Subgroups — #34082778

Order 19328.

1658 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#18012785	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#41×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#23752881	C₂	1	1	yes	maximal, characteristic, complemented
4	#23752874	C₂	1	1	yes	maximal, characteristic, complemented
5	#23752869	C₂	1	1	yes	maximal, characteristic, complemented
6	#23752859	C₂	1	3	yes	maximal, complemented
7	#23752858	C₂	1	3	yes	maximal, complemented
8	#23752847	C₂	1	3	yes	maximal, complemented
9	#23752846	C₂	1	3	yes	maximal, complemented
10	#23752791	C₂	1	3	yes	maximal, complemented
11	#23752775	C₂	1	3	yes	maximal, complemented
12	#23752721	C₂	1	3	yes	maximal, complemented
13	#121×D₁₅₁	C₂	1	3	yes	maximal, complemented
14	#23752694	C₂	1	1	yes	maximal, characteristic, complemented
15	#550×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#18012785	—	2	8	no	—
17	C₂×#14559005	C₂²	1	1	yes	characteristic
18	C₂×#14559005	C₂²	1	1	yes	characteristic, complemented
19	C₂×#14559004	C₂²	1	3	yes	complemented
20	C₂×#14559004	C₂²	1	3	yes	complemented
21	C₂×#14559003	C₂²	1	3	yes	complemented
22	#41×D₁₅₁	—	2	8	no	—
23	C₂×Q₈×D₁₅₁	C₂²	1	1	yes	characteristic, complemented
24	C₂²×D₆₀₄	C₂²	1	3	yes	complemented
25	C₂×D₄×D₁₅₁	C₂²	1	3	yes	complemented
26	C₂×D₄×D₁₅₁	C₂²	1	3	yes	complemented
27	C₂×D₄×D₁₅₁	C₂²	1	3	yes	complemented
28	C₂×D₄×D₁₅₁	C₂²	1	6	yes	complemented
29	C₂²×C₄×D₁₅₁	C₂²	1	3	yes	complemented
30	#18012735	C₂²	1	3	yes	complemented
31	#18012727	C₂²	1	3	yes	complemented
32	#18012726	C₂²	1	3	yes	complemented
33	#18012724	C₂²	1	3	yes	complemented
34	#18012721	C₂²	1	3	yes	complemented
35	#18012719	C₂²	1	3	yes	complemented
36	#18012718	C₂²	1	3	yes	complemented
37	#18012717	C₂²	1	1	yes	characteristic, complemented
38	#18012716	C₂²	1	3	yes	complemented
39	#18012714	C₂²	1	3	yes	complemented
40	#18012713	C₂²	1	3	yes	complemented
41	#18012712	C₂²	1	3	yes	complemented
42	#18012712	C₂²	1	6	yes	complemented
43	#18012711	C₂²	1	3	yes	complemented
44	#18012711	C₂²	1	6	yes	complemented
45	#18012710	C₂²	1	6	yes	complemented
46	#18012710	C₂²	1	3	yes	complemented
47	#18012710	C₂²	1	3	yes	complemented
48	#18012709	C₂²	1	3	yes	complemented
49	#18012707	C₂²	1	3	yes	complemented
50	#18012707	C₂²	1	6	yes	complemented
51	#18012707	C₂²	1	6	yes	complemented
52	Q₈×Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₆₀₄	C₂²	1	3	yes	complemented
54	C₄×D₆₀₄	C₂²	1	3	yes	complemented
55	#18012701	C₂²	1	3	yes	complemented
56	C₄×C₂²⋊D₁₅₁	C₂²	1	3	yes	complemented
57	C₄×C₂²⋊D₁₅₁	C₂²	1	3	yes	complemented
58	#18012696	C₂²	1	3	yes	complemented
59	C₄⋊C₄×D₁₅₁	C₂²	1	3	yes	complemented
60	C₂²⋊C₄×D₁₅₁	C₂²	1	6	yes	complemented
61	C₂×#41×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
62	C₂×#41×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
63	#127×C₁₅₁	C₂²	1	3	yes	complemented
64	#121×C₁₅₁	C₂²	1	3	yes	complemented
65	#121×C₁₅₁	C₂²	1	3	yes	complemented
66	C₄×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₄×C₁₅₁	C₂²	1	3	yes	complemented
68	C₂³×D₁₅₁	C₂³	1	3	yes	—
69	C₂³×D₁₅₁	C₂³	1	6	yes	—
70	#14559005	—	2	4	no	—
71	#14559005	D₄	1	8	yes	complemented
72	#14559004	—	2	12	no	—
73	#14559004	—	2	12	no	—
74	#14559003	—	2	12	no	—
75	C₂×Dic₃₀₂	C₂³	1	1	yes	characteristic
76	C₂×Dic₃₀₂	C₂³	1	3	yes	—
77	Q₈×D₁₅₁	—	2	4	no	—
78	C₂×D₆₀₄	—	2	12	no	—
79	C₂×D₆₀₄	C₂³	1	3	yes	—
80	C₂×D₆₀₄	C₂³	1	3	yes	—
81	C₂×D₆₀₄	C₂³	1	3	yes	—
82	C₂×D₆₀₄	C₂³	1	3	yes	—
83	C₂×C₂²⋊D₁₅₁	C₂³	1	3	yes	—
84	C₂×C₂²⋊D₁₅₁	C₂³	1	6	yes	—
85	C₂×C₂²⋊D₁₅₁	C₂³	1	3	yes	—
86	C₂×C₂²⋊D₁₅₁	C₂³	1	3	yes	—
87	C₂×C₂²⋊D₁₅₁	C₂³	1	3	yes	—
88	C₂×C₂²⋊D₁₅₁	C₂³	1	6	yes	—
89	D₄×D₁₅₁	—	2	12	no	—
90	D₄×D₁₅₁	—	2	12	no	—
91	D₄×D₁₅₁	—	2	12	no	—
92	D₄×D₁₅₁	—	4	12	no	—
93	C₂²×Dic₁₅₁	C₂³	1	3	yes	—
94	C₂×C₄×D₁₅₁	—	2	12	no	—
95	C₂×C₄×D₁₅₁	C₂³	1	3	yes	—
96	C₂×C₄×D₁₅₁	C₂³	1	3	yes	—
97	C₂×C₄×D₁₅₁	C₂³	1	3	yes	—
98	C₂×C₄×D₁₅₁	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₅₁	C₂³	1	6	yes	—
100	C₂×C₄×D₁₅₁	C₂³	1	3	yes	—
101	C₄⋊Dic₁₅₁	C₂³	1	3	yes	—
102	C₄⋊Dic₁₅₁	C₂³	1	3	yes	—
103	Dic₁₅₁⋊C₄	C₂³	1	3	yes	—
104	Dic₁₅₁⋊C₄	C₂³	1	1	yes	characteristic
105	Dic₁₅₁⋊C₄	C₂³	1	1	yes	characteristic
106	Dic₁₅₁⋊C₄	C₂³	1	3	yes	—
107	C₂²⋊Dic₁₅₁	C₂³	1	6	yes	—
108	C₂²⋊Dic₁₅₁	C₂³	1	3	yes	—
109	C₂²⋊Dic₁₅₁	C₂³	1	3	yes	—
110	(C₂×D₁₅₁)⋊C₄	C₂³	1	3	yes	—
111	(C₂×D₁₅₁)⋊C₄	C₂³	1	6	yes	—
112	(C₂×D₁₅₁)⋊C₄	C₂³	1	3	yes	—
113	(C₂×D₁₅₁)⋊C₄	C₂³	1	3	yes	—
114	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
115	(C₂×D₁₅₁)⋊C₄	C₂³	1	1	yes	characteristic
116	(C₂×D₁₅₁)⋊C₄	C₂³	1	3	yes	—
117	C₄×Dic₁₅₁	C₂³	1	3	yes	—
118	#41×C₁₅₁	—	2	4	no	—
119	#41×C₁₅₁	—	2	4	no	—
120	C₂×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
121	C₂×D₄×C₁₅₁	C₂³	1	3	yes	—
122	C₂×D₄×C₁₅₁	C₂³	1	3	yes	—
123	C₂×D₄×C₁₅₁	C₂³	1	3	yes	—
124	C₂×D₄×C₁₅₁	C₂³	1	6	yes	—
125	C₂²×C₄×C₁₅₁	C₂³	1	3	yes	—
126	C₂²×C₄×C₁₅₁	C₂³	1	3	yes	—
127	C₄⋊C₄×C₁₅₁	C₂³	1	3	yes	—
128	C₄⋊C₄×C₁₅₁	C₂³	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₅₁	C₂³	1	3	yes	—
130	C₂²⋊C₄×C₁₅₁	C₂³	1	3	yes	—
131	C₄²×C₁₅₁	C₂³	1	3	yes	—
132	C₂²×D₁₅₁	—	2	6	no	—
133	C₂²×D₁₅₁	—	2	6	no	—
134	C₂²×D₁₅₁	—	2	12	no	—
135	C₂²×D₁₅₁	—	4	3	no	—
136	C₂²×D₁₅₁	—	4	6	no	—
137	C₂²×D₁₅₁	—	4	6	no	—
138	C₂²×D₁₅₁	C₂⁴	1	3	yes	—
139	C₂²×D₁₅₁	C₂⁴	1	3	yes	—
140	C₂²×D₁₅₁	C₂⁴	1	1	yes	characteristic
141	Dic₃₀₂	—	2	6	no	—
142	Dic₃₀₂	—	2	2	no	—
143	D₆₀₄	—	2	6	no	—
144	D₆₀₄	—	2	6	no	—
145	D₆₀₄	—	2	6	no	—
146	D₆₀₄	C₂×D₄	1	12	yes	complemented
147	C₂²⋊D₁₅₁	—	2	6	no	—
148	C₂²⋊D₁₅₁	—	2	12	no	—
149	C₂²⋊D₁₅₁	—	2	6	no	—
150	C₂²⋊D₁₅₁	—	2	6	no	—
151	C₂²⋊D₁₅₁	—	4	6	no	—
152	C₂²⋊D₁₅₁	—	4	3	no	—
153	C₂×Dic₁₅₁	—	2	6	no	—
154	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
155	C₂×Dic₁₅₁	C₂⁴	1	3	yes	—
156	C₂×Dic₁₅₁	C₂⁴	1	3	yes	—
157	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
158	C₂×Dic₁₅₁	C₂⁴	1	1	yes	characteristic
159	C₄×D₁₅₁	—	2	6	no	—
160	C₄×D₁₅₁	—	2	6	no	—
161	C₄×D₁₅₁	—	2	6	no	—
162	C₄×D₁₅₁	—	2	2	no	—
163	C₄×D₁₅₁	—	4	6	no	—
164	C₄×D₁₅₁	C₂×D₄	1	12	yes	complemented
165	C₂³×C₁₅₁	C₂⁴	1	3	yes	—
166	C₂³×C₁₅₁	C₂⁴	1	3	yes	—
167	Q₈×C₁₅₁	C₂×D₄	1	4	yes	complemented
168	D₄×C₁₅₁	—	2	6	no	—
169	D₄×C₁₅₁	—	2	6	no	—
170	D₄×C₁₅₁	—	4	6	no	—
171	D₄×C₁₅₁	—	4	3	no	—
172	C₂×C₄×C₁₅₁	—	2	6	no	—
173	C₂×C₄×C₁₅₁	—	2	6	no	—
174	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₅₁	C₂⁴	1	3	yes	—
176	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₅₁	C₂⁴	1	3	yes	—
179	C₂²×C₁₅₁	—	2	3	no	—
180	C₂²×C₁₅₁	—	2	3	no	—
181	C₂²×C₁₅₁	—	2	3	no	—
182	C₂²×C₁₅₁	—	2	3	no	—
183	C₂²×C₁₅₁	—	2	3	no	—
184	C₂²×C₁₅₁	—	2	3	no	—
185	C₂²×C₁₅₁	C₂⁵	1	1	yes	characteristic
186	C₂×D₁₅₁	—	2	1	no	—
187	C₂×D₁₅₁	—	2	3	no	—
188	C₂×D₁₅₁	—	2	1	no	—
189	C₂×D₁₅₁	—	2	3	no	—
190	C₂×D₁₅₁	—	2	3	no	—
191	C₂×D₁₅₁	—	2	3	no	—
192	C₂×D₁₅₁	—	2	3	no	—
193	C₂×D₁₅₁	—	4	12	no	—
194	C₂×D₁₅₁	—	8	12	no	—
195	C₂×D₁₅₁	C₂²×D₄	1	6	yes	—
196	C₂×D₁₅₁	H(5,𝔽₂)	1	2	yes	complemented
197	C₄×C₁₅₁	—	2	1	no	—
198	C₄×C₁₅₁	—	2	1	no	—
199	C₄×C₁₅₁	—	2	3	no	—
200	C₄×C₁₅₁	—	2	1	no	—
201	C₄×C₁₅₁	C₂²×D₄	1	6	yes	—
202	Dic₁₅₁	—	2	1	no	—
203	Dic₁₅₁	—	2	3	no	—
204	Dic₁₅₁	—	2	3	no	—
205	Dic₁₅₁	—	2	1	no	—
206	Dic₁₅₁	C₂²×D₄	1	2	yes	—
207	C₂×C₁₅₁	—	4	3	no	—
208	C₂×C₁₅₁	—	4	3	no	—
209	C₂×C₁₅₁	C₂³×D₄	1	1	yes	characteristic
210	C₂×C₁₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₁₅₁	#585	1	1	yes	characteristic
212	D₁₅₁	—	2	2	no	—
213	D₁₅₁	—	2	6	no	—
214	D₁₅₁	—	4	3	no	—
215	C₁₅₁	#3488	1	1	yes	characteristic, complemented, Sylow
216	#3488	—	151	1	no	maximal, Sylow
217	C₂×H(5,𝔽₂)	—	151	1	no	—
218	C₂²×#41	—	151	1	no	—
219	#550	—	151	1	no	—
220	#550	D₁₅₁	1	1	yes	characteristic, complemented
221	#548	—	151	1	no	—
222	#548	—	151	1	no	—
223	#546	—	151	3	no	—
224	#546	—	151	3	no	—
225	D₄²	—	151	3	no	—
226	D₄²	—	151	3	no	—
227	#537	—	151	3	no	—
228	#535	—	151	3	no	—
229	#525	—	151	3	no	—
230	C₂×#121	—	151	3	no	—
231	#520	—	151	1	no	—
232	H(5,𝔽₂)	—	302	8	no	—
233	C₂×#41	—	302	8	no	—
234	C₂×#41	—	151	1	no	—
235	C₂×#41	—	151	1	no	—
236	C₂×#41	—	151	3	no	—
237	C₂×#41	—	151	3	no	—
238	C₂×#41	—	151	3	no	—
239	C₂×#41	C₂×D₁₅₁	1	1	yes	characteristic, complemented
240	C₂×#41	C₂×D₁₅₁	1	1	yes	characteristic, complemented
241	C₂²×Q₈	—	151	1	no	—
242	C₂²×D₄	—	151	3	no	—
243	C₂²×D₄	—	151	3	no	—
244	C₂²×D₄	—	151	3	no	—
245	C₂²×D₄	—	151	6	no	—
246	C₂²×D₄	—	151	3	no	—
247	C₂³×C₄	—	151	3	no	—
248	#127	—	151	3	no	—
249	#127	C₂×D₁₅₁	1	3	yes	complemented
250	#124	—	151	3	no	—
251	#124	—	151	3	no	—
252	#123	—	151	3	no	—
253	#123	—	151	3	no	—
254	C₂²⋊Q₈	—	151	3	no	—
255	C₂²⋊Q₈	—	151	1	no	—
256	C₂²⋊Q₈	—	151	3	no	—
257	C₂²⋊Q₈	—	151	3	no	—
258	#121	—	151	6	no	—
259	#121	—	151	3	no	—
260	#121	—	151	3	no	—
261	#121	—	151	6	no	—
262	#121	—	151	3	no	—
263	#121	—	151	3	no	—
264	#121	—	151	3	no	—
265	#121	—	151	3	no	—
266	#121	—	151	6	no	—
267	#121	C₂×D₁₅₁	1	3	yes	complemented
268	#121	C₂×D₁₅₁	1	3	yes	complemented
269	#120	—	151	3	no	—
270	#120	—	151	6	no	—
271	#120	—	151	6	no	—
272	#120	—	151	3	no	—
273	C₄×Q₈	—	151	1	no	—
274	C₄×Q₈	C₂×D₁₅₁	1	1	yes	characteristic, complemented
275	C₄×D₄	—	151	3	no	—
276	C₄×D₄	—	151	3	no	—
277	C₄×D₄	—	151	3	no	—
278	C₄×D₄	—	151	3	no	—
279	C₄×D₄	—	151	3	no	—
280	C₄×D₄	C₂×D₁₅₁	1	3	yes	complemented
281	#117	—	151	3	no	—
282	C₂×C₄⋊C₄	—	151	3	no	—
283	C₂×C₂²⋊C₄	—	151	6	no	—
284	C₂⁴	—	151	3	no	—
285	C₂⁴	—	151	6	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	302	12	no	—
289	#41	—	302	12	no	—
290	#41	—	302	4	no	—
291	#41	—	302	12	no	—
292	#41	—	151	8	no	—
293	C₂×Q₈	—	302	4	no	—
294	C₂×Q₈	—	151	1	no	—
295	C₂×Q₈	—	151	3	no	—
296	C₂×Q₈	C₂²×D₁₅₁	1	1	yes	characteristic
297	C₂×D₄	—	302	12	no	—
298	C₂×D₄	—	302	12	no	—
299	C₂×D₄	—	302	12	no	—
300	C₂×D₄	—	302	12	no	—
301	C₂×D₄	—	604	12	no	—
302	C₂×D₄	—	151	3	no	—
303	C₂×D₄	—	151	6	no	—
304	C₂×D₄	—	151	3	no	—
305	C₂×D₄	—	151	3	no	—
306	C₂×D₄	—	151	3	no	—
307	C₂×D₄	—	151	6	no	—
308	C₂×D₄	—	151	3	no	—
309	C₂×D₄	—	151	3	no	—
310	C₂×D₄	—	151	3	no	—
311	C₂×D₄	—	151	3	no	—
312	C₂×D₄	C₂²×D₁₅₁	1	3	yes	—
313	C₂×D₄	C₂²×D₁₅₁	1	3	yes	—
314	C₂×D₄	C₂²×D₁₅₁	1	3	yes	—
315	C₂×D₄	C₂²×D₁₅₁	1	6	yes	—
316	C₂²×C₄	—	302	12	no	—
317	C₂²×C₄	—	151	3	no	—
318	C₂²×C₄	—	151	3	no	—
319	C₂²×C₄	—	151	3	no	—
320	C₂²×C₄	—	151	3	no	—
321	C₂²×C₄	—	151	1	no	—
322	C₂²×C₄	—	151	6	no	—
323	C₂²×C₄	—	151	3	no	—
324	C₂²×C₄	C₂²×D₁₅₁	1	3	yes	—
325	C₂²×C₄	C₂²×D₁₅₁	1	3	yes	—
326	C₄⋊C₄	—	151	3	no	—
327	C₄⋊C₄	—	151	1	no	—
328	C₄⋊C₄	—	151	1	no	—
329	C₄⋊C₄	—	151	3	no	—
330	C₄⋊C₄	—	151	3	no	—
331	C₄⋊C₄	—	151	3	no	—
332	C₄⋊C₄	C₂²×D₁₅₁	1	3	yes	—
333	C₄⋊C₄	C₂²×D₁₅₁	1	1	yes	characteristic
334	C₂²⋊C₄	—	151	6	no	—
335	C₂²⋊C₄	—	151	3	no	—
336	C₂²⋊C₄	—	151	3	no	—
337	C₂²⋊C₄	—	151	3	no	—
338	C₂²⋊C₄	—	151	6	no	—
339	C₂²⋊C₄	—	151	3	no	—
340	C₂²⋊C₄	—	151	3	no	—
341	C₂²⋊C₄	—	151	1	no	—
342	C₂²⋊C₄	—	151	1	no	—
343	C₂²⋊C₄	—	151	3	no	—
344	C₂²⋊C₄	C₂²×D₁₅₁	1	3	yes	—
345	C₂²⋊C₄	C₂²×D₁₅₁	1	3	yes	—
346	C₄²	—	151	3	no	—
347	C₄²	C₂²×D₁₅₁	1	3	yes	—
348	C₂³	—	302	6	no	—
349	C₂³	—	302	6	no	—
350	C₂³	—	302	12	no	—
351	C₂³	—	604	3	no	—
352	C₂³	—	604	6	no	—
353	C₂³	—	604	6	no	—
354	C₂³	—	151	3	no	—
355	C₂³	—	151	1	no	—
356	C₂³	—	151	3	no	—
357	C₂³	C₂³×D₁₅₁	1	3	yes	—
358	C₂³	C₂³×D₁₅₁	1	3	yes	—
359	Q₈	—	302	2	no	—
360	Q₈	—	302	6	no	—
361	Q₈	D₄×D₁₅₁	1	4	yes	complemented
362	D₄	—	2	6	no	—
363	D₄	—	2	6	no	—
364	D₄	—	4	6	no	—
365	D₄	—	4	3	no	—
366	D₄	—	302	6	no	—
367	D₄	—	302	6	no	—
368	D₄	—	302	6	no	—
369	D₄	—	302	12	no	—
370	D₄	—	302	6	no	—
371	D₄	—	302	6	no	—
372	D₄	—	302	6	no	—
373	D₄	—	604	6	no	—
374	D₄	—	604	3	no	—
375	D₄	—	151	12	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	6	no	—
378	C₂×C₄	—	302	6	no	—
379	C₂×C₄	—	302	2	no	—
380	C₂×C₄	—	302	6	no	—
381	C₂×C₄	—	302	6	no	—
382	C₂×C₄	—	302	6	no	—
383	C₂×C₄	—	604	6	no	—
384	C₂×C₄	—	151	1	no	—
385	C₂×C₄	—	151	3	no	—
386	C₂×C₄	—	151	3	no	—
387	C₂×C₄	—	151	1	no	—
388	C₂×C₄	—	151	1	no	—
389	C₂×C₄	—	151	12	no	—
390	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₁₅₁	1	3	yes	—
392	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₁₅₁	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₁₅₁	1	3	yes	—
395	C₂²	—	2	3	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	3	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	2	3	no	—
401	C₂²	—	302	1	no	—
402	C₂²	—	302	3	no	—
403	C₂²	—	302	1	no	—
404	C₂²	—	302	3	no	—
405	C₂²	—	302	3	no	—
406	C₂²	—	302	3	no	—
407	C₂²	—	302	3	no	—
408	C₂²	—	604	12	no	—
409	C₂²	—	151	6	no	—
410	C₂²	—	151	2	no	—
411	C₂²	—	1208	12	no	—
412	C₂²	C₂⁴×D₁₅₁	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	3	no	—
416	C₄	—	2	1	no	—
417	C₄	—	302	1	no	—
418	C₄	—	302	3	no	—
419	C₄	—	302	3	no	—
420	C₄	—	302	1	no	—
421	C₄	—	151	2	no	—
422	C₄	C₂×D₄×D₁₅₁	1	6	yes	—
423	C₂	—	4	3	no	—
424	C₂	—	4	3	no	—
425	C₂	—	302	2	no	—
426	C₂	—	302	6	no	—
427	C₂	—	604	3	no	—
428	C₂	C₂²×D₄×D₁₅₁	1	1	yes	characteristic
429	C₂	H(5,𝔽₂)×D₁₅₁	1	1	yes	characteristic
430	C₂	#23753048	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₅₁
commutator, socle, cosocle	C₂²×C₁₅₁	C₂⁵
Fitting	#550×C₁₅₁	C₂
hypercenter	#550	D₁₅₁
hypocenter	C₁₅₁	#3488
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. C₂×#18012785	C₂	semidirect
2. C₂×#41×D₁₅₁	C₂	semidirect
3. #23752881	C₂	semidirect
4. #23752874	C₂	semidirect
5. #23752869	C₂	semidirect
6. #23752859	C₂	semidirect
7. #23752858	C₂	semidirect
8. #23752847	C₂	semidirect
9. #23752846	C₂	semidirect
10. #23752791	C₂	semidirect
11. #23752775	C₂	semidirect
12. #23752721	C₂	semidirect
13. #121×D₁₅₁	C₂	semidirect
14. #23752694	C₂	semidirect
15. #550×C₁₅₁	C₂	semidirect
18. C₂×#14559005	C₂²	semidirect
19. C₂×#14559004	C₂²	semidirect
20. C₂×#14559004	C₂²	semidirect
21. C₂×#14559003	C₂²	semidirect
23. C₂×Q₈×D₁₅₁	C₂²	semidirect
24. C₂²×D₆₀₄	C₂²	semidirect
25. C₂×D₄×D₁₅₁	C₂²	semidirect
26. C₂×D₄×D₁₅₁	C₂²	semidirect
27. C₂×D₄×D₁₅₁	C₂²	semidirect
28. C₂×D₄×D₁₅₁	C₂²	semidirect
29. C₂²×C₄×D₁₅₁	C₂²	semidirect
30. #18012735	C₂²	semidirect
31. #18012727	C₂²	semidirect
32. #18012726	C₂²	semidirect
33. #18012724	C₂²	semidirect
34. #18012721	C₂²	semidirect
35. #18012719	C₂²	semidirect
36. #18012718	C₂²	semidirect
37. #18012717	C₂²	semidirect
38. #18012716	C₂²	semidirect
39. #18012714	C₂²	semidirect
40. #18012713	C₂²	semidirect
41. #18012712	C₂²	semidirect
42. #18012712	C₂²	semidirect
43. #18012711	C₂²	semidirect
44. #18012711	C₂²	semidirect
45. #18012710	C₂²	semidirect
46. #18012710	C₂²	semidirect
47. #18012710	C₂²	semidirect
48. #18012709	C₂²	semidirect
49. #18012707	C₂²	semidirect
50. #18012707	C₂²	semidirect
51. #18012707	C₂²	semidirect
52. Q₈×Dic₁₅₁	C₂²	semidirect
53. C₄×D₆₀₄	C₂²	semidirect
54. C₄×D₆₀₄	C₂²	semidirect
55. #18012701	C₂²	semidirect
56. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
57. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
58. #18012696	C₂²	semidirect
59. C₄⋊C₄×D₁₅₁	C₂²	semidirect
60. C₂²⋊C₄×D₁₅₁	C₂²	semidirect
61. C₂×#41×C₁₅₁	C₂²	semidirect
62. C₂×#41×C₁₅₁	C₂²	semidirect
63. #127×C₁₅₁	C₂²	semidirect
64. #121×C₁₅₁	C₂²	semidirect
65. #121×C₁₅₁	C₂²	semidirect
66. C₄×Q₈×C₁₅₁	C₂²	semidirect
67. C₄×D₄×C₁₅₁	C₂²	semidirect
71. #14559005	D₄	semidirect
146. D₆₀₄	C₂×D₄	semidirect
164. C₄×D₁₅₁	C₂×D₄	semidirect
167. Q₈×C₁₅₁	C₂×D₄	semidirect
196. C₂×D₁₅₁	H(5,𝔽₂)	semidirect
215. C₁₅₁	#3488	semidirect
220. #550	D₁₅₁	semidirect
239. C₂×#41	C₂×D₁₅₁	semidirect
240. C₂×#41	C₂×D₁₅₁	semidirect
249. #127	C₂×D₁₅₁	semidirect
267. #121	C₂×D₁₅₁	semidirect
268. #121	C₂×D₁₅₁	semidirect
274. C₄×Q₈	C₂×D₁₅₁	semidirect
280. C₄×D₄	C₂×D₁₅₁	semidirect
361. Q₈	D₄×D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#18012785	2
C₂×#41×D₁₅₁	2
#23752881	2
#23752874	2
#23752869	2
#23752859	2
#23752858	2
#23752847	2
#23752846	2
#23752791	2
#23752775	2
#23752721	2
#121×D₁₅₁	2
#23752694	2
#550×C₁₅₁	2
#3488	151