Subgroups — #30652358

Order 16256.

1900 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16861254	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#22550523	C₂	1	1	yes	maximal, characteristic, complemented
4	#22550522	C₂	1	1	yes	maximal, characteristic, complemented
5	#22550521	C₂	1	1	yes	maximal, characteristic, complemented
6	#22550520	C₂	1	1	yes	maximal, characteristic, complemented
7	#22550515	C₂	1	2	yes	maximal, complemented
8	#22550513	C₂	1	2	yes	maximal, complemented
9	#22550511	C₂	1	1	yes	maximal, characteristic, complemented
10	#22550510	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₂²⋊D₁₂₇	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#22550508	C₂	1	2	yes	maximal, complemented
14	#22550442	C₂	1	1	yes	maximal, characteristic, complemented
15	#22550439	C₂	1	1	yes	maximal, characteristic, complemented
16	#22550436	C₂	1	2	yes	maximal, complemented
17	#22550434	C₂	1	2	yes	maximal, complemented
18	#22550386	C₂	1	1	yes	maximal, characteristic, complemented
19	#22550385	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16861177	C₂	1	2	yes	maximal, complemented
21	#120×D₁₂₇	C₂	1	2	yes	maximal, complemented
22	#22550348	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄²×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×D₁₂₇	C₂²	1	2	yes	complemented
25	#16861254	—	2	8	no	—
26	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14523248	C₂²	1	1	yes	characteristic, complemented
28	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
29	C₂×#14523247	C₂²	1	1	yes	characteristic, complemented
30	C₂×#14523247	C₂²	1	2	yes	complemented
31	C₂²×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
34	C₂²×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
35	C₂²×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
36	C₂×D₄×D₁₂₇	—	2	8	no	—
37	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
39	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
41	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
44	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
45	C₂×D₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
46	C₂×D₄×D₁₂₇	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₁₂₇	C₂²	1	1	yes	characteristic, complemented
48	#16861205	C₂²	1	2	yes	complemented
49	#16861205	C₂²	1	1	yes	characteristic, complemented
50	#16861197	C₂²	1	1	yes	characteristic, complemented
51	#16861196	C₂²	1	1	yes	characteristic, complemented
52	#16861195	C₂²	1	2	yes	complemented
53	#16861194	C₂²	1	1	yes	characteristic, complemented
54	#16861194	C₂²	1	2	yes	complemented
55	#16861193	C₂²	1	2	yes	complemented
56	#16861191	C₂²	1	1	yes	characteristic, complemented
57	#16861191	C₂²	1	2	yes	complemented
58	#16861191	C₂²	1	2	yes	complemented
59	#16861190	C₂²	1	2	yes	complemented
60	#16861189	C₂²	1	1	yes	characteristic, complemented
61	#16861188	C₂²	1	1	yes	characteristic, complemented
62	#16861187	C₂²	1	1	yes	characteristic, complemented
63	#16861186	C₂²	1	1	yes	characteristic, complemented
64	#16861184	C₂²	1	1	yes	characteristic, complemented
65	#16861183	C₂²	1	2	yes	complemented
66	#16861183	C₂²	1	1	yes	characteristic, complemented
67	#16861182	C₂²	1	1	yes	characteristic, complemented
68	#16861182	C₂²	1	2	yes	complemented
69	#16861182	C₂²	1	2	yes	complemented
70	#16861181	C₂²	1	1	yes	characteristic, complemented
71	#16861181	C₂²	1	2	yes	complemented
72	#16861181	C₂²	1	2	yes	complemented
73	#16861181	C₂²	1	2	yes	complemented
74	#16861181	C₂²	1	2	yes	complemented
75	#16861180	C₂²	1	1	yes	characteristic, complemented
76	#16861180	C₂²	1	1	yes	characteristic, complemented
77	#16861180	C₂²	1	2	yes	complemented
78	#16861180	C₂²	1	2	yes	complemented
79	#16861179	C₂²	1	1	yes	characteristic, complemented
80	#16861179	C₂²	1	2	yes	complemented
81	#16861179	C₂²	1	2	yes	complemented
82	#16861179	C₂²	1	2	yes	complemented
83	#16861178	C₂²	1	2	yes	complemented
84	#16861178	C₂²	1	2	yes	complemented
85	#16861177	C₂²	1	2	yes	complemented
86	#16861177	C₂²	1	1	yes	characteristic, complemented
87	#16861177	C₂²	1	2	yes	complemented
88	#16861177	C₂²	1	2	yes	complemented
89	#16861177	C₂²	1	2	yes	complemented
90	#16861177	C₂²	1	2	yes	complemented
91	#16861177	C₂²	1	2	yes	complemented
92	#16861177	C₂²	1	2	yes	complemented
93	#16861177	C₂²	1	2	yes	complemented
94	#16861177	C₂²	1	2	yes	complemented
95	#16861177	C₂²	1	2	yes	complemented
96	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₅₀₈	C₂²	1	1	yes	characteristic, complemented
98	D₄×Dic₁₂₇	C₂²	1	2	yes	complemented
99	D₄×Dic₁₂₇	C₂²	1	1	yes	characteristic, complemented
100	#16861171	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₂²⋊D₁₂₇	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₁₂₇	C₂²	1	2	yes	complemented
104	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
105	(C₂²⋊D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
106	#16861167	C₂²	1	1	yes	characteristic, complemented
107	#16861166	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₂²⋊Dic₁₂₇	C₂²	1	2	yes	complemented
109	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
110	C₂×(C₂×D₁₂₇)⋊C₄	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
112	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₁₂₇	C₂²	1	2	yes	complemented
114	C₂²×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
115	C₂²×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
116	C₂²×D₄×C₁₂₇	C₂²	1	2	yes	complemented
117	#127×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
118	#121×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₂₇	C₂²	1	2	yes	complemented
120	#121×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
121	#120×C₁₂₇	C₂²	1	2	yes	complemented
122	#120×C₁₂₇	C₂²	1	2	yes	complemented
123	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
124	C₄×D₄×C₁₂₇	C₂²	1	1	yes	characteristic, complemented
125	C₂³×D₁₂₇	—	2	8	no	—
126	C₂³×D₁₂₇	—	4	4	no	—
127	C₂³×D₁₂₇	—	4	4	no	—
128	C₂³×D₁₂₇	C₂³	1	1	yes	characteristic
129	C₂³×D₁₂₇	C₂³	1	2	yes	—
130	C₂³×D₁₂₇	C₂³	1	2	yes	—
131	C₂³×D₁₂₇	C₂³	1	2	yes	—
132	C₂³×D₁₂₇	C₂³	1	2	yes	—
133	C₂³×D₁₂₇	C₂³	1	2	yes	—
134	C₂³×D₁₂₇	C₂³	1	2	yes	complemented
135	#14523248	—	2	4	no	—
136	#14523248	—	2	4	no	—
137	#14523247	—	2	8	no	—
138	#14523247	—	2	4	no	—
139	#14523247	—	2	4	no	—
140	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic, complemented
141	C₂×Dic₂₅₄	C₂³	1	1	yes	characteristic, complemented
142	C₂×D₅₀₈	—	2	4	no	—
143	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
144	C₂×D₅₀₈	C₂³	1	2	yes	—
145	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
146	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
147	C₂×D₅₀₈	C₂³	1	1	yes	characteristic
148	C₂×D₅₀₈	C₂³	1	2	yes	complemented
149	C₂×C₂²⋊D₁₂₇	—	2	8	no	—
150	C₂×C₂²⋊D₁₂₇	—	2	8	no	—
151	C₂×C₂²⋊D₁₂₇	—	2	8	no	—
152	C₂×C₂²⋊D₁₂₇	—	4	4	no	—
153	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊D₁₂₇	C₂³	1	1	yes	characteristic, complemented
163	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	complemented
164	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	complemented
165	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	complemented
166	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	complemented
167	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	complemented
168	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	complemented
169	C₂×C₂²⋊D₁₂₇	C₂³	1	2	yes	complemented
170	D₄×D₁₂₇	—	2	8	no	—
171	D₄×D₁₂₇	—	2	8	no	—
172	D₄×D₁₂₇	—	2	4	no	—
173	D₄×D₁₂₇	—	2	4	no	—
174	D₄×D₁₂₇	—	2	8	no	—
175	D₄×D₁₂₇	—	2	4	no	—
176	D₄×D₁₂₇	—	2	4	no	—
177	D₄×D₁₂₇	—	4	4	no	—
178	D₄×D₁₂₇	—	4	4	no	—
179	D₄×D₁₂₇	D₄	1	8	yes	complemented
180	C₂²×Dic₁₂₇	C₂³	1	1	yes	characteristic
181	C₂²×Dic₁₂₇	C₂³	1	2	yes	complemented
182	C₂²×Dic₁₂₇	C₂³	1	2	yes	complemented
183	C₂²×Dic₁₂₇	C₂³	1	2	yes	complemented
184	C₂×C₄×D₁₂₇	—	2	4	no	—
185	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
186	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
187	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
188	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic
189	C₂×C₄×D₁₂₇	C₂³	1	1	yes	characteristic, complemented
190	C₂×C₄×D₁₂₇	C₂³	1	2	yes	complemented
191	C₂×C₄×D₁₂₇	C₂³	1	2	yes	complemented
192	C₂×C₄×D₁₂₇	C₂³	1	2	yes	complemented
193	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
194	C₄⋊Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
195	C₄⋊Dic₁₂₇	C₂³	1	2	yes	complemented
196	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
197	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
198	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
199	Dic₁₂₇⋊C₄	C₂³	1	1	yes	characteristic, complemented
200	Dic₁₂₇⋊C₄	C₂³	1	2	yes	complemented
201	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic
202	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	—
203	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	complemented
204	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	complemented
205	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	complemented
206	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	complemented
207	C₂²⋊Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
208	C₂²⋊Dic₁₂₇	C₂³	1	2	yes	complemented
209	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
210	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
211	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
212	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
213	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	—
214	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic
215	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
216	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
217	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
218	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
219	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
220	(C₂×D₁₂₇)⋊C₄	C₂³	1	2	yes	complemented
221	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
222	(C₂×D₁₂₇)⋊C₄	C₂³	1	1	yes	characteristic, complemented
223	C₄×Dic₁₂₇	C₂³	1	2	yes	complemented
224	C₄×Dic₁₂₇	C₂³	1	1	yes	characteristic, complemented
225	C₂⁴×C₁₂₇	C₂³	1	2	yes	—
226	C₂⁴×C₁₂₇	C₂³	1	2	yes	complemented
227	C₂×D₄×C₁₂₇	—	2	4	no	—
228	C₂×D₄×C₁₂₇	—	2	4	no	—
229	C₂×D₄×C₁₂₇	—	4	4	no	—
230	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
231	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
232	C₂×D₄×C₁₂₇	C₂³	1	2	yes	—
233	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
234	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic
235	C₂×D₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
236	C₂×D₄×C₁₂₇	C₂³	1	2	yes	complemented
237	C₂×D₄×C₁₂₇	C₂³	1	2	yes	complemented
238	C₂×D₄×C₁₂₇	C₂³	1	2	yes	complemented
239	C₂×D₄×C₁₂₇	C₂³	1	2	yes	complemented
240	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic
241	C₂²×C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
242	C₂²×C₄×C₁₂₇	C₂³	1	2	yes	complemented
243	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
244	C₄⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
245	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic
246	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	complemented
247	C₂²⋊C₄×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
248	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	complemented
249	C₂²⋊C₄×C₁₂₇	C₂³	1	2	yes	complemented
250	C₄²×C₁₂₇	C₂³	1	1	yes	characteristic, complemented
251	C₂²×D₁₂₇	—	2	2	no	—
252	C₂²×D₁₂₇	—	2	2	no	—
253	C₂²×D₁₂₇	—	2	2	no	—
254	C₂²×D₁₂₇	—	2	4	no	—
255	C₂²×D₁₂₇	—	2	4	no	—
256	C₂²×D₁₂₇	—	2	4	no	—
257	C₂²×D₁₂₇	—	2	4	no	—
258	C₂²×D₁₂₇	—	2	4	no	—
259	C₂²×D₁₂₇	—	2	4	no	—
260	C₂²×D₁₂₇	—	2	4	no	—
261	C₂²×D₁₂₇	—	2	4	no	—
262	C₂²×D₁₂₇	—	4	2	no	—
263	C₂²×D₁₂₇	—	4	2	no	—
264	C₂²×D₁₂₇	—	4	2	no	—
265	C₂²×D₁₂₇	—	4	2	no	—
266	C₂²×D₁₂₇	—	4	2	no	—
267	C₂²×D₁₂₇	—	4	2	no	—
268	C₂²×D₁₂₇	—	4	2	no	—
269	C₂²×D₁₂₇	—	4	2	no	—
270	C₂²×D₁₂₇	—	4	2	no	—
271	C₂²×D₁₂₇	—	4	32	no	—
272	C₂²×D₁₂₇	C₂×D₄	1	8	yes	complemented
273	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
274	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
275	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
276	C₂²×D₁₂₇	C₂⁴	1	2	yes	—
277	C₂²×D₁₂₇	C₂⁴	1	1	yes	characteristic
278	Dic₂₅₄	—	2	2	no	—
279	Dic₂₅₄	—	2	2	no	—
280	D₅₀₈	—	2	4	no	—
281	D₅₀₈	—	2	2	no	—
282	D₅₀₈	—	2	2	no	—
283	D₅₀₈	—	2	2	no	—
284	D₅₀₈	—	4	2	no	—
285	D₅₀₈	C₂×D₄	1	4	yes	complemented
286	C₂²⋊D₁₂₇	—	2	4	no	—
287	C₂²⋊D₁₂₇	—	2	4	no	—
288	C₂²⋊D₁₂₇	—	2	2	no	—
289	C₂²⋊D₁₂₇	—	2	4	no	—
290	C₂²⋊D₁₂₇	—	2	4	no	—
291	C₂²⋊D₁₂₇	—	2	4	no	—
292	C₂²⋊D₁₂₇	—	2	2	no	—
293	C₂²⋊D₁₂₇	—	2	4	no	—
294	C₂²⋊D₁₂₇	—	2	4	no	—
295	C₂²⋊D₁₂₇	—	2	2	no	—
296	C₂²⋊D₁₂₇	—	2	4	no	—
297	C₂²⋊D₁₂₇	—	2	2	no	—
298	C₂²⋊D₁₂₇	—	4	2	no	—
299	C₂²⋊D₁₂₇	—	4	2	no	—
300	C₂²⋊D₁₂₇	—	4	2	no	—
301	C₂²⋊D₁₂₇	—	4	2	no	—
302	C₂²⋊D₁₂₇	C₂×D₄	1	8	yes	complemented
303	C₂×Dic₁₂₇	—	2	4	no	—
304	C₂×Dic₁₂₇	—	2	2	no	—
305	C₂×Dic₁₂₇	—	2	4	no	—
306	C₂×Dic₁₂₇	—	4	2	no	—
307	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
308	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
309	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
310	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
311	C₂×Dic₁₂₇	C₂⁴	1	2	yes	—
312	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
313	C₂×Dic₁₂₇	C₂⁴	1	1	yes	characteristic
314	C₄×D₁₂₇	—	2	2	no	—
315	C₄×D₁₂₇	—	2	4	no	—
316	C₄×D₁₂₇	—	2	2	no	—
317	C₄×D₁₂₇	—	2	2	no	—
318	C₄×D₁₂₇	—	2	2	no	—
319	C₄×D₁₂₇	—	4	2	no	—
320	C₄×D₁₂₇	—	4	2	no	—
321	C₄×D₁₂₇	C₂×D₄	1	4	yes	complemented
322	C₂³×C₁₂₇	—	2	4	no	—
323	C₂³×C₁₂₇	—	2	4	no	—
324	C₂³×C₁₂₇	—	2	4	no	—
325	C₂³×C₁₂₇	—	4	2	no	—
326	C₂³×C₁₂₇	—	4	2	no	—
327	C₂³×C₁₂₇	—	4	2	no	—
328	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
329	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
330	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
331	C₂³×C₁₂₇	C₂⁴	1	2	yes	—
332	C₂³×C₁₂₇	C₂⁴	1	1	yes	characteristic
333	D₄×C₁₂₇	—	2	4	no	—
334	D₄×C₁₂₇	—	2	4	no	—
335	D₄×C₁₂₇	—	2	2	no	—
336	D₄×C₁₂₇	—	2	4	no	—
337	D₄×C₁₂₇	—	2	2	no	—
338	D₄×C₁₂₇	—	2	2	no	—
339	D₄×C₁₂₇	—	4	2	no	—
340	D₄×C₁₂₇	—	4	2	no	—
341	D₄×C₁₂₇	—	4	2	no	—
342	D₄×C₁₂₇	C₂×D₄	1	4	yes	complemented
343	C₂×C₄×C₁₂₇	—	2	2	no	—
344	C₂×C₄×C₁₂₇	—	2	2	no	—
345	C₂×C₄×C₁₂₇	—	4	2	no	—
346	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
347	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
348	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
349	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
350	C₂×C₄×C₁₂₇	C₂⁴	1	2	yes	—
351	C₂×C₄×C₁₂₇	C₂⁴	1	1	yes	characteristic
352	C₂²×C₁₂₇	—	2	1	no	—
353	C₂²×C₁₂₇	—	2	2	no	—
354	C₂²×C₁₂₇	—	2	2	no	—
355	C₂²×C₁₂₇	—	2	1	no	—
356	C₂²×C₁₂₇	—	2	1	no	—
357	C₂²×C₁₂₇	—	2	2	no	—
358	C₂²×C₁₂₇	—	2	2	no	—
359	C₂²×C₁₂₇	—	2	1	no	—
360	C₂²×C₁₂₇	—	2	2	no	—
361	C₂²×C₁₂₇	—	2	2	no	—
362	C₂²×C₁₂₇	—	2	2	no	—
363	C₂²×C₁₂₇	—	2	2	no	—
364	C₂²×C₁₂₇	—	2	1	no	—
365	C₂²×C₁₂₇	—	4	8	no	—
366	C₂²×C₁₂₇	—	8	4	no	—
367	C₂²×C₁₂₇	C₂²×D₄	1	4	yes	—
368	C₂²×C₁₂₇	H(5,𝔽₂)	1	2	yes	complemented
369	C₂²×C₁₂₇	C₂⁵	1	1	yes	characteristic
370	C₂×D₁₂₇	—	2	8	no	—
371	C₂×D₁₂₇	—	2	1	no	—
372	C₂×D₁₂₇	—	2	2	no	—
373	C₂×D₁₂₇	—	2	2	no	—
374	C₂×D₁₂₇	—	2	1	no	—
375	C₂×D₁₂₇	—	2	1	no	—
376	C₂×D₁₂₇	—	2	1	no	—
377	C₂×D₁₂₇	—	2	1	no	—
378	C₂×D₁₂₇	—	2	2	no	—
379	C₂×D₁₂₇	—	2	1	no	—
380	C₂×D₁₂₇	—	2	1	no	—
381	C₂×D₁₂₇	—	2	2	no	—
382	C₂×D₁₂₇	—	2	2	no	—
383	C₂×D₁₂₇	—	4	8	no	—
384	C₂×D₁₂₇	—	4	8	no	—
385	C₂×D₁₂₇	—	4	8	no	—
386	C₂×D₁₂₇	—	4	8	no	—
387	C₂×D₁₂₇	—	4	8	no	—
388	C₂×D₁₂₇	—	8	4	no	—
389	C₂×D₁₂₇	C₂²×D₄	1	2	yes	—
390	C₂×D₁₂₇	C₂²×D₄	1	4	yes	—
391	C₂×D₁₂₇	H(5,𝔽₂)	1	2	yes	complemented
392	C₄×C₁₂₇	—	2	1	no	—
393	C₄×C₁₂₇	—	2	1	no	—
394	C₄×C₁₂₇	—	2	1	no	—
395	C₄×C₁₂₇	—	2	2	no	—
396	C₄×C₁₂₇	—	2	1	no	—
397	C₄×C₁₂₇	C₂²×D₄	1	2	yes	—
398	Dic₁₂₇	—	2	1	no	—
399	Dic₁₂₇	—	2	2	no	—
400	Dic₁₂₇	—	2	1	no	—
401	Dic₁₂₇	—	2	1	no	—
402	Dic₁₂₇	—	2	2	no	—
403	Dic₁₂₇	—	2	1	no	—
404	Dic₁₂₇	C₂²×D₄	1	2	yes	—
405	C₂×C₁₂₇	—	2	2	no	—
406	C₂×C₁₂₇	—	2	4	no	—
407	C₂×C₁₂₇	—	4	2	no	—
408	C₂×C₁₂₇	—	4	2	no	—
409	C₂×C₁₂₇	—	4	1	no	—
410	C₂×C₁₂₇	C₂³×D₄	1	1	yes	characteristic
411	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
412	C₂×C₁₂₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
413	D₁₂₇	—	2	2	no	—
414	D₁₂₇	—	2	2	no	—
415	D₁₂₇	—	2	4	no	—
416	D₁₂₇	—	4	2	no	—
417	D₁₂₇	—	4	1	no	—
418	#3484	—	127	1	no	maximal, Sylow
419	C₁₂₇	#3484	1	1	yes	characteristic, complemented, Sylow
420	C₂×H(5,𝔽₂)	—	127	1	no	—
421	C₂³×D₄	—	127	1	no	—
422	#546	—	127	1	no	—
423	#546	—	127	2	no	—
424	#546	—	127	1	no	—
425	#546	—	127	2	no	—
426	#546	—	127	1	no	—
427	#546	—	127	1	no	—
428	D₄²	—	127	1	no	—
429	D₄²	—	127	2	no	—
430	D₄²	—	127	1	no	—
431	D₄²	—	127	1	no	—
432	D₄²	—	127	2	no	—
433	D₄²	D₁₂₇	1	1	yes	characteristic, complemented
434	#535	—	127	1	no	—
435	#535	—	127	1	no	—
436	#534	—	127	2	no	—
437	#534	—	127	2	no	—
438	#525	—	127	1	no	—
439	#525	—	127	1	no	—
440	C₂×#120	—	127	2	no	—
441	C₂×#120	—	127	2	no	—
442	#518	—	127	1	no	—
443	C₂⁵	—	127	2	no	—
444	H(5,𝔽₂)	—	254	8	no	—
445	C₂×#41	—	127	1	no	—
446	C₂×#41	—	127	1	no	—
447	C₂×#41	—	127	2	no	—
448	C₂×#41	—	127	1	no	—
449	C₂×#41	—	127	1	no	—
450	C₂²×D₄	—	127	1	no	—
451	C₂²×D₄	—	127	2	no	—
452	C₂²×D₄	—	127	2	no	—
453	C₂²×D₄	—	127	2	no	—
454	C₂²×D₄	—	127	2	no	—
455	C₂²×D₄	—	127	2	no	—
456	C₂²×D₄	—	127	2	no	—
457	C₂²×D₄	—	127	2	no	—
458	C₂²×D₄	—	127	1	no	—
459	C₂²×D₄	—	127	2	no	—
460	C₂²×D₄	—	127	1	no	—
461	C₂²×D₄	—	127	1	no	—
462	C₂²×D₄	—	127	2	no	—
463	C₂²×D₄	—	127	1	no	—
464	C₂²×D₄	—	127	1	no	—
465	C₂²×D₄	—	254	8	no	—
466	C₂²×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
467	C₂²×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
468	C₂²×D₄	C₂×D₁₂₇	1	2	yes	complemented
469	C₂³×C₄	—	127	1	no	—
470	#127	—	127	1	no	—
471	#127	—	127	2	no	—
472	#127	C₂×D₁₂₇	1	1	yes	characteristic, complemented
473	#124	—	127	1	no	—
474	#124	—	127	2	no	—
475	#124	—	127	1	no	—
476	#123	—	127	2	no	—
477	#123	—	127	1	no	—
478	#123	—	127	2	no	—
479	#123	—	127	2	no	—
480	#123	—	127	1	no	—
481	#123	—	127	2	no	—
482	#123	—	127	2	no	—
483	C₂²⋊Q₈	—	127	1	no	—
484	C₂²⋊Q₈	—	127	1	no	—
485	C₂²⋊Q₈	—	127	1	no	—
486	C₂²⋊Q₈	—	127	1	no	—
487	#121	—	127	1	no	—
488	#121	—	127	2	no	—
489	#121	—	127	1	no	—
490	#121	—	127	1	no	—
491	#121	—	127	2	no	—
492	#121	—	127	2	no	—
493	#121	—	127	2	no	—
494	#121	—	127	2	no	—
495	#121	—	127	2	no	—
496	#121	—	127	2	no	—
497	#121	—	127	1	no	—
498	#121	—	127	1	no	—
499	#121	—	127	1	no	—
500	#121	—	127	2	no	—
501	#121	—	127	2	no	—
502	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
503	#121	C₂×D₁₂₇	1	2	yes	complemented
504	#121	C₂×D₁₂₇	1	1	yes	characteristic, complemented
505	#120	—	127	2	no	—
506	#120	—	127	2	no	—
507	#120	—	127	2	no	—
508	#120	—	127	1	no	—
509	#120	—	127	2	no	—
510	#120	—	127	2	no	—
511	#120	—	127	2	no	—
512	#120	—	127	2	no	—
513	#120	—	127	2	no	—
514	#120	—	127	2	no	—
515	#120	—	127	2	no	—
516	#120	—	127	2	no	—
517	#120	—	127	2	no	—
518	#120	—	127	1	no	—
519	#120	—	127	2	no	—
520	#120	—	127	2	no	—
521	#120	—	127	2	no	—
522	#120	C₂×D₁₂₇	1	2	yes	complemented
523	#120	C₂×D₁₂₇	1	2	yes	complemented
524	C₄×D₄	—	127	1	no	—
525	C₄×D₄	—	127	2	no	—
526	C₄×D₄	—	127	1	no	—
527	C₄×D₄	—	127	2	no	—
528	C₄×D₄	—	127	1	no	—
529	C₄×D₄	—	127	1	no	—
530	C₄×D₄	—	127	2	no	—
531	C₄×D₄	—	127	2	no	—
532	C₄×D₄	—	127	1	no	—
533	C₄×D₄	—	127	1	no	—
534	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
535	C₄×D₄	C₂×D₁₂₇	1	1	yes	characteristic, complemented
536	#117	—	127	1	no	—
537	#117	—	127	1	no	—
538	C₂×C₂²⋊C₄	—	127	2	no	—
539	C₂×C₂²⋊C₄	—	127	2	no	—
540	C₂×C₂²⋊C₄	—	127	2	no	—
541	C₂×C₂²⋊C₄	—	127	2	no	—
542	C₂×C₂²⋊C₄	—	127	2	no	—
543	C₂×C₂²⋊C₄	—	127	2	no	—
544	C₂⁴	—	127	2	no	—
545	C₂⁴	—	127	2	no	—
546	C₂⁴	—	127	2	no	—
547	C₂⁴	—	127	2	no	—
548	C₂⁴	—	127	2	no	—
549	C₂⁴	—	127	2	no	—
550	C₂⁴	—	127	1	no	—
551	C₂⁴	—	508	4	no	—
552	C₂⁴	—	508	4	no	—
553	C₂⁴	—	254	8	no	—
554	C₂⁴	C₂²×D₁₂₇	1	2	yes	—
555	C₂⁴	C₂²×D₁₂₇	1	2	yes	complemented
556	#41	—	254	4	no	—
557	#41	—	254	4	no	—
558	#41	—	254	4	no	—
559	#41	—	254	8	no	—
560	#41	—	254	4	no	—
561	C₂×Q₈	—	127	1	no	—
562	C₂×Q₈	—	127	1	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	127	2	no	—
567	C₂×D₄	—	127	8	no	—
568	C₂×D₄	—	127	2	no	—
569	C₂×D₄	—	127	2	no	—
570	C₂×D₄	—	127	2	no	—
571	C₂×D₄	—	127	2	no	—
572	C₂×D₄	—	127	2	no	—
573	C₂×D₄	—	127	1	no	—
574	C₂×D₄	—	127	1	no	—
575	C₂×D₄	—	127	2	no	—
576	C₂×D₄	—	127	1	no	—
577	C₂×D₄	—	127	2	no	—
578	C₂×D₄	—	127	2	no	—
579	C₂×D₄	—	127	2	no	—
580	C₂×D₄	—	127	2	no	—
581	C₂×D₄	—	127	2	no	—
582	C₂×D₄	—	127	2	no	—
583	C₂×D₄	—	127	1	no	—
584	C₂×D₄	—	127	1	no	—
585	C₂×D₄	—	127	2	no	—
586	C₂×D₄	—	127	1	no	—
587	C₂×D₄	—	127	1	no	—
588	C₂×D₄	—	127	2	no	—
589	C₂×D₄	—	127	1	no	—
590	C₂×D₄	—	508	4	no	—
591	C₂×D₄	—	508	4	no	—
592	C₂×D₄	—	508	4	no	—
593	C₂×D₄	—	254	4	no	—
594	C₂×D₄	—	254	4	no	—
595	C₂×D₄	—	254	8	no	—
596	C₂×D₄	—	254	4	no	—
597	C₂×D₄	—	254	4	no	—
598	C₂×D₄	—	254	8	no	—
599	C₂×D₄	—	254	8	no	—
600	C₂×D₄	—	254	8	no	—
601	C₂×D₄	—	254	8	no	—
602	C₂×D₄	—	254	8	no	—
603	C₂×D₄	—	254	4	no	—
604	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
605	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
606	C₂×D₄	C₂²×D₁₂₇	1	2	yes	—
607	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
608	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic
609	C₂×D₄	C₂²×D₁₂₇	1	2	yes	complemented
610	C₂×D₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
611	C₂×D₄	C₂²×D₁₂₇	1	2	yes	complemented
612	C₂×D₄	C₂²×D₁₂₇	1	2	yes	complemented
613	C₂×D₄	C₂²×D₁₂₇	1	2	yes	complemented
614	C₂²×C₄	—	127	1	no	—
615	C₂²×C₄	—	127	2	no	—
616	C₂²×C₄	—	127	1	no	—
617	C₂²×C₄	—	127	2	no	—
618	C₂²×C₄	—	127	2	no	—
619	C₂²×C₄	—	127	2	no	—
620	C₂²×C₄	—	127	2	no	—
621	C₂²×C₄	—	127	1	no	—
622	C₂²×C₄	—	127	1	no	—
623	C₂²×C₄	—	127	1	no	—
624	C₂²×C₄	—	127	2	no	—
625	C₂²×C₄	—	127	1	no	—
626	C₂²×C₄	—	254	4	no	—
627	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic
628	C₂²×C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
629	C₂²×C₄	C₂²×D₁₂₇	1	2	yes	complemented
630	C₄⋊C₄	—	127	1	no	—
631	C₄⋊C₄	—	127	1	no	—
632	C₄⋊C₄	—	127	1	no	—
633	C₄⋊C₄	—	127	2	no	—
634	C₄⋊C₄	—	127	1	no	—
635	C₄⋊C₄	—	127	1	no	—
636	C₄⋊C₄	—	127	2	no	—
637	C₄⋊C₄	—	127	1	no	—
638	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
639	C₄⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
640	C₂²⋊C₄	—	127	1	no	—
641	C₂²⋊C₄	—	127	2	no	—
642	C₂²⋊C₄	—	127	2	no	—
643	C₂²⋊C₄	—	127	2	no	—
644	C₂²⋊C₄	—	127	2	no	—
645	C₂²⋊C₄	—	127	2	no	—
646	C₂²⋊C₄	—	127	2	no	—
647	C₂²⋊C₄	—	127	1	no	—
648	C₂²⋊C₄	—	127	2	no	—
649	C₂²⋊C₄	—	127	1	no	—
650	C₂²⋊C₄	—	127	1	no	—
651	C₂²⋊C₄	—	127	1	no	—
652	C₂²⋊C₄	—	127	2	no	—
653	C₂²⋊C₄	—	127	1	no	—
654	C₂²⋊C₄	—	127	2	no	—
655	C₂²⋊C₄	—	127	2	no	—
656	C₂²⋊C₄	—	127	2	no	—
657	C₂²⋊C₄	—	127	2	no	—
658	C₂²⋊C₄	—	127	2	no	—
659	C₂²⋊C₄	—	127	2	no	—
660	C₂²⋊C₄	—	127	1	no	—
661	C₂²⋊C₄	—	127	1	no	—
662	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic
663	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	complemented
664	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	complemented
665	C₂²⋊C₄	C₂²×D₁₂₇	1	2	yes	complemented
666	C₂²⋊C₄	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
667	C₄²	—	127	2	no	—
668	C₄²	—	127	1	no	—
669	C₄²	C₂²×D₁₂₇	1	1	yes	characteristic, complemented
670	C₂³	—	2	4	no	—
671	C₂³	—	2	4	no	—
672	C₂³	—	2	4	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	2	no	—
675	C₂³	—	4	2	no	—
676	C₂³	—	127	8	no	—
677	C₂³	—	127	1	no	—
678	C₂³	—	127	1	no	—
679	C₂³	—	127	2	no	—
680	C₂³	—	127	2	no	—
681	C₂³	—	127	1	no	—
682	C₂³	—	508	2	no	—
683	C₂³	—	508	2	no	—
684	C₂³	—	508	2	no	—
685	C₂³	—	508	2	no	—
686	C₂³	—	508	2	no	—
687	C₂³	—	508	2	no	—
688	C₂³	—	508	2	no	—
689	C₂³	—	508	2	no	—
690	C₂³	—	508	2	no	—
691	C₂³	—	508	32	no	—
692	C₂³	—	254	4	no	—
693	C₂³	—	254	4	no	—
694	C₂³	—	254	4	no	—
695	C₂³	—	254	4	no	—
696	C₂³	—	254	4	no	—
697	C₂³	—	254	4	no	—
698	C₂³	—	254	2	no	—
699	C₂³	—	254	2	no	—
700	C₂³	—	254	4	no	—
701	C₂³	—	254	4	no	—
702	C₂³	—	254	2	no	—
703	C₂³	C₂³×D₁₂₇	1	2	yes	—
704	C₂³	C₂³×D₁₂₇	1	2	yes	—
705	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
706	C₂³	C₂³×D₁₂₇	1	2	yes	—
707	C₂³	C₂³×D₁₂₇	1	1	yes	characteristic
708	Q₈	—	254	2	no	—
709	Q₈	—	254	2	no	—
710	D₄	—	2	4	no	—
711	D₄	—	2	4	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	4	no	—
714	D₄	—	2	2	no	—
715	D₄	—	2	2	no	—
716	D₄	—	4	2	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	2	no	—
719	D₄	—	127	8	no	—
720	D₄	—	127	4	no	—
721	D₄	—	508	2	no	—
722	D₄	—	508	2	no	—
723	D₄	—	508	2	no	—
724	D₄	—	508	2	no	—
725	D₄	—	508	2	no	—
726	D₄	—	254	2	no	—
727	D₄	—	254	4	no	—
728	D₄	—	254	2	no	—
729	D₄	—	254	4	no	—
730	D₄	—	254	2	no	—
731	D₄	—	254	4	no	—
732	D₄	—	254	2	no	—
733	D₄	—	254	4	no	—
734	D₄	—	254	2	no	—
735	D₄	—	254	4	no	—
736	D₄	—	254	4	no	—
737	D₄	—	254	4	no	—
738	D₄	—	254	4	no	—
739	D₄	—	254	4	no	—
740	D₄	—	254	2	no	—
741	D₄	—	254	2	no	—
742	D₄	D₄×D₁₂₇	1	4	yes	complemented
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	127	1	no	—
747	C₂×C₄	—	127	4	no	—
748	C₂×C₄	—	127	2	no	—
749	C₂×C₄	—	127	1	no	—
750	C₂×C₄	—	127	1	no	—
751	C₂×C₄	—	127	1	no	—
752	C₂×C₄	—	127	2	no	—
753	C₂×C₄	—	127	1	no	—
754	C₂×C₄	—	508	2	no	—
755	C₂×C₄	—	508	2	no	—
756	C₂×C₄	—	508	2	no	—
757	C₂×C₄	—	254	2	no	—
758	C₂×C₄	—	254	2	no	—
759	C₂×C₄	—	254	4	no	—
760	C₂×C₄	—	254	2	no	—
761	C₂×C₄	—	254	4	no	—
762	C₂×C₄	—	254	4	no	—
763	C₂×C₄	—	254	2	no	—
764	C₂×C₄	—	254	2	no	—
765	C₂×C₄	C₂³×D₁₂₇	1	2	yes	—
766	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
767	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
768	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
769	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
770	C₂×C₄	C₂³×D₁₂₇	1	1	yes	characteristic
771	C₂²	—	2	1	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	1	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	4	8	no	—
785	C₂²	—	8	4	no	—
786	C₂²	—	127	2	no	—
787	C₂²	—	127	4	no	—
788	C₂²	—	127	2	no	—
789	C₂²	—	1016	4	no	—
790	C₂²	—	508	8	no	—
791	C₂²	—	508	8	no	—
792	C₂²	—	508	8	no	—
793	C₂²	—	508	8	no	—
794	C₂²	—	508	8	no	—
795	C₂²	—	254	8	no	—
796	C₂²	—	254	1	no	—
797	C₂²	—	254	2	no	—
798	C₂²	—	254	1	no	—
799	C₂²	—	254	2	no	—
800	C₂²	—	254	1	no	—
801	C₂²	—	254	2	no	—
802	C₂²	—	254	1	no	—
803	C₂²	—	254	2	no	—
804	C₂²	—	254	1	no	—
805	C₂²	—	254	2	no	—
806	C₂²	—	254	1	no	—
807	C₂²	—	254	1	no	—
808	C₂²	C₂×D₄×D₁₂₇	1	4	yes	—
809	C₂²	#16861254	1	2	yes	complemented
810	C₂²	C₂⁴×D₁₂₇	1	1	yes	characteristic
811	C₄	—	2	1	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	2	no	—
816	C₄	—	127	2	no	—
817	C₄	—	254	1	no	—
818	C₄	—	254	2	no	—
819	C₄	—	254	1	no	—
820	C₄	—	254	2	no	—
821	C₄	—	254	1	no	—
822	C₄	—	254	1	no	—
823	C₄	C₂×D₄×D₁₂₇	1	2	yes	—
824	C₂	—	2	2	no	—
825	C₂	—	2	4	no	—
826	C₂	—	4	2	no	—
827	C₂	—	4	1	no	—
828	C₂	—	4	2	no	—
829	C₂	—	508	1	no	—
830	C₂	—	508	2	no	—
831	C₂	—	254	4	no	—
832	C₂	—	254	2	no	—
833	C₂	—	254	2	no	—
834	C₂	C₂²×D₄×D₁₂₇	1	1	yes	characteristic
835	C₂	H(5,𝔽₂)×D₁₂₇	1	1	yes	characteristic
836	C₂	C₂×#16861254	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₂₇
commutator, socle, cosocle	C₂²×C₁₂₇	C₂⁵
Fitting	D₄²×C₁₂₇	C₂
hypercenter	D₄²	D₁₂₇
hypocenter	C₁₂₇	#3484
LCS	G ▷ C₂²×C₁₂₇ ▷ C₁₂₇
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₂×#16861254	C₂	semidirect
2. C₂²×D₄×D₁₂₇	C₂	semidirect
3. #22550523	C₂	semidirect
4. #22550522	C₂	semidirect
5. #22550521	C₂	semidirect
6. #22550520	C₂	semidirect
7. #22550515	C₂	semidirect
8. #22550513	C₂	semidirect
9. #22550511	C₂	semidirect
10. #22550510	C₂	semidirect
11. D₄×C₂²⋊D₁₂₇	C₂	semidirect
12. D₄×C₂²⋊D₁₂₇	C₂	semidirect
13. #22550508	C₂	semidirect
14. #22550442	C₂	semidirect
15. #22550439	C₂	semidirect
16. #22550436	C₂	semidirect
17. #22550434	C₂	semidirect
18. #22550386	C₂	semidirect
19. #22550385	C₂	semidirect
20. C₂×#16861177	C₂	semidirect
21. #120×D₁₂₇	C₂	semidirect
22. #22550348	C₂	semidirect
23. D₄²×C₁₂₇	C₂	semidirect
24. C₂⁴×D₁₂₇	C₂²	semidirect
26. C₂×#14523248	C₂²	semidirect
27. C₂×#14523248	C₂²	semidirect
28. C₂×#14523247	C₂²	semidirect
29. C₂×#14523247	C₂²	semidirect
30. C₂×#14523247	C₂²	semidirect
31. C₂²×D₅₀₈	C₂²	semidirect
32. C₂²×C₂²⋊D₁₂₇	C₂²	semidirect
33. C₂²×C₂²⋊D₁₂₇	C₂²	semidirect
34. C₂²×C₂²⋊D₁₂₇	C₂²	semidirect
35. C₂²×C₂²⋊D₁₂₇	C₂²	semidirect
38. C₂×D₄×D₁₂₇	C₂²	semidirect
39. C₂×D₄×D₁₂₇	C₂²	semidirect
40. C₂×D₄×D₁₂₇	C₂²	semidirect
41. C₂×D₄×D₁₂₇	C₂²	semidirect
42. C₂×D₄×D₁₂₇	C₂²	semidirect
43. C₂×D₄×D₁₂₇	C₂²	semidirect
44. C₂×D₄×D₁₂₇	C₂²	semidirect
45. C₂×D₄×D₁₂₇	C₂²	semidirect
46. C₂×D₄×D₁₂₇	C₂²	semidirect
47. C₂²×C₄×D₁₂₇	C₂²	semidirect
48. #16861205	C₂²	semidirect
49. #16861205	C₂²	semidirect
50. #16861197	C₂²	semidirect
51. #16861196	C₂²	semidirect
52. #16861195	C₂²	semidirect
53. #16861194	C₂²	semidirect
54. #16861194	C₂²	semidirect
55. #16861193	C₂²	semidirect
56. #16861191	C₂²	semidirect
57. #16861191	C₂²	semidirect
58. #16861191	C₂²	semidirect
59. #16861190	C₂²	semidirect
60. #16861189	C₂²	semidirect
61. #16861188	C₂²	semidirect
62. #16861187	C₂²	semidirect
63. #16861186	C₂²	semidirect
64. #16861184	C₂²	semidirect
65. #16861183	C₂²	semidirect
66. #16861183	C₂²	semidirect
67. #16861182	C₂²	semidirect
68. #16861182	C₂²	semidirect
69. #16861182	C₂²	semidirect
70. #16861181	C₂²	semidirect
71. #16861181	C₂²	semidirect
72. #16861181	C₂²	semidirect
73. #16861181	C₂²	semidirect
74. #16861181	C₂²	semidirect
75. #16861180	C₂²	semidirect
76. #16861180	C₂²	semidirect
77. #16861180	C₂²	semidirect
78. #16861180	C₂²	semidirect
79. #16861179	C₂²	semidirect
80. #16861179	C₂²	semidirect
81. #16861179	C₂²	semidirect
82. #16861179	C₂²	semidirect
83. #16861178	C₂²	semidirect
84. #16861178	C₂²	semidirect
85. #16861177	C₂²	semidirect
86. #16861177	C₂²	semidirect
87. #16861177	C₂²	semidirect
88. #16861177	C₂²	semidirect
89. #16861177	C₂²	semidirect
90. #16861177	C₂²	semidirect
91. #16861177	C₂²	semidirect
92. #16861177	C₂²	semidirect
93. #16861177	C₂²	semidirect
94. #16861177	C₂²	semidirect
95. #16861177	C₂²	semidirect
96. C₄×D₅₀₈	C₂²	semidirect
97. C₄×D₅₀₈	C₂²	semidirect
98. D₄×Dic₁₂₇	C₂²	semidirect
99. D₄×Dic₁₂₇	C₂²	semidirect
100. #16861171	C₂²	semidirect
101. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
102. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
103. C₄×C₂²⋊D₁₂₇	C₂²	semidirect
104. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
105. (C₂²⋊D₁₂₇)⋊C₄	C₂²	semidirect
106. #16861167	C₂²	semidirect
107. #16861166	C₂²	semidirect
108. C₂×C₂²⋊Dic₁₂₇	C₂²	semidirect
109. C₂×(C₂×D₁₂₇)⋊C₄	C₂²	semidirect
110. C₂×(C₂×D₁₂₇)⋊C₄	C₂²	semidirect
111. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
112. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
113. C₂²⋊C₄×D₁₂₇	C₂²	semidirect
114. C₂²×D₄×C₁₂₇	C₂²	semidirect
115. C₂²×D₄×C₁₂₇	C₂²	semidirect
116. C₂²×D₄×C₁₂₇	C₂²	semidirect
117. #127×C₁₂₇	C₂²	semidirect
118. #121×C₁₂₇	C₂²	semidirect
119. #121×C₁₂₇	C₂²	semidirect
120. #121×C₁₂₇	C₂²	semidirect
121. #120×C₁₂₇	C₂²	semidirect
122. #120×C₁₂₇	C₂²	semidirect
123. C₄×D₄×C₁₂₇	C₂²	semidirect
124. C₄×D₄×C₁₂₇	C₂²	semidirect
134. C₂³×D₁₂₇	C₂³	semidirect
140. C₂×Dic₂₅₄	C₂³	semidirect
141. C₂×Dic₂₅₄	C₂³	semidirect
148. C₂×D₅₀₈	C₂³	semidirect
162. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
163. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
164. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
165. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
166. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
167. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
168. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
169. C₂×C₂²⋊D₁₂₇	C₂³	semidirect
179. D₄×D₁₂₇	D₄	semidirect
181. C₂²×Dic₁₂₇	C₂³	semidirect
182. C₂²×Dic₁₂₇	C₂³	semidirect
183. C₂²×Dic₁₂₇	C₂³	semidirect
189. C₂×C₄×D₁₂₇	C₂³	semidirect
190. C₂×C₄×D₁₂₇	C₂³	semidirect
191. C₂×C₄×D₁₂₇	C₂³	semidirect
192. C₂×C₄×D₁₂₇	C₂³	semidirect
193. C₄⋊Dic₁₂₇	C₂³	semidirect
194. C₄⋊Dic₁₂₇	C₂³	semidirect
195. C₄⋊Dic₁₂₇	C₂³	semidirect
196. Dic₁₂₇⋊C₄	C₂³	semidirect
197. Dic₁₂₇⋊C₄	C₂³	semidirect
198. Dic₁₂₇⋊C₄	C₂³	semidirect
199. Dic₁₂₇⋊C₄	C₂³	semidirect
200. Dic₁₂₇⋊C₄	C₂³	semidirect
203. C₂²⋊Dic₁₂₇	C₂³	semidirect
204. C₂²⋊Dic₁₂₇	C₂³	semidirect
205. C₂²⋊Dic₁₂₇	C₂³	semidirect
206. C₂²⋊Dic₁₂₇	C₂³	semidirect
207. C₂²⋊Dic₁₂₇	C₂³	semidirect
208. C₂²⋊Dic₁₂₇	C₂³	semidirect
215. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
216. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
217. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
218. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
219. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
220. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
221. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
222. (C₂×D₁₂₇)⋊C₄	C₂³	semidirect
223. C₄×Dic₁₂₇	C₂³	semidirect
224. C₄×Dic₁₂₇	C₂³	semidirect
226. C₂⁴×C₁₂₇	C₂³	semidirect
235. C₂×D₄×C₁₂₇	C₂³	semidirect
236. C₂×D₄×C₁₂₇	C₂³	semidirect
237. C₂×D₄×C₁₂₇	C₂³	semidirect
238. C₂×D₄×C₁₂₇	C₂³	semidirect
239. C₂×D₄×C₁₂₇	C₂³	semidirect
241. C₂²×C₄×C₁₂₇	C₂³	semidirect
242. C₂²×C₄×C₁₂₇	C₂³	semidirect
243. C₄⋊C₄×C₁₂₇	C₂³	semidirect
244. C₄⋊C₄×C₁₂₇	C₂³	semidirect
246. C₂²⋊C₄×C₁₂₇	C₂³	semidirect
247. C₂²⋊C₄×C₁₂₇	C₂³	semidirect
248. C₂²⋊C₄×C₁₂₇	C₂³	semidirect
249. C₂²⋊C₄×C₁₂₇	C₂³	semidirect
250. C₄²×C₁₂₇	C₂³	semidirect
272. C₂²×D₁₂₇	C₂×D₄	semidirect
285. D₅₀₈	C₂×D₄	semidirect
302. C₂²⋊D₁₂₇	C₂×D₄	semidirect
321. C₄×D₁₂₇	C₂×D₄	semidirect
342. D₄×C₁₂₇	C₂×D₄	semidirect
368. C₂²×C₁₂₇	H(5,𝔽₂)	semidirect
391. C₂×D₁₂₇	H(5,𝔽₂)	semidirect
419. C₁₂₇	#3484	semidirect
433. D₄²	D₁₂₇	semidirect
466. C₂²×D₄	C₂×D₁₂₇	semidirect
467. C₂²×D₄	C₂×D₁₂₇	semidirect
468. C₂²×D₄	C₂×D₁₂₇	semidirect
472. #127	C₂×D₁₂₇	semidirect
502. #121	C₂×D₁₂₇	semidirect
503. #121	C₂×D₁₂₇	semidirect
504. #121	C₂×D₁₂₇	semidirect
522. #120	C₂×D₁₂₇	semidirect
523. #120	C₂×D₁₂₇	semidirect
534. C₄×D₄	C₂×D₁₂₇	semidirect
535. C₄×D₄	C₂×D₁₂₇	semidirect
555. C₂⁴	C₂²×D₁₂₇	semidirect
609. C₂×D₄	C₂²×D₁₂₇	semidirect
610. C₂×D₄	C₂²×D₁₂₇	semidirect
611. C₂×D₄	C₂²×D₁₂₇	semidirect
612. C₂×D₄	C₂²×D₁₂₇	semidirect
613. C₂×D₄	C₂²×D₁₂₇	semidirect
628. C₂²×C₄	C₂²×D₁₂₇	semidirect
629. C₂²×C₄	C₂²×D₁₂₇	semidirect
638. C₄⋊C₄	C₂²×D₁₂₇	semidirect
639. C₄⋊C₄	C₂²×D₁₂₇	semidirect
663. C₂²⋊C₄	C₂²×D₁₂₇	semidirect
664. C₂²⋊C₄	C₂²×D₁₂₇	semidirect
665. C₂²⋊C₄	C₂²×D₁₂₇	semidirect
666. C₂²⋊C₄	C₂²×D₁₂₇	semidirect
669. C₄²	C₂²×D₁₂₇	semidirect
742. D₄	D₄×D₁₂₇	semidirect
809. C₂²	#16861254	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16861254	2
C₂²×D₄×D₁₂₇	2
#22550523	2
#22550522	2
#22550521	2
#22550520	2
#22550515	2
#22550513	2
#22550511	2
#22550510	2
D₄×C₂²⋊D₁₂₇	2
#22550508	2
#22550442	2
#22550439	2
#22550436	2
#22550434	2
#22550386	2
#22550385	2
C₂×#16861177	2
#120×D₁₂₇	2
#22550348	2
D₄²×C₁₂₇	2
#3484	127