉	C₂³	1	4	yes	—
102	D₄×D₁₄₉	—	2	8	no	—
103	D₄×D₁₄₉	—	4	4	no	—
104	D₄×D₁₄₉	—	4	4	no	—
105	C₂²×Dic₁₄₉	C₂³	1	4	yes	—
106	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
109	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
110	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
111	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
112	C₂×C₄×D₁₄₉	C₂³	1	4	yes	—
113	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
114	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
115	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
117	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
118	#14558715	C₂³	1	2	yes	—
119	#14558715	C₂³	1	2	yes	—
120	#14558715	C₂³	1	2	yes	—
121	#14558715	C₂³	1	2	yes	—
122	#14558715	C₂³	1	2	yes	—
123	C₂²⋊Dic₁₄₉	C₂³	1	4	yes	—
124	#14558713	C₂³	1	2	yes	—
125	#14558713	C₂³	1	2	yes	—
126	#14558713	C₂³	1	2	yes	—
127	#14558713	C₂³	1	4	yes	—
128	#14558713	C₂³	1	4	yes	—
129	#14558713	C₂³	1	2	yes	—
130	#14558713	C₂³	1	2	yes	—
131	#14558713	C₂³	1	4	yes	—
132	#14558713	C₂³	1	4	yes	—
133	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
134	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
135	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
136	C₄×Dic₁₄₉	C₂³	1	2	yes	—
137	C₄×Dic₁₄₉	C₂³	1	2	yes	—
138	C₄×Dic₁₄₉	C₂³	1	2	yes	—
139	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
140	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
142	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
143	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
144	C₂²×C₄×C₁₄₉	C₂³	1	4	yes	—
145	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
148	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
150	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
151	C₂²⋊C₄×C₁₄₉	C₂³	1	4	yes	—
152	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
153	C₄²×C₁₄₉	C₂³	1	2	yes	—
154	C₄²×C₁₄₉	C₂³	1	2	yes	—
155	C₂²×D₁₄₉	—	2	8	no	—
156	C₂²×D₁₄₉	—	4	4	no	—
157	C₂²×D₁₄₉	—	4	4	no	—
158	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
159	C₂²×D₁₄₉	C₂⁴	1	4	yes	—
160	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
161	Dic₂₉₈	—	2	2	no	—
162	Dic₂₉₈	—	2	4	no	—
163	D₅₉₆	—	2	4	no	—
164	D₅₉₆	—	2	4	no	—
165	D₅₉₆	—	2	2	no	—
166	D₅₉₆	—	2	4	no	—
167	D₅₉₆	—	4	2	no	—
168	D₅₉₆	—	4	4	no	—
169	D₅₉₆	—	4	4	no	—
170	C₂²⋊D₁₄₉	—	2	8	no	—
171	C₂²⋊D₁₄₉	—	2	8	no	—
172	C₂²⋊D₁₄₉	—	4	4	no	—
173	C₂²⋊D₁₄₉	—	4	4	no	—
174	C₂²⋊D₁₄₉	—	4	4	no	—
175	C₂×Dic₁₄₉	—	4	4	no	—
176	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
177	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
178	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
180	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
181	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
182	C₄×D₁₄₉	—	2	2	no	—
183	C₄×D₁₄₉	—	2	4	no	—
184	C₄×D₁₄₉	—	2	4	no	—
185	C₄×D₁₄₉	—	2	2	no	—
186	C₄×D₁₄₉	—	2	4	no	—
187	C₄×D₁₄₉	—	4	4	no	—
188	C₄×D₁₄₉	—	4	4	no	—
189	C₄×D₁₄₉	#41	1	4	yes	complemented
190	C₂³×C₁₄₉	C₂⁴	1	4	yes	—
191	Q₈×C₁₄₉	—	2	2	no	—
192	Q₈×C₁₄₉	—	2	2	no	—
193	D₄×C₁₄₉	—	2	4	no	—
194	D₄×C₁₄₉	—	2	4	no	—
195	D₄×C₁₄₉	—	4	2	no	—
196	C₂×C₄×C₁₄₉	—	4	4	no	—
197	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
198	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
199	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
200	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
201	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
202	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
203	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
204	C₂²×C₁₄₉	—	2	4	no	—
205	C₂²×C₁₄₉	—	2	4	no	—
206	C₂²×C₁₄₉	—	2	4	no	—
207	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
208	C₂×D₁₄₉	—	2	1	no	—
209	C₂×D₁₄₉	—	2	1	no	—
210	C₂×D₁₄₉	—	2	2	no	—
211	C₂×D₁₄₉	—	2	4	no	—
212	C₂×D₁₄₉	—	2	2	no	—
213	C₂×D₁₄₉	—	2	2	no	—
214	C₂×D₁₄₉	—	2	4	no	—
215	C₂×D₁₄₉	—	2	4	no	—
216	C₂×D₁₄₉	—	8	8	no	—
217	C₂×D₁₄₉	C₂×#41	1	2	yes	—
218	C₄×C₁₄₉	—	2	2	no	—
219	C₄×C₁₄₉	—	2	2	no	—
220	C₄×C₁₄₉	—	2	2	no	—
221	C₄×C₁₄₉	—	2	1	no	—
222	C₄×C₁₄₉	—	2	2	no	—
223	C₄×C₁₄₉	C₂×#41	1	2	yes	—
224	C₄×C₁₄₉	H(5,𝔽₂)	1	2	yes	—
225	Dic₁₄₉	—	2	2	no	—
226	Dic₁₄₉	—	2	1	no	—
227	Dic₁₄₉	—	2	2	no	—
228	Dic₁₄₉	—	2	2	no	—
229	Dic₁₄₉	C₂×#41	1	2	yes	—
230	Dic₁₄₉	H(5,𝔽₂)	1	2	yes	—
231	C₂×C₁₄₉	—	4	4	no	—
232	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
233	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	D₁₄₉	—	2	2	no	—
236	D₁₄₉	—	4	2	no	—
237	D₁₄₉	—	4	4	no	—
238	C₁₄₉	#3508	1	1	yes	characteristic, complemented, Sylow
239	#3508	—	149	1	no	maximal, Sylow
240	#559	—	149	2	no	—
241	#559	—	149	1	no	—
242	#559	D₁₄₉	1	1	yes	characteristic, complemented
243	#550	—	149	1	no	—
244	#550	—	149	1	no	—
245	#550	—	149	2	no	—
246	#546	—	149	2	no	—
247	#546	—	149	4	no	—
248	#546	—	149	2	no	—
249	#540	—	149	4	no	—
250	#535	—	149	2	no	—
251	#533	—	149	1	no	—
252	#532	—	149	2	no	—
253	#532	—	149	2	no	—
254	C₂×#127	—	149	1	no	—
255	#518	—	149	2	no	—
256	C₄×#41	—	149	1	no	—
257	C₂×#41	—	149	1	no	—
258	C₂×#41	—	149	2	no	—
259	C₂×#41	—	149	2	no	—
260	C₂×#41	—	149	4	no	—
261	C₂²×D₄	—	149	2	no	—
262	C₂²×D₄	—	149	2	no	—
263	C₂²×D₄	—	149	2	no	—
264	C₄⋊Q₈	—	149	1	no	—
265	C₄⋊Q₈	—	149	1	no	—
266	#127	—	149	2	no	—
267	#127	—	149	2	no	—
268	#127	—	149	2	no	—
269	#127	—	149	2	no	—
270	#127	—	149	1	no	—
271	#127	—	149	2	no	—
272	#127	C₂×D₁₄₉	1	1	yes	characteristic
273	#125	—	149	2	no	—
274	#124	—	149	2	no	—
275	#124	—	149	4	no	—
276	#124	—	149	2	no	—
277	#124	C₂×D₁₄₉	1	2	yes	complemented
278	#124	C₂×D₁₄₉	1	2	yes	complemented
279	#123	—	149	4	no	—
280	#123	—	149	4	no	—
281	#123	—	149	4	no	—
282	#123	C₂×D₁₄₉	1	4	yes	complemented
283	C₂²⋊Q₈	—	149	1	no	—
284	C₂²⋊Q₈	—	149	2	no	—
285	C₂²⋊Q₈	—	149	1	no	—
286	#121	—	149	2	no	—
287	#121	—	149	4	no	—
288	#121	—	149	4	no	—
289	#121	—	149	2	no	—
290	#121	—	149	4	no	—
291	#121	—	149	4	no	—
292	#121	—	149	4	no	—
293	#121	—	149	4	no	—
294	#121	—	149	4	no	—
295	#120	—	149	4	no	—
296	#120	—	149	4	no	—
297	C₄×Q₈	—	149	1	no	—
298	C₄×Q₈	—	149	2	no	—
299	C₄×Q₈	—	149	1	no	—
300	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
301	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic, complemented
302	C₄×D₄	—	149	2	no	—
303	C₄×D₄	—	149	4	no	—
304	C₄×D₄	—	149	2	no	—
305	C₄×D₄	—	149	1	no	—
306	C₄×D₄	—	149	2	no	—
307	C₄×D₄	—	149	4	no	—
308	C₄×D₄	—	149	4	no	—
309	C₄×D₄	—	149	2	no	—
310	C₄×D₄	—	149	1	no	—
311	C₄×D₄	—	149	2	no	—
312	C₄×D₄	—	149	2	no	—
313	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
314	C₄×D₄	C₂×D₁₄₉	1	2	yes	complemented
315	#117	—	149	1	no	—
316	#117	—	149	2	no	—
317	#117	—	149	2	no	—
318	C₂×C₂²⋊C₄	—	149	4	no	—
319	C₂×C₂²⋊C₄	—	149	4	no	—
320	C₂×C₄²	—	149	1	no	—
321	C₂×C₄²	—	149	2	no	—
322	C₂⁴	—	149	4	no	—
323	#41	—	298	4	no	—
324	#41	—	596	8	no	—
325	#41	—	596	4	no	—
326	#41	—	596	4	no	—
327	C₂×Q₈	—	149	1	no	—
328	C₂×Q₈	—	149	2	no	—
329	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
330	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
331	C₂×D₄	—	298	8	no	—
332	C₂×D₄	—	596	4	no	—
333	C₂×D₄	—	596	4	no	—
334	C₂×D₄	—	149	4	no	—
335	C₂×D₄	—	149	4	no	—
336	C₂×D₄	—	149	4	no	—
337	C₂×D₄	—	149	4	no	—
338	C₂×D₄	—	149	4	no	—
339	C₂×D₄	—	149	2	no	—
340	C₂×D₄	—	149	2	no	—
341	C₂×D₄	—	149	1	no	—
342	C₂×D₄	—	149	2	no	—
343	C₂×D₄	—	149	4	no	—
344	C₂×D₄	—	149	4	no	—
345	C₂×D₄	—	149	2	no	—
346	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
347	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
348	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
349	C₂²×C₄	—	149	2	no	—
350	C₂²×C₄	—	149	2	no	—
351	C₂²×C₄	—	149	2	no	—
352	C₂²×C₄	—	149	1	no	—
353	C₂²×C₄	—	149	1	no	—
354	C₂²×C₄	—	149	4	no	—
355	C₂²×C₄	—	149	4	no	—
356	C₂²×C₄	—	149	4	no	—
357	C₂²×C₄	—	149	1	no	—
358	C₂²×C₄	C₂²×D₁₄₉	1	4	yes	—
359	C₄⋊C₄	—	149	1	no	—
360	C₄⋊C₄	—	149	2	no	—
361	C₄⋊C₄	—	149	2	no	—
362	C₄⋊C₄	—	149	2	no	—
363	C₄⋊C₄	—	149	2	no	—
364	C₄⋊C₄	—	149	1	no	—
365	C₄⋊C₄	—	149	2	no	—
366	C₄⋊C₄	—	149	2	no	—
367	C₄⋊C₄	—	149	2	no	—
368	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
370	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
371	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
372	C₂²⋊C₄	—	149	4	no	—
373	C₂²⋊C₄	—	149	2	no	—
374	C₂²⋊C₄	—	149	2	no	—
375	C₂²⋊C₄	—	149	2	no	—
376	C₂²⋊C₄	—	149	4	no	—
377	C₂²⋊C₄	—	149	4	no	—
378	C₂²⋊C₄	—	149	2	no	—
379	C₂²⋊C₄	—	149	2	no	—
380	C₂²⋊C₄	—	149	4	no	—
381	C₂²⋊C₄	—	149	4	no	—
382	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
383	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
384	C₂²⋊C₄	C₂²×D₁₄₉	1	4	yes	—
385	C₄²	—	149	1	no	—
386	C₄²	—	149	2	no	—
387	C₄²	—	149	1	no	—
388	C₄²	—	149	2	no	—
389	C₄²	—	149	1	no	—
390	C₄²	—	149	2	no	—
391	C₄²	C₂²×D₁₄₉	1	2	yes	—
392	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
393	C₄²	C₂²×D₁₄₉	1	2	yes	—
394	C₂³	—	298	8	no	—
395	C₂³	—	596	4	no	—
396	C₂³	—	596	4	no	—
397	C₂³	—	149	4	no	—
398	C₂³	—	149	2	no	—
399	C₂³	—	149	1	no	—
400	C₂³	C₂³×D₁₄₉	1	4	yes	—
401	Q₈	—	2	2	no	—
402	Q₈	—	2	2	no	—
403	Q₈	—	298	4	no	—
404	Q₈	—	298	2	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	2	no	—
408	D₄	—	298	4	no	—
409	D₄	—	298	8	no	—
410	D₄	—	298	8	no	—
411	D₄	—	298	4	no	—
412	D₄	—	298	2	no	—
413	D₄	—	298	4	no	—
414	D₄	—	596	2	no	—
415	D₄	—	596	4	no	—
416	D₄	—	596	4	no	—
417	D₄	—	596	4	no	—
418	D₄	—	596	4	no	—
419	D₄	—	596	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	298	2	no	—
422	C₂×C₄	—	298	4	no	—
423	C₂×C₄	—	298	4	no	—
424	C₂×C₄	—	298	2	no	—
425	C₂×C₄	—	298	4	no	—
426	C₂×C₄	—	596	4	no	—
427	C₂×C₄	—	596	4	no	—
428	C₂×C₄	—	596	4	no	—
429	C₂×C₄	—	149	2	no	—
430	C₂×C₄	—	149	1	no	—
431	C₂×C₄	—	149	2	no	—
432	C₂×C₄	—	149	2	no	—
433	C₂×C₄	—	149	1	no	—
434	C₂×C₄	—	149	1	no	—
435	C₂×C₄	—	149	4	no	—
436	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
437	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
438	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
440	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
441	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
442	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	298	1	no	—
447	C₂²	—	298	1	no	—
448	C₂²	—	298	2	no	—
449	C₂²	—	298	4	no	—
450	C₂²	—	298	2	no	—
451	C₂²	—	298	4	no	—
452	C₂²	—	298	2	no	—
453	C₂²	—	298	4	no	—
454	C₂²	—	149	2	no	—
455	C₂²	—	1192	8	no	—
456	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	2	no	—
462	C₄	—	298	2	no	—
463	C₄	—	298	2	no	—
464	C₄	—	298	1	no	—
465	C₄	—	298	2	no	—
466	C₄	—	149	2	no	—
467	C₄	—	149	2	no	—
468	C₄	#41×D₁₄₉	1	2	yes	—
469	C₄	#18011957	1	2	yes	—
470	C₂	—	4	4	no	—
471	C₂	—	298	2	no	—
472	C₂	—	596	4	no	—
473	C₂	—	596	2	no	—
474	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
475	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic
476	C₂	C₂×#18011957	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#559×C₁₄₉	C₂
hypercenter	#559	D₁₄₉
hypocenter	C₁₄₉	#3508
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #559

Complements

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

N	H ≅ G/N	type
1. #23750360	C₂	semidirect
2. #23750357	C₂	semidirect
3. #23750297	C₂	semidirect
4. #23750296	C₂	semidirect
5. #23750295	C₂	semidirect
6. #23750270	C₂	semidirect
7. #23750268	C₂	semidirect
8. #23750267	C₂	semidirect
9. #23750227	C₂	semidirect
10. #23750193	C₂	semidirect
11. #23750179	C₂	semidirect
12. #23750174	C₂	semidirect
13. #23750172	C₂	semidirect
14. #127×D₁₄₉	C₂	semidirect
15. #23750097	C₂	semidirect
16. C₄×#14558737	C₂	semidirect
17. #559×C₁₄₉	C₂	semidirect
19. C₂×#14558737	C₂²	semidirect
20. C₂×#14558736	C₂²	semidirect
21. C₂×#14558735	C₂²	semidirect
25. #18011910	C₂²	semidirect
26. #18011909	C₂²	semidirect
28. #18011908	C₂²	semidirect
32. #18011907	C₂²	semidirect
33. #18011901	C₂²	semidirect
34. #18011900	C₂²	semidirect
35. #18011899	C₂²	semidirect
36. #18011897	C₂²	semidirect
37. #18011896	C₂²	semidirect
38. #18011895	C₂²	semidirect
39. #18011893	C₂²	semidirect
43. #18011886	C₂²	semidirect
44. #18011886	C₂²	semidirect
45. #18011885	C₂²	semidirect
46. #18011884	C₂²	semidirect
47. #18011884	C₂²	semidirect
48. #18011884	C₂²	semidirect
49. #18011884	C₂²	semidirect
50. #18011883	C₂²	semidirect
51. #18011882	C₂²	semidirect
54. Q₈×Dic₁₄₉	C₂²	semidirect
55. C₄×Dic₂₉₈	C₂²	semidirect
56. C₄×Dic₂₉₈	C₂²	semidirect
58. C₄×D₅₉₆	C₂²	semidirect
59. C₄×D₅₉₆	C₂²	semidirect
60. C₄×D₅₉₆	C₂²	semidirect
61. D₄×Dic₁₄₉	C₂²	semidirect
63. #18011873	C₂²	semidirect
64. #18011873	C₂²	semidirect
65. C₄×C₂²⋊D₁₄₉	C₂²	semidirect
66. #18011871	C₂²	semidirect
67. #18011871	C₂²	semidirect
69. #18011869	C₂²	semidirect
74. C₄²×D₁₄₉	C₂²	semidirect
76. #124×C₁₄₉	C₂²	semidirect
77. #124×C₁₄₉	C₂²	semidirect
78. #123×C₁₄₉	C₂²	semidirect
79. C₄×Q₈×C₁₄₉	C₂²	semidirect
80. C₄×Q₈×C₁₄₉	C₂²	semidirect
81. C₄×D₄×C₁₄₉	C₂²	semidirect
82. C₄×D₄×C₁₄₉	C₂²	semidirect
189. C₄×D₁₄₉	#41	semidirect
238. C₁₄₉	#3508	semidirect
242. #559	D₁₄₉	semidirect
277. #124	C₂×D₁₄₉	semidirect
278. #124	C₂×D₁₄₉	semidirect
282. #123	C₂×D₁₄₉	semidirect
300. C₄×Q₈	C₂×D₁₄₉	semidirect
301. C₄×Q₈	C₂×D₁₄₉	semidirect
313. C₄×D₄	C₂×D₁₄₉	semidirect
314. C₄×D₄	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750360	2
#23750357	2
#23750297	2
#23750296	2
#23750295	2
#23750270	2
#23750268	2
#23750267	2
#23750227	2
#23750193	2
#23750179	2
#23750174	2
#23750172	2
#127×D₁₄₉	2
#23750097	2
C₄×#14558737	2
#559×C₁₄₉	2
#3508	149