Subgroups — C₄×#529×C₁₀₇ #41059999

Order 27392.

2670 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₄×#125×C₁₀₇	C₂	1	2	yes	maximal, complemented
3	C₄×#126×C₁₀₇	C₂	1	4	yes	maximal, complemented
4	C₄×#124×C₁₀₇	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊Q₈×C₁₀₇	C₂	1	2	yes	maximal, complemented
6	C₄×#123×C₁₀₇	C₂	1	4	yes	maximal, complemented
7	C₄×#121×C₁₀₇	C₂	1	2	yes	maximal
8	C₁₀₇×#2298	C₂	1	2	yes	maximal, complemented
9	C₁₀₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₇×#2290	C₂	1	2	yes	maximal, complemented
12	C₁₀₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄²×Q₈×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×D₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄²×D₄×C₁₀₇	C₂	1	2	yes	maximal, complemented
16	C₄×#117×C₁₀₇	C₂	1	2	yes	maximal, complemented
17	C₂×C₄³×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
18	#529×C₁₀₇	C₄	1	16	yes	direct product factor
19	C₂×#126×C₁₀₇	C₂²	1	2	yes	—
20	C₂×#125×C₁₀₇	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₀₇	C₂²	1	1	yes	characteristic
22	C₂×#123×C₁₀₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
24	C₂×#121×C₁₀₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₀₇	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₀₇	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₀₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₀₇	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₀₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₁₀₇	C₂²	1	2	yes	—
32	C₂×#117×C₁₀₇	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₀₇	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₀₇	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₁₀₇	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
39	#391×C₁₀₇	C₂²	1	2	yes	—
40	#390×C₁₀₇	C₂²	1	2	yes	—
41	#389×C₁₀₇	C₂²	1	2	yes	—
42	#389×C₁₀₇	C₂²	1	2	yes	—
43	#388×C₁₀₇	C₂²	1	4	yes	—
44	#388×C₁₀₇	C₂²	1	4	yes	—
45	#388×C₁₀₇	C₂²	1	4	yes	—
46	#388×C₁₀₇	C₂²	1	4	yes	—
47	#387×C₁₀₇	C₂²	1	4	yes	—
48	#387×C₁₀₇	C₂²	1	4	yes	—
49	#387×C₁₀₇	C₂²	1	4	yes	—
50	#387×C₁₀₇	C₂²	1	4	yes	—
51	#386×C₁₀₇	C₂²	1	4	yes	—
52	#385×C₁₀₇	C₂²	1	4	yes	—
53	#383×C₁₀₇	C₂²	1	2	yes	—
54	#382×C₁₀₇	C₂²	1	2	yes	—
55	#381×C₁₀₇	C₂²	1	2	yes	—
56	#380×C₁₀₇	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	4	yes	—
59	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
64	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₁₀₇	C₂²	1	4	yes	—
67	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	4	yes	—
68	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	4	yes	—
69	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	4	yes	—
73	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₁₀₇	C₂²	1	4	yes	—
75	#376×C₁₀₇	C₂²	1	2	yes	—
76	#376×C₁₀₇	C₂²	1	2	yes	—
77	C₄³×C₁₀₇	C₂²	1	1	yes	characteristic
78	C₄³×C₁₀₇	C₂²	1	1	yes	characteristic
79	C₄³×C₁₀₇	C₂²	1	2	yes	—
80	C₄³×C₁₀₇	C₂²	1	2	yes	—
81	C₄³×C₁₀₇	C₂²	1	1	yes	characteristic
82	C₄³×C₁₀₇	C₂²	1	1	yes	characteristic
83	C₄³×C₁₀₇	C₂²	1	2	yes	—
84	C₂²×Q₈×C₁₀₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₀₇	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₀₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₀₇	C₂³	1	4	yes	—
88	C₂³×C₄×C₁₀₇	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₀₇	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₀₇	C₂³	1	2	yes	—
94	#126×C₁₀₇	C₂×C₄	1	16	yes	complemented
95	#125×C₁₀₇	C₂×C₄	1	8	yes	complemented
96	#124×C₁₀₇	C₂×C₄	1	8	yes	complemented
97	#123×C₁₀₇	C₂×C₄	1	16	yes	complemented
98	C₂²⋊Q₈×C₁₀₇	C₂×C₄	1	8	yes	complemented
99	#121×C₁₀₇	C₂×C₄	1	8	yes	—
100	C₄×Q₈×C₁₀₇	—	2	8	no	—
101	C₄×Q₈×C₁₀₇	C₂×C₄	1	8	yes	complemented
102	C₄×D₄×C₁₀₇	—	2	16	no	—
103	C₄×D₄×C₁₀₇	—	2	8	no	—
104	C₄×D₄×C₁₀₇	C₂×C₄	1	8	yes	complemented
105	C₄×D₄×C₁₀₇	C₂×C₄	1	16	yes	complemented
106	#117×C₁₀₇	—	2	8	no	—
107	#117×C₁₀₇	C₂×C₄	1	16	yes	complemented
108	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₀₇	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₁₀₇	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₀₇	—	2	8	no	—
129	C₂×C₄²×C₁₀₇	—	2	4	no	—
130	C₂×C₄²×C₁₀₇	—	2	8	no	—
131	C₂×C₄²×C₁₀₇	—	2	4	no	—
132	C₂×C₄²×C₁₀₇	—	2	8	no	—
133	C₂×C₄²×C₁₀₇	C₂×C₄	1	8	yes	complemented
134	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
143	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₀₇	C₂³	1	4	yes	—
147	C₂×C₄²×C₁₀₇	C₂³	1	4	yes	—
148	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₀₇	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₁₀₇	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₀₇	C₂³	1	1	yes	characteristic
158	#95×C₁₀₇	C₂³	1	4	yes	—
159	#95×C₁₀₇	C₂³	1	4	yes	—
160	#95×C₁₀₇	C₂³	1	4	yes	—
161	#95×C₁₀₇	C₂³	1	4	yes	—
162	#95×C₁₀₇	C₂³	1	2	yes	—
163	#95×C₁₀₇	C₂³	1	4	yes	—
164	#95×C₁₀₇	C₂³	1	4	yes	—
165	#95×C₁₀₇	C₂³	1	4	yes	—
166	#95×C₁₀₇	C₂³	1	4	yes	—
167	#95×C₁₀₇	C₂³	1	2	yes	—
168	#95×C₁₀₇	C₂³	1	4	yes	—
169	C₂⁴×C₁₀₇	C₂⁴	1	2	yes	—
170	C₂⁴×C₁₀₇	C₂⁴	1	1	yes	characteristic
171	C₂×Q₈×C₁₀₇	—	2	4	no	—
172	C₂×Q₈×C₁₀₇	C₂²×C₄	1	4	yes	—
173	C₂×D₄×C₁₀₇	—	2	8	no	—
174	C₂×D₄×C₁₀₇	—	2	4	no	—
175	C₂×D₄×C₁₀₇	C₂²×C₄	1	8	yes	—
176	C₂×D₄×C₁₀₇	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₁₀₇	—	2	4	no	—
178	C₂²×C₄×C₁₀₇	—	2	4	no	—
179	C₂²×C₄×C₁₀₇	—	2	4	no	—
180	C₂²×C₄×C₁₀₇	—	2	4	no	—
181	C₂²×C₄×C₁₀₇	—	2	2	no	—
182	C₂²×C₄×C₁₀₇	—	2	2	no	—
183	C₂²×C₄×C₁₀₇	—	2	4	no	—
184	C₂²×C₄×C₁₀₇	—	2	4	no	—
185	C₂²×C₄×C₁₀₇	—	2	4	no	—
186	C₂²×C₄×C₁₀₇	—	2	4	no	—
187	C₂²×C₄×C₁₀₇	—	2	4	no	—
188	C₂²×C₄×C₁₀₇	—	2	8	no	—
189	C₂²×C₄×C₁₀₇	—	2	8	no	—
190	C₂²×C₄×C₁₀₇	—	2	8	no	—
191	C₂²×C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
192	C₂²×C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
193	C₂²×C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
195	C₂²×C₄×C₁₀₇	#41	1	8	yes	—
196	C₂²×C₄×C₁₀₇	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₀₇	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₀₇	C₂⁴	1	2	yes	—
211	C₄⋊C₄×C₁₀₇	—	2	8	no	—
212	C₄⋊C₄×C₁₀₇	—	2	8	no	—
213	C₄⋊C₄×C₁₀₇	—	2	4	no	—
214	C₄⋊C₄×C₁₀₇	—	2	8	no	—
215	C₄⋊C₄×C₁₀₇	—	2	4	no	—
216	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
217	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
218	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
219	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
220	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
222	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
223	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
224	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
225	C₂²⋊C₄×C₁₀₇	—	2	8	no	—
226	C₂²⋊C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
227	C₂²⋊C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
228	C₂²⋊C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
229	C₂²⋊C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
230	C₂²⋊C₄×C₁₀₇	C₂²×C₄	1	8	yes	—
231	C₄²×C₁₀₇	—	2	4	no	—
232	C₄²×C₁₀₇	—	2	4	no	—
233	C₄²×C₁₀₇	—	2	4	no	—
234	C₄²×C₁₀₇	—	2	4	no	—
235	C₄²×C₁₀₇	—	2	2	no	—
236	C₄²×C₁₀₇	—	2	2	no	—
237	C₄²×C₁₀₇	—	2	4	no	—
238	C₄²×C₁₀₇	—	2	4	no	—
239	C₄²×C₁₀₇	—	2	4	no	—
240	C₄²×C₁₀₇	—	2	4	no	—
241	C₄²×C₁₀₇	—	2	4	no	—
242	C₄²×C₁₀₇	—	2	8	no	—
243	C₄²×C₁₀₇	—	2	4	no	—
244	C₄²×C₁₀₇	—	2	4	no	—
245	C₄²×C₁₀₇	—	2	8	no	—
246	C₄²×C₁₀₇	—	2	8	no	—
247	C₄²×C₁₀₇	C₂²×C₄	1	4	yes	—
248	C₄²×C₁₀₇	C₂²×C₄	1	4	yes	—
249	C₄²×C₁₀₇	C₂²×C₄	1	4	yes	—
250	C₄²×C₁₀₇	C₂²×C₄	1	4	yes	—
251	C₄²×C₁₀₇	C₂²×C₄	1	8	yes	—
252	C₄²×C₁₀₇	#41	1	4	yes	—
253	C₄²×C₁₀₇	#41	1	4	yes	—
254	C₄²×C₁₀₇	#41	1	8	yes	—
255	C₂³×C₁₀₇	—	2	1	no	—
256	C₂³×C₁₀₇	—	2	2	no	—
257	C₂³×C₁₀₇	—	2	1	no	—
258	C₂³×C₁₀₇	—	2	2	no	—
259	C₂³×C₁₀₇	—	2	4	no	—
260	C₂³×C₁₀₇	—	2	4	no	—
261	C₂³×C₁₀₇	—	2	2	no	—
262	C₂³×C₁₀₇	C₂³×C₄	1	4	yes	—
263	C₂³×C₁₀₇	C₂³×C₄	1	2	yes	—
264	C₂³×C₁₀₇	C₂×#41	1	4	yes	—
265	C₂³×C₁₀₇	C₂⁵	1	1	yes	characteristic
266	Q₈×C₁₀₇	—	2	8	no	—
267	D₄×C₁₀₇	—	2	16	no	—
268	D₄×C₁₀₇	—	2	8	no	—
269	C₂×C₄×C₁₀₇	—	2	16	no	—
270	C₂×C₄×C₁₀₇	—	2	8	no	—
271	C₂×C₄×C₁₀₇	—	2	1	no	—
272	C₂×C₄×C₁₀₇	—	2	2	no	—
273	C₂×C₄×C₁₀₇	—	2	2	no	—
274	C₂×C₄×C₁₀₇	—	2	2	no	—
275	C₂×C₄×C₁₀₇	—	2	2	no	—
276	C₂×C₄×C₁₀₇	—	2	1	no	—
277	C₂×C₄×C₁₀₇	—	2	2	no	—
278	C₂×C₄×C₁₀₇	—	2	2	no	—
279	C₂×C₄×C₁₀₇	—	2	2	no	—
280	C₂×C₄×C₁₀₇	—	2	2	no	—
281	C₂×C₄×C₁₀₇	—	2	2	no	—
282	C₂×C₄×C₁₀₇	—	2	2	no	—
283	C₂×C₄×C₁₀₇	—	2	4	no	—
284	C₂×C₄×C₁₀₇	—	2	4	no	—
285	C₂×C₄×C₁₀₇	—	2	2	no	—
286	C₂×C₄×C₁₀₇	—	2	8	no	—
287	C₂×C₄×C₁₀₇	—	2	16	no	—
288	C₂×C₄×C₁₀₇	—	2	8	no	—
289	C₂×C₄×C₁₀₇	—	2	16	no	—
290	C₂×C₄×C₁₀₇	—	2	4	no	—
291	C₂×C₄×C₁₀₇	—	2	4	no	—
292	C₂×C₄×C₁₀₇	—	2	4	no	—
293	C₂×C₄×C₁₀₇	—	2	4	no	—
294	C₂×C₄×C₁₀₇	—	2	4	no	—
295	C₂×C₄×C₁₀₇	—	2	4	no	—
296	C₂×C₄×C₁₀₇	—	4	16	no	—
297	C₂×C₄×C₁₀₇	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₁₀₇	C₂³×C₄	1	2	yes	—
299	C₂×C₄×C₁₀₇	C₂³×C₄	1	2	yes	—
300	C₂×C₄×C₁₀₇	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₁₀₇	C₂³×C₄	1	4	yes	—
302	C₂×C₄×C₁₀₇	C₂³×C₄	1	4	yes	—
303	C₂×C₄×C₁₀₇	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₁₀₇	C₂³×C₄	1	2	yes	—
305	C₂×C₄×C₁₀₇	C₂³×C₄	1	2	yes	—
306	C₂×C₄×C₁₀₇	C₂×#41	1	4	yes	—
307	C₂×C₄×C₁₀₇	C₂×#41	1	4	yes	—
308	C₂×C₄×C₁₀₇	C₂×#41	1	4	yes	—
309	C₂×C₄×C₁₀₇	C₂×#41	1	2	yes	—
310	C₂×C₄×C₁₀₇	C₂×#41	1	2	yes	—
311	C₂×C₄×C₁₀₇	C₂×#41	1	4	yes	—
312	C₂×C₄×C₁₀₇	C₂×#41	1	4	yes	—
313	C₂×C₄×C₁₀₇	C₂×#41	1	4	yes	—
314	C₂×C₄×C₁₀₇	C₂×#41	1	4	yes	—
315	C₂²×C₁₀₇	—	2	2	no	—
316	C₂²×C₁₀₇	—	2	2	no	—
317	C₂²×C₁₀₇	—	2	4	no	—
318	C₂²×C₁₀₇	—	2	4	no	—
319	C₂²×C₁₀₇	—	2	4	no	—
320	C₂²×C₁₀₇	—	2	4	no	—
321	C₂²×C₁₀₇	—	2	4	no	—
322	C₂²×C₁₀₇	—	4	4	no	—
323	C₂²×C₁₀₇	—	4	4	no	—
324	C₂²×C₁₀₇	C₄×#41	1	4	yes	—
325	C₂²×C₁₀₇	C₂⁴×C₄	1	1	yes	characteristic
326	C₂²×C₁₀₇	C₂²×#41	1	1	yes	characteristic
327	C₂²×C₁₀₇	C₂²×#41	1	2	yes	—
328	C₂²×C₁₀₇	C₂²×#41	1	2	yes	—
329	C₂²×C₁₀₇	C₂²×#41	1	1	yes	characteristic
330	C₄×C₁₀₇	—	2	2	no	—
331	C₄×C₁₀₇	—	2	2	no	—
332	C₄×C₁₀₇	—	2	2	no	—
333	C₄×C₁₀₇	—	2	2	no	—
334	C₄×C₁₀₇	—	2	4	no	—
335	C₄×C₁₀₇	—	2	4	no	—
336	C₄×C₁₀₇	—	2	4	no	—
337	C₄×C₁₀₇	—	2	4	no	—
338	C₄×C₁₀₇	—	2	4	no	—
339	C₄×C₁₀₇	—	2	4	no	—
340	C₄×C₁₀₇	—	4	4	no	—
341	C₄×C₁₀₇	—	4	4	no	—
342	C₄×C₁₀₇	C₄×#41	1	4	yes	—
343	C₄×C₁₀₇	C₄×#41	1	4	yes	—
344	C₄×C₁₀₇	#529	1	8	yes	direct product factor
345	C₄×#529	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
346	C₂×C₁₀₇	—	2	4	no	—
347	C₂×C₁₀₇	—	4	4	no	—
348	C₂×C₁₀₇	C₂×C₄×#41	1	1	yes	characteristic
349	C₂×C₁₀₇	C₂×C₄×#41	1	1	yes	characteristic
350	C₂×C₁₀₇	C₂×C₄×#41	1	1	yes	characteristic
351	C₂×C₁₀₇	C₂×#529	1	2	yes	—
352	C₂×C₁₀₇	#3444	1	2	yes	—
353	C₂×#529	C₂×C₁₀₇	1	1	yes	characteristic
354	C₄×#125	C₂×C₁₀₇	1	2	yes	complemented
355	C₄×#126	C₂×C₁₀₇	1	4	yes	complemented
356	C₄×#124	C₂×C₁₀₇	1	2	yes	complemented
357	C₄×C₂²⋊Q₈	C₂×C₁₀₇	1	2	yes	complemented
358	C₄×#123	C₂×C₁₀₇	1	4	yes	complemented
359	C₄×#121	C₂×C₁₀₇	1	2	yes	—
360	#2298	C₂×C₁₀₇	1	2	yes	complemented
361	#2295	C₂×C₁₀₇	1	1	yes	characteristic, complemented
362	#2293	C₂×C₁₀₇	1	1	yes	characteristic, complemented
363	#2290	C₂×C₁₀₇	1	2	yes	complemented
364	#2283	C₂×C₁₀₇	1	1	yes	characteristic, complemented
365	C₄²×Q₈	C₂×C₁₀₇	1	1	yes	characteristic, complemented
366	C₄²×D₄	C₂×C₁₀₇	1	2	yes	complemented
367	C₄²×D₄	C₂×C₁₀₇	1	1	yes	characteristic, complemented
368	C₄×#117	C₂×C₁₀₇	1	2	yes	complemented
369	C₂×C₄³	C₂×C₁₀₇	1	1	yes	characteristic, complemented
370	C₁₀₇	C₄×#529	1	1	yes	characteristic, direct product factor, Sylow
371	#529	C₄×C₁₀₇	1	16	yes	direct product factor
372	C₂×#126	C₂²×C₁₀₇	1	2	yes	—
373	C₂×#125	C₂²×C₁₀₇	1	1	yes	characteristic
374	C₂×#124	C₂²×C₁₀₇	1	1	yes	characteristic
375	C₂×#123	C₂²×C₁₀₇	1	2	yes	—
376	C₂×C₂²⋊Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
377	C₂×#121	C₂²×C₁₀₇	1	1	yes	characteristic
378	C₂×C₄×Q₈	C₂²×C₁₀₇	1	2	yes	—
379	C₂×C₄×Q₈	C₂²×C₁₀₇	1	1	yes	characteristic
380	C₂×C₄×D₄	C₂²×C₁₀₇	1	4	yes	—
381	C₂×C₄×D₄	C₂²×C₁₀₇	1	2	yes	—
382	C₂×C₄×D₄	C₂²×C₁₀₇	1	2	yes	—
383	C₂×C₄×D₄	C₂²×C₁₀₇	1	1	yes	characteristic
384	C₂×#117	C₂²×C₁₀₇	1	2	yes	—
385	C₂×#117	C₂²×C₁₀₇	1	2	yes	—
386	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
387	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
388	C₂²×C₄²	C₂²×C₁₀₇	1	2	yes	—
389	C₂²×C₄²	C₂²×C₁₀₇	1	2	yes	—
390	C₂²×C₄²	C₂²×C₁₀₇	1	2	yes	—
391	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
392	#391	C₂²×C₁₀₇	1	2	yes	—
393	#390	C₂²×C₁₀₇	1	2	yes	—
394	#389	C₂²×C₁₀₇	1	2	yes	—
395	#389	C₂²×C₁₀₇	1	2	yes	—
396	#388	C₂²×C₁₀₇	1	4	yes	—
397	#388	C₂²×C₁₀₇	1	4	yes	—
398	#388	C₂²×C₁₀₇	1	4	yes	—
399	#388	C₂²×C₁₀₇	1	4	yes	—
400	#387	C₂²×C₁₀₇	1	4	yes	—
401	#387	C₂²×C₁₀₇	1	4	yes	—
402	#387	C₂²×C₁₀₇	1	4	yes	—
403	#387	C₂²×C₁₀₇	1	4	yes	—
404	#386	C₂²×C₁₀₇	1	4	yes	—
405	#385	C₂²×C₁₀₇	1	4	yes	—
406	#383	C₂²×C₁₀₇	1	2	yes	—
407	#382	C₂²×C₁₀₇	1	2	yes	—
408	#381	C₂²×C₁₀₇	1	2	yes	—
409	#380	C₂²×C₁₀₇	1	2	yes	—
410	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	4	yes	—
411	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	4	yes	—
412	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	4	yes	—
413	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	4	yes	—
414	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
415	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
416	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
417	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
418	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	1	yes	characteristic
419	C₄×C₄⋊C₄	C₂²×C₁₀₇	1	2	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	4	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	4	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	4	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	4	yes	—
424	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
425	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
426	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	2	yes	—
427	C₄×C₂²⋊C₄	C₂²×C₁₀₇	1	4	yes	—
428	#376	C₂²×C₁₀₇	1	2	yes	—
429	#376	C₂²×C₁₀₇	1	2	yes	—
430	C₄³	C₂²×C₁₀₇	1	2	yes	—
431	C₄³	C₂²×C₁₀₇	1	2	yes	—
432	C₄³	C₂²×C₁₀₇	1	1	yes	characteristic
433	C₄³	C₂²×C₁₀₇	1	1	yes	characteristic
434	C₄³	C₂²×C₁₀₇	1	1	yes	characteristic
435	C₄³	C₂²×C₁₀₇	1	1	yes	characteristic
436	C₄³	C₂²×C₁₀₇	1	2	yes	—
437	C₂²×Q₈	C₂³×C₁₀₇	1	1	yes	characteristic
438	C₂²×D₄	C₂³×C₁₀₇	1	2	yes	—
439	C₂²×D₄	C₂³×C₁₀₇	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₁₀₇	1	4	yes	—
441	C₂³×C₄	C₂³×C₁₀₇	1	2	yes	—
442	C₂³×C₄	C₂³×C₁₀₇	1	2	yes	—
443	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
445	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₁₀₇	1	2	yes	—
447	#126	C₂×C₄×C₁₀₇	1	16	yes	complemented
448	#125	C₂×C₄×C₁₀₇	1	8	yes	complemented
449	#124	C₂×C₄×C₁₀₇	1	8	yes	complemented
450	#123	C₂×C₄×C₁₀₇	1	16	yes	complemented
451	C₂²⋊Q₈	C₂×C₄×C₁₀₇	1	8	yes	complemented
452	#121	C₂×C₄×C₁₀₇	1	8	yes	—
453	C₄×Q₈	—	2	8	no	—
454	C₄×Q₈	C₂×C₄×C₁₀₇	1	8	yes	complemented
455	C₄×D₄	—	2	16	no	—
456	C₄×D₄	—	2	8	no	—
457	C₄×D₄	C₂×C₄×C₁₀₇	1	8	yes	complemented
458	C₄×D₄	C₂×C₄×C₁₀₇	1	16	yes	complemented
459	#117	—	2	8	no	—
460	#117	C₂×C₄×C₁₀₇	1	16	yes	complemented
461	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
462	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂³×C₁₀₇	1	2	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₀₇	1	2	yes	—
481	C₂×C₄²	—	2	8	no	—
482	C₂×C₄²	—	2	4	no	—
483	C₂×C₄²	—	2	8	no	—
484	C₂×C₄²	—	2	4	no	—
485	C₂×C₄²	—	2	8	no	—
486	C₂×C₄²	C₂×C₄×C₁₀₇	1	8	yes	complemented
487	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
488	C₂×C₄²	C₂³×C₁₀₇	1	4	yes	—
489	C₂×C₄²	C₂³×C₁₀₇	1	4	yes	—
490	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
491	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
492	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
493	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
494	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
495	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
497	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
498	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
499	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
500	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
501	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
502	C₂×C₄²	C₂³×C₁₀₇	1	4	yes	—
503	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
505	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₁₀₇	1	2	yes	—
510	C₂×C₄²	C₂³×C₁₀₇	1	1	yes	characteristic
511	#95	C₂³×C₁₀₇	1	4	yes	—
512	#95	C₂³×C₁₀₇	1	4	yes	—
513	#95	C₂³×C₁₀₇	1	4	yes	—
514	#95	C₂³×C₁₀₇	1	4	yes	—
515	#95	C₂³×C₁₀₇	1	2	yes	—
516	#95	C₂³×C₁₀₇	1	4	yes	—
517	#95	C₂³×C₁₀₇	1	4	yes	—
518	#95	C₂³×C₁₀₇	1	4	yes	—
519	#95	C₂³×C₁₀₇	1	4	yes	—
520	#95	C₂³×C₁₀₇	1	2	yes	—
521	#95	C₂³×C₁₀₇	1	4	yes	—
522	C₂⁴	C₂⁴×C₁₀₇	1	2	yes	—
523	C₂⁴	C₂⁴×C₁₀₇	1	1	yes	characteristic
524	C₂×Q₈	—	2	4	no	—
525	C₂×Q₈	C₂²×C₄×C₁₀₇	1	4	yes	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	C₂²×C₄×C₁₀₇	1	8	yes	—
529	C₂×D₄	C₂²×C₄×C₁₀₇	1	4	yes	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	8	no	—
542	C₂²×C₄	—	2	8	no	—
543	C₂²×C₄	—	2	8	no	—
544	C₂²×C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
545	C₂²×C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
546	C₂²×C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
547	C₂²×C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
548	C₂²×C₄	#41×C₁₀₇	1	8	yes	—
549	C₂²×C₄	C₂⁴×C₁₀₇	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₁₀₇	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
552	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
553	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
554	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
556	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
560	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₁₀₇	1	2	yes	—
564	C₄⋊C₄	—	2	8	no	—
565	C₄⋊C₄	—	2	8	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	8	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
570	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
571	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
572	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
573	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	4	yes	—
574	C₄⋊C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
575	C₂²⋊C₄	—	2	8	no	—
576	C₂²⋊C₄	—	2	8	no	—
577	C₂²⋊C₄	—	2	8	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
580	C₂²⋊C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
581	C₂²⋊C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
582	C₂²⋊C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
583	C₂²⋊C₄	C₂²×C₄×C₁₀₇	1	8	yes	—
584	C₄²	—	2	4	no	—
585	C₄²	—	2	4	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	4	no	—
592	C₄²	—	2	4	no	—
593	C₄²	—	2	4	no	—
594	C₄²	—	2	4	no	—
595	C₄²	—	2	8	no	—
596	C₄²	—	2	4	no	—
597	C₄²	—	2	4	no	—
598	C₄²	—	2	8	no	—
599	C₄²	—	2	8	no	—
600	C₄²	C₂²×C₄×C₁₀₇	1	4	yes	—
601	C₄²	C₂²×C₄×C₁₀₇	1	4	yes	—
602	C₄²	C₂²×C₄×C₁₀₇	1	4	yes	—
603	C₄²	C₂²×C₄×C₁₀₇	1	4	yes	—
604	C₄²	C₂²×C₄×C₁₀₇	1	8	yes	—
605	C₄²	#41×C₁₀₇	1	4	yes	—
606	C₄²	#41×C₁₀₇	1	4	yes	—
607	C₄²	#41×C₁₀₇	1	8	yes	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	2	no	—
615	C₂³	C₂³×C₄×C₁₀₇	1	4	yes	—
616	C₂³	C₂³×C₄×C₁₀₇	1	2	yes	—
617	C₂³	C₂×#41×C₁₀₇	1	4	yes	—
618	C₂³	C₂⁵×C₁₀₇	1	1	yes	characteristic
619	Q₈	—	2	8	no	—
620	D₄	—	2	16	no	—
621	D₄	—	2	8	no	—
622	C₂×C₄	—	2	16	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	8	no	—
640	C₂×C₄	—	2	16	no	—
641	C₂×C₄	—	2	8	no	—
642	C₂×C₄	—	2	16	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	4	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	4	16	no	—
650	C₂×C₄	C₂³×C₄×C₁₀₇	1	2	yes	—
651	C₂×C₄	C₂³×C₄×C₁₀₇	1	2	yes	—
652	C₂×C₄	C₂³×C₄×C₁₀₇	1	2	yes	—
653	C₂×C₄	C₂³×C₄×C₁₀₇	1	2	yes	—
654	C₂×C₄	C₂³×C₄×C₁₀₇	1	4	yes	—
655	C₂×C₄	C₂³×C₄×C₁₀₇	1	4	yes	—
656	C₂×C₄	C₂³×C₄×C₁₀₇	1	4	yes	—
657	C₂×C₄	C₂³×C₄×C₁₀₇	1	2	yes	—
658	C₂×C₄	C₂³×C₄×C₁₀₇	1	2	yes	—
659	C₂×C₄	C₂×#41×C₁₀₇	1	4	yes	—
660	C₂×C₄	C₂×#41×C₁₀₇	1	4	yes	—
661	C₂×C₄	C₂×#41×C₁₀₇	1	4	yes	—
662	C₂×C₄	C₂×#41×C₁₀₇	1	2	yes	—
663	C₂×C₄	C₂×#41×C₁₀₇	1	2	yes	—
664	C₂×C₄	C₂×#41×C₁₀₇	1	4	yes	—
665	C₂×C₄	C₂×#41×C₁₀₇	1	4	yes	—
666	C₂×C₄	C₂×#41×C₁₀₇	1	4	yes	—
667	C₂×C₄	C₂×#41×C₁₀₇	1	4	yes	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	4	4	no	—
676	C₂²	—	4	4	no	—
677	C₂²	C₄×#41×C₁₀₇	1	4	yes	—
678	C₂²	C₂⁴×C₄×C₁₀₇	1	1	yes	characteristic
679	C₂²	C₂²×#41×C₁₀₇	1	1	yes	characteristic
680	C₂²	C₂²×#41×C₁₀₇	1	2	yes	—
681	C₂²	C₂²×#41×C₁₀₇	1	2	yes	—
682	C₂²	C₂²×#41×C₁₀₇	1	1	yes	characteristic
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	4	no	—
690	C₄	—	2	4	no	—
691	C₄	—	2	4	no	—
692	C₄	—	2	4	no	—
693	C₄	—	4	4	no	—
694	C₄	—	4	4	no	—
695	C₄	C₄×#41×C₁₀₇	1	4	yes	—
696	C₄	C₄×#41×C₁₀₇	1	4	yes	—
697	C₄	#529×C₁₀₇	1	8	yes	direct product factor
698	C₂	—	2	4	no	—
699	C₂	—	4	4	no	—
700	C₂	C₂×C₄×#41×C₁₀₇	1	1	yes	characteristic
701	C₂	C₂×C₄×#41×C₁₀₇	1	1	yes	characteristic
702	C₂	C₂×C₄×#41×C₁₀₇	1	1	yes	characteristic
703	C₂	C₂×#529×C₁₀₇	1	2	yes	—
704	C₂	C₁₀₇×#3444	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₀₇	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₀₇
Frattini, cosocle	C₂³	C₂⁵×C₁₀₇
socle	C₂³×C₁₀₇	C₂⁵
prime radical	C₂×#121×C₁₀₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×#125×C₁₀₇	C₂	semidirect
3. C₄×#126×C₁₀₇	C₂	semidirect
4. C₄×#124×C₁₀₇	C₂	semidirect
5. C₄×C₂²⋊Q₈×C₁₀₇	C₂	semidirect
6. C₄×#123×C₁₀₇	C₂	semidirect
8. C₁₀₇×#2298	C₂	semidirect
9. C₁₀₇×#2295	C₂	semidirect
10. C₁₀₇×#2293	C₂	semidirect
11. C₁₀₇×#2290	C₂	semidirect
12. C₁₀₇×#2283	C₂	semidirect
13. C₄²×Q₈×C₁₀₇	C₂	semidirect
14. C₄²×D₄×C₁₀₇	C₂	semidirect
15. C₄²×D₄×C₁₀₇	C₂	semidirect
16. C₄×#117×C₁₀₇	C₂	semidirect
17. C₂×C₄³×C₁₀₇	C₂	semidirect
18. #529×C₁₀₇	C₄	direct (N × H)
94. #126×C₁₀₇	C₂×C₄	semidirect
95. #125×C₁₀₇	C₂×C₄	semidirect
96. #124×C₁₀₇	C₂×C₄	semidirect
97. #123×C₁₀₇	C₂×C₄	semidirect
98. C₂²⋊Q₈×C₁₀₇	C₂×C₄	semidirect
101. C₄×Q₈×C₁₀₇	C₂×C₄	semidirect
104. C₄×D₄×C₁₀₇	C₂×C₄	semidirect
105. C₄×D₄×C₁₀₇	C₂×C₄	semidirect
107. #117×C₁₀₇	C₂×C₄	semidirect
133. C₂×C₄²×C₁₀₇	C₂×C₄	semidirect
344. C₄×C₁₀₇	#529	direct (N × H)
345. C₄×#529	C₁₀₇	direct (N × H)
354. C₄×#125	C₂×C₁₀₇	semidirect
355. C₄×#126	C₂×C₁₀₇	semidirect
356. C₄×#124	C₂×C₁₀₇	semidirect
357. C₄×C₂²⋊Q₈	C₂×C₁₀₇	semidirect
358. C₄×#123	C₂×C₁₀₇	semidirect
360. #2298	C₂×C₁₀₇	semidirect
361. #2295	C₂×C₁₀₇	semidirect
362. #2293	C₂×C₁₀₇	semidirect
363. #2290	C₂×C₁₀₇	semidirect
364. #2283	C₂×C₁₀₇	semidirect
365. C₄²×Q₈	C₂×C₁₀₇	semidirect
366. C₄²×D₄	C₂×C₁₀₇	semidirect
367. C₄²×D₄	C₂×C₁₀₇	semidirect
368. C₄×#117	C₂×C₁₀₇	semidirect
369. C₂×C₄³	C₂×C₁₀₇	semidirect
370. C₁₀₇	C₄×#529	direct (N × H)
371. #529	C₄×C₁₀₇	direct (N × H)
447. #126	C₂×C₄×C₁₀₇	semidirect
448. #125	C₂×C₄×C₁₀₇	semidirect
449. #124	C₂×C₄×C₁₀₇	semidirect
450. #123	C₂×C₄×C₁₀₇	semidirect
451. C₂²⋊Q₈	C₂×C₄×C₁₀₇	semidirect
454. C₄×Q₈	C₂×C₄×C₁₀₇	semidirect
457. C₄×D₄	C₂×C₄×C₁₀₇	semidirect
458. C₄×D₄	C₂×C₄×C₁₀₇	semidirect
460. #117	C₂×C₄×C₁₀₇	semidirect
486. C₂×C₄²	C₂×C₄×C₁₀₇	semidirect
697. C₄	#529×C₁₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#529×C₁₀₇	2
C₄×#125×C₁₀₇	2
C₄×#126×C₁₀₇	2
C₄×#124×C₁₀₇	2
C₄×C₂²⋊Q₈×C₁₀₇	2
C₄×#123×C₁₀₇	2
C₄×#121×C₁₀₇	2
C₁₀₇×#2298	2
C₁₀₇×#2295	2
C₁₀₇×#2293	2
C₁₀₇×#2290	2
C₁₀₇×#2283	2
C₄²×Q₈×C₁₀₇	2
C₄²×D₄×C₁₀₇	2
C₄×#117×C₁₀₇	2
C₂×C₄³×C₁₀₇	2
C₄×#529	107

Subgroups — C4×#529×C107 #41059999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#529×C₁₀₇ #41059999