Subgroups — #34058828

Order 19072.

1058 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750379	C₂	1	1	yes	maximal, characteristic, complemented
2	#23750376	C₂	1	2	yes	maximal, complemented
3	#23750372	C₂	1	2	yes	maximal, complemented
4	#23750371	C₂	1	2	yes	maximal, complemented
5	#23750369	C₂	1	1	yes	maximal, characteristic, complemented
6	#23750367	C₂	1	1	yes	maximal, characteristic, complemented
7	#23750365	C₂	1	2	yes	maximal, complemented
8	#23750363	C₂	1	2	yes	maximal, complemented
9	#23750363	C₂	1	2	yes	maximal, complemented
10	#23750174	C₂	1	1	yes	maximal, characteristic, complemented
11	#23750170	C₂	1	2	yes	maximal, complemented
12	#23750161	C₂	1	2	yes	maximal, complemented
13	#23750160	C₂	1	1	yes	maximal, characteristic, complemented
14	#23750154	C₂	1	1	yes	maximal, characteristic, complemented
15	#23750152	C₂	1	2	yes	maximal, complemented
16	#23750138	C₂	1	2	yes	maximal, complemented
17	#23750135	C₂	1	2	yes	maximal, complemented
18	#23750133	C₂	1	2	yes	maximal, complemented
19	#562×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#14558737	C₂²	1	1	yes	characteristic
21	C₂×#14558735	C₂²	1	2	yes	—
22	C₂×#14558735	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₄×D₁₄₉	C₂²	1	2	yes	complemented
24	#18011910	C₂²	1	2	yes	complemented
25	#18011909	C₂²	1	1	yes	characteristic, complemented
26	#18011907	C₂²	1	2	yes	—
27	#18011907	C₂²	1	1	yes	characteristic
28	#18011906	C₂²	1	2	yes	complemented
29	#18011906	C₂²	1	2	yes	complemented
30	#18011906	C₂²	1	2	yes	complemented
31	#18011906	C₂²	1	2	yes	complemented
32	#18011904	C₂²	1	2	yes	complemented
33	#18011904	C₂²	1	2	yes	complemented
34	#18011903	C₂²	1	1	yes	characteristic, complemented
35	#18011902	C₂²	1	2	yes	complemented
36	#18011901	C₂²	1	2	yes	complemented
37	#18011900	C₂²	1	2	yes	—
38	#18011899	C₂²	1	1	yes	characteristic
39	#18011899	C₂²	1	1	yes	characteristic
40	#18011897	C₂²	1	2	yes	—
41	#18011897	C₂²	1	2	yes	—
42	#18011897	C₂²	1	2	yes	complemented
43	#18011896	C₂²	1	2	yes	—
44	#18011896	C₂²	1	2	yes	complemented
45	#18011896	C₂²	1	2	yes	complemented
46	#18011895	C₂²	1	2	yes	complemented
47	#18011895	C₂²	1	2	yes	complemented
48	#18011894	C₂²	1	2	yes	—
49	#18011894	C₂²	1	2	yes	complemented
50	#18011893	C₂²	1	2	yes	—
51	#18011893	C₂²	1	2	yes	complemented
52	#18011893	C₂²	1	2	yes	complemented
53	#18011891	C₂²	1	1	yes	characteristic, complemented
54	#18011891	C₂²	1	2	yes	complemented
55	#18011890	C₂²	1	2	yes	complemented
56	#18011889	C₂²	1	2	yes	complemented
57	#18011889	C₂²	1	2	yes	complemented
58	#18011888	C₂²	1	2	yes	complemented
59	#18011887	C₂²	1	1	yes	characteristic, complemented
60	#18011887	C₂²	1	2	yes	complemented
61	#18011886	C₂²	1	1	yes	characteristic
62	#18011886	C₂²	1	2	yes	—
63	#18011885	C₂²	1	2	yes	—
64	#18011885	C₂²	1	2	yes	—
65	#18011885	C₂²	1	2	yes	complemented
66	#18011884	C₂²	1	2	yes	—
67	#18011884	C₂²	1	2	yes	—
68	#18011884	C₂²	1	2	yes	complemented
69	#18011884	C₂²	1	2	yes	complemented
70	#18011883	C₂²	1	2	yes	—
71	#18011883	C₂²	1	2	yes	complemented
72	#18011883	C₂²	1	2	yes	complemented
73	#18011882	C₂²	1	1	yes	characteristic
74	#18011882	C₂²	1	2	yes	—
75	#18011881	C₂²	1	2	yes	—
76	#18011881	C₂²	1	2	yes	—
77	#18011881	C₂²	1	2	yes	complemented
78	#18011879	C₂²	1	2	yes	—
79	#18011879	C₂²	1	2	yes	complemented
80	#18011879	C₂²	1	2	yes	complemented
81	Q₈×Dic₁₄₉	C₂²	1	1	yes	characteristic, complemented
82	#18011876	C₂²	1	1	yes	characteristic, complemented
83	D₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
84	D₄×Dic₁₄₉	C₂²	1	2	yes	complemented
85	#18011873	C₂²	1	1	yes	characteristic
86	#18011873	C₂²	1	2	yes	—
87	#18011873	C₂²	1	2	yes	complemented
88	#18011871	C₂²	1	2	yes	—
89	#18011871	C₂²	1	2	yes	complemented
90	#18011871	C₂²	1	2	yes	complemented
91	#18011871	C₂²	1	2	yes	complemented
92	#18011871	C₂²	1	2	yes	complemented
93	#18011869	C₂²	1	2	yes	complemented
94	#18011869	C₂²	1	2	yes	complemented
95	#18011867	C₂²	1	2	yes	complemented
96	C₂×C₄×Dic₁₄₉	C₂²	1	2	yes	complemented
97	C₄²×D₁₄₉	C₂²	1	1	yes	characteristic, complemented
98	#125×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
99	#124×C₁₄₉	C₂²	1	1	yes	characteristic
100	#124×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
101	#123×C₁₄₉	C₂²	1	2	yes	complemented
102	#123×C₁₄₉	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
104	C₂²⋊Q₈×C₁₄₉	C₂²	1	2	yes	complemented
105	#121×C₁₄₉	C₂²	1	2	yes	—
106	#121×C₁₄₉	C₂²	1	2	yes	complemented
107	C₂³×D₁₄₉	C₂³	1	2	yes	—
108	#14558737	—	4	2	no	—
109	#14558735	—	4	4	no	—
110	#14558735	—	4	2	no	—
111	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
112	C₂×Dic₂₉₈	C₂³	1	2	yes	—
113	C₂×Dic₂₉₈	C₂³	1	1	yes	characteristic
114	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
115	C₂×D₅₉₆	C₂³	1	2	yes	—
116	C₂×D₅₉₆	C₂³	1	2	yes	—
117	C₂×D₅₉₆	C₂³	1	1	yes	characteristic
118	C₂×D₅₉₆	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₁₄₉	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	C₂×C₂²⋊D₁₄₉	C₂³	1	2	yes	—
127	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
128	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
129	C₂²×Dic₁₄₉	C₂³	1	2	yes	—
130	C₂×C₄×D₁₄₉	—	4	4	no	—
131	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
132	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
133	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
135	C₂×C₄×D₁₄₉	C₂³	1	2	yes	—
136	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
138	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
139	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
140	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
142	C₄⋊Dic₁₄₉	C₂³	1	2	yes	—
143	C₄⋊Dic₁₄₉	C₂³	1	1	yes	characteristic
144	#14558715	C₂³	1	2	yes	—
145	#14558715	C₂³	1	2	yes	—
146	#14558715	C₂³	1	2	yes	—
147	#14558715	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	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
153	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
154	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
155	C₂²⋊Dic₁₄₉	C₂³	1	2	yes	—
156	#14558713	C₂³	1	2	yes	—
157	#14558713	C₂³	1	2	yes	—
158	#14558713	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	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
171	C₄×Dic₁₄₉	C₂³	1	2	yes	—
172	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
173	C₄×Dic₁₄₉	C₂³	1	1	yes	characteristic
174	C₄×Dic₁₄₉	C₂³	1	2	yes	—
175	C₄×Dic₁₄₉	C₂³	1	2	yes	—
176	C₄×Dic₁₄₉	C₂³	1	2	yes	—
177	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
178	C₂×Q₈×C₁₄₉	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
181	C₂×D₄×C₁₄₉	C₂³	1	2	yes	—
182	C₂×D₄×C₁₄₉	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
184	C₂²×C₄×C₁₄₉	C₂³	1	2	yes	—
185	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
186	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
187	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
188	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
189	C₄⋊C₄×C₁₄₉	C₂³	1	2	yes	—
190	C₄⋊C₄×C₁₄₉	C₂³	1	1	yes	characteristic
191	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
197	C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
198	C₂²×D₁₄₉	—	4	2	no	—
199	C₂²×D₁₄₉	—	4	2	no	—
200	C₂²×D₁₄₉	—	4	2	no	—
201	C₂²×D₁₄₉	C₂⁴	1	1	yes	characteristic
202	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
203	C₂²×D₁₄₉	C₂⁴	1	2	yes	—
204	Dic₂₉₈	—	4	1	no	—
205	Dic₂₉₈	—	4	2	no	—
206	Dic₂₉₈	—	4	1	no	—
207	D₅₉₆	—	4	2	no	—
208	D₅₉₆	—	4	2	no	—
209	D₅₉₆	—	4	1	no	—
210	D₅₉₆	—	4	2	no	—
211	D₅₉₆	—	4	1	no	—
212	C₂²⋊D₁₄₉	—	4	2	no	—
213	C₂²⋊D₁₄₉	—	4	2	no	—
214	C₂²⋊D₁₄₉	—	4	2	no	—
215	C₂²⋊D₁₄₉	—	4	2	no	—
216	C₂²⋊D₁₄₉	—	4	2	no	—
217	C₂²⋊D₁₄₉	—	4	2	no	—
218	C₂²⋊D₁₄₉	—	4	2	no	—
219	C₂²⋊D₁₄₉	—	4	2	no	—
220	C₂×Dic₁₄₉	—	2	4	no	—
221	C₂×Dic₁₄₉	—	2	4	no	—
222	C₂×Dic₁₄₉	—	4	2	no	—
223	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
224	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
225	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
226	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
227	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
228	C₂×Dic₁₄₉	C₂⁴	1	2	yes	—
229	C₂×Dic₁₄₉	C₂⁴	1	1	yes	characteristic
230	C₄×D₁₄₉	—	2	4	no	—
231	C₄×D₁₄₉	—	2	4	no	—
232	C₄×D₁₄₉	—	2	2	no	—
233	C₄×D₁₄₉	—	4	2	no	—
234	C₄×D₁₄₉	—	4	2	no	—
235	C₄×D₁₄₉	—	4	1	no	—
236	C₄×D₁₄₉	—	4	1	no	—
237	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
238	C₂³×C₁₄₉	C₂⁴	1	2	yes	—
239	Q₈×C₁₄₉	—	4	1	no	—
240	Q₈×C₁₄₉	—	4	1	no	—
241	D₄×C₁₄₉	—	4	2	no	—
242	D₄×C₁₄₉	—	4	1	no	—
243	D₄×C₁₄₉	—	4	2	no	—
244	D₄×C₁₄₉	—	4	1	no	—
245	C₂×C₄×C₁₄₉	—	4	2	no	—
246	C₂×C₄×C₁₄₉	—	4	2	no	—
247	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₄₉	C₂⁴	1	2	yes	—
254	C₂²×C₁₄₉	—	2	2	no	—
255	C₂²×C₁₄₉	—	2	2	no	—
256	C₂²×C₁₄₉	—	2	2	no	—
257	C₂²×C₁₄₉	—	2	2	no	—
258	C₂²×C₁₄₉	—	2	2	no	—
259	C₂²×C₁₄₉	—	2	2	no	—
260	C₂²×C₁₄₉	C₂⁵	1	1	yes	characteristic
261	C₂×D₁₄₉	—	2	2	no	—
262	C₂×D₁₄₉	—	2	2	no	—
263	C₂×D₁₄₉	—	2	1	no	—
264	C₂×D₁₄₉	—	2	1	no	—
265	C₂×D₁₄₉	—	2	1	no	—
266	C₂×D₁₄₉	—	2	2	no	—
267	C₂×D₁₄₉	—	2	2	no	—
268	C₂×D₁₄₉	—	2	2	no	—
269	C₂×D₁₄₉	—	2	2	no	—
270	C₂×D₁₄₉	—	4	8	no	—
271	C₄×C₁₄₉	—	2	2	no	—
272	C₄×C₁₄₉	—	2	2	no	—
273	C₄×C₁₄₉	—	2	1	no	—
274	C₄×C₁₄₉	—	2	2	no	—
275	C₄×C₁₄₉	—	2	2	no	—
276	C₄×C₁₄₉	—	2	1	no	—
277	C₄×C₁₄₉	—	2	1	no	—
278	Dic₁₄₉	—	2	2	no	—
279	Dic₁₄₉	—	2	2	no	—
280	Dic₁₄₉	—	2	1	no	—
281	Dic₁₄₉	—	2	1	no	—
282	Dic₁₄₉	—	2	2	no	—
283	Dic₁₄₉	—	2	2	no	—
284	Dic₁₄₉	H(5,𝔽₂)	1	2	yes	—
285	C₂×C₁₄₉	—	4	2	no	—
286	C₂×C₁₄₉	—	4	2	no	—
287	C₂×C₁₄₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₁₄₉	#585	1	1	yes	characteristic
289	C₂×C₁₄₉	#585	1	1	yes	characteristic
290	D₁₄₉	—	4	1	no	—
291	D₁₄₉	—	4	2	no	—
292	D₁₄₉	—	4	2	no	—
293	C₁₄₉	#3529	1	1	yes	characteristic, complemented, Sylow
294	#3529	—	149	1	no	maximal, Sylow
295	#563	—	149	1	no	—
296	#563	—	149	2	no	—
297	#562	—	149	1	no	—
298	#562	—	149	2	no	—
299	#562	—	149	2	no	—
300	#562	D₁₄₉	1	1	yes	characteristic, complemented
301	H(3,𝔽₄)	—	149	1	no	—
302	#560	—	149	2	no	—
303	#560	—	149	2	no	—
304	#560	—	149	2	no	—
305	#532	—	149	1	no	—
306	#532	—	149	2	no	—
307	#529	—	149	1	no	—
308	#529	—	149	1	no	—
309	#529	—	149	2	no	—
310	#529	—	149	2	no	—
311	#525	—	149	2	no	—
312	#525	—	149	2	no	—
313	#525	—	149	2	no	—
314	C₂×#41	—	149	1	no	—
315	C₂×#41	—	149	2	no	—
316	C₂×#41	—	149	1	no	—
317	C₂³×C₄	—	149	2	no	—
318	C₄⋊Q₈	—	149	1	no	—
319	C₄⋊Q₈	—	149	2	no	—
320	#127	—	149	1	no	—
321	#127	—	149	2	no	—
322	#126	—	149	2	no	—
323	#126	—	149	2	no	—
324	#126	—	149	2	no	—
325	#126	—	149	2	no	—
326	#126	—	149	2	no	—
327	#126	—	149	2	no	—
328	#125	—	149	2	no	—
329	#125	—	149	2	no	—
330	#125	—	149	1	no	—
331	#125	C₂×D₁₄₉	1	1	yes	characteristic, complemented
332	#124	—	149	2	no	—
333	#124	—	149	2	no	—
334	#124	—	149	2	no	—
335	#124	—	149	2	no	—
336	#124	—	149	1	no	—
337	#124	—	149	1	no	—
338	#124	C₂×D₁₄₉	1	1	yes	characteristic
339	#124	C₂×D₁₄₉	1	1	yes	characteristic, complemented
340	#123	—	149	2	no	—
341	#123	—	149	2	no	—
342	#123	—	149	2	no	—
343	#123	—	149	2	no	—
344	#123	—	149	2	no	—
345	#123	—	149	2	no	—
346	#123	—	149	2	no	—
347	#123	—	149	2	no	—
348	#123	—	149	2	no	—
349	#123	—	149	2	no	—
350	#123	C₂×D₁₄₉	1	2	yes	complemented
351	#123	C₂×D₁₄₉	1	2	yes	complemented
352	C₂²⋊Q₈	—	149	2	no	—
353	C₂²⋊Q₈	—	149	1	no	—
354	C₂²⋊Q₈	—	149	2	no	—
355	C₂²⋊Q₈	—	149	2	no	—
356	C₂²⋊Q₈	—	149	2	no	—
357	C₂²⋊Q₈	—	149	2	no	—
358	C₂²⋊Q₈	—	149	1	no	—
359	C₂²⋊Q₈	—	149	2	no	—
360	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
361	C₂²⋊Q₈	C₂×D₁₄₉	1	2	yes	complemented
362	#121	—	149	2	no	—
363	#121	—	149	1	no	—
364	#121	—	149	2	no	—
365	#121	—	149	2	no	—
366	#121	—	149	2	no	—
367	#121	—	149	2	no	—
368	#121	—	149	2	no	—
369	#121	—	149	2	no	—
370	#121	—	149	2	no	—
371	#121	—	149	1	no	—
372	#121	—	149	2	no	—
373	#121	—	149	2	no	—
374	#121	—	149	2	no	—
375	#121	—	149	2	no	—
376	#121	C₂×D₁₄₉	1	2	yes	—
377	#121	C₂×D₁₄₉	1	2	yes	complemented
378	#120	—	149	2	no	—
379	#120	—	149	2	no	—
380	#120	—	149	2	no	—
381	#120	—	149	2	no	—
382	#120	—	149	2	no	—
383	#120	—	149	2	no	—
384	C₄×Q₈	—	149	1	no	—
385	C₄×Q₈	—	149	1	no	—
386	C₄×D₄	—	149	1	no	—
387	C₄×D₄	—	149	2	no	—
388	C₄×D₄	—	149	1	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	#117	—	149	2	no	—
397	#117	—	149	2	no	—
398	#117	—	149	2	no	—
399	C₂×C₄²	—	149	2	no	—
400	C₂×C₄²	—	149	1	no	—
401	C₂⁴	—	149	2	no	—
402	#41	—	596	4	no	—
403	#41	—	596	2	no	—
404	#41	—	596	2	no	—
405	C₂×Q₈	—	149	1	no	—
406	C₂×Q₈	—	149	2	no	—
407	C₂×Q₈	—	149	1	no	—
408	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
409	C₂×Q₈	C₂²×D₁₄₉	1	1	yes	characteristic
410	C₂×D₄	—	149	2	no	—
411	C₂×D₄	—	149	2	no	—
412	C₂×D₄	—	149	2	no	—
413	C₂×D₄	—	149	2	no	—
414	C₂×D₄	—	149	2	no	—
415	C₂×D₄	—	149	2	no	—
416	C₂×D₄	—	149	2	no	—
417	C₂×D₄	—	149	2	no	—
418	C₂×D₄	—	149	2	no	—
419	C₂×D₄	—	149	1	no	—
420	C₂×D₄	—	149	2	no	—
421	C₂×D₄	—	149	1	no	—
422	C₂×D₄	—	149	2	no	—
423	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
424	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
425	C₂×D₄	C₂²×D₁₄₉	1	2	yes	—
426	C₂×D₄	C₂²×D₁₄₉	1	1	yes	characteristic
427	C₂²×C₄	—	596	4	no	—
428	C₂²×C₄	—	149	2	no	—
429	C₂²×C₄	—	149	2	no	—
430	C₂²×C₄	—	149	1	no	—
431	C₂²×C₄	—	149	2	no	—
432	C₂²×C₄	—	149	2	no	—
433	C₂²×C₄	—	149	2	no	—
434	C₂²×C₄	—	149	1	no	—
435	C₂²×C₄	—	149	1	no	—
436	C₂²×C₄	—	149	2	no	—
437	C₂²×C₄	—	149	2	no	—
438	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
439	C₂²×C₄	C₂²×D₁₄₉	1	2	yes	—
440	C₄⋊C₄	—	149	2	no	—
441	C₄⋊C₄	—	149	2	no	—
442	C₄⋊C₄	—	149	2	no	—
443	C₄⋊C₄	—	149	2	no	—
444	C₄⋊C₄	—	149	2	no	—
445	C₄⋊C₄	—	149	2	no	—
446	C₄⋊C₄	—	149	2	no	—
447	C₄⋊C₄	—	149	2	no	—
448	C₄⋊C₄	—	149	2	no	—
449	C₄⋊C₄	—	149	2	no	—
450	C₄⋊C₄	—	149	1	no	—
451	C₄⋊C₄	—	149	2	no	—
452	C₄⋊C₄	—	149	2	no	—
453	C₄⋊C₄	—	149	1	no	—
454	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
455	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
456	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
457	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
458	C₄⋊C₄	C₂²×D₁₄₉	1	2	yes	—
459	C₄⋊C₄	C₂²×D₁₄₉	1	1	yes	characteristic
460	C₂²⋊C₄	—	149	2	no	—
461	C₂²⋊C₄	—	149	2	no	—
462	C₂²⋊C₄	—	149	2	no	—
463	C₂²⋊C₄	—	149	2	no	—
464	C₂²⋊C₄	—	149	2	no	—
465	C₂²⋊C₄	—	149	2	no	—
466	C₂²⋊C₄	—	149	2	no	—
467	C₂²⋊C₄	—	149	2	no	—
468	C₂²⋊C₄	—	149	2	no	—
469	C₂²⋊C₄	—	149	2	no	—
470	C₂²⋊C₄	—	149	2	no	—
471	C₂²⋊C₄	—	149	2	no	—
472	C₂²⋊C₄	—	149	2	no	—
473	C₂²⋊C₄	—	149	2	no	—
474	C₂²⋊C₄	—	149	2	no	—
475	C₂²⋊C₄	—	149	2	no	—
476	C₂²⋊C₄	—	149	2	no	—
477	C₂²⋊C₄	—	149	2	no	—
478	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
479	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
480	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₁₄₉	1	2	yes	—
484	C₄²	—	149	2	no	—
485	C₄²	—	149	2	no	—
486	C₄²	—	149	1	no	—
487	C₄²	—	149	1	no	—
488	C₄²	—	149	2	no	—
489	C₄²	—	149	1	no	—
490	C₄²	—	149	2	no	—
491	C₄²	C₂²×D₁₄₉	1	1	yes	characteristic
492	C₂³	—	596	2	no	—
493	C₂³	—	596	2	no	—
494	C₂³	—	596	2	no	—
495	C₂³	—	149	2	no	—
496	C₂³	—	149	2	no	—
497	C₂³	—	149	1	no	—
498	C₂³	C₂³×D₁₄₉	1	2	yes	—
499	C₂³	C₂³×D₁₄₉	1	2	yes	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	596	1	no	—
503	Q₈	—	596	2	no	—
504	Q₈	—	596	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	1	no	—
509	D₄	—	596	2	no	—
510	D₄	—	596	2	no	—
511	D₄	—	596	1	no	—
512	D₄	—	596	2	no	—
513	D₄	—	596	1	no	—
514	D₄	—	596	2	no	—
515	D₄	—	596	2	no	—
516	D₄	—	596	2	no	—
517	D₄	—	596	2	no	—
518	D₄	—	596	2	no	—
519	D₄	—	596	2	no	—
520	D₄	—	596	2	no	—
521	D₄	—	596	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	298	4	no	—
525	C₂×C₄	—	298	4	no	—
526	C₂×C₄	—	298	2	no	—
527	C₂×C₄	—	298	4	no	—
528	C₂×C₄	—	298	4	no	—
529	C₂×C₄	—	596	2	no	—
530	C₂×C₄	—	596	2	no	—
531	C₂×C₄	—	596	1	no	—
532	C₂×C₄	—	596	1	no	—
533	C₂×C₄	—	596	2	no	—
534	C₂×C₄	—	149	2	no	—
535	C₂×C₄	—	149	1	no	—
536	C₂×C₄	—	149	1	no	—
537	C₂×C₄	—	149	2	no	—
538	C₂×C₄	—	149	2	no	—
539	C₂×C₄	—	149	2	no	—
540	C₂×C₄	—	149	1	no	—
541	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
542	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
543	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₁₄₉	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
547	C₂×C₄	C₂³×D₁₄₉	1	2	yes	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	298	2	no	—
555	C₂²	—	298	2	no	—
556	C₂²	—	298	1	no	—
557	C₂²	—	298	1	no	—
558	C₂²	—	298	2	no	—
559	C₂²	—	298	2	no	—
560	C₂²	—	298	1	no	—
561	C₂²	—	298	2	no	—
562	C₂²	—	298	2	no	—
563	C₂²	—	596	8	no	—
564	C₂²	C₂⁴×D₁₄₉	1	1	yes	characteristic
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	298	2	no	—
573	C₄	—	298	2	no	—
574	C₄	—	298	1	no	—
575	C₄	—	298	1	no	—
576	C₄	—	298	2	no	—
577	C₄	—	298	2	no	—
578	C₄	—	149	2	no	—
579	C₂	—	4	2	no	—
580	C₂	—	4	2	no	—
581	C₂	—	596	2	no	—
582	C₂	—	596	2	no	—
583	C₂	—	596	1	no	—
584	C₂	H(5,𝔽₂)×D₁₄₉	1	1	yes	characteristic
585	C₂	#23750460	1	1	yes	characteristic
586	C₂	#23750462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₄₉
commutator, socle, cosocle	C₂²×C₁₄₉	C₂⁵
Fitting	#562×C₁₄₉	C₂
hypercenter	#562	D₁₄₉
hypocenter	C₁₄₉	#3529
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #23750379	C₂	semidirect
2. #23750376	C₂	semidirect
3. #23750372	C₂	semidirect
4. #23750371	C₂	semidirect
5. #23750369	C₂	semidirect
6. #23750367	C₂	semidirect
7. #23750365	C₂	semidirect
8. #23750363	C₂	semidirect
9. #23750363	C₂	semidirect
10. #23750174	C₂	semidirect
11. #23750170	C₂	semidirect
12. #23750161	C₂	semidirect
13. #23750160	C₂	semidirect
14. #23750154	C₂	semidirect
15. #23750152	C₂	semidirect
16. #23750138	C₂	semidirect
17. #23750135	C₂	semidirect
18. #23750133	C₂	semidirect
19. #562×C₁₄₉	C₂	semidirect
22. C₂×#14558735	C₂²	semidirect
23. C₂²×C₄×D₁₄₉	C₂²	semidirect
24. #18011910	C₂²	semidirect
25. #18011909	C₂²	semidirect
28. #18011906	C₂²	semidirect
29. #18011906	C₂²	semidirect
30. #18011906	C₂²	semidirect
31. #18011906	C₂²	semidirect
32. #18011904	C₂²	semidirect
33. #18011904	C₂²	semidirect
34. #18011903	C₂²	semidirect
35. #18011902	C₂²	semidirect
36. #18011901	C₂²	semidirect
42. #18011897	C₂²	semidirect
44. #18011896	C₂²	semidirect
45. #18011896	C₂²	semidirect
46. #18011895	C₂²	semidirect
47. #18011895	C₂²	semidirect
49. #18011894	C₂²	semidirect
51. #18011893	C₂²	semidirect
52. #18011893	C₂²	semidirect
53. #18011891	C₂²	semidirect
54. #18011891	C₂²	semidirect
55. #18011890	C₂²	semidirect
56. #18011889	C₂²	semidirect
57. #18011889	C₂²	semidirect
58. #18011888	C₂²	semidirect
59. #18011887	C₂²	semidirect
60. #18011887	C₂²	semidirect
65. #18011885	C₂²	semidirect
68. #18011884	C₂²	semidirect
69. #18011884	C₂²	semidirect
71. #18011883	C₂²	semidirect
72. #18011883	C₂²	semidirect
77. #18011881	C₂²	semidirect
79. #18011879	C₂²	semidirect
80. #18011879	C₂²	semidirect
81. Q₈×Dic₁₄₉	C₂²	semidirect
82. #18011876	C₂²	semidirect
84. D₄×Dic₁₄₉	C₂²	semidirect
87. #18011873	C₂²	semidirect
89. #18011871	C₂²	semidirect
90. #18011871	C₂²	semidirect
91. #18011871	C₂²	semidirect
92. #18011871	C₂²	semidirect
93. #18011869	C₂²	semidirect
94. #18011869	C₂²	semidirect
95. #18011867	C₂²	semidirect
96. C₂×C₄×Dic₁₄₉	C₂²	semidirect
97. C₄²×D₁₄₉	C₂²	semidirect
98. #125×C₁₄₉	C₂²	semidirect
100. #124×C₁₄₉	C₂²	semidirect
101. #123×C₁₄₉	C₂²	semidirect
102. #123×C₁₄₉	C₂²	semidirect
103. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
104. C₂²⋊Q₈×C₁₄₉	C₂²	semidirect
106. #121×C₁₄₉	C₂²	semidirect
293. C₁₄₉	#3529	semidirect
300. #562	D₁₄₉	semidirect
331. #125	C₂×D₁₄₉	semidirect
339. #124	C₂×D₁₄₉	semidirect
350. #123	C₂×D₁₄₉	semidirect
351. #123	C₂×D₁₄₉	semidirect
360. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
361. C₂²⋊Q₈	C₂×D₁₄₉	semidirect
377. #121	C₂×D₁₄₉	semidirect

Maximal subgroups

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

subgroup	index
#23750379	2
#23750376	2
#23750372	2
#23750371	2
#23750369	2
#23750367	2
#23750365	2
#23750363	2
#23750174	2
#23750170	2
#23750161	2
#23750160	2
#23750154	2
#23750152	2
#23750138	2
#23750135	2
#23750133	2
#562×C₁₄₉	2
#3529	149