Subgroups — C₁₀₇×#17592 #41043556

Order 27392.

1510 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#407×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#380×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₇×#1520	C₂	1	2	yes	maximal, complemented
5	C₁₀₇×#1519	C₂	1	2	yes	maximal, complemented
6	C₁₀₇×#1513	C₂	1	4	yes	maximal, complemented
7	C₁₀₇×#1504	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₀₇	C₄	1	1	yes	characteristic, complemented
9	C₂⁴×C₄×C₁₀₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₀₇	—	2	1	no	—
11	#525×C₁₀₇	—	2	1	no	—
12	#525×C₁₀₇	—	2	1	no	—
13	#525×C₁₀₇	—	2	1	no	—
14	#525×C₁₀₇	—	2	1	no	—
15	#525×C₁₀₇	C₄	1	2	yes	complemented
16	#525×C₁₀₇	C₄	1	2	yes	complemented
17	#525×C₁₀₇	C₂²	1	2	yes	—
18	#525×C₁₀₇	C₂²	1	2	yes	—
19	C₂×#123×C₁₀₇	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₁₀₇	C₄	1	1	yes	characteristic, complemented
21	C₂×C₂²⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂×#121×C₁₀₇	C₄	1	1	yes	characteristic, complemented
23	C₂×#121×C₁₀₇	C₂²	1	1	yes	characteristic
24	C₂×#120×C₁₀₇	—	2	1	no	—
25	C₂×C₄×D₄×C₁₀₇	—	2	1	no	—
26	C₂×C₄×D₄×C₁₀₇	—	2	1	no	—
27	C₂×#117×C₁₀₇	C₄	1	1	yes	characteristic, complemented
28	C₂²×C₄⋊C₄×C₁₀₇	—	2	1	no	—
29	C₂²×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
30	#407×C₁₀₇	—	2	1	no	—
31	#407×C₁₀₇	—	2	1	no	—
32	#407×C₁₀₇	C₂²	1	2	yes	complemented
33	#407×C₁₀₇	C₂²	1	2	yes	complemented
34	C₂×C₂²⋊C₈×C₁₀₇	—	2	1	no	—
35	C₂×C₂²⋊C₈×C₁₀₇	C₂²	1	2	yes	—
36	#380×C₁₀₇	—	2	1	no	—
37	#380×C₁₀₇	—	2	1	no	—
38	#380×C₁₀₇	C₂²	1	2	yes	—
39	#380×C₁₀₇	C₂²	1	2	yes	complemented
40	C₂×#95×C₁₀₇	C₂²	1	2	yes	complemented
41	#328×C₁₀₇	C₂²	1	8	yes	complemented
42	#327×C₁₀₇	C₂²	1	8	yes	complemented
43	C₂⁵×C₁₀₇	D₄	1	1	yes	characteristic
44	C₂×#41×C₁₀₇	—	2	1	no	—
45	C₂×#41×C₁₀₇	—	2	1	no	—
46	C₂×#41×C₁₀₇	—	4	4	no	—
47	C₂×#41×C₁₀₇	C₂×C₄	1	2	yes	—
48	C₂×#41×C₁₀₇	C₂×C₄	1	2	yes	complemented
49	C₂²×Q₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂²×D₄×C₁₀₇	—	2	1	no	—
51	C₂²×D₄×C₁₀₇	—	2	1	no	—
52	C₂²×D₄×C₁₀₇	—	2	1	no	—
53	C₂²×D₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic, complemented
54	C₂³×C₄×C₁₀₇	—	2	1	no	—
55	C₂³×C₄×C₁₀₇	—	2	2	no	—
56	C₂³×C₄×C₁₀₇	—	4	4	no	—
57	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₁₀₇	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₁₀₇	—	2	2	no	—
72	C₂×M₁₆×C₁₀₇	—	2	2	no	—
73	C₂×M₁₆×C₁₀₇	—	4	4	no	—
74	C₂²×C₈×C₁₀₇	—	2	2	no	—
75	#123×C₁₀₇	—	2	2	no	—
76	#123×C₁₀₇	—	2	2	no	—
77	#123×C₁₀₇	—	2	2	no	—
78	#123×C₁₀₇	—	2	2	no	—
79	C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
80	C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
81	C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
82	C₂²⋊Q₈×C₁₀₇	—	2	1	no	—
83	C₂²⋊Q₈×C₁₀₇	C₂×C₄	1	2	yes	—
84	C₂²⋊Q₈×C₁₀₇	C₂×C₄	1	2	yes	complemented
85	C₂²⋊Q₈×C₁₀₇	C₂×C₄	1	2	yes	complemented
86	C₂²⋊Q₈×C₁₀₇	C₂³	1	2	yes	—
87	#121×C₁₀₇	—	2	1	no	—
88	#121×C₁₀₇	—	2	1	no	—
89	#121×C₁₀₇	—	2	1	no	—
90	#121×C₁₀₇	—	2	1	no	—
91	#121×C₁₀₇	C₂×C₄	1	2	yes	—
92	#121×C₁₀₇	C₂×C₄	1	2	yes	complemented
93	#121×C₁₀₇	C₂×C₄	1	2	yes	complemented
94	#121×C₁₀₇	C₂³	1	2	yes	—
95	#120×C₁₀₇	—	2	2	no	—
96	#120×C₁₀₇	—	2	2	no	—
97	#120×C₁₀₇	—	2	2	no	—
98	#120×C₁₀₇	—	2	2	no	—
99	C₄×D₄×C₁₀₇	—	2	2	no	—
100	C₄×D₄×C₁₀₇	—	2	2	no	—
101	C₄×D₄×C₁₀₇	—	2	2	no	—
102	C₄×D₄×C₁₀₇	—	2	2	no	—
103	C₄×D₄×C₁₀₇	—	2	2	no	—
104	C₄×D₄×C₁₀₇	—	2	2	no	—
105	C₄×D₄×C₁₀₇	—	2	2	no	—
106	C₄×D₄×C₁₀₇	—	2	2	no	—
107	#117×C₁₀₇	—	2	1	no	—
108	#117×C₁₀₇	—	2	1	no	—
109	#117×C₁₀₇	C₂×C₄	1	2	yes	—
110	#117×C₁₀₇	C₂×C₄	1	2	yes	complemented
111	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₀₇	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
114	C₂×C₄⋊C₄×C₁₀₇	—	2	2	no	—
115	C₂×C₄⋊C₄×C₁₀₇	—	4	4	no	—
116	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic, complemented
117	C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	1	1	yes	characteristic, complemented
118	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₁₀₇	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
124	C₂×C₂²⋊C₄×C₁₀₇	—	2	2	no	—
125	C₂×C₂²⋊C₄×C₁₀₇	—	4	4	no	—
126	C₂×C₄²×C₁₀₇	—	2	1	no	—
127	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
128	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
129	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
130	C₂²⋊C₈×C₁₀₇	C₂³	1	4	yes	—
131	#95×C₁₀₇	—	2	2	no	—
132	#95×C₁₀₇	C₂³	1	4	yes	—
133	C₂⁴×C₁₀₇	—	2	2	no	—
134	C₂⁴×C₁₀₇	—	2	2	no	—
135	C₂⁴×C₁₀₇	—	2	1	no	—
136	C₂⁴×C₁₀₇	—	4	2	no	—
137	C₂⁴×C₁₀₇	—	4	2	no	—
138	C₂⁴×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
139	C₂⁴×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
140	C₂⁴×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
141	C₂⁴×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
142	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×C₁₀₇	C₂×D₄	1	1	yes	characteristic
145	#41×C₁₀₇	—	4	4	no	—
146	#41×C₁₀₇	—	4	4	no	—
147	#41×C₁₀₇	—	4	4	no	—
148	#41×C₁₀₇	—	4	4	no	—
149	C₂×Q₈×C₁₀₇	—	2	1	no	—
150	C₂×Q₈×C₁₀₇	—	4	2	no	—
151	C₂×Q₈×C₁₀₇	C₂²×C₄	1	2	yes	—
152	C₂×D₄×C₁₀₇	—	2	2	no	—
153	C₂×D₄×C₁₀₇	—	2	2	no	—
154	C₂×D₄×C₁₀₇	—	2	2	no	—
155	C₂×D₄×C₁₀₇	—	2	2	no	—
156	C₂×D₄×C₁₀₇	—	2	2	no	—
157	C₂×D₄×C₁₀₇	—	2	2	no	—
158	C₂×D₄×C₁₀₇	—	2	1	no	—
159	C₂×D₄×C₁₀₇	—	4	2	no	—
160	C₂×D₄×C₁₀₇	—	4	4	no	—
161	C₂×D₄×C₁₀₇	—	4	4	no	—
162	C₂×D₄×C₁₀₇	—	4	2	no	—
163	C₂×D₄×C₁₀₇	—	4	2	no	—
164	C₂×D₄×C₁₀₇	C₂²×C₄	1	2	yes	—
165	C₂²×C₄×C₁₀₇	—	2	4	no	—
166	C₂²×C₄×C₁₀₇	—	2	4	no	—
167	C₂²×C₄×C₁₀₇	—	2	4	no	—
168	C₂²×C₄×C₁₀₇	—	2	1	no	—
169	C₂²×C₄×C₁₀₇	—	2	1	no	—
170	C₂²×C₄×C₁₀₇	—	2	1	no	—
171	C₂²×C₄×C₁₀₇	—	2	2	no	—
172	C₂²×C₄×C₁₀₇	—	2	2	no	—
173	C₂²×C₄×C₁₀₇	—	2	4	no	—
174	C₂²×C₄×C₁₀₇	—	4	2	no	—
175	C₂²×C₄×C₁₀₇	—	4	2	no	—
176	C₂²×C₄×C₁₀₇	—	4	2	no	—
177	C₂²×C₄×C₁₀₇	—	4	2	no	—
178	C₂²×C₄×C₁₀₇	—	4	2	no	—
179	C₂²×C₄×C₁₀₇	—	4	2	no	—
180	C₂²×C₄×C₁₀₇	—	4	2	no	—
181	C₂²×C₄×C₁₀₇	—	4	2	no	—
182	C₂²×C₄×C₁₀₇	—	4	2	no	—
183	C₂²×C₄×C₁₀₇	—	4	2	no	—
184	C₂²×C₄×C₁₀₇	—	4	2	no	—
185	C₂²×C₄×C₁₀₇	—	4	4	no	—
186	C₂²×C₄×C₁₀₇	—	4	4	no	—
187	C₂²×C₄×C₁₀₇	—	4	4	no	—
188	C₂²×C₄×C₁₀₇	—	4	4	no	—
189	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₀₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
217	M₁₆×C₁₀₇	—	4	4	no	—
218	M₁₆×C₁₀₇	—	4	4	no	—
219	C₂×C₈×C₁₀₇	—	2	4	no	—
220	C₂×C₈×C₁₀₇	—	4	4	no	—
221	C₄⋊C₄×C₁₀₇	—	2	2	no	—
222	C₄⋊C₄×C₁₀₇	—	2	2	no	—
223	C₄⋊C₄×C₁₀₇	—	2	2	no	—
224	C₄⋊C₄×C₁₀₇	—	2	1	no	—
225	C₄⋊C₄×C₁₀₇	—	2	1	no	—
226	C₄⋊C₄×C₁₀₇	—	2	2	no	—
227	C₄⋊C₄×C₁₀₇	—	4	4	no	—
228	C₄⋊C₄×C₁₀₇	—	4	4	no	—
229	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
230	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	2	yes	—
231	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
232	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
233	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
234	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
235	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
236	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
237	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
238	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
239	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
240	C₂²⋊C₄×C₁₀₇	—	2	2	no	—
241	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
242	C₂²⋊C₄×C₁₀₇	—	4	4	no	—
243	C₄²×C₁₀₇	—	2	2	no	—
244	C₄²×C₁₀₇	—	2	2	no	—
245	C₂³×C₁₀₇	—	2	1	no	—
246	C₂³×C₁₀₇	—	2	1	no	—
247	C₂³×C₁₀₇	—	2	2	no	—
248	C₂³×C₁₀₇	—	2	2	no	—
249	C₂³×C₁₀₇	—	2	1	no	—
250	C₂³×C₁₀₇	—	2	1	no	—
251	C₂³×C₁₀₇	—	2	2	no	—
252	C₂³×C₁₀₇	—	2	2	no	—
253	C₂³×C₁₀₇	—	2	2	no	—
254	C₂³×C₁₀₇	—	2	2	no	—
255	C₂³×C₁₀₇	—	2	2	no	—
256	C₂³×C₁₀₇	—	2	2	no	—
257	C₂³×C₁₀₇	—	2	2	no	—
258	C₂³×C₁₀₇	—	2	2	no	—
259	C₂³×C₁₀₇	—	2	2	no	—
260	C₂³×C₁₀₇	—	4	1	no	—
261	C₂³×C₁₀₇	—	4	1	no	—
262	C₂³×C₁₀₇	—	4	1	no	—
263	C₂³×C₁₀₇	—	4	1	no	—
264	C₂³×C₁₀₇	—	4	1	no	—
265	C₂³×C₁₀₇	—	4	1	no	—
266	C₂³×C₁₀₇	—	4	1	no	—
267	C₂³×C₁₀₇	—	4	1	no	—
268	C₂³×C₁₀₇	—	4	8	no	—
269	C₂³×C₁₀₇	—	4	8	no	—
270	C₂³×C₁₀₇	—	4	2	no	—
271	C₂³×C₁₀₇	—	4	2	no	—
272	C₂³×C₁₀₇	—	4	2	no	—
273	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂³×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂³×C₁₀₇	AGL(1,ℤ/8)	1	2	yes	—
280	C₂³×C₁₀₇	#137	1	2	yes	—
281	C₂³×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
282	Q₈×C₁₀₇	—	4	2	no	—
283	Q₈×C₁₀₇	—	4	2	no	—
284	D₄×C₁₀₇	—	4	2	no	—
285	D₄×C₁₀₇	—	4	4	no	—
286	D₄×C₁₀₇	—	4	4	no	—
287	D₄×C₁₀₇	—	4	2	no	—
288	D₄×C₁₀₇	—	4	2	no	—
289	D₄×C₁₀₇	—	4	4	no	—
290	D₄×C₁₀₇	—	4	4	no	—
291	D₄×C₁₀₇	—	4	4	no	—
292	D₄×C₁₀₇	—	4	2	no	—
293	C₂×C₄×C₁₀₇	—	2	2	no	—
294	C₂×C₄×C₁₀₇	—	2	2	no	—
295	C₂×C₄×C₁₀₇	—	2	2	no	—
296	C₂×C₄×C₁₀₇	—	2	2	no	—
297	C₂×C₄×C₁₀₇	—	2	2	no	—
298	C₂×C₄×C₁₀₇	—	2	2	no	—
299	C₂×C₄×C₁₀₇	—	2	2	no	—
300	C₂×C₄×C₁₀₇	—	2	2	no	—
301	C₂×C₄×C₁₀₇	—	2	2	no	—
302	C₂×C₄×C₁₀₇	—	2	2	no	—
303	C₂×C₄×C₁₀₇	—	2	2	no	—
304	C₂×C₄×C₁₀₇	—	2	2	no	—
305	C₂×C₄×C₁₀₇	—	2	2	no	—
306	C₂×C₄×C₁₀₇	—	2	2	no	—
307	C₂×C₄×C₁₀₇	—	2	2	no	—
308	C₂×C₄×C₁₀₇	—	2	2	no	—
309	C₂×C₄×C₁₀₇	—	2	2	no	—
310	C₂×C₄×C₁₀₇	—	2	2	no	—
311	C₂×C₄×C₁₀₇	—	4	1	no	—
312	C₂×C₄×C₁₀₇	—	4	1	no	—
313	C₂×C₄×C₁₀₇	—	4	1	no	—
314	C₂×C₄×C₁₀₇	—	4	1	no	—
315	C₂×C₄×C₁₀₇	—	4	1	no	—
316	C₂×C₄×C₁₀₇	—	4	1	no	—
317	C₂×C₄×C₁₀₇	—	4	1	no	—
318	C₂×C₄×C₁₀₇	—	4	1	no	—
319	C₂×C₄×C₁₀₇	—	4	1	no	—
320	C₂×C₄×C₁₀₇	—	4	1	no	—
321	C₂×C₄×C₁₀₇	—	4	1	no	—
322	C₂×C₄×C₁₀₇	—	4	1	no	—
323	C₂×C₄×C₁₀₇	—	4	4	no	—
324	C₂×C₄×C₁₀₇	—	4	2	no	—
325	C₂×C₄×C₁₀₇	—	4	2	no	—
326	C₂×C₄×C₁₀₇	—	4	2	no	—
327	C₂×C₄×C₁₀₇	—	4	4	no	—
328	C₂×C₄×C₁₀₇	—	4	4	no	—
329	C₂×C₄×C₁₀₇	—	4	4	no	—
330	C₂×C₄×C₁₀₇	—	4	4	no	—
331	C₂×C₄×C₁₀₇	—	8	8	no	—
332	C₂×C₄×C₁₀₇	#99	1	4	yes	—
333	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
334	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
335	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×C₄×C₁₀₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	C₂×C₄×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
340	C₂×C₄×C₁₀₇	C₂²×D₄	1	1	yes	characteristic
341	C₈×C₁₀₇	—	4	4	no	—
342	C₂²×C₁₀₇	—	2	4	no	—
343	C₂²×C₁₀₇	—	2	4	no	—
344	C₂²×C₁₀₇	—	2	1	no	—
345	C₂²×C₁₀₇	—	2	1	no	—
346	C₂²×C₁₀₇	—	2	1	no	—
347	C₂²×C₁₀₇	—	2	1	no	—
348	C₂²×C₁₀₇	—	2	1	no	—
349	C₂²×C₁₀₇	—	2	1	no	—
350	C₂²×C₁₀₇	—	2	1	no	—
351	C₂²×C₁₀₇	—	2	1	no	—
352	C₂²×C₁₀₇	—	2	1	no	—
353	C₂²×C₁₀₇	—	2	1	no	—
354	C₂²×C₁₀₇	—	2	1	no	—
355	C₂²×C₁₀₇	—	2	1	no	—
356	C₂²×C₁₀₇	—	2	1	no	—
357	C₂²×C₁₀₇	—	2	1	no	—
358	C₂²×C₁₀₇	—	2	1	no	—
359	C₂²×C₁₀₇	—	2	1	no	—
360	C₂²×C₁₀₇	—	4	2	no	—
361	C₂²×C₁₀₇	—	4	2	no	—
362	C₂²×C₁₀₇	—	4	4	no	—
363	C₂²×C₁₀₇	—	4	4	no	—
364	C₂²×C₁₀₇	—	4	4	no	—
365	C₂²×C₁₀₇	—	4	4	no	—
366	C₂²×C₁₀₇	—	4	2	no	—
367	C₂²×C₁₀₇	—	4	2	no	—
368	C₂²×C₁₀₇	—	4	2	no	—
369	C₂²×C₁₀₇	—	4	2	no	—
370	C₂²×C₁₀₇	—	4	2	no	—
371	C₂²×C₁₀₇	—	8	4	no	—
372	C₂²×C₁₀₇	C₂×#99	1	2	yes	—
373	C₂²×C₁₀₇	#417	1	2	yes	—
374	C₂²×C₁₀₇	#417	1	2	yes	—
375	C₂²×C₁₀₇	#421	1	2	yes	—
376	C₂²×C₁₀₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
377	C₂²×C₁₀₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
378	C₂²×C₁₀₇	C₂×#137	1	1	yes	characteristic
379	C₄×C₁₀₇	—	2	1	no	—
380	C₄×C₁₀₇	—	2	1	no	—
381	C₄×C₁₀₇	—	2	1	no	—
382	C₄×C₁₀₇	—	2	1	no	—
383	C₄×C₁₀₇	—	2	1	no	—
384	C₄×C₁₀₇	—	2	1	no	—
385	C₄×C₁₀₇	—	4	2	no	—
386	C₄×C₁₀₇	—	4	2	no	—
387	C₄×C₁₀₇	—	4	2	no	—
388	C₄×C₁₀₇	—	8	4	no	—
389	C₄×C₁₀₇	C₂×#99	1	2	yes	—
390	C₄×C₁₀₇	C₂×#99	1	2	yes	—
391	#17592	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
392	C₂×C₁₀₇	—	2	1	no	—
393	C₂×C₁₀₇	—	2	1	no	—
394	C₂×C₁₀₇	—	2	2	no	—
395	C₂×C₁₀₇	—	2	2	no	—
396	C₂×C₁₀₇	—	2	2	no	—
397	C₂×C₁₀₇	—	2	2	no	—
398	C₂×C₁₀₇	—	4	1	no	—
399	C₂×C₁₀₇	—	4	1	no	—
400	C₂×C₁₀₇	—	8	2	no	—
401	C₂×C₁₀₇	C₂²×#99	1	1	yes	characteristic
402	C₂×C₁₀₇	C₂×#417	1	1	yes	characteristic
403	C₂×C₁₀₇	C₂×#421	1	1	yes	characteristic
404	C₂×#525	C₂×C₁₀₇	1	1	yes	characteristic
405	C₂×#407	C₂×C₁₀₇	1	1	yes	characteristic, complemented
406	C₂×#380	C₂×C₁₀₇	1	1	yes	characteristic, complemented
407	#1520	C₂×C₁₀₇	1	2	yes	complemented
408	#1519	C₂×C₁₀₇	1	2	yes	complemented
409	#1513	C₂×C₁₀₇	1	4	yes	complemented
410	#1504	C₂×C₁₀₇	1	4	yes	complemented
411	C₁₀₇	#17592	1	1	yes	characteristic, direct product factor, Sylow
412	C₂²×#41	C₄×C₁₀₇	1	1	yes	characteristic, complemented
413	C₂⁴×C₄	C₂²×C₁₀₇	1	1	yes	characteristic
414	C₂²×M₁₆	—	2	1	no	—
415	#525	—	2	1	no	—
416	#525	—	2	1	no	—
417	#525	—	2	1	no	—
418	#525	—	2	1	no	—
419	#525	C₄×C₁₀₇	1	2	yes	complemented
420	#525	C₄×C₁₀₇	1	2	yes	complemented
421	#525	C₂²×C₁₀₇	1	2	yes	—
422	#525	C₂²×C₁₀₇	1	2	yes	—
423	C₂×#123	—	2	1	no	—
424	C₂×C₂²⋊Q₈	C₄×C₁₀₇	1	1	yes	characteristic, complemented
425	C₂×C₂²⋊Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
426	C₂×#121	C₄×C₁₀₇	1	1	yes	characteristic, complemented
427	C₂×#121	C₂²×C₁₀₇	1	1	yes	characteristic
428	C₂×#120	—	2	1	no	—
429	C₂×C₄×D₄	—	2	1	no	—
430	C₂×C₄×D₄	—	2	1	no	—
431	C₂×#117	C₄×C₁₀₇	1	1	yes	characteristic, complemented
432	C₂²×C₄⋊C₄	—	2	1	no	—
433	C₂²×C₂²⋊C₄	—	2	1	no	—
434	#407	—	2	1	no	—
435	#407	—	2	1	no	—
436	#407	C₂²×C₁₀₇	1	2	yes	complemented
437	#407	C₂²×C₁₀₇	1	2	yes	complemented
438	C₂×C₂²⋊C₈	—	2	1	no	—
439	C₂×C₂²⋊C₈	C₂²×C₁₀₇	1	2	yes	—
440	#380	—	2	1	no	—
441	#380	—	2	1	no	—
442	#380	C₂²×C₁₀₇	1	2	yes	—
443	#380	C₂²×C₁₀₇	1	2	yes	complemented
444	C₂×#95	C₂²×C₁₀₇	1	2	yes	complemented
445	#328	C₂²×C₁₀₇	1	8	yes	complemented
446	#327	C₂²×C₁₀₇	1	8	yes	complemented
447	C₂⁵	D₄×C₁₀₇	1	1	yes	characteristic
448	C₂×#41	—	2	1	no	—
449	C₂×#41	—	2	1	no	—
450	C₂×#41	—	4	4	no	—
451	C₂×#41	C₂×C₄×C₁₀₇	1	2	yes	—
452	C₂×#41	C₂×C₄×C₁₀₇	1	2	yes	complemented
453	C₂²×Q₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic, complemented
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	—	2	1	no	—
457	C₂²×D₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic, complemented
458	C₂³×C₄	—	2	1	no	—
459	C₂³×C₄	—	2	2	no	—
460	C₂³×C₄	—	4	4	no	—
461	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
462	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
463	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
464	C₂³×C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic
465	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
466	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
467	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
468	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
469	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
470	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
471	C₂³×C₄	D₄×C₁₀₇	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
475	C₂×M₁₆	—	2	2	no	—
476	C₂×M₁₆	—	2	2	no	—
477	C₂×M₁₆	—	4	4	no	—
478	C₂²×C₈	—	2	2	no	—
479	#123	—	2	2	no	—
480	#123	—	2	2	no	—
481	#123	—	2	2	no	—
482	#123	—	2	2	no	—
483	C₂²⋊Q₈	—	2	1	no	—
484	C₂²⋊Q₈	—	2	1	no	—
485	C₂²⋊Q₈	—	2	1	no	—
486	C₂²⋊Q₈	—	2	1	no	—
487	C₂²⋊Q₈	C₂×C₄×C₁₀₇	1	2	yes	—
488	C₂²⋊Q₈	C₂×C₄×C₁₀₇	1	2	yes	complemented
489	C₂²⋊Q₈	C₂×C₄×C₁₀₇	1	2	yes	complemented
490	C₂²⋊Q₈	C₂³×C₁₀₇	1	2	yes	—
491	#121	—	2	1	no	—
492	#121	—	2	1	no	—
493	#121	—	2	1	no	—
494	#121	—	2	1	no	—
495	#121	C₂×C₄×C₁₀₇	1	2	yes	—
496	#121	C₂×C₄×C₁₀₇	1	2	yes	complemented
497	#121	C₂×C₄×C₁₀₇	1	2	yes	complemented
498	#121	C₂³×C₁₀₇	1	2	yes	—
499	#120	—	2	2	no	—
500	#120	—	2	2	no	—
501	#120	—	2	2	no	—
502	#120	—	2	2	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	#117	—	2	1	no	—
512	#117	—	2	1	no	—
513	#117	C₂×C₄×C₁₀₇	1	2	yes	—
514	#117	C₂×C₄×C₁₀₇	1	2	yes	complemented
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄⋊C₄	—	2	2	no	—
518	C₂×C₄⋊C₄	—	2	2	no	—
519	C₂×C₄⋊C₄	—	4	4	no	—
520	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic, complemented
521	C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	1	1	yes	characteristic, complemented
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	2	no	—
528	C₂×C₂²⋊C₄	—	2	2	no	—
529	C₂×C₂²⋊C₄	—	4	4	no	—
530	C₂×C₄²	—	2	1	no	—
531	C₂²⋊C₈	—	2	2	no	—
532	C₂²⋊C₈	—	2	2	no	—
533	C₂²⋊C₈	—	2	2	no	—
534	C₂²⋊C₈	C₂³×C₁₀₇	1	4	yes	—
535	#95	—	2	2	no	—
536	#95	C₂³×C₁₀₇	1	4	yes	—
537	C₂⁴	—	2	2	no	—
538	C₂⁴	—	2	2	no	—
539	C₂⁴	—	2	1	no	—
540	C₂⁴	—	4	2	no	—
541	C₂⁴	—	4	2	no	—
542	C₂⁴	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
543	C₂⁴	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
544	C₂⁴	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
545	C₂⁴	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
546	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
547	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
548	C₂⁴	C₂×D₄×C₁₀₇	1	1	yes	characteristic
549	#41	—	4	4	no	—
550	#41	—	4	4	no	—
551	#41	—	4	4	no	—
552	#41	—	4	4	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	4	2	no	—
555	C₂×Q₈	C₂²×C₄×C₁₀₇	1	2	yes	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	4	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	C₂²×C₄×C₁₀₇	1	2	yes	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	—	4	4	no	—
593	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
594	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
595	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
596	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
597	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
598	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
599	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
600	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
601	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
602	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
603	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
604	C₂²×C₄	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
605	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
606	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
607	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
608	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
609	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
610	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₁₀₇	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
621	M₁₆	—	4	4	no	—
622	M₁₆	—	4	4	no	—
623	C₂×C₈	—	2	4	no	—
624	C₂×C₈	—	4	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	4	4	no	—
632	C₄⋊C₄	—	4	4	no	—
633	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
634	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	2	yes	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	4	4	no	—
646	C₂²⋊C₄	—	4	4	no	—
647	C₄²	—	2	2	no	—
648	C₄²	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	8	no	—
673	C₂³	—	4	8	no	—
674	C₂³	—	4	2	no	—
675	C₂³	—	4	2	no	—
676	C₂³	—	4	2	no	—
677	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
678	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
679	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
680	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
681	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
682	C₂³	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
683	C₂³	AGL(1,ℤ/8)×C₁₀₇	1	2	yes	—
684	C₂³	#137×C₁₀₇	1	2	yes	—
685	C₂³	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
686	Q₈	—	4	2	no	—
687	Q₈	—	4	2	no	—
688	D₄	—	4	2	no	—
689	D₄	—	4	4	no	—
690	D₄	—	4	4	no	—
691	D₄	—	4	4	no	—
692	D₄	—	4	4	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	2	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	4	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	—	4	4	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	8	8	no	—
736	C₂×C₄	#99×C₁₀₇	1	4	yes	—
737	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
738	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
739	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
740	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
741	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
742	C₂×C₄	C₂×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
743	C₂×C₄	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
744	C₂×C₄	C₂²×D₄×C₁₀₇	1	1	yes	characteristic
745	C₈	—	4	4	no	—
746	C₂²	—	2	4	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	1	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	4	no	—
767	C₂²	—	4	4	no	—
768	C₂²	—	4	4	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	8	4	no	—
776	C₂²	C₂×#99×C₁₀₇	1	2	yes	—
777	C₂²	#417×C₁₀₇	1	2	yes	—
778	C₂²	#417×C₁₀₇	1	2	yes	—
779	C₂²	#421×C₁₀₇	1	2	yes	—
780	C₂²	C₂²×C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
781	C₂²	C₂×AGL(1,ℤ/8)×C₁₀₇	1	1	yes	characteristic
782	C₂²	C₂×#137×C₁₀₇	1	1	yes	characteristic
783	C₄	—	2	1	no	—
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	1	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	8	4	no	—
793	C₄	C₂×#99×C₁₀₇	1	2	yes	—
794	C₄	C₂×#99×C₁₀₇	1	2	yes	—
795	C₂	—	2	1	no	—
796	C₂	—	2	2	no	—
797	C₂	—	2	2	no	—
798	C₂	—	2	1	no	—
799	C₂	—	2	2	no	—
800	C₂	—	2	2	no	—
801	C₂	—	4	1	no	—
802	C₂	—	4	1	no	—
803	C₂	—	8	2	no	—
804	C₂	C₂²×#99×C₁₀₇	1	1	yes	characteristic
805	C₂	C₂×#417×C₁₀₇	1	1	yes	characteristic
806	C₂	C₂×#421×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₇	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₀₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₇
prime radical	C₂×#525×C₁₀₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₇ ◁ C₂⁴×C₄×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#407×C₁₀₇	C₂	semidirect
3. C₂×#380×C₁₀₇	C₂	semidirect
4. C₁₀₇×#1520	C₂	semidirect
5. C₁₀₇×#1519	C₂	semidirect
6. C₁₀₇×#1513	C₂	semidirect
7. C₁₀₇×#1504	C₂	semidirect
8. C₂²×#41×C₁₀₇	C₄	semidirect
15. #525×C₁₀₇	C₄	semidirect
16. #525×C₁₀₇	C₄	semidirect
20. C₂×C₂²⋊Q₈×C₁₀₇	C₄	semidirect
22. C₂×#121×C₁₀₇	C₄	semidirect
27. C₂×#117×C₁₀₇	C₄	semidirect
32. #407×C₁₀₇	C₂²	semidirect
33. #407×C₁₀₇	C₂²	semidirect
39. #380×C₁₀₇	C₂²	semidirect
40. C₂×#95×C₁₀₇	C₂²	semidirect
41. #328×C₁₀₇	C₂²	semidirect
42. #327×C₁₀₇	C₂²	semidirect
48. C₂×#41×C₁₀₇	C₂×C₄	semidirect
49. C₂²×Q₈×C₁₀₇	C₂×C₄	semidirect
53. C₂²×D₄×C₁₀₇	C₂×C₄	semidirect
84. C₂²⋊Q₈×C₁₀₇	C₂×C₄	semidirect
85. C₂²⋊Q₈×C₁₀₇	C₂×C₄	semidirect
92. #121×C₁₀₇	C₂×C₄	semidirect
93. #121×C₁₀₇	C₂×C₄	semidirect
110. #117×C₁₀₇	C₂×C₄	semidirect
116. C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	semidirect
117. C₂×C₄⋊C₄×C₁₀₇	C₂×C₄	semidirect
391. #17592	C₁₀₇	direct (N × H)
405. C₂×#407	C₂×C₁₀₇	semidirect
406. C₂×#380	C₂×C₁₀₇	semidirect
407. #1520	C₂×C₁₀₇	semidirect
408. #1519	C₂×C₁₀₇	semidirect
409. #1513	C₂×C₁₀₇	semidirect
410. #1504	C₂×C₁₀₇	semidirect
411. C₁₀₇	#17592	direct (N × H)
412. C₂²×#41	C₄×C₁₀₇	semidirect
419. #525	C₄×C₁₀₇	semidirect
420. #525	C₄×C₁₀₇	semidirect
424. C₂×C₂²⋊Q₈	C₄×C₁₀₇	semidirect
426. C₂×#121	C₄×C₁₀₇	semidirect
431. C₂×#117	C₄×C₁₀₇	semidirect
436. #407	C₂²×C₁₀₇	semidirect
437. #407	C₂²×C₁₀₇	semidirect
443. #380	C₂²×C₁₀₇	semidirect
444. C₂×#95	C₂²×C₁₀₇	semidirect
445. #328	C₂²×C₁₀₇	semidirect
446. #327	C₂²×C₁₀₇	semidirect
452. C₂×#41	C₂×C₄×C₁₀₇	semidirect
453. C₂²×Q₈	C₂×C₄×C₁₀₇	semidirect
457. C₂²×D₄	C₂×C₄×C₁₀₇	semidirect
488. C₂²⋊Q₈	C₂×C₄×C₁₀₇	semidirect
489. C₂²⋊Q₈	C₂×C₄×C₁₀₇	semidirect
496. #121	C₂×C₄×C₁₀₇	semidirect
497. #121	C₂×C₄×C₁₀₇	semidirect
514. #117	C₂×C₄×C₁₀₇	semidirect
520. C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	semidirect
521. C₂×C₄⋊C₄	C₂×C₄×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₁₀₇	2
C₂×#407×C₁₀₇	2
C₂×#380×C₁₀₇	2
C₁₀₇×#1520	2
C₁₀₇×#1519	2
C₁₀₇×#1513	2
C₁₀₇×#1504	2
#17592	107

Subgroups — C107×#17592 #41043556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#17592 #41043556