Subgroups — C₁₃₉×#35686 #48030282

Order 35584.

2412 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2633×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2616×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2599×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2584×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2502×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2486×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2466×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2455×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2441×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2415×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2392×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2388×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	#2360×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	D₄×C₄⋊C₄×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2347×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
19	#552×C₁₃₉	—	2	8	no	—
20	C₂×#126×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#125×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
28	#520×C₁₃₉	—	2	8	no	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
36	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
38	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	#399×C₁₃₉	C₂²	1	4	yes	—
43	#398×C₁₃₉	C₂²	1	2	yes	—
44	#398×C₁₃₉	C₂²	1	2	yes	—
45	#398×C₁₃₉	C₂²	1	2	yes	—
46	#397×C₁₃₉	C₂²	1	2	yes	—
47	#397×C₁₃₉	C₂²	1	4	yes	—
48	#396×C₁₃₉	C₂²	1	4	yes	—
49	#395×C₁₃₉	C₂²	1	1	yes	characteristic
50	#395×C₁₃₉	C₂²	1	2	yes	—
51	#394×C₁₃₉	C₂²	1	2	yes	—
52	#394×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	1	yes	characteristic
54	#394×C₁₃₉	C₂²	1	2	yes	—
55	#394×C₁₃₉	C₂²	1	4	yes	—
56	#393×C₁₃₉	C₂²	1	1	yes	characteristic
57	#392×C₁₃₉	C₂²	1	1	yes	characteristic
58	#392×C₁₃₉	C₂²	1	2	yes	—
59	#391×C₁₃₉	C₂²	1	2	yes	—
60	#389×C₁₃₉	C₂²	1	4	yes	—
61	#389×C₁₃₉	C₂²	1	4	yes	—
62	#389×C₁₃₉	C₂²	1	4	yes	—
63	#389×C₁₃₉	C₂²	1	4	yes	—
64	#389×C₁₃₉	C₂²	1	2	yes	—
65	#389×C₁₃₉	C₂²	1	2	yes	—
66	#388×C₁₃₉	C₂²	1	4	yes	—
67	#388×C₁₃₉	C₂²	1	4	yes	—
68	#387×C₁₃₉	C₂²	1	4	yes	—
69	#387×C₁₃₉	C₂²	1	4	yes	—
70	#385×C₁₃₉	C₂²	1	4	yes	—
71	#385×C₁₃₉	C₂²	1	4	yes	—
72	#385×C₁₃₉	C₂²	1	4	yes	—
73	#385×C₁₃₉	C₂²	1	4	yes	—
74	#384×C₁₃₉	C₂²	1	2	yes	—
75	#383×C₁₃₉	C₂²	1	2	yes	—
76	#381×C₁₃₉	C₂²	1	2	yes	—
77	#380×C₁₃₉	C₂²	1	1	yes	characteristic
78	#380×C₁₃₉	C₂²	1	2	yes	—
79	#380×C₁₃₉	C₂²	1	2	yes	—
80	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
85	C₂×#41×C₁₃₉	—	2	4	no	—
86	C₂×#41×C₁₃₉	—	2	8	no	—
87	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
99	#126×C₁₃₉	—	2	8	no	—
100	#125×C₁₃₉	—	2	4	no	—
101	#125×C₁₃₉	—	2	8	no	—
102	#123×C₁₃₉	—	2	8	no	—
103	#123×C₁₃₉	—	4	4	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
106	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
107	C₄×Q₈×C₁₃₉	—	2	4	no	—
108	C₄×Q₈×C₁₃₉	—	2	8	no	—
109	C₄×D₄×C₁₃₉	—	2	4	no	—
110	C₄×D₄×C₁₃₉	—	2	8	no	—
111	C₄×D₄×C₁₃₉	—	2	16	no	—
112	C₄×D₄×C₁₃₉	—	2	8	no	—
113	C₄×D₄×C₁₃₉	—	4	8	no	—
114	#117×C₁₃₉	—	2	8	no	—
115	#117×C₁₃₉	—	2	8	no	—
116	#117×C₁₃₉	D₄	1	8	yes	complemented
117	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
119	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
160	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
161	#95×C₁₃₉	C₂³	1	2	yes	—
162	#95×C₁₃₉	C₂³	1	1	yes	characteristic
163	#95×C₁₃₉	C₂³	1	2	yes	—
164	#95×C₁₃₉	C₂³	1	4	yes	—
165	#95×C₁₃₉	C₂³	1	4	yes	—
166	#95×C₁₃₉	C₂³	1	4	yes	—
167	#95×C₁₃₉	C₂³	1	4	yes	—
168	#95×C₁₃₉	C₂³	1	4	yes	—
169	#95×C₁₃₉	C₂³	1	1	yes	characteristic
170	#95×C₁₃₉	C₂³	1	4	yes	—
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	4	yes	—
173	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
174	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
175	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	#41×C₁₃₉	—	2	32	no	—
177	C₂×Q₈×C₁₃₉	—	2	2	no	—
178	C₂×Q₈×C₁₃₉	—	2	2	no	—
179	C₂×Q₈×C₁₃₉	—	2	4	no	—
180	C₂×Q₈×C₁₃₉	—	2	4	no	—
181	C₂×D₄×C₁₃₉	—	2	4	no	—
182	C₂×D₄×C₁₃₉	—	2	4	no	—
183	C₂×D₄×C₁₃₉	—	2	4	no	—
184	C₂×D₄×C₁₃₉	—	2	4	no	—
185	C₂×D₄×C₁₃₉	—	2	4	no	—
186	C₂×D₄×C₁₃₉	—	2	2	no	—
187	C₂×D₄×C₁₃₉	—	2	2	no	—
188	C₂×D₄×C₁₃₉	—	2	2	no	—
189	C₂×D₄×C₁₃₉	—	2	4	no	—
190	C₂×D₄×C₁₃₉	—	2	4	no	—
191	C₂×D₄×C₁₃₉	—	4	1	no	—
192	C₂²×C₄×C₁₃₉	—	2	4	no	—
193	C₂²×C₄×C₁₃₉	—	2	4	no	—
194	C₂²×C₄×C₁₃₉	—	2	4	no	—
195	C₂²×C₄×C₁₃₉	—	2	4	no	—
196	C₂²×C₄×C₁₃₉	—	2	4	no	—
197	C₂²×C₄×C₁₃₉	—	2	4	no	—
198	C₂²×C₄×C₁₃₉	—	2	2	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	2	8	no	—
201	C₂²×C₄×C₁₃₉	—	4	2	no	—
202	C₂²×C₄×C₁₃₉	—	4	4	no	—
203	C₂²×C₄×C₁₃₉	—	4	2	no	—
204	C₂²×C₄×C₁₃₉	—	4	4	no	—
205	C₂²×C₄×C₁₃₉	—	4	2	no	—
206	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
222	C₄⋊C₄×C₁₃₉	—	2	4	no	—
223	C₄⋊C₄×C₁₃₉	—	2	8	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	2	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	4	no	—
228	C₄⋊C₄×C₁₃₉	—	2	4	no	—
229	C₄⋊C₄×C₁₃₉	—	2	2	no	—
230	C₄⋊C₄×C₁₃₉	—	2	4	no	—
231	C₄⋊C₄×C₁₃₉	—	2	4	no	—
232	C₄⋊C₄×C₁₃₉	—	2	4	no	—
233	C₄⋊C₄×C₁₃₉	—	2	4	no	—
234	C₄⋊C₄×C₁₃₉	—	2	4	no	—
235	C₄⋊C₄×C₁₃₉	—	2	8	no	—
236	C₄⋊C₄×C₁₃₉	—	2	8	no	—
237	C₄⋊C₄×C₁₃₉	—	4	4	no	—
238	C₄⋊C₄×C₁₃₉	—	4	4	no	—
239	C₄⋊C₄×C₁₃₉	—	4	4	no	—
240	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
241	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
242	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
248	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
249	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
251	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
252	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
253	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
254	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
255	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
256	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
257	C₄²×C₁₃₉	—	2	8	no	—
258	C₄²×C₁₃₉	—	2	4	no	—
259	C₄²×C₁₃₉	—	2	2	no	—
260	C₄²×C₁₃₉	—	2	4	no	—
261	C₄²×C₁₃₉	—	4	4	no	—
262	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
263	C₂³×C₁₃₉	—	2	1	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	2	no	—
266	C₂³×C₁₃₉	—	2	2	no	—
267	C₂³×C₁₃₉	—	2	2	no	—
268	C₂³×C₁₃₉	—	2	1	no	—
269	C₂³×C₁₃₉	—	2	2	no	—
270	C₂³×C₁₃₉	—	2	2	no	—
271	C₂³×C₁₃₉	—	2	2	no	—
272	C₂³×C₁₃₉	—	2	2	no	—
273	C₂³×C₁₃₉	—	2	2	no	—
274	C₂³×C₁₃₉	—	2	2	no	—
275	C₂³×C₁₃₉	—	2	1	no	—
276	C₂³×C₁₃₉	—	2	1	no	—
277	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
278	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
279	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
280	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
281	Q₈×C₁₃₉	—	2	8	no	—
282	Q₈×C₁₃₉	—	4	4	no	—
283	D₄×C₁₃₉	—	2	16	no	—
284	D₄×C₁₃₉	—	2	8	no	—
285	D₄×C₁₃₉	—	2	16	no	—
286	D₄×C₁₃₉	—	4	4	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	4	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	8	no	—
296	C₂×C₄×C₁₃₉	—	2	16	no	—
297	C₂×C₄×C₁₃₉	—	2	1	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	4	no	—
300	C₂×C₄×C₁₃₉	—	2	1	no	—
301	C₂×C₄×C₁₃₉	—	2	1	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	2	no	—
304	C₂×C₄×C₁₃₉	—	2	4	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	4	no	—
307	C₂×C₄×C₁₃₉	—	2	4	no	—
308	C₂×C₄×C₁₃₉	—	2	4	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	1	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	4	no	—
314	C₂×C₄×C₁₃₉	—	2	1	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	4	no	—
318	C₂×C₄×C₁₃₉	—	4	8	no	—
319	C₂×C₄×C₁₃₉	—	4	4	no	—
320	C₂×C₄×C₁₃₉	—	8	8	no	—
321	C₂×C₄×C₁₃₉	—	8	4	no	—
322	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
323	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
324	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
327	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
328	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
329	C₂²×C₁₃₉	—	2	2	no	—
330	C₂²×C₁₃₉	—	2	4	no	—
331	C₂²×C₁₃₉	—	2	2	no	—
332	C₂²×C₁₃₉	—	2	2	no	—
333	C₂²×C₁₃₉	—	2	4	no	—
334	C₂²×C₁₃₉	—	2	4	no	—
335	C₂²×C₁₃₉	—	2	2	no	—
336	C₂²×C₁₃₉	—	2	4	no	—
337	C₂²×C₁₃₉	—	4	1	no	—
338	C₂²×C₁₃₉	—	4	2	no	—
339	C₂²×C₁₃₉	—	4	2	no	—
340	C₂²×C₁₃₉	—	4	2	no	—
341	C₂²×C₁₃₉	—	4	1	no	—
342	C₂²×C₁₃₉	—	4	2	no	—
343	C₂²×C₁₃₉	—	4	2	no	—
344	C₂²×C₁₃₉	—	4	2	no	—
345	C₂²×C₁₃₉	—	4	2	no	—
346	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
347	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
348	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
349	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
350	C₂²×C₁₃₉	#585	1	1	yes	characteristic
351	C₄×C₁₃₉	—	2	2	no	—
352	C₄×C₁₃₉	—	2	4	no	—
353	C₄×C₁₃₉	—	2	4	no	—
354	C₄×C₁₃₉	—	2	4	no	—
355	C₄×C₁₃₉	—	2	4	no	—
356	C₄×C₁₃₉	—	4	1	no	—
357	C₄×C₁₃₉	—	4	2	no	—
358	C₄×C₁₃₉	—	4	2	no	—
359	C₄×C₁₃₉	—	4	4	no	—
360	C₄×C₁₃₉	—	4	1	no	—
361	C₄×C₁₃₉	—	4	4	no	—
362	C₄×C₁₃₉	—	4	1	no	—
363	C₄×C₁₃₉	—	4	2	no	—
364	C₄×C₁₃₉	#525	1	4	yes	—
365	C₂×C₁₃₉	—	4	2	no	—
366	C₂×C₁₃₉	—	4	4	no	—
367	C₂×C₁₃₉	—	4	2	no	—
368	C₂×C₁₃₉	C₂×#525	1	1	yes	characteristic
369	C₂×C₁₃₉	#3488	1	1	yes	characteristic
370	C₂×C₁₃₉	#3492	1	2	yes	—
371	C₂×C₁₃₉	#3499	1	1	yes	characteristic
372	C₂×C₁₃₉	#3507	1	2	yes	—
373	#35686	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
374	C₁₃₉	#35686	1	1	yes	characteristic, direct product factor, Sylow
375	C₂×#552	C₂×C₁₃₉	1	1	yes	characteristic, complemented
376	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic, complemented
377	#2633	C₂×C₁₃₉	1	2	yes	complemented
378	#2616	C₂×C₁₃₉	1	1	yes	characteristic, complemented
379	#2599	C₂×C₁₃₉	1	2	yes	complemented
380	#2584	C₂×C₁₃₉	1	2	yes	complemented
381	#2502	C₂×C₁₃₉	1	1	yes	characteristic, complemented
382	#2486	C₂×C₁₃₉	1	1	yes	characteristic, complemented
383	#2466	C₂×C₁₃₉	1	4	yes	complemented
384	#2455	C₂×C₁₃₉	1	4	yes	complemented
385	#2441	C₂×C₁₃₉	1	2	yes	complemented
386	#2415	C₂×C₁₃₉	1	2	yes	complemented
387	#2392	C₂×C₁₃₉	1	2	yes	complemented
388	#2388	C₂×C₁₃₉	1	1	yes	characteristic
389	#2360	C₂×C₁₃₉	1	2	yes	complemented
390	D₄×C₄⋊C₄	C₂×C₁₃₉	1	2	yes	complemented
391	#2347	C₂×C₁₃₉	1	1	yes	characteristic, complemented
392	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
393	#552	—	2	8	no	—
394	C₂×#126	C₂²×C₁₃₉	1	2	yes	—
395	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
396	C₂×#125	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
398	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
399	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
400	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
402	#520	—	2	8	no	—
403	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
404	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
406	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
407	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
409	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
410	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
411	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
412	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
413	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
414	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
415	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
416	#399	C₂²×C₁₃₉	1	4	yes	—
417	#398	C₂²×C₁₃₉	1	2	yes	—
418	#398	C₂²×C₁₃₉	1	2	yes	—
419	#398	C₂²×C₁₃₉	1	2	yes	—
420	#397	C₂²×C₁₃₉	1	2	yes	—
421	#397	C₂²×C₁₃₉	1	4	yes	—
422	#396	C₂²×C₁₃₉	1	4	yes	—
423	#395	C₂²×C₁₃₉	1	1	yes	characteristic
424	#395	C₂²×C₁₃₉	1	2	yes	—
425	#394	C₂²×C₁₃₉	1	2	yes	—
426	#394	C₂²×C₁₃₉	1	4	yes	—
427	#394	C₂²×C₁₃₉	1	1	yes	characteristic
428	#394	C₂²×C₁₃₉	1	2	yes	—
429	#394	C₂²×C₁₃₉	1	4	yes	—
430	#393	C₂²×C₁₃₉	1	1	yes	characteristic
431	#392	C₂²×C₁₃₉	1	1	yes	characteristic
432	#392	C₂²×C₁₃₉	1	2	yes	—
433	#391	C₂²×C₁₃₉	1	2	yes	—
434	#389	C₂²×C₁₃₉	1	4	yes	—
435	#389	C₂²×C₁₃₉	1	4	yes	—
436	#389	C₂²×C₁₃₉	1	4	yes	—
437	#389	C₂²×C₁₃₉	1	4	yes	—
438	#389	C₂²×C₁₃₉	1	2	yes	—
439	#389	C₂²×C₁₃₉	1	2	yes	—
440	#388	C₂²×C₁₃₉	1	4	yes	—
441	#388	C₂²×C₁₃₉	1	4	yes	—
442	#387	C₂²×C₁₃₉	1	4	yes	—
443	#387	C₂²×C₁₃₉	1	4	yes	—
444	#385	C₂²×C₁₃₉	1	4	yes	—
445	#385	C₂²×C₁₃₉	1	4	yes	—
446	#385	C₂²×C₁₃₉	1	4	yes	—
447	#385	C₂²×C₁₃₉	1	4	yes	—
448	#384	C₂²×C₁₃₉	1	2	yes	—
449	#383	C₂²×C₁₃₉	1	2	yes	—
450	#381	C₂²×C₁₃₉	1	2	yes	—
451	#380	C₂²×C₁₃₉	1	1	yes	characteristic
452	#380	C₂²×C₁₃₉	1	2	yes	—
453	#380	C₂²×C₁₃₉	1	2	yes	—
454	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
455	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
456	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
457	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
458	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
459	C₂×#41	—	2	4	no	—
460	C₂×#41	—	2	8	no	—
461	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
462	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
464	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
466	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
469	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
471	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
472	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
473	#126	—	2	8	no	—
474	#125	—	2	4	no	—
475	#125	—	2	8	no	—
476	#123	—	2	8	no	—
477	#123	—	4	4	no	—
478	C₂²⋊Q₈	—	2	4	no	—
479	C₂²⋊Q₈	—	2	8	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₄×Q₈	—	2	4	no	—
482	C₄×Q₈	—	2	8	no	—
483	C₄×D₄	—	2	4	no	—
484	C₄×D₄	—	2	8	no	—
485	C₄×D₄	—	2	16	no	—
486	C₄×D₄	—	2	8	no	—
487	C₄×D₄	—	4	8	no	—
488	#117	—	2	8	no	—
489	#117	—	2	8	no	—
490	#117	D₄×C₁₃₉	1	8	yes	complemented
491	C₂×C₄⋊C₄	—	2	4	no	—
492	C₂×C₄⋊C₄	—	2	8	no	—
493	C₂×C₄⋊C₄	—	2	4	no	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
529	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
530	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
531	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
533	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
534	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
535	#95	C₂³×C₁₃₉	1	1	yes	characteristic
536	#95	C₂³×C₁₃₉	1	4	yes	—
537	#95	C₂³×C₁₃₉	1	1	yes	characteristic
538	#95	C₂³×C₁₃₉	1	4	yes	—
539	#95	C₂³×C₁₃₉	1	2	yes	—
540	#95	C₂³×C₁₃₉	1	2	yes	—
541	#95	C₂³×C₁₃₉	1	2	yes	—
542	#95	C₂³×C₁₃₉	1	4	yes	—
543	#95	C₂³×C₁₃₉	1	4	yes	—
544	#95	C₂³×C₁₃₉	1	4	yes	—
545	#95	C₂³×C₁₃₉	1	4	yes	—
546	#95	C₂³×C₁₃₉	1	4	yes	—
547	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
548	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
549	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
550	#41	—	2	32	no	—
551	C₂×Q₈	—	2	2	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	4	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	4	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	8	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	4	no	—
577	C₂²×C₄	—	4	2	no	—
578	C₂²×C₄	—	4	4	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
581	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
582	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
585	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	2	8	no	—
611	C₄⋊C₄	—	4	4	no	—
612	C₄⋊C₄	—	4	4	no	—
613	C₄⋊C₄	—	4	4	no	—
614	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
615	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	4	no	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₂²⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
631	C₄²	—	2	8	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	4	4	no	—
636	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
652	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
653	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
654	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
655	Q₈	—	2	8	no	—
656	Q₈	—	4	4	no	—
657	D₄	—	2	8	no	—
658	D₄	—	2	16	no	—
659	D₄	—	2	16	no	—
660	D₄	—	4	4	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	8	no	—
670	C₂×C₄	—	2	16	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	8	8	no	—
695	C₂×C₄	—	8	4	no	—
696	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
697	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
698	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
700	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
701	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
702	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	4	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
721	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
722	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
723	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
724	C₂²	#585×C₁₃₉	1	1	yes	characteristic
725	C₄	—	2	2	no	—
726	C₄	—	2	4	no	—
727	C₄	—	2	4	no	—
728	C₄	—	2	4	no	—
729	C₄	—	2	4	no	—
730	C₄	—	4	1	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	4	no	—
734	C₄	—	4	1	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	1	no	—
737	C₄	—	4	2	no	—
738	C₄	#525×C₁₃₉	1	4	yes	—
739	C₂	—	4	2	no	—
740	C₂	—	4	4	no	—
741	C₂	—	4	2	no	—
742	C₂	C₂×#525×C₁₃₉	1	1	yes	characteristic
743	C₂	#3488×C₁₃₉	1	1	yes	characteristic
744	C₂	#3492×C₁₃₉	1	2	yes	—
745	C₂	#3499×C₁₃₉	1	1	yes	characteristic
746	C₂	#3507×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2388×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#552×C₁₃₉	C₂	semidirect
2. C₂×#520×C₁₃₉	C₂	semidirect
3. #2633×C₁₃₉	C₂	semidirect
4. #2616×C₁₃₉	C₂	semidirect
5. #2599×C₁₃₉	C₂	semidirect
6. #2584×C₁₃₉	C₂	semidirect
7. #2502×C₁₃₉	C₂	semidirect
8. #2486×C₁₃₉	C₂	semidirect
9. #2466×C₁₃₉	C₂	semidirect
10. #2455×C₁₃₉	C₂	semidirect
11. #2441×C₁₃₉	C₂	semidirect
12. #2415×C₁₃₉	C₂	semidirect
13. #2392×C₁₃₉	C₂	semidirect
15. #2360×C₁₃₉	C₂	semidirect
16. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
17. #2347×C₁₃₉	C₂	semidirect
116. #117×C₁₃₉	D₄	semidirect
373. #35686	C₁₃₉	direct (N × H)
374. C₁₃₉	#35686	direct (N × H)
375. C₂×#552	C₂×C₁₃₉	semidirect
376. C₂×#520	C₂×C₁₃₉	semidirect
377. #2633	C₂×C₁₃₉	semidirect
378. #2616	C₂×C₁₃₉	semidirect
379. #2599	C₂×C₁₃₉	semidirect
380. #2584	C₂×C₁₃₉	semidirect
381. #2502	C₂×C₁₃₉	semidirect
382. #2486	C₂×C₁₃₉	semidirect
383. #2466	C₂×C₁₃₉	semidirect
384. #2455	C₂×C₁₃₉	semidirect
385. #2441	C₂×C₁₃₉	semidirect
386. #2415	C₂×C₁₃₉	semidirect
387. #2392	C₂×C₁₃₉	semidirect
389. #2360	C₂×C₁₃₉	semidirect
390. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
391. #2347	C₂×C₁₃₉	semidirect
490. #117	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#552×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2633×C₁₃₉	2
#2616×C₁₃₉	2
#2599×C₁₃₉	2
#2584×C₁₃₉	2
#2502×C₁₃₉	2
#2486×C₁₃₉	2
#2466×C₁₃₉	2
#2455×C₁₃₉	2
#2441×C₁₃₉	2
#2415×C₁₃₉	2
#2392×C₁₃₉	2
#2388×C₁₃₉	2
#2360×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#2347×C₁₃₉	2
#35686	139

Subgroups — C139×#35686 #48030282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35686 #48030282