Subgroups — #34058569

Order 19072.

992 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750352	C₂	1	2	yes	maximal, complemented
2	#23750352	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750351	C₂	1	1	yes	maximal, characteristic, complemented
4	#23750346	C₂	1	1	yes	maximal, characteristic, complemented
5	#23750343	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750342	C₂	1	2	yes	maximal, complemented
7	#23750317	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750315	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750312	C₂	1	2	yes	maximal, complemented
10	#23750310	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750308	C₂	1	2	yes	maximal, complemented
12	#23750234	C₂	1	2	yes	maximal, complemented
13	#23750232	C₂	1	2	yes	maximal, complemented
14	#23750197	C₂	1	2	yes	maximal
15	#23750181	C₂	1	1	yes	maximal, characteristic, complemented
16	#23750179	C₂	1	1	yes	maximal, characteristic, complemented
17	#23750178	C₂	1	1	yes	maximal, characteristic, complemented
18	#23750177	C₂	1	1	yes	maximal, characteristic, complemented
19	#23750177	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#18011910	C₂	1	1	yes	maximal, characteristic, complemented
21	#23750102	C₂	1	2	yes	maximal, complemented
22	C₄×#14558735	C₂	1	1	yes	maximal, characteristic
23	#552×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14558735	C₂²	1	1	yes	characteristic
25	C₂²×Dic₂₉₈	C₂²	1	2	yes	—
26	#18011910	C₂²	1	1	yes	characteristic
27	#18011910	C₂²	1	1	yes	characteristic
28	#18011910	C₂²	1	2	yes	—
29	#18011910	C₂²	1	2	yes	—
30	#18011910	C₂²	1	1	yes	characteristic
31	#18011910	C₂²	1	1	yes	characteristic
32	#18011910	C₂²	1	1	yes	characteristic
33	#18011910	C₂²	1	2	yes	—
34	#18011910	C₂²	1	2	yes	—
35	#18011909	C₂²	1	1	yes	characteristic
36	#18011906	C₂²	1	2	yes	—
37	#18011906	C₂²	1	2	yes	—
38	#18011906	C₂²	1	2	yes	—
39	#18011905	C₂²	1	2	yes	—
40	#18011904	C₂²	1	2	yes	—
41	#18011904	C₂²	1	2	yes	—
42	#18011904	C₂²	1	2	yes	—
43	#18011903	C₂²	1	1	yes	characteristic
44	#18011903	C₂²	1	2	yes	—
45	#18011902	C₂²	1	1	yes	characteristic
46	#18011902	C₂²	1	1	yes	characteristic
47	#18011902	C₂²	1	2	yes	—
48	#18011902	C₂²	1	2	yes	—
49	#18011901	C₂²	1	2	yes	—
50	#18011901	C₂²	1	2	yes	—
51	#18011901	C₂²	1	2	yes	—
52	#18011901	C₂²	1	2	yes	—
53	#18011901	C₂²	1	2	yes	—
54	#18011901	C₂²	1	2	yes	—
55	#18011901	C₂²	1	2	yes	—
56	#18011897	C₂²	1	2	yes	—
57	#18011897	C₂²	1	2	yes	—
58	#18011895	C₂²	1	2	yes	—
59	#18011894	C₂²	1	2	yes	—
60	#18011892	C₂²	1	2	yes	—
61	#18011891	C₂²	1	1	yes	characteristic
62	#18011890	C₂²	1	1	yes	characteristic
63	#18011890	C₂²	1	1	yes	characteristic
64	#18011889	C₂²	1	2	yes	—
65	#18011889	C₂²	1	2	yes	—
66	#18011889	C₂²	1	2	yes	—
67	#18011888	C₂²	1	2	yes	—
68	#18011888	C₂²	1	2	yes	—
69	#18011888	C₂²	1	2	yes	—
70	#18011888	C₂²	1	2	yes	—
71	#18011887	C₂²	1	1	yes	characteristic
72	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
73	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic
74	C₄×Dic₂₉₈	C₂²	1	2	yes	—
75	C₄×Dic₂₉₈	C₂²	1	2	yes	—
76	C₄×Dic₂₉₈	C₂²	1	2	yes	—
77	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
78	C₄×Dic₂₉₈	C₂²	1	2	yes	—
79	C₄×Dic₂₉₈	C₂²	1	2	yes	—
80	C₄×Dic₂₉₈	C₂²	1	1	yes	characteristic
81	#18011876	C₂²	1	2	yes	—
82	#18011876	C₂²	1	1	yes	characteristic
83	#18011876	C₂²	1	2	yes	—
84	#18011876	C₂²	1	1	yes	characteristic
85	#18011876	C₂²	1	2	yes	—
86	#18011876	C₂²	1	2	yes	—
87	#18011876	C₂²	1	2	yes	—
88	#18011876	C₂²	1	2	yes	—
89	#18011876	C₂²	1	1	yes	characteristic
90	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₁₄₉	C₂²	1	1	yes	characteristic
93	#18011871	C₂²	1	1	yes	characteristic
94	#18011871	C₂²	1	1	yes	characteristic
95	#18011870	C₂²	1	1	yes	characteristic
96	#18011870	C₂²	1	2	yes	—
97	#18011869	C₂²	1	1	yes	characteristic
98	#18011869	C₂²	1	1	yes	characteristic
99	#18011869	C₂²	1	1	yes	characteristic
100	#18011868	C₂²	1	2	yes	—
101	#18011867	C₂²	1	2	yes	—
102	#18011867	C₂²	1	2	yes	—
103	#18011867	C₂²	1	1	yes	characteristic
104	#18011867	C₂²	1	2	yes	—
105	#18011867	C₂²	1	2	yes	—
106	#18011867	C₂²	1	1	yes	characteristic
107	C₂×C₄⋊Dic₁₄₉	C₂²	1	1	yes	characteristic
108	C₂×#14558715	C₂²	1	2	yes	—
109	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
110	C₂×C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
111	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic
112	#126×C₁₄₉	C₂²	1	2	yes	—
113	#125×C₁₄₉	C₂²	1	1	yes	characteristic
114	#125×C₁₄₉	C₂²	1	2	yes	—
115	#123×C₁₄₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₁₄₉	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
120	#117×C₁₄₉	C₂²	1	1	yes	characteristic
121	#117×C₁₄₉	C₂²	1	2	yes	—
122	C₂×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic
123	#14558735	—	2	4	no	—
124	C₂×Dic₂₉₈	—	2	8	no	—
125	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
126	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₂₉₈	C₂³	1	2	yes	—
128	C₂×Dic₂₉₈	C₂³	1	2	yes	—
129	C₂×Dic₂₉₈	C₂³	1	2	yes	—
130	C₂×Dic₂₉₈	C₂³	1	2	yes	—
131	C₂×Dic₂₉₈	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₄₉	C₂³	1	1	yes	characteristic
134	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
135	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
138	C₂²×Dic₁₄₉	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
143	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
144	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
145	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
146	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
150	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
151	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
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	#14558715	C₂³	1	2	yes	—
157	#14558715	C₂³	1	2	yes	—
158	#14558715	C₂³	1	2	yes	—
159	#14558715	C₂³	1	2	yes	—
160	#14558715	C₂³	1	2	yes	—
161	#14558715	C₂³	1	2	yes	—
162	#14558715	C₂³	1	2	yes	—
163	#14558715	C₂³	1	2	yes	—
164	#14558715	C₂³	1	2	yes	—
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	1	yes	characteristic
170	#14558715	C₂³	1	1	yes	characteristic
171	#14558715	C₂³	1	1	yes	characteristic
172	#14558715	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
178	#14558713	C₂³	1	1	yes	characteristic
179	#14558713	C₂³	1	2	yes	—
180	#14558713	C₂³	1	2	yes	—
181	#14558713	C₂³	1	1	yes	characteristic
182	#14558713	C₂³	1	2	yes	—
183	#14558713	C₂³	1	2	yes	—
184	C₄×Dic₁₄₉	C₂³	1	2	yes	—
185	C₄×Dic₁₄₉	C₂³	1	2	yes	—
186	C₄×Dic₁₄₉	C₂³	1	2	yes	—
187	C₄×Dic₁₄₉	C₂³	1	2	yes	—
188	C₄×Dic₁₄₉	C₂³	1	2	yes	—
189	C₄×Dic₁₄₉	C₂³	1	2	yes	—
190	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
191	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
192	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
198	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
201	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
202	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
204	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
206	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
207	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
208	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
209	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
216	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
221	C₄²×C₁₄₉	C₂³	1	2	yes	—
222	C₄²×C₁₄₉	C₂³	1	2	yes	—
223	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
224	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
225	Dic₂₉₈	—	2	2	no	—
226	Dic₂₉₈	—	2	4	no	—
227	Dic₂₉₈	—	2	4	no	—
228	Dic₂₉₈	—	2	4	no	—
229	Dic₂₉₈	—	2	4	no	—
230	Dic₂₉₈	—	2	2	no	—
231	Dic₂₉₈	—	2	4	no	—
232	C₂²⋊D₁₄₉	—	2	2	no	—
233	C₂²⋊D₁₄₉	—	2	2	no	—
234	C₂×Dic₁₄₉	—	2	4	no	—
235	C₂×Dic₁₄₉	—	2	2	no	—
236	C₂×Dic₁₄₉	—	2	2	no	—
237	C₂×Dic₁₄₉	—	2	2	no	—
238	C₂×Dic₁₄₉	#41	1	4	yes	—
239	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
240	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
241	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
242	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
243	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
246	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
247	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
250	C₄×D₁₄₉	—	2	2	no	—
251	C₄×D₁₄₉	—	2	2	no	—
252	C₄×D₁₄₉	—	2	2	no	—
253	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
254	C₂³×C₁₄₉	C₂⁴	1	1	yes	characteristic
255	Q₈×C₁₄₉	—	2	2	no	—
256	D₄×C₁₄₉	—	2	2	no	—
257	C₂×C₄×C₁₄₉	—	2	4	no	—
258	C₂×C₄×C₁₄₉	—	2	2	no	—
259	C₂×C₄×C₁₄₉	—	2	2	no	—
260	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
263	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
264	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
265	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
267	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₁₄₉	—	2	1	no	—
270	C₂²×C₁₄₉	—	2	1	no	—
271	C₂²×C₁₄₉	—	2	1	no	—
272	C₂²×C₁₄₉	—	2	1	no	—
273	C₂²×C₁₄₉	—	2	1	no	—
274	C₂²×C₁₄₉	C₂×#41	1	2	yes	—
275	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
276	C₂×D₁₄₉	—	2	1	no	—
277	C₂×D₁₄₉	—	2	1	no	—
278	C₂×D₁₄₉	—	2	1	no	—
279	C₄×C₁₄₉	—	2	2	no	—
280	C₄×C₁₄₉	—	2	2	no	—
281	C₄×C₁₄₉	—	2	1	no	—
282	C₄×C₁₄₉	—	2	1	no	—
283	C₄×C₁₄₉	—	2	1	no	—
284	C₄×C₁₄₉	—	2	2	no	—
285	C₄×C₁₄₉	—	2	1	no	—
286	C₄×C₁₄₉	—	2	2	no	—
287	C₄×C₁₄₉	2₋¹⁺⁴	1	2	yes	—
288	Dic₁₄₉	—	2	1	no	—
289	Dic₁₄₉	—	2	2	no	—
290	Dic₁₄₉	—	2	2	no	—
291	Dic₁₄₉	—	2	1	no	—
292	Dic₁₄₉	—	2	1	no	—
293	Dic₁₄₉	—	2	1	no	—
294	Dic₁₄₉	—	2	2	no	—
295	Dic₁₄₉	—	2	2	no	—
296	Dic₁₄₉	C₂×#41	1	2	yes	—
297	Dic₁₄₉	C₂×#41	1	2	yes	—
298	Dic₁₄₉	2₋¹⁺⁴	1	2	yes	—
299	C₂×C₁₄₉	—	2	2	no	—
300	C₂×C₁₄₉	—	4	1	no	—
301	C₂×C₁₄₉	C₂²×#41	1	1	yes	characteristic
302	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
303	C₂×C₁₄₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	D₁₄₉	—	4	1	no	—
305	C₁₄₉	#3509	1	1	yes	characteristic, complemented, Sylow
306	#3509	—	149	1	no	maximal, Sylow
307	#557	—	149	2	no	—
308	#557	—	149	1	no	—
309	#557	—	149	1	no	—
310	#556	—	149	2	no	—
311	#556	—	149	1	no	—
312	#556	—	149	1	no	—
313	#552	—	149	2	no	—
314	#552	—	149	1	no	—
315	#552	—	149	1	no	—
316	#552	—	149	2	no	—
317	#552	—	149	1	no	—
318	#552	D₁₄₉	1	1	yes	characteristic, complemented
319	#541	—	149	2	no	—
320	#541	—	149	2	no	—
321	#536	—	149	2	no	—
322	#533	—	149	1	no	—
323	#533	—	149	1	no	—
324	#533	—	149	1	no	—
325	#533	—	149	1	no	—
326	#533	—	149	1	no	—
327	C₂×C₄⋊Q₈	—	149	1	no	—
328	#519	—	149	2	no	—
329	C₄×#41	—	149	1	no	—
330	C₂×#41	—	149	1	no	—
331	C₂²×Q₈	—	149	2	no	—
332	C₄⋊Q₈	—	149	1	no	—
333	C₄⋊Q₈	—	149	1	no	—
334	C₄⋊Q₈	—	149	1	no	—
335	C₄⋊Q₈	—	149	2	no	—
336	C₄⋊Q₈	—	149	2	no	—
337	C₄⋊Q₈	—	149	1	no	—
338	C₄⋊Q₈	—	149	1	no	—
339	C₄⋊Q₈	—	149	1	no	—
340	C₄⋊Q₈	—	149	2	no	—
341	C₄⋊Q₈	—	149	2	no	—
342	#126	—	149	2	no	—
343	#126	—	149	2	no	—
344	#126	—	149	2	no	—
345	#126	—	149	2	no	—
346	#126	—	149	2	no	—
347	#126	—	149	2	no	—
348	#126	—	149	2	no	—
349	#126	C₂×D₁₄₉	1	2	yes	—
350	#125	—	149	2	no	—
351	#125	—	149	2	no	—
352	#125	—	149	2	no	—
353	#125	—	149	1	no	—
354	#125	—	149	1	no	—
355	#125	—	149	2	no	—
356	#125	—	149	2	no	—
357	#125	—	149	2	no	—
358	#125	—	149	2	no	—
359	#125	—	149	2	no	—
360	#125	—	149	2	no	—
361	#125	—	149	1	no	—
362	#125	—	149	2	no	—
363	#125	C₂×D₁₄₉	1	1	yes	characteristic
364	#125	C₂×D₁₄₉	1	2	yes	—
365	#124	—	149	2	no	—
366	#124	—	149	2	no	—
367	#123	—	149	2	no	—
368	#123	—	149	2	no	—
369	#123	—	149	2	no	—
370	#123	C₂×D₁₄₉	1	2	yes	—
371	C₂²⋊Q₈	—	149	1	no	—
372	C₂²⋊Q₈	—	149	1	no	—
373	C₂²⋊Q₈	—	149	1	no	—
374	C₂²⋊Q₈	—	149	2	no	—
375	C₂²⋊Q₈	—	149	2	no	—
376	C₂²⋊Q₈	—	149	2	no	—
377	C₂²⋊Q₈	—	149	1	no	—
378	C₂²⋊Q₈	—	149	2	no	—
379	C₂²⋊Q₈	—	149	2	no	—
380	C₂²⋊Q₈	—	149	2	no	—
381	C₂²⋊Q₈	—	149	2	no	—
382	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
383	C₂²⋊Q₈	C₂×D₁₄₉	1	1	yes	characteristic
384	C₄×Q₈	—	149	1	no	—
385	C₄×Q₈	—	149	1	no	—
386	C₄×Q₈	—	149	1	no	—
387	C₄×Q₈	—	149	2	no	—
388	C₄×Q₈	—	149	2	no	—
389	C₄×Q₈	—	149	2	no	—
390	C₄×Q₈	—	149	2	no	—
391	C₄×Q₈	—	149	2	no	—
392	C₄×Q₈	—	149	1	no	—
393	C₄×Q₈	—	149	2	no	—
394	C₄×Q₈	—	149	1	no	—
395	C₄×Q₈	—	149	1	no	—
396	C₄×Q₈	—	149	2	no	—
397	C₄×Q₈	—	149	2	no	—
398	C₄×Q₈	—	149	2	no	—
399	C₄×Q₈	—	149	2	no	—
400	C₄×Q₈	—	149	2	no	—
401	C₄×Q₈	—	149	1	no	—
402	C₄×Q₈	C₂×D₁₄₉	1	1	yes	characteristic
403	C₄×D₄	—	149	1	no	—
404	C₄×D₄	—	149	1	no	—
405	C₄×D₄	—	149	1	no	—
406	C₄×D₄	—	149	1	no	—
407	C₄×D₄	—	149	1	no	—
408	C₄×D₄	C₂×D₁₄₉	1	1	yes	characteristic
409	#117	—	149	2	no	—
410	#117	—	149	1	no	—
411	#117	—	149	1	no	—
412	#117	—	149	1	no	—
413	#117	—	149	1	no	—
414	#117	—	149	1	no	—
415	#117	—	149	1	no	—
416	#117	—	149	2	no	—
417	#117	—	149	2	no	—
418	#117	—	149	2	no	—
419	#117	—	149	2	no	—
420	#117	—	149	2	no	—
421	#117	C₂×D₁₄₉	1	2	yes	—
422	#117	C₂×D₁₄₉	1	1	yes	characteristic
423	C₂×C₄⋊C₄	—	149	2	no	—
424	C₂×C₄⋊C₄	—	149	1	no	—
425	C₂×C₄⋊C₄	C₂×D₁₄₉	1	1	yes	characteristic
426	C₂×C₄²	—	149	1	no	—
427	C₂×C₄²	—	149	1	no	—
428	C₂×C₄²	—	149	1	no	—
429	#41	—	298	4	no	—
430	C₂×Q₈	—	298	8	no	—
431	C₂×Q₈	—	149	1	no	—
432	C₂×Q₈	—	149	2	no	—
433	C₂×Q₈	—	149	2	no	—
434	C₂×Q₈	—	149	2	no	—
435	C₂×Q₈	—	149	2	no	—
436	C₂×Q₈	—	149	2	no	—
437	C₂×Q₈	—	149	1	no	—
438	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
439	C₂×D₄	—	149	1	no	—
440	C₂×D₄	—	149	1	no	—
441	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
442	C₂²×C₄	—	149	1	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	1	no	—
448	C₂²×C₄	—	149	1	no	—
449	C₂²×C₄	—	149	1	no	—
450	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
451	C₂²×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
452	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
453	C₄⋊C₄	—	149	2	no	—
454	C₄⋊C₄	—	149	2	no	—
455	C₄⋊C₄	—	149	1	no	—
456	C₄⋊C₄	—	149	1	no	—
457	C₄⋊C₄	—	149	2	no	—
458	C₄⋊C₄	—	149	2	no	—
459	C₄⋊C₄	—	149	2	no	—
460	C₄⋊C₄	—	149	2	no	—
461	C₄⋊C₄	—	149	1	no	—
462	C₄⋊C₄	—	149	1	no	—
463	C₄⋊C₄	—	149	1	no	—
464	C₄⋊C₄	—	149	1	no	—
465	C₄⋊C₄	—	149	1	no	—
466	C₄⋊C₄	—	149	1	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	—	149	2	no	—
472	C₄⋊C₄	—	149	2	no	—
473	C₄⋊C₄	—	149	2	no	—
474	C₄⋊C₄	—	149	2	no	—
475	C₄⋊C₄	—	149	2	no	—
476	C₄⋊C₄	—	149	2	no	—
477	C₄⋊C₄	—	149	2	no	—
478	C₄⋊C₄	—	149	2	no	—
479	C₄⋊C₄	—	149	2	no	—
480	C₄⋊C₄	—	149	2	no	—
481	C₄⋊C₄	—	149	2	no	—
482	C₄⋊C₄	—	149	2	no	—
483	C₄⋊C₄	—	149	2	no	—
484	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
486	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
487	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
490	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
491	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
492	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
493	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
494	C₂²⋊C₄	—	149	1	no	—
495	C₂²⋊C₄	—	149	2	no	—
496	C₂²⋊C₄	—	149	1	no	—
497	C₂²⋊C₄	—	149	2	no	—
498	C₂²⋊C₄	—	149	2	no	—
499	C₂²⋊C₄	—	149	1	no	—
500	C₂²⋊C₄	—	149	1	no	—
501	C₂²⋊C₄	—	149	2	no	—
502	C₂²⋊C₄	—	149	2	no	—
503	C₂²⋊C₄	—	149	2	no	—
504	C₂²⋊C₄	—	149	2	no	—
505	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
506	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
507	C₂²⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
508	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
510	C₄²	—	149	1	no	—
511	C₄²	—	149	1	no	—
512	C₄²	—	149	1	no	—
513	C₄²	—	149	1	no	—
514	C₄²	—	149	1	no	—
515	C₄²	—	149	1	no	—
516	C₄²	—	149	1	no	—
517	C₄²	—	149	1	no	—
518	C₄²	—	149	1	no	—
519	C₄²	—	149	2	no	—
520	C₄²	—	149	2	no	—
521	C₄²	—	149	2	no	—
522	C₄²	—	149	2	no	—
523	C₄²	—	149	2	no	—
524	C₄²	—	149	2	no	—
525	C₄²	—	149	2	no	—
526	C₄²	—	149	2	no	—
527	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
528	C₄²	C₂²×D₁₄₉	1	2	yes	—
529	C₄²	C₂²×D₁₄₉	1	2	yes	—
530	C₂³	—	149	1	no	—
531	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
532	C₂³	C₂³×D₁₄₉	1	1	yes	characteristic
533	Q₈	—	2	2	no	—
534	Q₈	—	298	4	no	—
535	Q₈	—	298	4	no	—
536	Q₈	—	298	4	no	—
537	Q₈	—	298	4	no	—
538	Q₈	—	298	4	no	—
539	Q₈	—	298	2	no	—
540	Q₈	—	298	2	no	—
541	D₄	—	2	2	no	—
542	D₄	—	298	2	no	—
543	D₄	—	298	2	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	298	2	no	—
548	C₂×C₄	—	298	2	no	—
549	C₂×C₄	—	298	4	no	—
550	C₂×C₄	—	298	2	no	—
551	C₂×C₄	—	298	2	no	—
552	C₂×C₄	—	298	2	no	—
553	C₂×C₄	—	298	2	no	—
554	C₂×C₄	—	149	1	no	—
555	C₂×C₄	—	149	1	no	—
556	C₂×C₄	—	149	2	no	—
557	C₂×C₄	—	149	2	no	—
558	C₂×C₄	—	149	1	no	—
559	C₂×C₄	—	149	2	no	—
560	C₂×C₄	—	149	2	no	—
561	C₂×C₄	—	149	1	no	—
562	C₂×C₄	—	149	4	no	—
563	C₂×C₄	—	149	1	no	—
564	C₂×C₄	—	149	1	no	—
565	C₂×C₄	—	149	1	no	—
566	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
568	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
569	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
570	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
572	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
573	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
574	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	298	1	no	—
581	C₂²	—	298	1	no	—
582	C₂²	—	298	1	no	—
583	C₂²	#41×D₁₄₉	1	2	yes	—
584	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	2	no	—
593	C₄	—	298	1	no	—
594	C₄	—	298	2	no	—
595	C₄	—	298	2	no	—
596	C₄	—	298	1	no	—
597	C₄	—	298	1	no	—
598	C₄	—	298	2	no	—
599	C₄	—	298	1	no	—
600	C₄	—	298	2	no	—
601	C₄	—	149	2	no	—
602	C₄	—	149	2	no	—
603	C₄	—	149	2	no	—
604	C₄	#18011958	1	2	yes	—
605	C₂	—	2	2	no	—
606	C₂	—	4	1	no	—
607	C₂	—	596	1	no	—
608	C₂	C₂×#41×D₁₄₉	1	1	yes	characteristic
609	C₂	2₋¹⁺⁴×D₁₄₉	1	1	yes	characteristic
610	C₂	C₂×#18011958	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#552×C₁₄₉	C₂
prime radical	C₂×#14558735	C₂²
hypercenter	#552	D₁₄₉
hypocenter	C₁₄₉	#3509
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #23750352	C₂	semidirect
2. #23750352	C₂	semidirect
3. #23750351	C₂	semidirect
4. #23750346	C₂	semidirect
5. #23750343	C₂	semidirect
6. #23750342	C₂	semidirect
7. #23750317	C₂	semidirect
8. #23750315	C₂	semidirect
9. #23750312	C₂	semidirect
10. #23750310	C₂	semidirect
11. #23750308	C₂	semidirect
12. #23750234	C₂	semidirect
13. #23750232	C₂	semidirect
15. #23750181	C₂	semidirect
16. #23750179	C₂	semidirect
17. #23750178	C₂	semidirect
18. #23750177	C₂	semidirect
19. #23750177	C₂	semidirect
20. C₂×#18011910	C₂	semidirect
21. #23750102	C₂	semidirect
23. #552×C₁₄₉	C₂	semidirect
305. C₁₄₉	#3509	semidirect
318. #552	D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750352	2
#23750351	2
#23750346	2
#23750343	2
#23750342	2
#23750317	2
#23750315	2
#23750312	2
#23750310	2
#23750308	2
#23750234	2
#23750232	2
#23750197	2
#23750181	2
#23750179	2
#23750178	2
#23750177	2
C₂×#18011910	2
#23750102	2
C₄×#14558735	2
#552×C₁₄₉	2
#3509	149