Subgroups — #28350719

Order 13696.

1050 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20293368	C₂	1	1	yes	maximal, characteristic, complemented
2	#20293367	C₂	1	1	yes	maximal, characteristic, complemented
3	#20293367	C₂	1	1	yes	maximal, characteristic, complemented
4	#20293365	C₂	1	1	yes	maximal, characteristic, complemented
5	#20293330	C₂	1	1	yes	maximal, characteristic, complemented
6	#20293328	C₂	1	1	yes	maximal, characteristic, complemented
7	#20293328	C₂	1	1	yes	maximal, characteristic, complemented
8	#20293326	C₂	1	1	yes	maximal, characteristic, complemented
9	#20293325	C₂	1	1	yes	maximal, characteristic, complemented
10	#20293322	C₂	1	1	yes	maximal, characteristic, complemented
11	#20293313	C₂	1	1	yes	maximal, characteristic, complemented
12	#20293309	C₂	1	1	yes	maximal, characteristic, complemented
13	#20293298	C₂	1	1	yes	maximal, characteristic, complemented
14	#20293295	C₂	1	1	yes	maximal, characteristic, complemented
15	#20293278	C₂	1	1	yes	maximal, characteristic, complemented
16	#20293275	C₂	1	1	yes	maximal, characteristic, complemented
17	#20293236	C₂	1	1	yes	maximal, characteristic, complemented
18	#20293233	C₂	1	1	yes	maximal, characteristic, complemented
19	#20293229	C₂	1	1	yes	maximal, characteristic, complemented
20	#20293229	C₂	1	1	yes	maximal, characteristic, complemented
21	#20293229	C₂	1	1	yes	maximal, characteristic, complemented
22	#20293228	C₂	1	1	yes	maximal, characteristic, complemented
23	#20293226	C₂	1	1	yes	maximal, characteristic, complemented
24	#20293223	C₂	1	1	yes	maximal, characteristic, complemented
25	#20293223	C₂	1	1	yes	maximal, characteristic, complemented
26	#20293207	C₂	1	1	yes	maximal, characteristic, complemented
27	#20293207	C₂	1	1	yes	maximal, characteristic, complemented
28	#20293140	C₂	1	1	yes	maximal, characteristic, complemented
29	#20293136	C₂	1	1	yes	maximal, characteristic, complemented
30	#20293135	C₂	1	1	yes	maximal, characteristic, complemented
31	#539×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133819	C₂²	1	1	yes	characteristic
33	C₂×#13133818	C₂²	1	1	yes	characteristic
34	C₂×#13133818	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13133818	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13133817	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₁₀₇	C₂²	1	1	yes	characteristic
38	#16812108	C₂²	1	1	yes	characteristic, complemented
39	#16812106	C₂²	1	1	yes	characteristic
40	#16812105	C₂²	1	1	yes	characteristic
41	#16812105	C₂²	1	1	yes	characteristic
42	#16812105	C₂²	1	1	yes	characteristic
43	#16812105	C₂²	1	1	yes	characteristic, complemented
44	#16812104	C₂²	1	1	yes	characteristic
45	#16812104	C₂²	1	1	yes	characteristic
46	#16812104	C₂²	1	1	yes	characteristic
47	#16812104	C₂²	1	1	yes	characteristic
48	#16812104	C₂²	1	1	yes	characteristic
49	#16812104	C₂²	1	1	yes	characteristic, complemented
50	#16812104	C₂²	1	1	yes	characteristic, complemented
51	#16812103	C₂²	1	1	yes	characteristic
52	#16812102	C₂²	1	1	yes	characteristic
53	#16812102	C₂²	1	1	yes	characteristic, complemented
54	#16812100	C₂²	1	1	yes	characteristic, complemented
55	#16812100	C₂²	1	1	yes	characteristic, complemented
56	#16812099	C₂²	1	1	yes	characteristic, complemented
57	#16812099	C₂²	1	1	yes	characteristic, complemented
58	#16812099	C₂²	1	1	yes	characteristic, complemented
59	#16812099	C₂²	1	1	yes	characteristic, complemented
60	#16812099	C₂²	1	1	yes	characteristic, complemented
61	#16812099	C₂²	1	1	yes	characteristic, complemented
62	#16812094	C₂²	1	1	yes	characteristic
63	#16812094	C₂²	1	1	yes	characteristic
64	#16812094	C₂²	1	1	yes	characteristic
65	#16812094	C₂²	1	1	yes	characteristic
66	#16812094	C₂²	1	1	yes	characteristic
67	#16812094	C₂²	1	1	yes	characteristic
68	#16812094	C₂²	1	1	yes	characteristic
69	#16812094	C₂²	1	1	yes	characteristic, complemented
70	#16812094	C₂²	1	1	yes	characteristic, complemented
71	#16812094	C₂²	1	1	yes	characteristic, complemented
72	#16812093	C₂²	1	1	yes	characteristic
73	#16812093	C₂²	1	1	yes	characteristic, complemented
74	#16812093	C₂²	1	1	yes	characteristic, complemented
75	#16812092	C₂²	1	1	yes	characteristic
76	#16812092	C₂²	1	1	yes	characteristic
77	#16812092	C₂²	1	1	yes	characteristic, complemented
78	#16812091	C₂²	1	1	yes	characteristic
79	#16812091	C₂²	1	1	yes	characteristic
80	#16812091	C₂²	1	1	yes	characteristic
81	#16812091	C₂²	1	1	yes	characteristic
82	#16812091	C₂²	1	1	yes	characteristic
83	#16812091	C₂²	1	1	yes	characteristic, complemented
84	#16812087	C₂²	1	1	yes	characteristic
85	#16812087	C₂²	1	1	yes	characteristic
86	#16812087	C₂²	1	1	yes	characteristic
87	#16812087	C₂²	1	1	yes	characteristic, complemented
88	#16812087	C₂²	1	1	yes	characteristic, complemented
89	#16812086	C₂²	1	1	yes	characteristic
90	#16812085	C₂²	1	1	yes	characteristic
91	#16812085	C₂²	1	1	yes	characteristic, complemented
92	#16812085	C₂²	1	1	yes	characteristic, complemented
93	#16812084	C₂²	1	1	yes	characteristic
94	#16812084	C₂²	1	1	yes	characteristic
95	#16812084	C₂²	1	1	yes	characteristic
96	#16812084	C₂²	1	1	yes	characteristic
97	#16812084	C₂²	1	1	yes	characteristic
98	#16812084	C₂²	1	1	yes	characteristic
99	#16812084	C₂²	1	1	yes	characteristic
100	#16812084	C₂²	1	1	yes	characteristic
101	#16812084	C₂²	1	1	yes	characteristic, complemented
102	#16812084	C₂²	1	1	yes	characteristic, complemented
103	#16812084	C₂²	1	1	yes	characteristic, complemented
104	#16812083	C₂²	1	1	yes	characteristic
105	#16812083	C₂²	1	1	yes	characteristic
106	#16812083	C₂²	1	1	yes	characteristic
107	#16812083	C₂²	1	1	yes	characteristic
108	#16812083	C₂²	1	1	yes	characteristic
109	#16812083	C₂²	1	1	yes	characteristic
110	#16812083	C₂²	1	1	yes	characteristic, complemented
111	#16812082	C₂²	1	1	yes	characteristic
112	#16812082	C₂²	1	1	yes	characteristic
113	#16812082	C₂²	1	1	yes	characteristic
114	#16812082	C₂²	1	1	yes	characteristic
115	#16812082	C₂²	1	1	yes	characteristic
116	#16812082	C₂²	1	1	yes	characteristic
117	#16812082	C₂²	1	1	yes	characteristic
118	#16812082	C₂²	1	1	yes	characteristic
119	#16812082	C₂²	1	1	yes	characteristic
120	#16812082	C₂²	1	1	yes	characteristic
121	#16812082	C₂²	1	1	yes	characteristic
122	#16812082	C₂²	1	1	yes	characteristic, complemented
123	#16812082	C₂²	1	1	yes	characteristic, complemented
124	#16812082	C₂²	1	1	yes	characteristic, complemented
125	#16812082	C₂²	1	1	yes	characteristic, complemented
126	#16812082	C₂²	1	1	yes	characteristic, complemented
127	#16812081	C₂²	1	1	yes	characteristic
128	#16812081	C₂²	1	1	yes	characteristic
129	#16812081	C₂²	1	1	yes	characteristic
130	#16812081	C₂²	1	1	yes	characteristic, complemented
131	#16812080	C₂²	1	1	yes	characteristic
132	#16812079	C₂²	1	1	yes	characteristic
133	#16812079	C₂²	1	1	yes	characteristic
134	#16812079	C₂²	1	1	yes	characteristic
135	#16812079	C₂²	1	1	yes	characteristic
136	#16812077	C₂²	1	1	yes	characteristic
137	#16812077	C₂²	1	1	yes	characteristic
138	C₄×Dic₂₁₄	C₂²	1	1	yes	characteristic, complemented
139	#16812074	C₂²	1	1	yes	characteristic, complemented
140	C₄×D₄₂₈	C₂²	1	1	yes	characteristic
141	C₄×D₄₂₈	C₂²	1	1	yes	characteristic, complemented
142	#16812071	C₂²	1	1	yes	characteristic
143	#16812071	C₂²	1	1	yes	characteristic
144	#16812071	C₂²	1	1	yes	characteristic
145	#16812071	C₂²	1	1	yes	characteristic
146	#16812071	C₂²	1	1	yes	characteristic, complemented
147	#16812071	C₂²	1	1	yes	characteristic, complemented
148	C₄×C₂²⋊D₁₀₇	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊D₁₀₇	C₂²	1	1	yes	characteristic
150	C₄×C₂²⋊D₁₀₇	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊D₁₀₇	C₂²	1	1	yes	characteristic, complemented
152	C₄×C₂²⋊D₁₀₇	C₂²	1	1	yes	characteristic, complemented
153	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic
154	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic
155	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic
156	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic
157	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
158	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
159	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
160	#16812067	C₂²	1	1	yes	characteristic
161	#16812067	C₂²	1	1	yes	characteristic, complemented
162	#16812067	C₂²	1	1	yes	characteristic, complemented
163	#16812066	C₂²	1	1	yes	characteristic
164	#16812066	C₂²	1	1	yes	characteristic, complemented
165	#16812066	C₂²	1	1	yes	characteristic, complemented
166	#16812065	C₂²	1	1	yes	characteristic
167	C₂×Dic₁₀₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
168	C₄⋊C₄×D₁₀₇	C₂²	1	1	yes	characteristic, complemented
169	C₄⋊C₄×D₁₀₇	C₂²	1	1	yes	characteristic, complemented
170	C₄⋊C₄×D₁₀₇	C₂²	1	1	yes	characteristic, complemented
171	C₄⋊C₄×D₁₀₇	C₂²	1	1	yes	characteristic, complemented
172	#126×C₁₀₇	C₂²	1	1	yes	characteristic
173	#126×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
174	#125×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
175	#125×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
176	#123×C₁₀₇	C₂²	1	1	yes	characteristic
177	#123×C₁₀₇	C₂²	1	1	yes	characteristic
178	#123×C₁₀₇	C₂²	1	1	yes	characteristic
179	#123×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
181	C₂²⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
182	C₂²⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
183	#121×C₁₀₇	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
185	C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₀₇	C₂³	1	1	yes	characteristic
188	#13133819	—	4	2	no	—
189	#13133818	—	4	2	no	—
190	#13133818	—	4	2	no	—
191	#13133818	—	4	2	no	—
192	#13133817	—	4	2	no	—
193	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
194	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
195	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
196	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
197	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
198	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
199	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
200	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
201	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
202	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
203	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
204	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
205	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
206	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
207	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
208	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
219	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
223	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
224	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
225	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
226	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
227	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₁₀₇	—	4	2	no	—
229	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
245	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
246	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
247	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
248	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
249	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
250	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
251	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
252	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
253	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
259	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
260	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
261	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
262	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
263	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
264	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
265	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
266	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
267	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
268	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
269	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
270	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
271	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
272	Dic₁₀₇⋊C₄	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
277	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₁₀₇)⋊C₄	C₂³	1	1	yes	characteristic
305	C₄×Dic₁₀₇	C₂³	1	1	yes	characteristic
306	C₄×Dic₁₀₇	C₂³	1	1	yes	characteristic
307	C₄×Dic₁₀₇	C₂³	1	1	yes	characteristic
308	C₄×Dic₁₀₇	C₂³	1	1	yes	characteristic
309	C₄×Dic₁₀₇	C₂³	1	1	yes	characteristic
310	C₄×Dic₁₀₇	C₂³	1	1	yes	characteristic
311	C₄×Dic₁₀₇	C₂³	1	1	yes	characteristic
312	C₄×Dic₁₀₇	C₂³	1	1	yes	characteristic
313	C₂×Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
314	C₂×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
317	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
318	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
319	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
320	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
321	C₂²×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
324	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
335	C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
346	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
347	C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
348	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
349	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
350	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
351	C₂²×D₁₀₇	—	4	1	no	—
352	C₂²×D₁₀₇	—	4	1	no	—
353	C₂²×D₁₀₇	—	4	1	no	—
354	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
355	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
356	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
357	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
358	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
359	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
360	Q₈×C₁₀₇	—	4	1	no	—
361	D₄×C₁₀₇	—	4	1	no	—
362	D₄×C₁₀₇	—	4	1	no	—
363	D₄×C₁₀₇	—	4	1	no	—
364	C₂×C₄×C₁₀₇	—	4	1	no	—
365	C₂×C₄×C₁₀₇	—	4	1	no	—
366	C₂×C₄×C₁₀₇	—	4	1	no	—
367	C₂×C₄×C₁₀₇	—	4	1	no	—
368	C₂×C₄×C₁₀₇	—	4	1	no	—
369	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
378	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
381	C₂²⋊D₁₀₇	—	2	2	no	—
382	C₂²⋊D₁₀₇	—	2	2	no	—
383	C₂²⋊D₁₀₇	—	4	1	no	—
384	C₂²⋊D₁₀₇	—	4	1	no	—
385	C₂²⋊D₁₀₇	—	4	1	no	—
386	C₂²⋊D₁₀₇	—	4	1	no	—
387	C₂²⋊D₁₀₇	—	4	1	no	—
388	C₂²⋊D₁₀₇	—	4	1	no	—
389	C₂²⋊D₁₀₇	—	4	1	no	—
390	C₂²⋊D₁₀₇	—	4	1	no	—
391	C₂²⋊D₁₀₇	—	4	1	no	—
392	C₂²⋊D₁₀₇	—	4	1	no	—
393	C₂²⋊D₁₀₇	—	4	1	no	—
394	C₂²⋊D₁₀₇	—	4	1	no	—
395	C₂²⋊D₁₀₇	—	4	1	no	—
396	C₂²⋊D₁₀₇	—	4	1	no	—
397	C₂×Dic₁₀₇	—	2	2	no	—
398	C₂×Dic₁₀₇	—	4	1	no	—
399	C₂×Dic₁₀₇	—	4	1	no	—
400	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
410	D₄₂₈	—	4	1	no	—
411	D₄₂₈	—	4	1	no	—
412	D₄₂₈	—	4	1	no	—
413	D₄₂₈	—	4	1	no	—
414	D₄₂₈	—	4	1	no	—
415	D₄₂₈	—	4	1	no	—
416	D₄₂₈	—	4	1	no	—
417	D₄₂₈	—	4	1	no	—
418	D₄₂₈	—	4	1	no	—
419	D₄₂₈	—	4	1	no	—
420	D₄₂₈	—	4	1	no	—
421	D₄₂₈	—	4	1	no	—
422	D₄₂₈	—	4	1	no	—
423	D₄₂₈	—	4	1	no	—
424	C₄×D₁₀₇	—	2	2	no	—
425	C₄×D₁₀₇	—	2	2	no	—
426	C₄×D₁₀₇	—	2	2	no	—
427	C₄×D₁₀₇	—	2	2	no	—
428	C₄×D₁₀₇	—	4	1	no	—
429	C₄×D₁₀₇	—	4	1	no	—
430	C₄×D₁₀₇	—	4	1	no	—
431	C₄×D₁₀₇	—	4	1	no	—
432	C₄×D₁₀₇	—	4	1	no	—
433	C₄×D₁₀₇	—	4	1	no	—
434	C₄×D₁₀₇	—	4	1	no	—
435	C₄×D₁₀₇	—	4	1	no	—
436	C₄×D₁₀₇	—	4	1	no	—
437	C₄×D₁₀₇	—	4	1	no	—
438	C₄×D₁₀₇	—	4	1	no	—
439	C₄×D₁₀₇	—	4	1	no	—
440	Dic₂₁₄	—	2	2	no	—
441	Dic₂₁₄	—	2	2	no	—
442	C₂²×C₁₀₇	—	2	1	no	—
443	C₂²×C₁₀₇	—	2	1	no	—
444	C₂²×C₁₀₇	—	2	1	no	—
445	C₂²×C₁₀₇	—	2	1	no	—
446	C₂²×C₁₀₇	—	2	1	no	—
447	C₂²×C₁₀₇	—	2	1	no	—
448	C₂²×C₁₀₇	—	2	1	no	—
449	C₂²×C₁₀₇	—	2	1	no	—
450	C₂²×C₁₀₇	—	2	1	no	—
451	C₂²×C₁₀₇	C₂⁵	1	1	yes	characteristic
452	C₂×D₁₀₇	—	2	1	no	—
453	C₂×D₁₀₇	—	2	1	no	—
454	C₂×D₁₀₇	—	2	1	no	—
455	C₂×D₁₀₇	—	2	1	no	—
456	C₂×D₁₀₇	—	2	1	no	—
457	C₂×D₁₀₇	—	2	1	no	—
458	C₂×D₁₀₇	—	2	1	no	—
459	C₂×D₁₀₇	—	2	1	no	—
460	C₂×D₁₀₇	—	2	1	no	—
461	C₂×D₁₀₇	—	2	1	no	—
462	C₂×D₁₀₇	—	2	1	no	—
463	C₂×D₁₀₇	—	2	1	no	—
464	C₂×D₁₀₇	—	2	1	no	—
465	C₂×D₁₀₇	—	2	1	no	—
466	C₂×D₁₀₇	—	2	1	no	—
467	C₂×D₁₀₇	—	2	1	no	—
468	C₂×D₁₀₇	—	2	1	no	—
469	C₂×D₁₀₇	—	2	1	no	—
470	C₂×D₁₀₇	—	4	4	no	—
471	C₄×C₁₀₇	—	2	1	no	—
472	C₄×C₁₀₇	—	2	1	no	—
473	C₄×C₁₀₇	—	2	1	no	—
474	C₄×C₁₀₇	—	2	1	no	—
475	C₄×C₁₀₇	—	2	1	no	—
476	C₄×C₁₀₇	—	2	1	no	—
477	C₄×C₁₀₇	—	2	1	no	—
478	C₄×C₁₀₇	—	2	1	no	—
479	C₄×C₁₀₇	—	2	1	no	—
480	C₄×C₁₀₇	—	2	1	no	—
481	C₄×C₁₀₇	—	2	1	no	—
482	C₄×C₁₀₇	—	2	1	no	—
483	Dic₁₀₇	—	2	1	no	—
484	Dic₁₀₇	—	2	1	no	—
485	Dic₁₀₇	—	2	1	no	—
486	Dic₁₀₇	—	2	1	no	—
487	Dic₁₀₇	—	2	1	no	—
488	Dic₁₀₇	—	2	1	no	—
489	Dic₁₀₇	—	2	1	no	—
490	Dic₁₀₇	—	2	1	no	—
491	Dic₁₀₇	—	2	1	no	—
492	Dic₁₀₇	H(5,𝔽₂)	1	2	yes	—
493	C₂×C₁₀₇	—	4	1	no	—
494	C₂×C₁₀₇	—	4	1	no	—
495	C₂×C₁₀₇	—	4	1	no	—
496	C₂×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
497	C₂×C₁₀₇	#585	1	1	yes	characteristic
498	C₂×C₁₀₇	#585	1	1	yes	characteristic
499	D₁₀₇	—	4	1	no	—
500	D₁₀₇	—	4	1	no	—
501	D₁₀₇	—	4	1	no	—
502	D₁₀₇	—	4	1	no	—
503	D₁₀₇	—	4	1	no	—
504	D₁₀₇	—	4	1	no	—
505	#3539	—	107	1	no	maximal, Sylow
506	C₁₀₇	#3539	1	1	yes	characteristic, complemented, Sylow
507	#560	—	107	1	no	—
508	#560	—	107	1	no	—
509	#560	—	107	1	no	—
510	#560	—	107	1	no	—
511	#553	—	107	1	no	—
512	#553	—	107	1	no	—
513	#553	—	107	1	no	—
514	#553	—	107	1	no	—
515	#553	—	107	1	no	—
516	#553	—	107	1	no	—
517	#552	—	107	1	no	—
518	#552	—	107	1	no	—
519	#550	—	107	1	no	—
520	#550	—	107	1	no	—
521	#547	—	107	1	no	—
522	#547	—	107	1	no	—
523	#541	—	107	1	no	—
524	#540	—	107	1	no	—
525	#540	—	107	1	no	—
526	#540	—	107	1	no	—
527	#540	—	107	1	no	—
528	#540	—	107	1	no	—
529	#539	—	107	1	no	—
530	#539	—	107	1	no	—
531	#539	—	107	1	no	—
532	#539	D₁₀₇	1	1	yes	characteristic, complemented
533	#537	—	107	1	no	—
534	#537	—	107	1	no	—
535	#525	—	107	1	no	—
536	#525	—	107	1	no	—
537	#525	—	107	1	no	—
538	C₂×#41	—	107	1	no	—
539	C₂×#41	—	107	1	no	—
540	C₂×#41	—	107	1	no	—
541	C₂×#41	—	107	1	no	—
542	C₂×#41	—	107	1	no	—
543	C₂³×C₄	—	107	1	no	—
544	C₄⋊Q₈	—	107	1	no	—
545	#127	—	107	1	no	—
546	#127	—	107	1	no	—
547	#127	—	107	1	no	—
548	#127	—	107	1	no	—
549	#127	—	107	1	no	—
550	#126	—	107	1	no	—
551	#126	—	107	1	no	—
552	#126	—	107	1	no	—
553	#126	—	107	1	no	—
554	#126	—	107	1	no	—
555	#126	—	107	1	no	—
556	#126	—	107	1	no	—
557	#126	—	107	1	no	—
558	#126	—	107	1	no	—
559	#126	—	107	1	no	—
560	#126	C₂×D₁₀₇	1	1	yes	characteristic
561	#126	C₂×D₁₀₇	1	1	yes	characteristic, complemented
562	#125	—	107	1	no	—
563	#125	—	107	1	no	—
564	#125	—	107	1	no	—
565	#125	—	107	1	no	—
566	#125	—	107	1	no	—
567	#125	—	107	1	no	—
568	#125	—	107	1	no	—
569	#125	—	107	1	no	—
570	#125	C₂×D₁₀₇	1	1	yes	characteristic, complemented
571	#125	C₂×D₁₀₇	1	1	yes	characteristic, complemented
572	#123	—	107	1	no	—
573	#123	—	107	1	no	—
574	#123	—	107	1	no	—
575	#123	—	107	1	no	—
576	#123	—	107	1	no	—
577	#123	—	107	1	no	—
578	#123	—	107	1	no	—
579	#123	—	107	1	no	—
580	#123	—	107	1	no	—
581	#123	—	107	1	no	—
582	#123	—	107	1	no	—
583	#123	—	107	1	no	—
584	#123	—	107	1	no	—
585	#123	—	107	1	no	—
586	#123	—	107	1	no	—
587	#123	—	107	1	no	—
588	#123	—	107	1	no	—
589	#123	—	107	1	no	—
590	#123	—	107	1	no	—
591	#123	—	107	1	no	—
592	#123	—	107	1	no	—
593	#123	—	107	1	no	—
594	#123	C₂×D₁₀₇	1	1	yes	characteristic
595	#123	C₂×D₁₀₇	1	1	yes	characteristic
596	#123	C₂×D₁₀₇	1	1	yes	characteristic
597	#123	C₂×D₁₀₇	1	1	yes	characteristic, complemented
598	C₂²⋊Q₈	—	107	1	no	—
599	C₂²⋊Q₈	—	107	1	no	—
600	C₂²⋊Q₈	—	107	1	no	—
601	C₂²⋊Q₈	—	107	1	no	—
602	C₂²⋊Q₈	—	107	1	no	—
603	C₂²⋊Q₈	—	107	1	no	—
604	C₂²⋊Q₈	—	107	1	no	—
605	C₂²⋊Q₈	—	107	1	no	—
606	C₂²⋊Q₈	—	107	1	no	—
607	C₂²⋊Q₈	C₂×D₁₀₇	1	1	yes	characteristic
608	C₂²⋊Q₈	C₂×D₁₀₇	1	1	yes	characteristic, complemented
609	C₂²⋊Q₈	C₂×D₁₀₇	1	1	yes	characteristic, complemented
610	#121	—	107	1	no	—
611	#121	—	107	1	no	—
612	#121	—	107	1	no	—
613	#121	—	107	1	no	—
614	#121	—	107	1	no	—
615	#121	—	107	1	no	—
616	#121	—	107	1	no	—
617	#121	—	107	1	no	—
618	#121	—	107	1	no	—
619	#121	—	107	1	no	—
620	#121	—	107	1	no	—
621	#121	—	107	1	no	—
622	#121	—	107	1	no	—
623	#121	—	107	1	no	—
624	#121	—	107	1	no	—
625	#121	—	107	1	no	—
626	#121	—	107	1	no	—
627	#121	—	107	1	no	—
628	#121	—	107	1	no	—
629	#121	—	107	1	no	—
630	#121	—	107	1	no	—
631	#121	—	107	1	no	—
632	#121	—	107	1	no	—
633	#121	—	107	1	no	—
634	#121	—	107	1	no	—
635	#121	—	107	1	no	—
636	#121	—	107	1	no	—
637	#121	—	107	1	no	—
638	#121	—	107	1	no	—
639	#121	—	107	1	no	—
640	#121	—	107	1	no	—
641	#121	—	107	1	no	—
642	#121	—	107	1	no	—
643	#121	—	107	1	no	—
644	#121	—	107	1	no	—
645	#121	—	107	1	no	—
646	#121	—	107	1	no	—
647	#121	—	107	1	no	—
648	#121	—	107	1	no	—
649	#121	C₂×D₁₀₇	1	1	yes	characteristic
650	#120	—	107	1	no	—
651	#120	—	107	1	no	—
652	#120	—	107	1	no	—
653	#120	—	107	1	no	—
654	#120	—	107	1	no	—
655	#120	—	107	1	no	—
656	C₄×Q₈	—	107	1	no	—
657	C₄×Q₈	—	107	1	no	—
658	C₄×D₄	—	107	1	no	—
659	C₄×D₄	—	107	1	no	—
660	C₄×D₄	—	107	1	no	—
661	C₄×D₄	—	107	1	no	—
662	C₄×D₄	—	107	1	no	—
663	C₄×D₄	—	107	1	no	—
664	C₄×D₄	—	107	1	no	—
665	C₄×D₄	—	107	1	no	—
666	C₄×D₄	—	107	1	no	—
667	C₄×D₄	—	107	1	no	—
668	C₄×D₄	—	107	1	no	—
669	C₄×D₄	—	107	1	no	—
670	C₄×D₄	—	107	1	no	—
671	C₄×D₄	—	107	1	no	—
672	C₄×D₄	—	107	1	no	—
673	C₄×D₄	—	107	1	no	—
674	C₄×D₄	—	107	1	no	—
675	C₄×D₄	—	107	1	no	—
676	C₄×D₄	—	107	1	no	—
677	C₄×D₄	—	107	1	no	—
678	C₄×D₄	C₂×D₁₀₇	1	1	yes	characteristic
679	C₄×D₄	C₂×D₁₀₇	1	1	yes	characteristic, complemented
680	#117	—	107	1	no	—
681	#117	—	107	1	no	—
682	#117	—	107	1	no	—
683	#117	—	107	1	no	—
684	#117	—	107	1	no	—
685	#117	—	107	1	no	—
686	#117	—	107	1	no	—
687	C₂×C₄⋊C₄	—	107	1	no	—
688	C₂×C₄⋊C₄	—	107	1	no	—
689	C₂×C₄⋊C₄	—	107	1	no	—
690	C₂×C₄⋊C₄	—	107	1	no	—
691	C₂×C₄⋊C₄	—	107	1	no	—
692	C₂×C₄⋊C₄	C₂×D₁₀₇	1	1	yes	characteristic, complemented
693	C₂⁴	—	107	1	no	—
694	#41	—	428	2	no	—
695	#41	—	428	2	no	—
696	#41	—	428	2	no	—
697	#41	—	428	2	no	—
698	#41	—	428	2	no	—
699	C₂×Q₈	—	107	1	no	—
700	C₂×Q₈	—	107	1	no	—
701	C₂×Q₈	C₂²×D₁₀₇	1	1	yes	characteristic
702	C₂×D₄	—	107	1	no	—
703	C₂×D₄	—	107	1	no	—
704	C₂×D₄	—	107	1	no	—
705	C₂×D₄	—	107	1	no	—
706	C₂×D₄	—	107	1	no	—
707	C₂×D₄	—	107	1	no	—
708	C₂×D₄	—	107	1	no	—
709	C₂×D₄	—	107	1	no	—
710	C₂×D₄	—	107	1	no	—
711	C₂×D₄	—	107	1	no	—
712	C₂×D₄	—	107	1	no	—
713	C₂×D₄	—	107	1	no	—
714	C₂×D₄	—	107	1	no	—
715	C₂×D₄	—	107	1	no	—
716	C₂×D₄	—	107	1	no	—
717	C₂×D₄	—	107	1	no	—
718	C₂×D₄	—	107	1	no	—
719	C₂×D₄	—	107	1	no	—
720	C₂×D₄	—	107	1	no	—
721	C₂×D₄	—	107	1	no	—
722	C₂×D₄	—	107	1	no	—
723	C₂×D₄	—	107	1	no	—
724	C₂×D₄	—	107	1	no	—
725	C₂×D₄	—	107	1	no	—
726	C₂×D₄	—	107	1	no	—
727	C₂×D₄	—	107	1	no	—
728	C₂×D₄	—	107	1	no	—
729	C₂×D₄	—	107	1	no	—
730	C₂×D₄	—	107	1	no	—
731	C₂×D₄	—	107	1	no	—
732	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
733	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
734	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
735	C₂²×C₄	—	107	1	no	—
736	C₂²×C₄	—	107	1	no	—
737	C₂²×C₄	—	107	1	no	—
738	C₂²×C₄	—	107	1	no	—
739	C₂²×C₄	—	107	1	no	—
740	C₂²×C₄	—	107	1	no	—
741	C₂²×C₄	—	107	1	no	—
742	C₂²×C₄	—	107	1	no	—
743	C₂²×C₄	—	107	1	no	—
744	C₂²×C₄	—	107	1	no	—
745	C₂²×C₄	—	107	1	no	—
746	C₂²×C₄	—	107	1	no	—
747	C₂²×C₄	—	107	1	no	—
748	C₂²×C₄	—	107	1	no	—
749	C₂²×C₄	—	107	1	no	—
750	C₂²×C₄	—	107	1	no	—
751	C₂²×C₄	—	107	1	no	—
752	C₂²×C₄	—	107	1	no	—
753	C₂²×C₄	—	107	1	no	—
754	C₂²×C₄	—	428	2	no	—
755	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
758	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
759	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
760	C₄⋊C₄	—	107	1	no	—
761	C₄⋊C₄	—	107	1	no	—
762	C₄⋊C₄	—	107	1	no	—
763	C₄⋊C₄	—	107	1	no	—
764	C₄⋊C₄	—	107	1	no	—
765	C₄⋊C₄	—	107	1	no	—
766	C₄⋊C₄	—	107	1	no	—
767	C₄⋊C₄	—	107	1	no	—
768	C₄⋊C₄	—	107	1	no	—
769	C₄⋊C₄	—	107	1	no	—
770	C₄⋊C₄	—	107	1	no	—
771	C₄⋊C₄	—	107	1	no	—
772	C₄⋊C₄	—	107	1	no	—
773	C₄⋊C₄	—	107	1	no	—
774	C₄⋊C₄	—	107	1	no	—
775	C₄⋊C₄	—	107	1	no	—
776	C₄⋊C₄	—	107	1	no	—
777	C₄⋊C₄	—	107	1	no	—
778	C₄⋊C₄	—	107	1	no	—
779	C₄⋊C₄	—	107	1	no	—
780	C₄⋊C₄	—	107	1	no	—
781	C₄⋊C₄	—	107	1	no	—
782	C₄⋊C₄	—	107	1	no	—
783	C₄⋊C₄	—	107	1	no	—
784	C₄⋊C₄	—	107	1	no	—
785	C₄⋊C₄	—	107	1	no	—
786	C₄⋊C₄	—	107	1	no	—
787	C₄⋊C₄	—	107	1	no	—
788	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
796	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
797	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
798	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
799	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
800	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
801	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
802	C₂²⋊C₄	—	107	1	no	—
803	C₂²⋊C₄	—	107	1	no	—
804	C₂²⋊C₄	—	107	1	no	—
805	C₂²⋊C₄	—	107	1	no	—
806	C₂²⋊C₄	—	107	1	no	—
807	C₂²⋊C₄	—	107	1	no	—
808	C₂²⋊C₄	—	107	1	no	—
809	C₂²⋊C₄	—	107	1	no	—
810	C₂²⋊C₄	—	107	1	no	—
811	C₂²⋊C₄	—	107	1	no	—
812	C₂²⋊C₄	—	107	1	no	—
813	C₂²⋊C₄	—	107	1	no	—
814	C₂²⋊C₄	—	107	1	no	—
815	C₂²⋊C₄	—	107	1	no	—
816	C₂²⋊C₄	—	107	1	no	—
817	C₂²⋊C₄	—	107	1	no	—
818	C₂²⋊C₄	—	107	1	no	—
819	C₂²⋊C₄	—	107	1	no	—
820	C₂²⋊C₄	—	107	1	no	—
821	C₂²⋊C₄	—	107	1	no	—
822	C₂²⋊C₄	—	107	1	no	—
823	C₂²⋊C₄	—	107	1	no	—
824	C₂²⋊C₄	—	107	1	no	—
825	C₂²⋊C₄	—	107	1	no	—
826	C₂²⋊C₄	—	107	1	no	—
827	C₂²⋊C₄	—	107	1	no	—
828	C₂²⋊C₄	—	107	1	no	—
829	C₂²⋊C₄	—	107	1	no	—
830	C₂²⋊C₄	—	107	1	no	—
831	C₂²⋊C₄	—	107	1	no	—
832	C₂²⋊C₄	—	107	1	no	—
833	C₂²⋊C₄	—	107	1	no	—
834	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
844	C₄²	—	107	1	no	—
845	C₄²	—	107	1	no	—
846	C₄²	—	107	1	no	—
847	C₄²	—	107	1	no	—
848	C₄²	—	107	1	no	—
849	C₄²	—	107	1	no	—
850	C₄²	—	107	1	no	—
851	C₄²	—	107	1	no	—
852	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
853	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
854	C₂³	—	107	1	no	—
855	C₂³	—	107	1	no	—
856	C₂³	—	107	1	no	—
857	C₂³	—	107	1	no	—
858	C₂³	—	107	1	no	—
859	C₂³	—	107	1	no	—
860	C₂³	—	428	1	no	—
861	C₂³	—	428	1	no	—
862	C₂³	—	428	1	no	—
863	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
864	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
865	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
866	Q₈	—	4	1	no	—
867	Q₈	—	214	2	no	—
868	Q₈	—	214	2	no	—
869	D₄	—	4	1	no	—
870	D₄	—	4	1	no	—
871	D₄	—	4	1	no	—
872	D₄	—	428	1	no	—
873	D₄	—	428	1	no	—
874	D₄	—	428	1	no	—
875	D₄	—	428	1	no	—
876	D₄	—	428	1	no	—
877	D₄	—	428	1	no	—
878	D₄	—	428	1	no	—
879	D₄	—	428	1	no	—
880	D₄	—	428	1	no	—
881	D₄	—	428	1	no	—
882	D₄	—	428	1	no	—
883	D₄	—	428	1	no	—
884	D₄	—	428	1	no	—
885	D₄	—	428	1	no	—
886	D₄	—	428	1	no	—
887	D₄	—	428	1	no	—
888	D₄	—	428	1	no	—
889	D₄	—	428	1	no	—
890	D₄	—	428	1	no	—
891	D₄	—	428	1	no	—
892	D₄	—	428	1	no	—
893	D₄	—	428	1	no	—
894	D₄	—	428	1	no	—
895	D₄	—	428	1	no	—
896	D₄	—	428	1	no	—
897	D₄	—	428	1	no	—
898	D₄	—	428	1	no	—
899	D₄	—	428	1	no	—
900	D₄	—	214	2	no	—
901	D₄	—	214	2	no	—
902	C₂×C₄	—	4	1	no	—
903	C₂×C₄	—	4	1	no	—
904	C₂×C₄	—	4	1	no	—
905	C₂×C₄	—	4	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	107	1	no	—
908	C₂×C₄	—	107	1	no	—
909	C₂×C₄	—	107	1	no	—
910	C₂×C₄	—	107	1	no	—
911	C₂×C₄	—	107	1	no	—
912	C₂×C₄	—	107	1	no	—
913	C₂×C₄	—	107	1	no	—
914	C₂×C₄	—	107	1	no	—
915	C₂×C₄	—	107	1	no	—
916	C₂×C₄	—	107	1	no	—
917	C₂×C₄	—	428	1	no	—
918	C₂×C₄	—	428	1	no	—
919	C₂×C₄	—	428	1	no	—
920	C₂×C₄	—	428	1	no	—
921	C₂×C₄	—	428	1	no	—
922	C₂×C₄	—	428	1	no	—
923	C₂×C₄	—	428	1	no	—
924	C₂×C₄	—	428	1	no	—
925	C₂×C₄	—	428	1	no	—
926	C₂×C₄	—	428	1	no	—
927	C₂×C₄	—	428	1	no	—
928	C₂×C₄	—	428	1	no	—
929	C₂×C₄	—	428	1	no	—
930	C₂×C₄	—	428	1	no	—
931	C₂×C₄	—	214	2	no	—
932	C₂×C₄	—	214	2	no	—
933	C₂×C₄	—	214	2	no	—
934	C₂×C₄	—	214	2	no	—
935	C₂×C₄	—	214	2	no	—
936	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
937	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
938	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
939	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
948	C₂²	—	2	1	no	—
949	C₂²	—	2	1	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	428	4	no	—
958	C₂²	—	214	1	no	—
959	C₂²	—	214	1	no	—
960	C₂²	—	214	1	no	—
961	C₂²	—	214	1	no	—
962	C₂²	—	214	1	no	—
963	C₂²	—	214	1	no	—
964	C₂²	—	214	1	no	—
965	C₂²	—	214	1	no	—
966	C₂²	—	214	1	no	—
967	C₂²	—	214	1	no	—
968	C₂²	—	214	1	no	—
969	C₂²	—	214	1	no	—
970	C₂²	—	214	1	no	—
971	C₂²	—	214	1	no	—
972	C₂²	—	214	1	no	—
973	C₂²	—	214	1	no	—
974	C₂²	—	214	1	no	—
975	C₂²	—	214	1	no	—
976	C₂²	C₂⁴×D₁₀₇	1	1	yes	characteristic
977	C₄	—	2	1	no	—
978	C₄	—	2	1	no	—
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	107	2	no	—
990	C₄	—	214	1	no	—
991	C₄	—	214	1	no	—
992	C₄	—	214	1	no	—
993	C₄	—	214	1	no	—
994	C₄	—	214	1	no	—
995	C₄	—	214	1	no	—
996	C₄	—	214	1	no	—
997	C₄	—	214	1	no	—
998	C₄	—	214	1	no	—
999	C₂	—	4	1	no	—
1000	C₂	—	4	1	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	428	1	no	—
1003	C₂	—	428	1	no	—
1004	C₂	—	428	1	no	—
1005	C₂	—	428	1	no	—
1006	C₂	—	428	1	no	—
1007	C₂	—	428	1	no	—
1008	C₂	H(5,𝔽₂)×D₁₀₇	1	1	yes	characteristic
1009	C₂	#20293463	1	1	yes	characteristic
1010	C₂	#20293464	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₇
commutator, socle, cosocle	C₂²×C₁₀₇	C₂⁵
Fitting	#539×C₁₀₇	C₂
hypercenter	#539	D₁₀₇
hypocenter	C₁₀₇	#3539
LCS	G ▷ C₂²×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #20293368	C₂	semidirect
2. #20293367	C₂	semidirect
3. #20293367	C₂	semidirect
4. #20293365	C₂	semidirect
5. #20293330	C₂	semidirect
6. #20293328	C₂	semidirect
7. #20293328	C₂	semidirect
8. #20293326	C₂	semidirect
9. #20293325	C₂	semidirect
10. #20293322	C₂	semidirect
11. #20293313	C₂	semidirect
12. #20293309	C₂	semidirect
13. #20293298	C₂	semidirect
14. #20293295	C₂	semidirect
15. #20293278	C₂	semidirect
16. #20293275	C₂	semidirect
17. #20293236	C₂	semidirect
18. #20293233	C₂	semidirect
19. #20293229	C₂	semidirect
20. #20293229	C₂	semidirect
21. #20293229	C₂	semidirect
22. #20293228	C₂	semidirect
23. #20293226	C₂	semidirect
24. #20293223	C₂	semidirect
25. #20293223	C₂	semidirect
26. #20293207	C₂	semidirect
27. #20293207	C₂	semidirect
28. #20293140	C₂	semidirect
29. #20293136	C₂	semidirect
30. #20293135	C₂	semidirect
31. #539×C₁₀₇	C₂	semidirect
34. C₂×#13133818	C₂²	semidirect
35. C₂×#13133818	C₂²	semidirect
38. #16812108	C₂²	semidirect
43. #16812105	C₂²	semidirect
49. #16812104	C₂²	semidirect
50. #16812104	C₂²	semidirect
53. #16812102	C₂²	semidirect
54. #16812100	C₂²	semidirect
55. #16812100	C₂²	semidirect
56. #16812099	C₂²	semidirect
57. #16812099	C₂²	semidirect
58. #16812099	C₂²	semidirect
59. #16812099	C₂²	semidirect
60. #16812099	C₂²	semidirect
61. #16812099	C₂²	semidirect
69. #16812094	C₂²	semidirect
70. #16812094	C₂²	semidirect
71. #16812094	C₂²	semidirect
73. #16812093	C₂²	semidirect
74. #16812093	C₂²	semidirect
77. #16812092	C₂²	semidirect
83. #16812091	C₂²	semidirect
87. #16812087	C₂²	semidirect
88. #16812087	C₂²	semidirect
91. #16812085	C₂²	semidirect
92. #16812085	C₂²	semidirect
101. #16812084	C₂²	semidirect
102. #16812084	C₂²	semidirect
103. #16812084	C₂²	semidirect
110. #16812083	C₂²	semidirect
122. #16812082	C₂²	semidirect
123. #16812082	C₂²	semidirect
124. #16812082	C₂²	semidirect
125. #16812082	C₂²	semidirect
126. #16812082	C₂²	semidirect
130. #16812081	C₂²	semidirect
138. C₄×Dic₂₁₄	C₂²	semidirect
139. #16812074	C₂²	semidirect
141. C₄×D₄₂₈	C₂²	semidirect
146. #16812071	C₂²	semidirect
147. #16812071	C₂²	semidirect
150. C₄×C₂²⋊D₁₀₇	C₂²	semidirect
151. C₄×C₂²⋊D₁₀₇	C₂²	semidirect
152. C₄×C₂²⋊D₁₀₇	C₂²	semidirect
157. (C₂²⋊D₁₀₇)⋊C₄	C₂²	semidirect
158. (C₂²⋊D₁₀₇)⋊C₄	C₂²	semidirect
159. (C₂²⋊D₁₀₇)⋊C₄	C₂²	semidirect
161. #16812067	C₂²	semidirect
162. #16812067	C₂²	semidirect
164. #16812066	C₂²	semidirect
165. #16812066	C₂²	semidirect
167. C₂×Dic₁₀₇⋊C₄	C₂²	semidirect
168. C₄⋊C₄×D₁₀₇	C₂²	semidirect
169. C₄⋊C₄×D₁₀₇	C₂²	semidirect
170. C₄⋊C₄×D₁₀₇	C₂²	semidirect
171. C₄⋊C₄×D₁₀₇	C₂²	semidirect
173. #126×C₁₀₇	C₂²	semidirect
174. #125×C₁₀₇	C₂²	semidirect
175. #125×C₁₀₇	C₂²	semidirect
179. #123×C₁₀₇	C₂²	semidirect
181. C₂²⋊Q₈×C₁₀₇	C₂²	semidirect
182. C₂²⋊Q₈×C₁₀₇	C₂²	semidirect
185. C₄×D₄×C₁₀₇	C₂²	semidirect
186. C₂×C₄⋊C₄×C₁₀₇	C₂²	semidirect
506. C₁₀₇	#3539	semidirect
532. #539	D₁₀₇	semidirect
561. #126	C₂×D₁₀₇	semidirect
570. #125	C₂×D₁₀₇	semidirect
571. #125	C₂×D₁₀₇	semidirect
597. #123	C₂×D₁₀₇	semidirect
608. C₂²⋊Q₈	C₂×D₁₀₇	semidirect
609. C₂²⋊Q₈	C₂×D₁₀₇	semidirect
679. C₄×D₄	C₂×D₁₀₇	semidirect
692. C₂×C₄⋊C₄	C₂×D₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
#20293368	2
#20293367	2
#20293365	2
#20293330	2
#20293328	2
#20293326	2
#20293325	2
#20293322	2
#20293313	2
#20293309	2
#20293298	2
#20293295	2
#20293278	2
#20293275	2
#20293236	2
#20293233	2
#20293229	2
#20293228	2
#20293226	2
#20293223	2
#20293207	2
#20293140	2
#20293136	2
#20293135	2
#539×C₁₀₇	2
#3539	107