Subgroups — #30652340

Order 16256.

1242 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22550611	C₂	1	1	yes	maximal, characteristic, complemented
2	#22550586	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550583	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550572	C₂	1	2	yes	maximal, complemented
5	#22550570	C₂	1	2	yes	maximal, complemented
6	#22550550	C₂	1	4	yes	maximal, complemented
7	#22550522	C₂	1	2	yes	maximal, complemented
8	#22550514	C₂	1	2	yes	maximal, complemented
9	D₄×D₅₀₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550426	C₂	1	1	yes	maximal, characteristic, complemented
11	#22550413	C₂	1	2	yes	maximal, complemented
12	#22550410	C₂	1	2	yes	maximal, complemented
13	#22550385	C₂	1	4	yes	maximal, complemented
14	C₄×#14523248	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₅₀₈	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₂₇	C₂	1	2	yes	maximal, complemented
17	C₄×#41×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14523248	C₂²	1	1	yes	characteristic
19	C₂×#14523248	C₂²	1	2	yes	complemented
20	C₂²×D₅₀₈	C₂²	1	2	yes	—
21	C₂×D₄×D₁₂₇	C₂²	1	2	yes	—
22	C₂²×C₄×D₁₂₇	C₂²	1	4	yes	complemented
23	#16861209	C₂²	1	1	yes	characteristic, complemented
24	#16861206	C₂²	1	1	yes	characteristic
25	#16861204	C₂²	1	4	yes	complemented
26	#16861203	C₂²	1	4	yes	complemented
27	#16861201	C₂²	1	2	yes	complemented
28	#16861200	C₂²	1	2	yes	complemented
29	#16861198	C₂²	1	2	yes	complemented
30	#16861197	C₂²	1	2	yes	complemented
31	#16861197	C₂²	1	2	yes	complemented
32	#16861194	C₂²	1	4	yes	complemented
33	#16861194	C₂²	1	4	yes	complemented
34	#16861192	C₂²	1	4	yes	complemented
35	#16861191	C₂²	1	4	yes	complemented
36	#16861188	C₂²	1	2	yes	complemented
37	#16861187	C₂²	1	4	yes	complemented
38	#16861186	C₂²	1	4	yes	complemented
39	#16861185	C₂²	1	2	yes	complemented
40	#16861184	C₂²	1	2	yes	—
41	#16861183	C₂²	1	2	yes	—
42	#16861183	C₂²	1	2	yes	complemented
43	#16861183	C₂²	1	2	yes	complemented
44	#16861182	C₂²	1	4	yes	complemented
45	#16861181	C₂²	1	4	yes	complemented
46	#16861179	C₂²	1	4	yes	—
47	#16861177	C₂²	1	4	yes	complemented
48	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
49	C₄×Dic₂₅₄	C₂²	1	1	yes	characteristic, complemented
50	C₄×D₅₀₈	C₂²	1	2	yes	—
51	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
52	C₄×D₅₀₈	C₂²	1	1	yes	characteristic
53	C₄×D₅₀₈	C₂²	1	4	yes	complemented
54	C₄×D₅₀₈	C₂²	1	2	yes	complemented
55	C₄×D₅₀₈	C₂²	1	2	yes	complemented
56	C₄×D₅₀₈	C₂²	1	4	yes	complemented
57	C₄×D₅₀₈	C₂²	1	2	yes	complemented
58	D₄×Dic₁₂₇	C₂²	1	2	yes	—
59	#16861171	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊D₁₂₇	C₂²	1	4	yes	complemented
62	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
63	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	4	yes	complemented
64	#16861168	C₂²	1	1	yes	characteristic, complemented
65	#16861166	C₂²	1	2	yes	complemented
66	#16861166	C₂²	1	4	yes	complemented
67	C₂×C₄⋊Dic₁₂₇	C₂²	1	2	yes	complemented
68	C₄⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
69	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	4	yes	complemented
70	C₂²⋊C₄×D₁₂₇	C₂²	1	4	yes	complemented
71	C₄²×D₁₂₇	C₂²	1	2	yes	complemented
72	C₂×#41×C₁₂₇	C₂²	1	1	yes	characteristic
73	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
74	C₄×Q₈×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
75	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
76	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic
77	C₄×D₄×C₁₂₇	C₂²	1	2	yes	complemented
78	C₄×D₄×C₁₂₇	C₂²	1	2	yes	complemented
79	#117×C₁₂₇	C₂²	1	2	yes	complemented
80	#117×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄²×C₁₂₇	C₂²	1	2	yes	complemented
82	C₂×C₄²×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₁₂₇	C₂³	1	4	yes	—
84	#14523248	—	2	4	no	—
85	#14523248	—	4	4	no	—
86	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic
87	C₂×Dic₂₅₄	C₂³	1	2	yes	—
88	C₂×D₅₀₈	—	2	8	no	—
89	C₂×D₅₀₈	C₂³	1	4	yes	—
90	C₂×D₅₀₈	C₂³	1	2	yes	—
91	C₂×D₅₀₈	C₂³	1	2	yes	—
92	C₂×D₅₀₈	C₂³	1	2	yes	—
93	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊D₁₂₇	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₁₂₇	C₂³	1	4	yes	—
97	D₄×D₁₂₇	—	2	8	no	—
98	C₂²×Dic₁₂₇	C₂³	1	4	yes	—
99	C₂×C₄×D₁₂₇	—	4	8	no	—
100	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
101	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
102	C₂×C₄×D₁₂₇	C₂³	1	2	yes	—
103	C₂×C₄×D₁₂₇	C₂³	1	4	yes	—
104	C₂×C₄×D₁₂₇	C₂³	1	4	yes	—
105	C₂×C₄×D₁₂₇	C₂³	1	4	yes	—
106	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
107	C₄⋊Dic₁₂₇	C₂³	1	4	yes	—
108	C₄⋊Dic₁₂₇	C₂³	1	2	yes	—
109	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
110	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
111	Dic₁₂₇⋊C₄	C₂³	1	4	yes	—
112	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
113	Dic₁₂₇⋊C₄	C₂³	1	4	yes	—
114	Dic₁₂₇⋊C₄	C₂³	1	4	yes	—
115	Dic₁₂₇⋊C₄	C₂³	1	2	yes	—
116	C₂²⋊Dic₁₂₇	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
118	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
121	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₁₂₇)⋊C₄	C₂³	1	4	yes	—
126	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
127	C₄×Dic₁₂₇	C₂³	1	2	yes	—
128	C₄×Dic₁₂₇	C₂³	1	2	yes	—
129	C₄×Dic₁₂₇	C₂³	1	2	yes	—
130	#41×C₁₂₇	—	2	4	no	—
131	C₂×Q₈×C₁₂₇	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
133	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
140	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₂₇	C₂³	1	2	yes	—
143	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
144	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
145	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	—
147	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
148	C₄²×C₁₂₇	C₂³	1	2	yes	—
149	C₄²×C₁₂₇	C₂³	1	2	yes	—
150	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
151	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
152	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic
153	C₄²×C₁₂₇	C₂³	1	2	yes	—
154	C₂²×D₁₂₇	—	2	8	no	—
155	C₂²×D₁₂₇	—	2	8	no	—
156	C₂²×D₁₂₇	—	4	4	no	—
157	C₂²×D₁₂₇	C₂⁴	1	4	yes	—
158	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
159	Dic₂₅₄	—	2	2	no	—
160	Dic₂₅₄	—	4	2	no	—
161	D₅₀₈	—	2	8	no	—
162	D₅₀₈	—	2	4	no	—
163	D₅₀₈	—	2	4	no	—
164	D₅₀₈	—	4	2	no	—
165	D₅₀₈	#41	1	4	yes	complemented
166	C₂²⋊D₁₂₇	—	2	8	no	—
167	C₂²⋊D₁₂₇	—	2	4	no	—
168	C₂²⋊D₁₂₇	—	4	4	no	—
169	C₂×Dic₁₂₇	—	4	4	no	—
170	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
171	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
172	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
173	C₂×Dic₁₂₇	C₂⁴	1	4	yes	—
174	C₄×D₁₂₇	—	2	4	no	—
175	C₄×D₁₂₇	—	2	4	no	—
176	C₄×D₁₂₇	—	2	4	no	—
177	C₄×D₁₂₇	—	2	8	no	—
178	C₄×D₁₂₇	—	4	4	no	—
179	C₄×D₁₂₇	—	4	4	no	—
180	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
181	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
182	Q₈×C₁₂₇	—	2	2	no	—
183	D₄×C₁₂₇	—	2	4	no	—
184	D₄×C₁₂₇	#41	1	4	yes	complemented
185	C₂×C₄×C₁₂₇	—	2	4	no	—
186	C₂×C₄×C₁₂₇	—	2	2	no	—
187	C₂×C₄×C₁₂₇	—	2	4	no	—
188	C₂×C₄×C₁₂₇	—	2	2	no	—
189	C₂×C₄×C₁₂₇	—	2	4	no	—
190	C₂×C₄×C₁₂₇	—	2	2	no	—
191	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
194	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
195	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
196	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
197	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
199	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
200	C₂²×C₁₂₇	—	2	2	no	—
201	C₂²×C₁₂₇	—	2	2	no	—
202	C₂²×C₁₂₇	—	2	1	no	—
203	C₂²×C₁₂₇	—	2	1	no	—
204	C₂²×C₁₂₇	—	2	1	no	—
205	C₂²×C₁₂₇	C₂×#41	1	4	yes	—
206	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
207	C₂×D₁₂₇	—	2	2	no	—
208	C₂×D₁₂₇	—	2	2	no	—
209	C₂×D₁₂₇	—	2	4	no	—
210	C₂×D₁₂₇	—	2	4	no	—
211	C₂×D₁₂₇	—	2	4	no	—
212	C₂×D₁₂₇	—	4	16	no	—
213	C₂×D₁₂₇	C₂×#41	1	4	yes	—
214	C₄×C₁₂₇	—	2	1	no	—
215	C₄×C₁₂₇	—	2	2	no	—
216	C₄×C₁₂₇	—	2	1	no	—
217	C₄×C₁₂₇	—	2	2	no	—
218	C₄×C₁₂₇	—	2	2	no	—
219	C₄×C₁₂₇	—	2	1	no	—
220	C₄×C₁₂₇	C₂×#41	1	2	yes	—
221	C₄×C₁₂₇	C₂×#41	1	2	yes	—
222	C₄×C₁₂₇	H(5,𝔽₂)	1	2	yes	—
223	Dic₁₂₇	—	2	2	no	—
224	Dic₁₂₇	—	2	2	no	—
225	Dic₁₂₇	—	2	2	no	—
226	Dic₁₂₇	—	2	4	no	—
227	C₂×C₁₂₇	—	2	4	no	—
228	C₂×C₁₂₇	—	4	1	no	—
229	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
230	C₂×C₁₂₇	C₂²×#41	1	1	yes	characteristic
231	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
232	D₁₂₇	—	2	4	no	—
233	D₁₂₇	—	4	4	no	—
234	#3481	—	127	1	no	maximal, Sylow
235	C₁₂₇	#3481	1	1	yes	characteristic, complemented, Sylow
236	#559	—	127	1	no	—
237	#554	—	127	1	no	—
238	#554	—	127	1	no	—
239	#553	—	127	2	no	—
240	#553	—	127	2	no	—
241	#551	—	127	4	no	—
242	#546	—	127	2	no	—
243	#546	—	127	2	no	—
244	D₄²	—	127	1	no	—
245	#532	—	127	1	no	—
246	#529	—	127	2	no	—
247	#529	—	127	2	no	—
248	#525	—	127	4	no	—
249	C₄×#41	—	127	1	no	—
250	C₄×#41	D₁₂₇	1	1	yes	characteristic, complemented
251	C₂×C₄×D₄	—	127	2	no	—
252	C₂×C₄×D₄	—	127	2	no	—
253	C₂×#41	—	127	2	no	—
254	C₂×#41	—	127	1	no	—
255	C₂×#41	C₂×D₁₂₇	1	1	yes	characteristic
256	C₂²×D₄	—	127	2	no	—
257	C₂²×D₄	—	127	2	no	—
258	C₂³×C₄	—	127	4	no	—
259	C₄⋊Q₈	—	127	1	no	—
260	#127	—	127	1	no	—
261	#126	—	127	4	no	—
262	#126	—	127	4	no	—
263	#125	—	127	2	no	—
264	#125	—	127	2	no	—
265	#124	—	127	2	no	—
266	#124	—	127	2	no	—
267	#124	—	127	2	no	—
268	#123	—	127	4	no	—
269	#123	—	127	4	no	—
270	#123	—	127	4	no	—
271	#123	—	127	4	no	—
272	C₂²⋊Q₈	—	127	2	no	—
273	C₂²⋊Q₈	—	127	2	no	—
274	C₂²⋊Q₈	—	127	4	no	—
275	C₂²⋊Q₈	—	127	4	no	—
276	#121	—	127	4	no	—
277	#121	—	127	2	no	—
278	#121	—	127	2	no	—
279	#121	—	127	2	no	—
280	#121	—	127	2	no	—
281	#121	—	127	4	no	—
282	#120	—	127	4	no	—
283	#120	—	127	4	no	—
284	C₄×Q₈	—	127	1	no	—
285	C₄×Q₈	—	127	1	no	—
286	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
287	C₄×Q₈	C₂×D₁₂₇	1	1	yes	characteristic, complemented
288	C₄×D₄	—	127	2	no	—
289	C₄×D₄	—	127	4	no	—
290	C₄×D₄	—	127	2	no	—
291	C₄×D₄	—	127	2	no	—
292	C₄×D₄	—	127	2	no	—
293	C₄×D₄	—	127	4	no	—
294	C₄×D₄	—	127	1	no	—
295	C₄×D₄	—	127	4	no	—
296	C₄×D₄	—	127	2	no	—
297	C₄×D₄	—	127	2	no	—
298	C₄×D₄	—	127	2	no	—
299	C₄×D₄	—	127	4	no	—
300	C₄×D₄	—	127	2	no	—
301	C₄×D₄	—	127	1	no	—
302	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
303	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic
304	C₄×D₄	C₂×D₁₂₇	1	2	yes	complemented
305	C₄×D₄	C₂×D₁₂₇	1	2	yes	complemented
306	#117	—	127	1	no	—
307	#117	—	127	2	no	—
308	#117	—	127	4	no	—
309	#117	C₂×D₁₂₇	1	2	yes	complemented
310	#117	C₂×D₁₂₇	1	1	yes	characteristic, complemented
311	C₂×C₄⋊C₄	—	127	2	no	—
312	C₂×C₄⋊C₄	—	127	2	no	—
313	C₂×C₂²⋊C₄	—	127	4	no	—
314	C₂×C₂²⋊C₄	—	127	4	no	—
315	C₂×C₄²	—	127	2	no	—
316	C₂×C₄²	C₂×D₁₂₇	1	2	yes	complemented
317	C₂×C₄²	C₂×D₁₂₇	1	1	yes	characteristic, complemented
318	C₂⁴	—	127	4	no	—
319	#41	—	2	4	no	—
320	#41	—	508	4	no	—
321	#41	—	254	4	no	—
322	C₂×Q₈	—	127	2	no	—
323	C₂×Q₈	—	127	1	no	—
324	C₂×Q₈	C₂²×D₁₂₇	1	1	yes	characteristic
325	C₂×D₄	—	127	4	no	—
326	C₂×D₄	—	127	2	no	—
327	C₂×D₄	—	127	4	no	—
328	C₂×D₄	—	127	1	no	—
329	C₂×D₄	—	127	2	no	—
330	C₂×D₄	—	127	4	no	—
331	C₂×D₄	—	127	2	no	—
332	C₂×D₄	—	127	2	no	—
333	C₂×D₄	—	254	8	no	—
334	C₂×D₄	—	254	8	no	—
335	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
336	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
337	C₂²×C₄	—	127	4	no	—
338	C₂²×C₄	—	127	4	no	—
339	C₂²×C₄	—	127	4	no	—
340	C₂²×C₄	—	127	2	no	—
341	C₂²×C₄	—	127	2	no	—
342	C₂²×C₄	—	127	2	no	—
343	C₂²×C₄	—	127	4	no	—
344	C₂²×C₄	—	508	8	no	—
345	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
346	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
347	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
348	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
349	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	—
350	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
351	C₄⋊C₄	—	127	4	no	—
352	C₄⋊C₄	—	127	2	no	—
353	C₄⋊C₄	—	127	2	no	—
354	C₄⋊C₄	—	127	4	no	—
355	C₄⋊C₄	—	127	4	no	—
356	C₄⋊C₄	—	127	1	no	—
357	C₄⋊C₄	—	127	2	no	—
358	C₄⋊C₄	—	127	2	no	—
359	C₄⋊C₄	—	127	4	no	—
360	C₄⋊C₄	—	127	1	no	—
361	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
362	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
364	C₄⋊C₄	C₂²×D₁₂₇	1	2	yes	—
365	C₂²⋊C₄	—	127	4	no	—
366	C₂²⋊C₄	—	127	2	no	—
367	C₂²⋊C₄	—	127	2	no	—
368	C₂²⋊C₄	—	127	4	no	—
369	C₂²⋊C₄	—	127	4	no	—
370	C₂²⋊C₄	—	127	4	no	—
371	C₂²⋊C₄	—	127	4	no	—
372	C₂²⋊C₄	—	127	4	no	—
373	C₂²⋊C₄	—	127	2	no	—
374	C₂²⋊C₄	—	127	4	no	—
375	C₂²⋊C₄	—	127	4	no	—
376	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
378	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	—
379	C₄²	—	127	2	no	—
380	C₄²	—	127	2	no	—
381	C₄²	—	127	2	no	—
382	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
383	C₄²	C₂²×D₁₂₇	1	2	yes	—
384	C₄²	C₂²×D₁₂₇	1	2	yes	—
385	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
386	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
387	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic
388	C₄²	C₂²×D₁₂₇	1	2	yes	—
389	C₂³	—	127	2	no	—
390	C₂³	—	127	4	no	—
391	C₂³	—	508	4	no	—
392	C₂³	—	254	8	no	—
393	C₂³	—	254	8	no	—
394	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
395	C₂³	C₂³×D₁₂₇	1	2	yes	—
396	Q₈	—	2	2	no	—
397	Q₈	—	508	2	no	—
398	Q₈	—	254	2	no	—
399	D₄	—	2	4	no	—
400	D₄	—	127	4	no	—
401	D₄	—	508	2	no	—
402	D₄	—	508	4	no	—
403	D₄	—	254	8	no	—
404	D₄	—	254	4	no	—
405	D₄	—	254	8	no	—
406	D₄	—	254	4	no	—
407	D₄	—	254	4	no	—
408	D₄	#14523248	1	4	yes	complemented
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	127	2	no	—
416	C₂×C₄	—	127	2	no	—
417	C₂×C₄	—	127	2	no	—
418	C₂×C₄	—	127	4	no	—
419	C₂×C₄	—	508	4	no	—
420	C₂×C₄	—	508	4	no	—
421	C₂×C₄	—	508	4	no	—
422	C₂×C₄	—	254	4	no	—
423	C₂×C₄	—	254	4	no	—
424	C₂×C₄	—	254	4	no	—
425	C₂×C₄	—	254	8	no	—
426	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
427	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
429	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
430	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
431	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
433	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	127	4	no	—
441	C₂²	—	508	16	no	—
442	C₂²	—	254	4	no	—
443	C₂²	—	254	4	no	—
444	C₂²	—	254	4	no	—
445	C₂²	—	254	2	no	—
446	C₂²	—	254	2	no	—
447	C₂²	C₂×#14523248	1	4	yes	—
448	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	1	no	—
455	C₄	—	254	2	no	—
456	C₄	—	254	2	no	—
457	C₄	—	254	2	no	—
458	C₄	—	254	4	no	—
459	C₄	#41×D₁₂₇	1	2	yes	—
460	C₄	C₂×#14523248	1	2	yes	—
461	C₄	#16861255	1	2	yes	—
462	C₂	—	2	4	no	—
463	C₂	—	4	1	no	—
464	C₂	—	508	4	no	—
465	C₂	—	254	4	no	—
466	C₂	C₂×#41×D₁₂₇	1	1	yes	characteristic
467	C₂	C₂²×#14523248	1	1	yes	characteristic
468	C₂	C₂×#16861255	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Frattini	C₂²	C₂⁴×D₁₂₇
Fitting	C₄×#41×C₁₂₇	C₂
hypercenter	C₄×#41	D₁₂₇
hypocenter	C₁₂₇	#3481
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
1. #22550611	C₂	semidirect
2. #22550586	C₂	semidirect
3. #22550583	C₂	semidirect
4. #22550572	C₂	semidirect
5. #22550570	C₂	semidirect
6. #22550550	C₂	semidirect
7. #22550522	C₂	semidirect
8. #22550514	C₂	semidirect
9. D₄×D₅₀₈	C₂	semidirect
10. #22550426	C₂	semidirect
11. #22550413	C₂	semidirect
12. #22550410	C₂	semidirect
13. #22550385	C₂	semidirect
14. C₄×#14523248	C₂	semidirect
15. C₂×C₄×D₅₀₈	C₂	semidirect
16. C₄×D₄×D₁₂₇	C₂	semidirect
17. C₄×#41×C₁₂₇	C₂	semidirect
19. C₂×#14523248	C₂²	semidirect
22. C₂²×C₄×D₁₂₇	C₂²	semidirect
23. #16861209	C₂²	semidirect
25. #16861204	C₂²	semidirect
26. #16861203	C₂²	semidirect
27. #16861201	C₂²	semidirect
28. #16861200	C₂²	semidirect
29. #16861198	C₂²	semidirect
30. #16861197	C₂²	semidirect
31. #16861197	C₂²	semidirect
32. #16861194	C₂²	semidirect
33. #16861194	C₂²	semidirect
34. #16861192	C₂²	semidirect
35. #16861191	C₂²	semidirect
36. #16861188	C₂²	semidirect
37. #16861187	C₂²	semidirect
38. #16861186	C₂²	semidirect
39. #16861185	C₂²	semidirect
42. #16861183	C₂²	semidirect
43. #16861183	C₂²	semidirect
44. #16861182	C₂²	semidirect
45. #16861181	C₂²	semidirect
47. #16861177	C₂²	semidirect
48. C₄×Dic₂₅₄	C₂²	semidirect
49. C₄×Dic₂₅₄	C₂²	semidirect
53. C₄×D₅₀₈	C₂²	semidirect
54. C₄×D₅₀₈	C₂²	semidirect
55. C₄×D₅₀₈	C₂²	semidirect
56. C₄×D₅₀₈	C₂²	semidirect
57. C₄×D₅₀₈	C₂²	semidirect
59. #16861171	C₂²	semidirect
60. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
61. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
62. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
63. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
64. #16861168	C₂²	semidirect
65. #16861166	C₂²	semidirect
66. #16861166	C₂²	semidirect
67. C₂×C₄⋊Dic₁₂₇	C₂²	semidirect
68. C₄⋊C₄×D₁₂₇	C₂²	semidirect
69. C₂×(C₂×D₁₂₇)⋊C₄	C₂²	semidirect
70. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
71. C₄²×D₁₂₇	C₂²	semidirect
73. C₄×Q₈×C₁₂₇	C₂²	semidirect
74. C₄×Q₈×C₁₂₇	C₂²	semidirect
77. C₄×D₄×C₁₂₇	C₂²	semidirect
78. C₄×D₄×C₁₂₇	C₂²	semidirect
79. #117×C₁₂₇	C₂²	semidirect
80. #117×C₁₂₇	C₂²	semidirect
81. C₂×C₄²×C₁₂₇	C₂²	semidirect
82. C₂×C₄²×C₁₂₇	C₂²	semidirect
165. D₅₀₈	#41	semidirect
184. D₄×C₁₂₇	#41	semidirect
235. C₁₂₇	#3481	semidirect
250. C₄×#41	D₁₂₇	semidirect
286. C₄×Q₈	C₂×D₁₂₇	semidirect
287. C₄×Q₈	C₂×D₁₂₇	semidirect
304. C₄×D₄	C₂×D₁₂₇	semidirect
305. C₄×D₄	C₂×D₁₂₇	semidirect
309. #117	C₂×D₁₂₇	semidirect
310. #117	C₂×D₁₂₇	semidirect
316. C₂×C₄²	C₂×D₁₂₇	semidirect
317. C₂×C₄²	C₂×D₁₂₇	semidirect
408. D₄	#14523248	semidirect

Maximal subgroups

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

subgroup	index
#22550611	2
#22550586	2
#22550583	2
#22550572	2
#22550570	2
#22550550	2
#22550522	2
#22550514	2
D₄×D₅₀₈	2
#22550426	2
#22550413	2
#22550410	2
#22550385	2
C₄×#14523248	2
C₂×C₄×D₅₀₈	2
C₄×D₄×D₁₂₇	2
C₄×#41×C₁₂₇	2
#3481	127