Subgroups — #34078324

Order 19328.

764 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#18012759	C₂	1	1	yes	maximal, characteristic, complemented
3	#23752719	C₂	1	1	yes	maximal, characteristic, complemented
4	#23752373	C₂	1	1	yes	maximal, characteristic, complemented
5	#23752371	C₂	1	1	yes	maximal, characteristic, complemented
6	#23752366	C₂	1	1	yes	maximal, characteristic, complemented
7	#23752361	C₂	1	1	yes	maximal, characteristic, complemented
8	#23752356	C₂	1	1	yes	maximal, characteristic, complemented
9	#23752354	C₂	1	1	yes	maximal, characteristic, complemented
10	#23752349	C₂	1	1	yes	maximal, characteristic, complemented
11	#23752344	C₂	1	1	yes	maximal, characteristic, complemented
12	#23752209	C₂	1	1	yes	maximal, characteristic, complemented
13	#23752208	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×(C₂×D₁₅₁)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#135×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14559005	C₂²	1	1	yes	characteristic
17	C₂×#14559004	—	2	1	no	—
18	C₂×#14559004	C₂²	1	1	yes	characteristic
19	C₂×#14559003	—	2	1	no	—
20	C₂×#14559003	C₂²	1	1	yes	characteristic
21	#41×D₁₅₁	—	2	4	no	—
22	#41×D₁₅₁	—	2	4	no	—
23	C₂×Q₈×D₁₅₁	C₂²	1	1	yes	characteristic
24	C₂×D₄×D₁₅₁	—	2	1	no	—
25	C₂×D₄×D₁₅₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₅₁	—	2	1	no	—
27	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic
28	#18012759	—	2	4	no	—
29	C₂×#14558994	C₂²	1	1	yes	characteristic, complemented
30	C₂×#14558992	C₂²	1	1	yes	characteristic, complemented
31	C₂×#14558991	C₂²	1	1	yes	characteristic, complemented
32	C₂×#14558989	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₁₅₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	#18012720	—	2	1	no	—
35	#18012715	C₂²	1	1	yes	characteristic
36	#18012715	C₂²	1	1	yes	characteristic, complemented
37	#18012710	C₂²	1	1	yes	characteristic
38	#18012710	C₂²	1	1	yes	characteristic, complemented
39	#18012707	—	2	1	no	—
40	C₄×C₂²⋊D₁₅₁	—	2	1	no	—
41	C₄×C₂²⋊D₁₅₁	—	2	1	no	—
42	#18012698	C₂²	1	1	yes	characteristic, complemented
43	#18012664	C₂²	1	1	yes	characteristic, complemented
44	#18012664	C₂²	1	1	yes	characteristic, complemented
45	#18012663	C₂²	1	1	yes	characteristic, complemented
46	#18012663	C₂²	1	1	yes	characteristic, complemented
47	#18012661	C₂²	1	1	yes	characteristic, complemented
48	#18012661	C₂²	1	1	yes	characteristic, complemented
49	#18012660	C₂²	1	1	yes	characteristic, complemented
50	#18012660	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₁₅₁)⋊C₈	C₂²	1	1	yes	characteristic
52	(C₂×D₁₅₁)⋊C₈	C₂²	1	1	yes	characteristic
53	(C₂×D₁₅₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₁₅₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×#41×C₁₅₁	C₂²	1	1	yes	characteristic
56	C₂×#41×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
57	#135×C₁₅₁	—	2	4	no	—
58	C₂×Q₁₆×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
59	C₂×SD₁₆×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
60	C₂×SD₁₆×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
61	C₂×D₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
62	C₂²×C₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₁₅₁	—	2	1	no	—
64	C₂³×D₁₅₁	D₄	1	1	yes	characteristic
65	#14559005	—	2	2	no	—
66	#14559005	—	2	2	no	—
67	#14559004	—	2	8	no	—
68	#14559004	—	2	2	no	—
69	#14559004	D₄	1	4	yes	complemented
70	#14559003	—	2	8	no	—
71	#14559003	—	2	2	no	—
72	#14559003	—	2	2	no	—
73	C₂×Dic₃₀₂	—	2	1	no	—
74	C₂×Dic₃₀₂	C₂³	1	1	yes	characteristic
75	Q₈×D₁₅₁	—	2	2	no	—
76	Q₈×D₁₅₁	—	2	2	no	—
77	C₂×D₆₀₄	—	2	1	no	—
78	C₂×D₆₀₄	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊D₁₅₁	—	2	1	no	—
80	C₂×C₂²⋊D₁₅₁	—	2	1	no	—
81	C₂×C₂²⋊D₁₅₁	—	2	1	no	—
82	C₂×C₂²⋊D₁₅₁	—	2	1	no	—
83	C₂×C₂²⋊D₁₅₁	—	2	1	no	—
84	D₄×D₁₅₁	—	2	8	no	—
85	D₄×D₁₅₁	—	2	2	no	—
86	D₄×D₁₅₁	—	2	2	no	—
87	C₂²×Dic₁₅₁	—	2	1	no	—
88	C₂²×Dic₁₅₁	D₄	1	1	yes	characteristic
89	C₂×C₄×D₁₅₁	—	2	8	no	—
90	C₂×C₄×D₁₅₁	—	2	1	no	—
91	C₂×C₄×D₁₅₁	—	2	1	no	—
92	C₂×C₄×D₁₅₁	—	2	1	no	—
93	C₂×C₄×D₁₅₁	—	2	2	no	—
94	C₂×C₄×D₁₅₁	—	2	2	no	—
95	C₂×C₄×D₁₅₁	D₄	1	1	yes	characteristic
96	C₂×C₄×D₁₅₁	D₄	1	1	yes	characteristic
97	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
99	#14558994	—	2	2	no	—
100	#14558992	—	2	2	no	—
101	#14558991	—	2	2	no	—
102	#14558989	—	2	2	no	—
103	C₂×C₁₅₁⋊C₈	—	2	2	no	—
104	C₂×C₁₅₁⋊C₈	C₂³	1	1	yes	characteristic
105	C₂×C₁₅₁⋊C₈	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₁₅₁	C₂³	1	1	yes	characteristic
108	Dic₁₅₁⋊C₄	—	2	1	no	—
109	Dic₁₅₁⋊C₄	—	2	1	no	—
110	C₂²⋊Dic₁₅₁	—	2	1	no	—
111	C₂²⋊Dic₁₅₁	—	2	1	no	—
112	C₂²⋊Dic₁₅₁	—	2	1	no	—
113	(C₂×D₁₅₁)⋊C₄	—	2	1	no	—
114	(C₂×D₁₅₁)⋊C₄	—	2	1	no	—
115	C₄×Dic₁₅₁	—	2	1	no	—
116	#41×C₁₅₁	—	2	2	no	—
117	#41×C₁₅₁	—	2	2	no	—
118	#41×C₁₅₁	—	2	2	no	—
119	#41×C₁₅₁	D₄	1	4	yes	complemented
120	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
121	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
122	C₂×D₄×C₁₅₁	—	2	1	no	—
123	C₂×D₄×C₁₅₁	—	2	1	no	—
124	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₅₁	—	2	1	no	—
127	C₂²×C₄×C₁₅₁	—	2	1	no	—
128	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
129	Q₁₆×C₁₅₁	—	2	2	no	—
130	SD₁₆×C₁₅₁	—	2	2	no	—
131	SD₁₆×C₁₅₁	—	2	2	no	—
132	D₈×C₁₅₁	—	2	2	no	—
133	C₂×C₈×C₁₅₁	—	2	2	no	—
134	C₂×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
135	C₂×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
136	C₂²×D₁₅₁	—	2	4	no	—
137	C₂²×D₁₅₁	—	2	2	no	—
138	C₂²×D₁₅₁	—	2	1	no	—
139	C₂²×D₁₅₁	—	2	2	no	—
140	C₂²×D₁₅₁	—	4	1	no	—
141	C₂²×D₁₅₁	—	4	2	no	—
142	C₂²×D₁₅₁	—	4	2	no	—
143	C₂²×D₁₅₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×D₁₅₁	C₂×D₄	1	1	yes	characteristic
145	Dic₃₀₂	—	2	4	no	—
146	Dic₃₀₂	—	2	1	no	—
147	Dic₃₀₂	C₂×D₄	1	2	yes	—
148	D₆₀₄	—	2	4	no	—
149	D₆₀₄	—	2	1	no	—
150	D₆₀₄	C₂×D₄	1	2	yes	—
151	C₂²⋊D₁₅₁	—	2	4	no	—
152	C₂²⋊D₁₅₁	—	2	4	no	—
153	C₂²⋊D₁₅₁	—	2	4	no	—
154	C₂²⋊D₁₅₁	—	4	2	no	—
155	C₂²⋊D₁₅₁	—	4	2	no	—
156	C₂×Dic₁₅₁	—	2	4	no	—
157	C₂×Dic₁₅₁	—	2	2	no	—
158	C₂×Dic₁₅₁	—	2	1	no	—
159	C₂×Dic₁₅₁	—	2	1	no	—
160	C₂×Dic₁₅₁	—	2	1	no	—
161	C₂×Dic₁₅₁	C₂×D₄	1	1	yes	characteristic
162	C₂×Dic₁₅₁	C₂×D₄	1	1	yes	characteristic
163	C₄×D₁₅₁	—	2	4	no	—
164	C₄×D₁₅₁	—	2	4	no	—
165	C₄×D₁₅₁	—	2	2	no	—
166	C₄×D₁₅₁	—	2	4	no	—
167	C₄×D₁₅₁	—	2	2	no	—
168	C₄×D₁₅₁	—	2	1	no	—
169	C₄×D₁₅₁	—	2	1	no	—
170	C₄×D₁₅₁	—	2	1	no	—
171	C₄×D₁₅₁	—	2	1	no	—
172	C₁₅₁⋊C₈	—	2	1	no	—
173	C₁₅₁⋊C₈	—	2	1	no	—
174	C₂³×C₁₅₁	—	2	1	no	—
175	C₂³×C₁₅₁	—	2	1	no	—
176	C₂³×C₁₅₁	C₂×D₄	1	1	yes	characteristic
177	Q₈×C₁₅₁	—	2	1	no	—
178	Q₈×C₁₅₁	—	2	1	no	—
179	Q₈×C₁₅₁	—	2	1	no	—
180	Q₈×C₁₅₁	C₂×D₄	1	2	yes	—
181	D₄×C₁₅₁	—	2	4	no	—
182	D₄×C₁₅₁	—	2	1	no	—
183	D₄×C₁₅₁	—	2	1	no	—
184	D₄×C₁₅₁	—	2	1	no	—
185	D₄×C₁₅₁	—	4	2	no	—
186	D₄×C₁₅₁	C₂×D₄	1	2	yes	—
187	C₂×C₄×C₁₅₁	—	2	1	no	—
188	C₂×C₄×C₁₅₁	—	2	4	no	—
189	C₂×C₄×C₁₅₁	—	2	1	no	—
190	C₂×C₄×C₁₅₁	—	4	2	no	—
191	C₂×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
192	C₂×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
194	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
195	C₈×C₁₅₁	—	2	1	no	—
196	C₈×C₁₅₁	—	2	1	no	—
197	C₂²×C₁₅₁	—	2	1	no	—
198	C₂²×C₁₅₁	—	2	1	no	—
199	C₂²×C₁₅₁	—	2	2	no	—
200	C₂²×C₁₅₁	—	4	1	no	—
201	C₂²×C₁₅₁	—	4	1	no	—
202	C₂²×C₁₅₁	—	4	1	no	—
203	C₂²×C₁₅₁	—	4	1	no	—
204	C₂²×C₁₅₁	—	4	1	no	—
205	C₂²×C₁₅₁	#120	1	2	yes	—
206	C₂²×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×D₁₅₁	—	2	1	no	—
208	C₂×D₁₅₁	—	2	1	no	—
209	C₂×D₁₅₁	—	2	1	no	—
210	C₂×D₁₅₁	—	2	2	no	—
211	C₂×D₁₅₁	—	2	1	no	—
212	C₂×D₁₅₁	—	2	1	no	—
213	C₂×D₁₅₁	—	4	4	no	—
214	C₂×D₁₅₁	—	4	8	no	—
215	C₂×D₁₅₁	—	4	1	no	—
216	C₂×D₁₅₁	—	4	1	no	—
217	C₂×D₁₅₁	#135	1	2	yes	complemented
218	C₄×C₁₅₁	—	2	2	no	—
219	C₄×C₁₅₁	—	4	1	no	—
220	C₄×C₁₅₁	#120	1	2	yes	—
221	C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
222	C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
223	Dic₁₅₁	—	2	1	no	—
224	Dic₁₅₁	—	2	2	no	—
225	Dic₁₅₁	—	2	1	no	—
226	Dic₁₅₁	—	4	1	no	—
227	Dic₁₅₁	—	4	1	no	—
228	C₂×C₁₅₁	—	2	2	no	—
229	C₂×C₁₅₁	—	4	2	no	—
230	C₂×C₁₅₁	—	8	1	no	—
231	C₂×C₁₅₁	C₂×#120	1	1	yes	characteristic
232	C₂×C₁₅₁	C₂×#135	1	1	yes	characteristic
233	C₂×C₁₅₁	#575	1	1	yes	characteristic
234	D₁₅₁	—	2	2	no	—
235	D₁₅₁	—	4	1	no	—
236	D₁₅₁	—	4	2	no	—
237	C₁₅₁	#3002	1	1	yes	characteristic, complemented, Sylow
238	#3002	—	151	1	no	maximal, Sylow
239	C₂²×#41	—	151	1	no	—
240	C₂×#135	—	151	1	no	—
241	C₂×#135	D₁₅₁	1	1	yes	characteristic, complemented
242	#525	—	151	1	no	—
243	#452	—	151	1	no	—
244	#452	—	151	1	no	—
245	#451	—	151	1	no	—
246	#450	—	151	1	no	—
247	#449	—	151	1	no	—
248	#449	—	151	1	no	—
249	#448	—	151	1	no	—
250	#447	—	151	1	no	—
251	#416	—	151	1	no	—
252	#416	—	151	1	no	—
253	C₂×C₂²⋊C₈	—	151	1	no	—
254	C₂×#41	—	302	1	no	—
255	C₂×#41	—	302	4	no	—
256	C₂×#41	—	302	4	no	—
257	C₂×#41	—	302	1	no	—
258	C₂×#41	—	151	1	no	—
259	C₂×#41	—	151	1	no	—
260	C₂×#41	—	151	1	no	—
261	C₂×#41	C₂×D₁₅₁	1	1	yes	characteristic
262	C₂×#41	C₂×D₁₅₁	1	1	yes	characteristic, complemented
263	C₂²×Q₈	—	151	1	no	—
264	C₂²×D₄	—	302	1	no	—
265	C₂²×D₄	—	151	1	no	—
266	C₂³×C₄	—	302	1	no	—
267	C₂³×C₄	—	151	1	no	—
268	#135	—	2	4	no	—
269	#135	—	302	4	no	—
270	C₂×Q₁₆	—	151	1	no	—
271	C₂×Q₁₆	C₂×D₁₅₁	1	1	yes	characteristic, complemented
272	C₂×SD₁₆	—	151	1	no	—
273	C₂×SD₁₆	—	151	1	no	—
274	C₂×SD₁₆	C₂×D₁₅₁	1	1	yes	characteristic, complemented
275	C₂×SD₁₆	C₂×D₁₅₁	1	1	yes	characteristic, complemented
276	C₂×D₈	—	151	1	no	—
277	C₂×D₈	C₂×D₁₅₁	1	1	yes	characteristic, complemented
278	C₂²×C₈	—	151	1	no	—
279	C₂²×C₈	C₂×D₁₅₁	1	1	yes	characteristic, complemented
280	#123	—	302	1	no	—
281	C₂²⋊Q₈	—	151	1	no	—
282	C₂²⋊Q₈	—	151	1	no	—
283	#121	—	151	1	no	—
284	#121	—	151	1	no	—
285	#120	—	302	1	no	—
286	C₄×D₄	—	302	1	no	—
287	C₄×D₄	—	302	1	no	—
288	#117	—	151	1	no	—
289	#103	—	151	1	no	—
290	#103	—	151	1	no	—
291	#103	—	151	1	no	—
292	#103	—	151	1	no	—
293	#102	—	151	1	no	—
294	#102	—	151	1	no	—
295	#102	—	151	1	no	—
296	#102	—	151	1	no	—
297	C₂²⋊C₈	—	151	1	no	—
298	C₂²⋊C₈	—	151	1	no	—
299	C₂²⋊C₈	—	151	1	no	—
300	C₂²⋊C₈	—	151	1	no	—
301	C₂⁴	—	302	1	no	—
302	C₂⁴	—	151	1	no	—
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	#41	—	302	8	no	—
307	#41	—	302	8	no	—
308	#41	—	302	2	no	—
309	#41	—	302	2	no	—
310	#41	—	302	2	no	—
311	#41	—	302	2	no	—
312	#41	—	302	2	no	—
313	#41	—	151	4	no	—
314	#41	C₂²⋊D₁₅₁	1	4	yes	complemented
315	C₂×Q₈	—	302	1	no	—
316	C₂×Q₈	—	302	2	no	—
317	C₂×Q₈	—	302	2	no	—
318	C₂×Q₈	—	151	1	no	—
319	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
320	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	302	1	no	—
324	C₂×D₄	—	302	8	no	—
325	C₂×D₄	—	302	2	no	—
326	C₂×D₄	—	302	1	no	—
327	C₂×D₄	—	302	1	no	—
328	C₂×D₄	—	302	2	no	—
329	C₂×D₄	—	302	1	no	—
330	C₂×D₄	—	302	1	no	—
331	C₂×D₄	—	302	1	no	—
332	C₂×D₄	—	151	1	no	—
333	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
334	C₂×D₄	C₂²×D₁₅₁	1	1	yes	characteristic
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	302	8	no	—
338	C₂²×C₄	—	302	1	no	—
339	C₂²×C₄	—	302	1	no	—
340	C₂²×C₄	—	302	1	no	—
341	C₂²×C₄	—	302	2	no	—
342	C₂²×C₄	—	302	1	no	—
343	C₂²×C₄	—	302	2	no	—
344	C₂²×C₄	—	151	1	no	—
345	C₂²×C₄	—	151	1	no	—
346	C₂²×C₄	—	151	1	no	—
347	C₂²×C₄	—	151	1	no	—
348	C₂²×C₄	—	151	1	no	—
349	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
350	Q₁₆	—	2	2	no	—
351	Q₁₆	—	302	2	no	—
352	SD₁₆	—	2	2	no	—
353	SD₁₆	—	2	2	no	—
354	SD₁₆	—	302	2	no	—
355	SD₁₆	—	302	2	no	—
356	D₈	—	2	2	no	—
357	D₈	—	302	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	302	2	no	—
360	C₂×C₈	—	151	1	no	—
361	C₂×C₈	—	151	1	no	—
362	C₂×C₈	C₂²×D₁₅₁	1	1	yes	characteristic
363	C₂×C₈	C₂²×D₁₅₁	1	1	yes	characteristic
364	C₄⋊C₄	—	302	1	no	—
365	C₄⋊C₄	—	302	1	no	—
366	C₄⋊C₄	—	151	1	no	—
367	C₄⋊C₄	—	151	1	no	—
368	C₂²⋊C₄	—	302	1	no	—
369	C₂²⋊C₄	—	302	1	no	—
370	C₂²⋊C₄	—	302	1	no	—
371	C₂²⋊C₄	—	302	1	no	—
372	C₂²⋊C₄	—	302	1	no	—
373	C₄²	—	302	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	302	4	no	—
377	C₂³	—	302	2	no	—
378	C₂³	—	302	2	no	—
379	C₂³	—	302	1	no	—
380	C₂³	—	604	1	no	—
381	C₂³	—	604	2	no	—
382	C₂³	—	604	2	no	—
383	C₂³	—	151	1	no	—
384	C₂³	—	151	1	no	—
385	C₂³	D₄×D₁₅₁	1	1	yes	characteristic
386	Q₈	—	2	1	no	—
387	Q₈	—	2	1	no	—
388	Q₈	—	2	1	no	—
389	Q₈	—	302	4	no	—
390	Q₈	—	302	1	no	—
391	Q₈	—	151	2	no	—
392	Q₈	C₂×C₂²⋊D₁₅₁	1	2	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	1	no	—
395	D₄	—	2	1	no	—
396	D₄	—	2	1	no	—
397	D₄	—	4	2	no	—
398	D₄	—	302	4	no	—
399	D₄	—	302	4	no	—
400	D₄	—	302	4	no	—
401	D₄	—	302	4	no	—
402	D₄	—	302	1	no	—
403	D₄	—	604	2	no	—
404	D₄	—	604	2	no	—
405	D₄	—	151	2	no	—
406	D₄	C₂×C₂²⋊D₁₅₁	1	2	yes	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	302	4	no	—
412	C₂×C₄	—	302	4	no	—
413	C₂×C₄	—	302	4	no	—
414	C₂×C₄	—	302	2	no	—
415	C₂×C₄	—	302	1	no	—
416	C₂×C₄	—	302	2	no	—
417	C₂×C₄	—	302	4	no	—
418	C₂×C₄	—	302	2	no	—
419	C₂×C₄	—	302	1	no	—
420	C₂×C₄	—	302	1	no	—
421	C₂×C₄	—	302	1	no	—
422	C₂×C₄	—	302	1	no	—
423	C₂×C₄	—	302	1	no	—
424	C₂×C₄	—	302	1	no	—
425	C₂×C₄	—	151	1	no	—
426	C₂×C₄	—	151	1	no	—
427	C₂×C₄	D₄×D₁₅₁	1	2	yes	—
428	C₂×C₄	D₄×D₁₅₁	1	1	yes	characteristic
429	C₂×C₄	C₂×C₂²⋊D₁₅₁	1	2	yes	—
430	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	302	1	no	—
434	C₈	—	302	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	302	1	no	—
444	C₂²	—	302	1	no	—
445	C₂²	—	302	1	no	—
446	C₂²	—	302	1	no	—
447	C₂²	—	302	1	no	—
448	C₂²	—	302	2	no	—
449	C₂²	—	604	4	no	—
450	C₂²	—	604	8	no	—
451	C₂²	—	604	1	no	—
452	C₂²	—	604	1	no	—
453	C₂²	—	151	2	no	—
454	C₂²	#18012707	1	2	yes	—
455	C₂²	C₂×D₄×D₁₅₁	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	302	1	no	—
459	C₄	—	302	2	no	—
460	C₄	—	302	1	no	—
461	C₄	—	604	1	no	—
462	C₄	—	604	1	no	—
463	C₄	#18012707	1	2	yes	—
464	C₄	C₂×D₄×D₁₅₁	1	1	yes	characteristic
465	C₄	C₂²×C₂²⋊D₁₅₁	1	1	yes	characteristic
466	C₂	—	2	2	no	—
467	C₂	—	4	2	no	—
468	C₂	—	8	1	no	—
469	C₂	—	302	2	no	—
470	C₂	—	604	1	no	—
471	C₂	—	604	2	no	—
472	C₂	C₂×#18012707	1	1	yes	characteristic
473	C₂	#135×D₁₅₁	1	1	yes	characteristic
474	C₂	#23753009	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₅₁
commutator, cosocle	C₂×C₄×C₁₅₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₅₁
Fitting	C₂×#135×C₁₅₁	C₂
socle	C₂²×C₁₅₁	C₂²×D₄
hypercenter	C₂×#135	D₁₅₁
hypocenter	C₁₅₁	#3002
LCS	G ▷ C₂×C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₅₁	C₂	semidirect
2. C₂×#18012759	C₂	semidirect
3. #23752719	C₂	semidirect
4. #23752373	C₂	semidirect
5. #23752371	C₂	semidirect
6. #23752366	C₂	semidirect
7. #23752361	C₂	semidirect
8. #23752356	C₂	semidirect
9. #23752354	C₂	semidirect
10. #23752349	C₂	semidirect
11. #23752344	C₂	semidirect
12. #23752209	C₂	semidirect
13. #23752208	C₂	semidirect
14. C₂×(C₂×D₁₅₁)⋊C₈	C₂	semidirect
15. C₂×#135×C₁₅₁	C₂	semidirect
29. C₂×#14558994	C₂²	semidirect
30. C₂×#14558992	C₂²	semidirect
31. C₂×#14558991	C₂²	semidirect
32. C₂×#14558989	C₂²	semidirect
33. C₂²×C₁₅₁⋊C₈	C₂²	semidirect
36. #18012715	C₂²	semidirect
38. #18012710	C₂²	semidirect
42. #18012698	C₂²	semidirect
43. #18012664	C₂²	semidirect
44. #18012664	C₂²	semidirect
45. #18012663	C₂²	semidirect
46. #18012663	C₂²	semidirect
47. #18012661	C₂²	semidirect
48. #18012661	C₂²	semidirect
49. #18012660	C₂²	semidirect
50. #18012660	C₂²	semidirect
53. (C₂×D₁₅₁)⋊C₈	C₂²	semidirect
54. (C₂×D₁₅₁)⋊C₈	C₂²	semidirect
56. C₂×#41×C₁₅₁	C₂²	semidirect
58. C₂×Q₁₆×C₁₅₁	C₂²	semidirect
59. C₂×SD₁₆×C₁₅₁	C₂²	semidirect
60. C₂×SD₁₆×C₁₅₁	C₂²	semidirect
61. C₂×D₈×C₁₅₁	C₂²	semidirect
62. C₂²×C₈×C₁₅₁	C₂²	semidirect
69. #14559004	D₄	semidirect
119. #41×C₁₅₁	D₄	semidirect
217. C₂×D₁₅₁	#135	semidirect
237. C₁₅₁	#3002	semidirect
241. C₂×#135	D₁₅₁	semidirect
262. C₂×#41	C₂×D₁₅₁	semidirect
271. C₂×Q₁₆	C₂×D₁₅₁	semidirect
274. C₂×SD₁₆	C₂×D₁₅₁	semidirect
275. C₂×SD₁₆	C₂×D₁₅₁	semidirect
277. C₂×D₈	C₂×D₁₅₁	semidirect
279. C₂²×C₈	C₂×D₁₅₁	semidirect
314. #41	C₂²⋊D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₅₁	2
C₂×#18012759	2
#23752719	2
#23752373	2
#23752371	2
#23752366	2
#23752361	2
#23752356	2
#23752354	2
#23752349	2
#23752344	2
#23752209	2
#23752208	2
C₂×(C₂×D₁₅₁)⋊C₈	2
C₂×#135×C₁₅₁	2
#3002	151