Subgroups — #28350666

Order 13696.

1038 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20293379	C₂	1	1	yes	maximal, characteristic, complemented
2	#20293379	C₂	1	1	yes	maximal, characteristic, complemented
3	#20293374	C₂	1	1	yes	maximal, characteristic, complemented
4	#20293371	C₂	1	1	yes	maximal, characteristic, complemented
5	#20293335	C₂	1	1	yes	maximal, characteristic, complemented
6	#20293334	C₂	1	1	yes	maximal, characteristic, complemented
7	#20293319	C₂	1	1	yes	maximal, characteristic, complemented
8	#20293310	C₂	1	1	yes	maximal, characteristic, complemented
9	#20293303	C₂	1	1	yes	maximal, characteristic, complemented
10	#20293301	C₂	1	1	yes	maximal, characteristic, complemented
11	#20293300	C₂	1	1	yes	maximal, characteristic, complemented
12	#20293281	C₂	1	1	yes	maximal, characteristic, complemented
13	#20293275	C₂	1	1	yes	maximal, characteristic, complemented
14	#20293267	C₂	1	1	yes	maximal, characteristic, complemented
15	#20293264	C₂	1	1	yes	maximal, characteristic, complemented
16	#20293255	C₂	1	1	yes	maximal, characteristic, complemented
17	#20293252	C₂	1	1	yes	maximal, characteristic, complemented
18	#20293246	C₂	1	1	yes	maximal, characteristic, complemented
19	#20293243	C₂	1	1	yes	maximal, characteristic, complemented
20	#20293226	C₂	1	1	yes	maximal, characteristic, complemented
21	#20293221	C₂	1	1	yes	maximal, characteristic, complemented
22	#20293221	C₂	1	1	yes	maximal, characteristic, complemented
23	#20293219	C₂	1	1	yes	maximal, characteristic, complemented
24	#20293218	C₂	1	1	yes	maximal, characteristic, complemented
25	#20293210	C₂	1	1	yes	maximal, characteristic, complemented
26	#20293203	C₂	1	1	yes	maximal, characteristic, complemented
27	#20293199	C₂	1	1	yes	maximal, characteristic, complemented
28	#20293133	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#16812093	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16812086	C₂	1	1	yes	maximal, characteristic, complemented
31	#551×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133818	C₂²	1	1	yes	characteristic
33	C₂×#13133817	C₂²	1	1	yes	characteristic
34	C₂×#13133817	C₂²	1	1	yes	characteristic, complemented
35	C₂²×Dic₂₁₄	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊D₁₀₇	C₂²	1	1	yes	characteristic
37	C₂³×Dic₁₀₇	C₂²	1	1	yes	characteristic
38	#16812109	C₂²	1	1	yes	characteristic, complemented
39	#16812109	C₂²	1	1	yes	characteristic, complemented
40	#16812109	C₂²	1	1	yes	characteristic, complemented
41	#16812108	C₂²	1	1	yes	characteristic, complemented
42	#16812108	C₂²	1	1	yes	characteristic, complemented
43	#16812108	C₂²	1	1	yes	characteristic, complemented
44	#16812104	C₂²	1	1	yes	characteristic, complemented
45	#16812104	C₂²	1	1	yes	characteristic, complemented
46	#16812104	C₂²	1	1	yes	characteristic, complemented
47	#16812104	C₂²	1	1	yes	characteristic, complemented
48	#16812104	C₂²	1	1	yes	characteristic, complemented
49	#16812103	C₂²	1	1	yes	characteristic, complemented
50	#16812103	C₂²	1	1	yes	characteristic, complemented
51	#16812102	C₂²	1	1	yes	characteristic, complemented
52	#16812102	C₂²	1	1	yes	characteristic, complemented
53	#16812102	C₂²	1	1	yes	characteristic, complemented
54	#16812101	C₂²	1	1	yes	characteristic, complemented
55	#16812101	C₂²	1	1	yes	characteristic, complemented
56	#16812100	C₂²	1	1	yes	characteristic, complemented
57	#16812100	C₂²	1	1	yes	characteristic, complemented
58	#16812100	C₂²	1	1	yes	characteristic, complemented
59	#16812100	C₂²	1	1	yes	characteristic, complemented
60	#16812100	C₂²	1	1	yes	characteristic, complemented
61	#16812099	C₂²	1	1	yes	characteristic, complemented
62	#16812099	C₂²	1	1	yes	characteristic, complemented
63	#16812099	C₂²	1	1	yes	characteristic, complemented
64	#16812097	C₂²	1	1	yes	characteristic, complemented
65	#16812097	C₂²	1	1	yes	characteristic, complemented
66	#16812095	C₂²	1	1	yes	characteristic
67	#16812095	C₂²	1	1	yes	characteristic
68	#16812095	C₂²	1	1	yes	characteristic, complemented
69	#16812095	C₂²	1	1	yes	characteristic, complemented
70	#16812095	C₂²	1	1	yes	characteristic, complemented
71	#16812094	C₂²	1	1	yes	characteristic, complemented
72	#16812094	C₂²	1	1	yes	characteristic, complemented
73	#16812094	C₂²	1	1	yes	characteristic, complemented
74	#16812093	C₂²	1	1	yes	characteristic
75	#16812093	C₂²	1	1	yes	characteristic
76	#16812093	C₂²	1	1	yes	characteristic
77	#16812093	C₂²	1	1	yes	characteristic
78	#16812093	C₂²	1	1	yes	characteristic
79	#16812093	C₂²	1	1	yes	characteristic
80	#16812093	C₂²	1	1	yes	characteristic
81	#16812093	C₂²	1	1	yes	characteristic
82	#16812093	C₂²	1	1	yes	characteristic
83	#16812093	C₂²	1	1	yes	characteristic, complemented
84	#16812093	C₂²	1	1	yes	characteristic, complemented
85	#16812093	C₂²	1	1	yes	characteristic, complemented
86	#16812093	C₂²	1	1	yes	characteristic, complemented
87	#16812092	C₂²	1	1	yes	characteristic
88	#16812092	C₂²	1	1	yes	characteristic
89	#16812092	C₂²	1	1	yes	characteristic, complemented
90	#16812091	C₂²	1	1	yes	characteristic
91	#16812091	C₂²	1	1	yes	characteristic
92	#16812091	C₂²	1	1	yes	characteristic, complemented
93	#16812091	C₂²	1	1	yes	characteristic, complemented
94	#16812091	C₂²	1	1	yes	characteristic, complemented
95	#16812090	C₂²	1	1	yes	characteristic, complemented
96	#16812089	C₂²	1	1	yes	characteristic, complemented
97	#16812089	C₂²	1	1	yes	characteristic, complemented
98	#16812089	C₂²	1	1	yes	characteristic, complemented
99	#16812089	C₂²	1	1	yes	characteristic, complemented
100	#16812089	C₂²	1	1	yes	characteristic, complemented
101	#16812089	C₂²	1	1	yes	characteristic, complemented
102	#16812088	C₂²	1	1	yes	characteristic
103	#16812088	C₂²	1	1	yes	characteristic, complemented
104	#16812087	C₂²	1	1	yes	characteristic, complemented
105	#16812087	C₂²	1	1	yes	characteristic, complemented
106	#16812087	C₂²	1	1	yes	characteristic, complemented
107	#16812087	C₂²	1	1	yes	characteristic, complemented
108	#16812087	C₂²	1	1	yes	characteristic, complemented
109	#16812086	C₂²	1	1	yes	characteristic
110	#16812086	C₂²	1	1	yes	characteristic
111	#16812086	C₂²	1	1	yes	characteristic
112	#16812086	C₂²	1	1	yes	characteristic
113	#16812086	C₂²	1	1	yes	characteristic
114	#16812086	C₂²	1	1	yes	characteristic
115	#16812086	C₂²	1	1	yes	characteristic
116	#16812086	C₂²	1	1	yes	characteristic, complemented
117	#16812086	C₂²	1	1	yes	characteristic, complemented
118	#16812086	C₂²	1	1	yes	characteristic, complemented
119	#16812086	C₂²	1	1	yes	characteristic, complemented
120	#16812086	C₂²	1	1	yes	characteristic, complemented
121	#16812086	C₂²	1	1	yes	characteristic, complemented
122	#16812086	C₂²	1	1	yes	characteristic, complemented
123	#16812086	C₂²	1	1	yes	characteristic, complemented
124	#16812086	C₂²	1	1	yes	characteristic, complemented
125	#16812085	C₂²	1	1	yes	characteristic, complemented
126	#16812085	C₂²	1	1	yes	characteristic, complemented
127	#16812085	C₂²	1	1	yes	characteristic, complemented
128	#16812083	C₂²	1	1	yes	characteristic
129	#16812083	C₂²	1	1	yes	characteristic, complemented
130	#16812082	C₂²	1	1	yes	characteristic
131	#16812082	C₂²	1	1	yes	characteristic
132	#16812082	C₂²	1	1	yes	characteristic, complemented
133	#16812081	C₂²	1	1	yes	characteristic
134	#16812081	C₂²	1	1	yes	characteristic
135	#16812081	C₂²	1	1	yes	characteristic
136	#16812081	C₂²	1	1	yes	characteristic, complemented
137	#16812080	C₂²	1	1	yes	characteristic
138	#16812079	C₂²	1	1	yes	characteristic
139	#16812078	C₂²	1	1	yes	characteristic
140	#16812077	C₂²	1	1	yes	characteristic
141	Q₈×Dic₁₀₇	C₂²	1	1	yes	characteristic, complemented
142	C₄×Dic₂₁₄	C₂²	1	1	yes	characteristic, complemented
143	C₄×D₄₂₈	C₂²	1	1	yes	characteristic, complemented
144	D₄×Dic₁₀₇	C₂²	1	1	yes	characteristic
145	D₄×Dic₁₀₇	C₂²	1	1	yes	characteristic
146	D₄×Dic₁₀₇	C₂²	1	1	yes	characteristic, complemented
147	C₄×C₂²⋊D₁₀₇	C₂²	1	1	yes	characteristic
148	C₄×C₂²⋊D₁₀₇	C₂²	1	1	yes	characteristic
149	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic
150	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic
151	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic
152	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
153	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
154	(C₂²⋊D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
155	#16812068	C₂²	1	1	yes	characteristic
156	#16812067	C₂²	1	1	yes	characteristic, complemented
157	#16812066	C₂²	1	1	yes	characteristic, complemented
158	#16812065	C₂²	1	1	yes	characteristic, complemented
159	#16812065	C₂²	1	1	yes	characteristic, complemented
160	C₂×C₄⋊Dic₁₀₇	C₂²	1	1	yes	characteristic
161	C₂×C₄⋊Dic₁₀₇	C₂²	1	1	yes	characteristic
162	C₂×C₄⋊Dic₁₀₇	C₂²	1	1	yes	characteristic, complemented
163	C₂×C₄⋊Dic₁₀₇	C₂²	1	1	yes	characteristic, complemented
164	C₂×Dic₁₀₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₂×Dic₁₀₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	C₄⋊C₄×D₁₀₇	C₂²	1	1	yes	characteristic, complemented
167	C₂×C₂²⋊Dic₁₀₇	C₂²	1	1	yes	characteristic
168	C₂×(C₂×D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic
169	C₂×(C₂×D₁₀₇)⋊C₄	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₁₀₇	C₂²	1	1	yes	characteristic
171	C₂²⋊C₄×D₁₀₇	C₂²	1	1	yes	characteristic
172	#126×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
173	#126×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
174	#124×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
175	#123×C₁₀₇	C₂²	1	1	yes	characteristic
176	#123×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
177	#123×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
178	C₂²⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
179	C₂²⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
180	#120×C₁₀₇	C₂²	1	1	yes	characteristic
181	C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
183	#117×C₁₀₇	C₂²	1	1	yes	characteristic
184	#117×C₁₀₇	C₂²	1	1	yes	characteristic, complemented
185	C₂×C₂²⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
187	C₂³×D₁₀₇	C₂³	1	1	yes	characteristic
188	#13133818	—	4	2	no	—
189	#13133817	—	4	2	no	—
190	#13133817	—	4	2	no	—
191	C₂×Dic₂₁₄	—	4	2	no	—
192	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
193	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
194	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
195	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
196	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
197	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
198	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
199	C₂×Dic₂₁₄	C₂³	1	1	yes	characteristic
200	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
201	C₂×D₄₂₈	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₁₀₇	—	4	2	no	—
203	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₀₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₀₇	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	C₂²×Dic₁₀₇	—	4	2	no	—
214	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
215	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
216	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
217	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
218	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
219	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
220	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
221	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
222	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
223	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
224	C₂²×Dic₁₀₇	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₁₀₇	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
244	C₄⋊Dic₁₀₇	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	Dic₁₀₇⋊C₄	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	Dic₁₀₇⋊C₄	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	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₁₀₇	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₁₀₇	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	(C₂×D₁₀₇)⋊C₄	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	C₂⁴×C₁₀₇	C₂³	1	1	yes	characteristic
314	C₂×Q₈×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	C₂×D₄×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	C₂²×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	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
335	C₂²⋊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	C₄²×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	—	2	2	no	—
349	C₂³×C₁₀₇	—	2	2	no	—
350	C₂³×C₁₀₇	—	4	1	no	—
351	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
352	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
353	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
354	C₂³×C₁₀₇	C₂⁴	1	1	yes	characteristic
355	C₂²×D₁₀₇	—	2	2	no	—
356	C₂²×D₁₀₇	—	4	1	no	—
357	C₂²×D₁₀₇	—	4	1	no	—
358	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
359	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
360	C₂²×D₁₀₇	C₂⁴	1	1	yes	characteristic
361	Q₈×C₁₀₇	—	4	1	no	—
362	D₄×C₁₀₇	—	2	2	no	—
363	D₄×C₁₀₇	—	2	2	no	—
364	D₄×C₁₀₇	—	4	1	no	—
365	C₂×C₄×C₁₀₇	—	2	2	no	—
366	C₂×C₄×C₁₀₇	—	2	2	no	—
367	C₂×C₄×C₁₀₇	—	4	1	no	—
368	C₂×C₄×C₁₀₇	—	4	1	no	—
369	C₂×C₄×C₁₀₇	—	4	1	no	—
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	—	2	2	no	—
384	C₂²⋊D₁₀₇	—	2	2	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	C₂×Dic₁₀₇	—	2	2	no	—
392	C₂×Dic₁₀₇	—	2	2	no	—
393	C₂×Dic₁₀₇	—	2	2	no	—
394	C₂×Dic₁₀₇	—	4	1	no	—
395	C₂×Dic₁₀₇	—	4	1	no	—
396	C₂×Dic₁₀₇	—	4	1	no	—
397	C₂×Dic₁₀₇	—	4	1	no	—
398	C₂×Dic₁₀₇	—	4	1	no	—
399	C₂×Dic₁₀₇	—	4	1	no	—
400	C₂×Dic₁₀₇	—	4	1	no	—
401	C₂×Dic₁₀₇	—	4	1	no	—
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	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
412	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₁₀₇	C₂⁴	1	1	yes	characteristic
415	D₄₂₈	—	4	1	no	—
416	D₄₂₈	—	4	1	no	—
417	C₄×D₁₀₇	—	4	1	no	—
418	C₄×D₁₀₇	—	4	1	no	—
419	C₄×D₁₀₇	—	4	1	no	—
420	C₄×D₁₀₇	—	4	1	no	—
421	C₄×D₁₀₇	—	4	1	no	—
422	C₄×D₁₀₇	—	4	1	no	—
423	C₄×D₁₀₇	—	4	1	no	—
424	Dic₂₁₄	—	4	1	no	—
425	Dic₂₁₄	—	4	1	no	—
426	Dic₂₁₄	—	4	1	no	—
427	Dic₂₁₄	—	4	1	no	—
428	Dic₂₁₄	—	4	1	no	—
429	Dic₂₁₄	—	4	1	no	—
430	Dic₂₁₄	—	4	1	no	—
431	Dic₂₁₄	—	4	1	no	—
432	C₂²×C₁₀₇	—	2	1	no	—
433	C₂²×C₁₀₇	—	2	1	no	—
434	C₂²×C₁₀₇	—	2	1	no	—
435	C₂²×C₁₀₇	—	2	1	no	—
436	C₂²×C₁₀₇	—	2	1	no	—
437	C₂²×C₁₀₇	—	2	1	no	—
438	C₂²×C₁₀₇	—	2	1	no	—
439	C₂²×C₁₀₇	—	2	1	no	—
440	C₂²×C₁₀₇	—	2	1	no	—
441	C₂²×C₁₀₇	—	2	1	no	—
442	C₂²×C₁₀₇	—	4	4	no	—
443	C₂²×C₁₀₇	H(5,𝔽₂)	1	2	yes	—
444	C₂²×C₁₀₇	2₋¹⁺⁴	1	2	yes	—
445	C₂²×C₁₀₇	C₂⁵	1	1	yes	characteristic
446	C₂×D₁₀₇	—	2	1	no	—
447	C₂×D₁₀₇	—	2	1	no	—
448	C₂×D₁₀₇	—	2	1	no	—
449	C₂×D₁₀₇	—	2	1	no	—
450	C₂×D₁₀₇	—	2	1	no	—
451	C₂×D₁₀₇	—	2	1	no	—
452	C₂×D₁₀₇	—	2	1	no	—
453	C₂×D₁₀₇	—	2	1	no	—
454	C₂×D₁₀₇	—	2	1	no	—
455	C₂×D₁₀₇	—	8	2	no	—
456	C₄×C₁₀₇	—	2	1	no	—
457	C₄×C₁₀₇	—	2	1	no	—
458	C₄×C₁₀₇	—	2	1	no	—
459	C₄×C₁₀₇	—	2	1	no	—
460	C₄×C₁₀₇	—	2	1	no	—
461	C₄×C₁₀₇	—	2	1	no	—
462	C₄×C₁₀₇	—	2	1	no	—
463	C₄×C₁₀₇	—	2	1	no	—
464	C₄×C₁₀₇	—	2	1	no	—
465	C₄×C₁₀₇	—	2	1	no	—
466	C₄×C₁₀₇	—	2	1	no	—
467	Dic₁₀₇	—	2	1	no	—
468	Dic₁₀₇	—	2	1	no	—
469	Dic₁₀₇	—	2	1	no	—
470	Dic₁₀₇	—	2	1	no	—
471	Dic₁₀₇	—	2	1	no	—
472	Dic₁₀₇	—	2	1	no	—
473	Dic₁₀₇	—	2	1	no	—
474	Dic₁₀₇	—	2	1	no	—
475	Dic₁₀₇	—	2	1	no	—
476	Dic₁₀₇	—	2	1	no	—
477	Dic₁₀₇	—	2	1	no	—
478	Dic₁₀₇	—	2	1	no	—
479	Dic₁₀₇	—	2	1	no	—
480	C₂×C₁₀₇	—	2	2	no	—
481	C₂×C₁₀₇	—	2	2	no	—
482	C₂×C₁₀₇	—	4	1	no	—
483	C₂×C₁₀₇	—	4	1	no	—
484	C₂×C₁₀₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
485	C₂×C₁₀₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
486	C₂×C₁₀₇	#585	1	1	yes	characteristic
487	D₁₀₇	—	4	1	no	—
488	D₁₀₇	—	4	1	no	—
489	D₁₀₇	—	4	1	no	—
490	#3535	—	107	1	no	maximal, Sylow
491	C₁₀₇	#3535	1	1	yes	characteristic, complemented, Sylow
492	#563	—	107	1	no	—
493	#563	—	107	1	no	—
494	#562	—	107	1	no	—
495	#562	—	107	1	no	—
496	#554	—	107	1	no	—
497	#554	—	107	1	no	—
498	#552	—	107	1	no	—
499	#552	—	107	1	no	—
500	#551	—	107	1	no	—
501	#551	—	107	1	no	—
502	#551	—	107	1	no	—
503	#551	D₁₀₇	1	1	yes	characteristic, complemented
504	#547	—	107	1	no	—
505	#547	—	107	1	no	—
506	#546	—	107	1	no	—
507	#546	—	107	1	no	—
508	#544	—	107	1	no	—
509	#543	—	107	1	no	—
510	#542	—	107	1	no	—
511	#542	—	107	1	no	—
512	#539	—	107	1	no	—
513	#539	—	107	1	no	—
514	#539	—	107	1	no	—
515	#539	—	107	1	no	—
516	#539	—	107	1	no	—
517	#538	—	107	1	no	—
518	#536	—	107	1	no	—
519	#536	—	107	1	no	—
520	#525	—	107	1	no	—
521	C₂×#123	—	107	1	no	—
522	C₂×C₂²⋊Q₈	—	107	1	no	—
523	C₂×#41	—	107	1	no	—
524	C₂×#41	—	107	1	no	—
525	C₂×#41	—	107	1	no	—
526	C₂²×Q₈	—	107	1	no	—
527	C₂²×D₄	—	107	1	no	—
528	C₂³×C₄	—	107	1	no	—
529	C₄⋊Q₈	—	107	1	no	—
530	C₄⋊Q₈	—	107	1	no	—
531	C₄⋊Q₈	—	107	1	no	—
532	C₄⋊Q₈	—	107	1	no	—
533	C₄⋊Q₈	—	107	1	no	—
534	C₄⋊Q₈	—	107	1	no	—
535	#126	—	107	1	no	—
536	#126	—	107	1	no	—
537	#126	—	107	1	no	—
538	#126	—	107	1	no	—
539	#126	—	107	1	no	—
540	#126	—	107	1	no	—
541	#126	—	107	1	no	—
542	#126	—	107	1	no	—
543	#126	—	107	1	no	—
544	#126	—	107	1	no	—
545	#126	C₂×D₁₀₇	1	1	yes	characteristic, complemented
546	#126	C₂×D₁₀₇	1	1	yes	characteristic, complemented
547	#125	—	107	1	no	—
548	#125	—	107	1	no	—
549	#125	—	107	1	no	—
550	#125	—	107	1	no	—
551	#125	—	107	1	no	—
552	#125	—	107	1	no	—
553	#125	—	107	1	no	—
554	#125	—	107	1	no	—
555	#125	—	107	1	no	—
556	#125	—	107	1	no	—
557	#124	—	107	1	no	—
558	#124	—	107	1	no	—
559	#124	—	107	1	no	—
560	#124	—	107	1	no	—
561	#124	—	107	1	no	—
562	#124	—	107	1	no	—
563	#124	—	107	1	no	—
564	#124	C₂×D₁₀₇	1	1	yes	characteristic, complemented
565	#123	—	107	1	no	—
566	#123	—	107	1	no	—
567	#123	—	107	1	no	—
568	#123	—	107	1	no	—
569	#123	—	107	1	no	—
570	#123	—	107	1	no	—
571	#123	—	107	1	no	—
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	C₂×D₁₀₇	1	1	yes	characteristic
591	#123	C₂×D₁₀₇	1	1	yes	characteristic, complemented
592	#123	C₂×D₁₀₇	1	1	yes	characteristic, complemented
593	C₂²⋊Q₈	—	107	1	no	—
594	C₂²⋊Q₈	—	107	1	no	—
595	C₂²⋊Q₈	—	107	1	no	—
596	C₂²⋊Q₈	—	107	1	no	—
597	C₂²⋊Q₈	—	107	1	no	—
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	—	107	1	no	—
608	C₂²⋊Q₈	—	107	1	no	—
609	C₂²⋊Q₈	—	107	1	no	—
610	C₂²⋊Q₈	—	107	1	no	—
611	C₂²⋊Q₈	—	107	1	no	—
612	C₂²⋊Q₈	—	107	1	no	—
613	C₂²⋊Q₈	—	107	1	no	—
614	C₂²⋊Q₈	—	107	1	no	—
615	C₂²⋊Q₈	—	107	1	no	—
616	C₂²⋊Q₈	—	107	1	no	—
617	C₂²⋊Q₈	—	107	1	no	—
618	C₂²⋊Q₈	—	107	1	no	—
619	C₂²⋊Q₈	—	107	1	no	—
620	C₂²⋊Q₈	—	107	1	no	—
621	C₂²⋊Q₈	—	107	1	no	—
622	C₂²⋊Q₈	—	107	1	no	—
623	C₂²⋊Q₈	—	107	1	no	—
624	C₂²⋊Q₈	—	107	1	no	—
625	C₂²⋊Q₈	C₂×D₁₀₇	1	1	yes	characteristic
626	C₂²⋊Q₈	C₂×D₁₀₇	1	1	yes	characteristic, complemented
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	#120	—	107	1	no	—
638	#120	—	107	1	no	—
639	#120	—	107	1	no	—
640	#120	C₂×D₁₀₇	1	1	yes	characteristic
641	C₄×Q₈	—	107	1	no	—
642	C₄×Q₈	—	107	1	no	—
643	C₄×D₄	—	107	1	no	—
644	C₄×D₄	—	107	1	no	—
645	C₄×D₄	—	107	1	no	—
646	C₄×D₄	—	107	1	no	—
647	C₄×D₄	—	107	1	no	—
648	C₄×D₄	—	107	1	no	—
649	C₄×D₄	—	107	1	no	—
650	C₄×D₄	—	107	1	no	—
651	C₄×D₄	—	107	1	no	—
652	C₄×D₄	—	107	1	no	—
653	C₄×D₄	—	107	1	no	—
654	C₄×D₄	—	107	1	no	—
655	C₄×D₄	C₂×D₁₀₇	1	1	yes	characteristic
656	C₄×D₄	C₂×D₁₀₇	1	1	yes	characteristic, complemented
657	#117	—	107	1	no	—
658	#117	—	107	1	no	—
659	#117	—	107	1	no	—
660	#117	—	107	1	no	—
661	#117	—	107	1	no	—
662	#117	C₂×D₁₀₇	1	1	yes	characteristic
663	#117	C₂×D₁₀₇	1	1	yes	characteristic, complemented
664	C₂×C₄⋊C₄	—	107	1	no	—
665	C₂×C₄⋊C₄	—	107	1	no	—
666	C₂×C₄⋊C₄	—	107	1	no	—
667	C₂×C₄⋊C₄	—	107	1	no	—
668	C₂×C₄⋊C₄	—	107	1	no	—
669	C₂×C₄⋊C₄	—	107	1	no	—
670	C₂×C₄⋊C₄	—	107	1	no	—
671	C₂×C₂²⋊C₄	—	107	1	no	—
672	C₂×C₂²⋊C₄	—	107	1	no	—
673	C₂×C₂²⋊C₄	—	107	1	no	—
674	C₂×C₂²⋊C₄	—	107	1	no	—
675	C₂×C₂²⋊C₄	—	107	1	no	—
676	C₂×C₂²⋊C₄	C₂×D₁₀₇	1	1	yes	characteristic
677	C₂×C₂²⋊C₄	C₂×D₁₀₇	1	1	yes	characteristic
678	C₂⁴	—	107	1	no	—
679	C₂⁴	C₂²×D₁₀₇	1	1	yes	characteristic
680	#41	—	428	2	no	—
681	#41	—	428	2	no	—
682	#41	—	428	2	no	—
683	C₂×Q₈	—	107	1	no	—
684	C₂×Q₈	—	107	1	no	—
685	C₂×Q₈	—	107	1	no	—
686	C₂×Q₈	—	107	1	no	—
687	C₂×Q₈	—	107	1	no	—
688	C₂×Q₈	—	107	1	no	—
689	C₂×Q₈	—	107	1	no	—
690	C₂×Q₈	—	107	1	no	—
691	C₂×Q₈	—	428	2	no	—
692	C₂×Q₈	C₂²×D₁₀₇	1	1	yes	characteristic
693	C₂×D₄	—	107	1	no	—
694	C₂×D₄	—	107	1	no	—
695	C₂×D₄	—	107	1	no	—
696	C₂×D₄	—	107	1	no	—
697	C₂×D₄	—	107	1	no	—
698	C₂×D₄	—	107	1	no	—
699	C₂×D₄	—	107	1	no	—
700	C₂×D₄	—	107	1	no	—
701	C₂×D₄	—	107	1	no	—
702	C₂×D₄	—	107	1	no	—
703	C₂×D₄	—	107	1	no	—
704	C₂×D₄	—	107	1	no	—
705	C₂×D₄	—	428	2	no	—
706	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
707	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
708	C₂×D₄	C₂²×D₁₀₇	1	1	yes	characteristic
709	C₂²×C₄	—	107	1	no	—
710	C₂²×C₄	—	107	1	no	—
711	C₂²×C₄	—	107	1	no	—
712	C₂²×C₄	—	107	1	no	—
713	C₂²×C₄	—	107	1	no	—
714	C₂²×C₄	—	107	1	no	—
715	C₂²×C₄	—	107	1	no	—
716	C₂²×C₄	—	107	1	no	—
717	C₂²×C₄	—	107	1	no	—
718	C₂²×C₄	—	107	1	no	—
719	C₂²×C₄	—	107	1	no	—
720	C₂²×C₄	—	107	1	no	—
721	C₂²×C₄	—	107	1	no	—
722	C₂²×C₄	—	107	1	no	—
723	C₂²×C₄	—	107	1	no	—
724	C₂²×C₄	—	107	1	no	—
725	C₂²×C₄	—	107	1	no	—
726	C₂²×C₄	—	107	1	no	—
727	C₂²×C₄	—	428	2	no	—
728	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
729	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
730	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
733	C₄⋊C₄	—	107	1	no	—
734	C₄⋊C₄	—	107	1	no	—
735	C₄⋊C₄	—	107	1	no	—
736	C₄⋊C₄	—	107	1	no	—
737	C₄⋊C₄	—	107	1	no	—
738	C₄⋊C₄	—	107	1	no	—
739	C₄⋊C₄	—	107	1	no	—
740	C₄⋊C₄	—	107	1	no	—
741	C₄⋊C₄	—	107	1	no	—
742	C₄⋊C₄	—	107	1	no	—
743	C₄⋊C₄	—	107	1	no	—
744	C₄⋊C₄	—	107	1	no	—
745	C₄⋊C₄	—	107	1	no	—
746	C₄⋊C₄	—	107	1	no	—
747	C₄⋊C₄	—	107	1	no	—
748	C₄⋊C₄	—	107	1	no	—
749	C₄⋊C₄	—	107	1	no	—
750	C₄⋊C₄	—	107	1	no	—
751	C₄⋊C₄	—	107	1	no	—
752	C₄⋊C₄	—	107	1	no	—
753	C₄⋊C₄	—	107	1	no	—
754	C₄⋊C₄	—	107	1	no	—
755	C₄⋊C₄	—	107	1	no	—
756	C₄⋊C₄	—	107	1	no	—
757	C₄⋊C₄	—	107	1	no	—
758	C₄⋊C₄	—	107	1	no	—
759	C₄⋊C₄	—	107	1	no	—
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	C₂²×D₁₀₇	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
783	C₂²⋊C₄	—	107	1	no	—
784	C₂²⋊C₄	—	107	1	no	—
785	C₂²⋊C₄	—	107	1	no	—
786	C₂²⋊C₄	—	107	1	no	—
787	C₂²⋊C₄	—	107	1	no	—
788	C₂²⋊C₄	—	107	1	no	—
789	C₂²⋊C₄	—	107	1	no	—
790	C₂²⋊C₄	—	107	1	no	—
791	C₂²⋊C₄	—	107	1	no	—
792	C₂²⋊C₄	—	107	1	no	—
793	C₂²⋊C₄	—	107	1	no	—
794	C₂²⋊C₄	—	107	1	no	—
795	C₂²⋊C₄	—	107	1	no	—
796	C₂²⋊C₄	—	107	1	no	—
797	C₂²⋊C₄	—	107	1	no	—
798	C₂²⋊C₄	—	107	1	no	—
799	C₂²⋊C₄	—	107	1	no	—
800	C₂²⋊C₄	—	107	1	no	—
801	C₂²⋊C₄	—	107	1	no	—
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	C₂²×D₁₀₇	1	1	yes	characteristic
816	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
819	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₁₀₇	1	1	yes	characteristic
829	C₄²	—	107	1	no	—
830	C₄²	—	107	1	no	—
831	C₄²	—	107	1	no	—
832	C₄²	—	107	1	no	—
833	C₄²	—	107	1	no	—
834	C₄²	—	107	1	no	—
835	C₄²	—	107	1	no	—
836	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
837	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
838	C₄²	C₂²×D₁₀₇	1	1	yes	characteristic
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	4	1	no	—
842	C₂³	—	107	1	no	—
843	C₂³	—	107	1	no	—
844	C₂³	—	107	1	no	—
845	C₂³	—	428	1	no	—
846	C₂³	—	428	1	no	—
847	C₂³	—	214	2	no	—
848	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
849	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
850	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
851	C₂³	C₂³×D₁₀₇	1	1	yes	characteristic
852	Q₈	—	4	1	no	—
853	Q₈	—	428	1	no	—
854	Q₈	—	428	1	no	—
855	Q₈	—	428	1	no	—
856	Q₈	—	428	1	no	—
857	Q₈	—	428	1	no	—
858	Q₈	—	428	1	no	—
859	Q₈	—	428	1	no	—
860	Q₈	—	428	1	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	4	1	no	—
864	D₄	—	428	1	no	—
865	D₄	—	428	1	no	—
866	D₄	—	428	1	no	—
867	D₄	—	428	1	no	—
868	D₄	—	428	1	no	—
869	D₄	—	428	1	no	—
870	D₄	—	428	1	no	—
871	D₄	—	428	1	no	—
872	D₄	—	214	2	no	—
873	D₄	—	214	2	no	—
874	D₄	—	214	2	no	—
875	D₄	—	214	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	107	1	no	—
882	C₂×C₄	—	107	1	no	—
883	C₂×C₄	—	107	1	no	—
884	C₂×C₄	—	107	1	no	—
885	C₂×C₄	—	107	1	no	—
886	C₂×C₄	—	107	1	no	—
887	C₂×C₄	—	107	1	no	—
888	C₂×C₄	—	107	1	no	—
889	C₂×C₄	—	107	1	no	—
890	C₂×C₄	—	107	1	no	—
891	C₂×C₄	—	107	1	no	—
892	C₂×C₄	—	107	1	no	—
893	C₂×C₄	—	107	1	no	—
894	C₂×C₄	—	428	1	no	—
895	C₂×C₄	—	428	1	no	—
896	C₂×C₄	—	428	1	no	—
897	C₂×C₄	—	428	1	no	—
898	C₂×C₄	—	428	1	no	—
899	C₂×C₄	—	428	1	no	—
900	C₂×C₄	—	428	1	no	—
901	C₂×C₄	—	428	1	no	—
902	C₂×C₄	—	428	1	no	—
903	C₂×C₄	—	428	1	no	—
904	C₂×C₄	—	428	1	no	—
905	C₂×C₄	—	428	1	no	—
906	C₂×C₄	—	428	1	no	—
907	C₂×C₄	—	428	1	no	—
908	C₂×C₄	—	428	1	no	—
909	C₂×C₄	—	214	2	no	—
910	C₂×C₄	—	214	2	no	—
911	C₂×C₄	—	214	2	no	—
912	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
922	C₂×C₄	C₂³×D₁₀₇	1	1	yes	characteristic
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	4	4	no	—
934	C₂²	—	856	2	no	—
935	C₂²	—	214	1	no	—
936	C₂²	—	214	1	no	—
937	C₂²	—	214	1	no	—
938	C₂²	—	214	1	no	—
939	C₂²	—	214	1	no	—
940	C₂²	—	214	1	no	—
941	C₂²	—	214	1	no	—
942	C₂²	—	214	1	no	—
943	C₂²	—	214	1	no	—
944	C₂²	#16812155	1	2	yes	—
945	C₂²	#16812156	1	2	yes	—
946	C₂²	C₂⁴×D₁₀₇	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	214	1	no	—
959	C₄	—	214	1	no	—
960	C₄	—	214	1	no	—
961	C₄	—	214	1	no	—
962	C₄	—	214	1	no	—
963	C₄	—	214	1	no	—
964	C₄	—	214	1	no	—
965	C₄	—	214	1	no	—
966	C₄	—	214	1	no	—
967	C₄	—	214	1	no	—
968	C₄	—	214	1	no	—
969	C₄	—	214	1	no	—
970	C₄	—	214	1	no	—
971	C₂	—	2	2	no	—
972	C₂	—	2	2	no	—
973	C₂	—	4	1	no	—
974	C₂	—	4	1	no	—
975	C₂	—	428	1	no	—
976	C₂	—	428	1	no	—
977	C₂	—	428	1	no	—
978	C₂	C₂×#16812155	1	1	yes	characteristic
979	C₂	C₂×#16812156	1	1	yes	characteristic
980	C₂	#20293462	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₇
commutator, socle, cosocle	C₂²×C₁₀₇	C₂⁵
Fitting	#551×C₁₀₇	C₂
hypercenter	#551	D₁₀₇
hypocenter	C₁₀₇	#3535
LCS	G ▷ C₂²×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #20293379	C₂	semidirect
2. #20293379	C₂	semidirect
3. #20293374	C₂	semidirect
4. #20293371	C₂	semidirect
5. #20293335	C₂	semidirect
6. #20293334	C₂	semidirect
7. #20293319	C₂	semidirect
8. #20293310	C₂	semidirect
9. #20293303	C₂	semidirect
10. #20293301	C₂	semidirect
11. #20293300	C₂	semidirect
12. #20293281	C₂	semidirect
13. #20293275	C₂	semidirect
14. #20293267	C₂	semidirect
15. #20293264	C₂	semidirect
16. #20293255	C₂	semidirect
17. #20293252	C₂	semidirect
18. #20293246	C₂	semidirect
19. #20293243	C₂	semidirect
20. #20293226	C₂	semidirect
21. #20293221	C₂	semidirect
22. #20293221	C₂	semidirect
23. #20293219	C₂	semidirect
24. #20293218	C₂	semidirect
25. #20293210	C₂	semidirect
26. #20293203	C₂	semidirect
27. #20293199	C₂	semidirect
28. #20293133	C₂	semidirect
29. C₂×#16812093	C₂	semidirect
30. C₂×#16812086	C₂	semidirect
31. #551×C₁₀₇	C₂	semidirect
34. C₂×#13133817	C₂²	semidirect
35. C₂²×Dic₂₁₄	C₂²	semidirect
38. #16812109	C₂²	semidirect
39. #16812109	C₂²	semidirect
40. #16812109	C₂²	semidirect
41. #16812108	C₂²	semidirect
42. #16812108	C₂²	semidirect
43. #16812108	C₂²	semidirect
44. #16812104	C₂²	semidirect
45. #16812104	C₂²	semidirect
46. #16812104	C₂²	semidirect
47. #16812104	C₂²	semidirect
48. #16812104	C₂²	semidirect
49. #16812103	C₂²	semidirect
50. #16812103	C₂²	semidirect
51. #16812102	C₂²	semidirect
52. #16812102	C₂²	semidirect
53. #16812102	C₂²	semidirect
54. #16812101	C₂²	semidirect
55. #16812101	C₂²	semidirect
56. #16812100	C₂²	semidirect
57. #16812100	C₂²	semidirect
58. #16812100	C₂²	semidirect
59. #16812100	C₂²	semidirect
60. #16812100	C₂²	semidirect
61. #16812099	C₂²	semidirect
62. #16812099	C₂²	semidirect
63. #16812099	C₂²	semidirect
64. #16812097	C₂²	semidirect
65. #16812097	C₂²	semidirect
68. #16812095	C₂²	semidirect
69. #16812095	C₂²	semidirect
70. #16812095	C₂²	semidirect
71. #16812094	C₂²	semidirect
72. #16812094	C₂²	semidirect
73. #16812094	C₂²	semidirect
83. #16812093	C₂²	semidirect
84. #16812093	C₂²	semidirect
85. #16812093	C₂²	semidirect
86. #16812093	C₂²	semidirect
89. #16812092	C₂²	semidirect
92. #16812091	C₂²	semidirect
93. #16812091	C₂²	semidirect
94. #16812091	C₂²	semidirect
95. #16812090	C₂²	semidirect
96. #16812089	C₂²	semidirect
97. #16812089	C₂²	semidirect
98. #16812089	C₂²	semidirect
99. #16812089	C₂²	semidirect
100. #16812089	C₂²	semidirect
101. #16812089	C₂²	semidirect
103. #16812088	C₂²	semidirect
104. #16812087	C₂²	semidirect
105. #16812087	C₂²	semidirect
106. #16812087	C₂²	semidirect
107. #16812087	C₂²	semidirect
108. #16812087	C₂²	semidirect
116. #16812086	C₂²	semidirect
117. #16812086	C₂²	semidirect
118. #16812086	C₂²	semidirect
119. #16812086	C₂²	semidirect
120. #16812086	C₂²	semidirect
121. #16812086	C₂²	semidirect
122. #16812086	C₂²	semidirect
123. #16812086	C₂²	semidirect
124. #16812086	C₂²	semidirect
125. #16812085	C₂²	semidirect
126. #16812085	C₂²	semidirect
127. #16812085	C₂²	semidirect
129. #16812083	C₂²	semidirect
132. #16812082	C₂²	semidirect
136. #16812081	C₂²	semidirect
141. Q₈×Dic₁₀₇	C₂²	semidirect
142. C₄×Dic₂₁₄	C₂²	semidirect
143. C₄×D₄₂₈	C₂²	semidirect
146. D₄×Dic₁₀₇	C₂²	semidirect
152. (C₂²⋊D₁₀₇)⋊C₄	C₂²	semidirect
153. (C₂²⋊D₁₀₇)⋊C₄	C₂²	semidirect
154. (C₂²⋊D₁₀₇)⋊C₄	C₂²	semidirect
156. #16812067	C₂²	semidirect
157. #16812066	C₂²	semidirect
158. #16812065	C₂²	semidirect
159. #16812065	C₂²	semidirect
162. C₂×C₄⋊Dic₁₀₇	C₂²	semidirect
163. C₂×C₄⋊Dic₁₀₇	C₂²	semidirect
164. C₂×Dic₁₀₇⋊C₄	C₂²	semidirect
165. C₂×Dic₁₀₇⋊C₄	C₂²	semidirect
166. C₄⋊C₄×D₁₀₇	C₂²	semidirect
172. #126×C₁₀₇	C₂²	semidirect
173. #126×C₁₀₇	C₂²	semidirect
174. #124×C₁₀₇	C₂²	semidirect
176. #123×C₁₀₇	C₂²	semidirect
177. #123×C₁₀₇	C₂²	semidirect
179. C₂²⋊Q₈×C₁₀₇	C₂²	semidirect
182. C₄×D₄×C₁₀₇	C₂²	semidirect
184. #117×C₁₀₇	C₂²	semidirect
491. C₁₀₇	#3535	semidirect
503. #551	D₁₀₇	semidirect
545. #126	C₂×D₁₀₇	semidirect
546. #126	C₂×D₁₀₇	semidirect
564. #124	C₂×D₁₀₇	semidirect
591. #123	C₂×D₁₀₇	semidirect
592. #123	C₂×D₁₀₇	semidirect
626. C₂²⋊Q₈	C₂×D₁₀₇	semidirect
656. C₄×D₄	C₂×D₁₀₇	semidirect
663. #117	C₂×D₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
#20293379	2
#20293374	2
#20293371	2
#20293335	2
#20293334	2
#20293319	2
#20293310	2
#20293303	2
#20293301	2
#20293300	2
#20293281	2
#20293275	2
#20293267	2
#20293264	2
#20293255	2
#20293252	2
#20293246	2
#20293243	2
#20293226	2
#20293221	2
#20293219	2
#20293218	2
#20293210	2
#20293203	2
#20293199	2
#20293133	2
C₂×#16812093	2
C₂×#16812086	2
#551×C₁₀₇	2
#3535	107