Subgroups — C₁₃₉×#37124 #48031720

Order 35584.

1562 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2853×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2789×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2785×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2783×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2782×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2781×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2775×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2769×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2767×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2765×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2744×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2627×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2618×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	#2510×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2505×C₁₃₉	C₂	1	2	yes	maximal, complemented
16	#2450×C₁₃₉	C₂	1	2	yes	maximal, complemented
17	#2444×C₁₃₉	C₂	1	2	yes	maximal
18	#2322×C₁₃₉	C₂	1	2	yes	maximal, complemented
19	C₂×#382×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
27	#401×C₁₃₉	C₂²	1	2	yes	—
28	#400×C₁₃₉	C₂²	1	2	yes	—
29	#400×C₁₃₉	C₂²	1	2	yes	—
30	#400×C₁₃₉	C₂²	1	2	yes	—
31	#400×C₁₃₉	C₂²	1	2	yes	—
32	#400×C₁₃₉	C₂²	1	1	yes	characteristic
33	#400×C₁₃₉	C₂²	1	2	yes	—
34	#400×C₁₃₉	C₂²	1	2	yes	—
35	#400×C₁₃₉	C₂²	1	1	yes	characteristic
36	#398×C₁₃₉	C₂²	1	1	yes	characteristic
37	#398×C₁₃₉	C₂²	1	2	yes	—
38	#398×C₁₃₉	C₂²	1	1	yes	characteristic
39	#398×C₁₃₉	C₂²	1	2	yes	—
40	#398×C₁₃₉	C₂²	1	2	yes	—
41	#398×C₁₃₉	C₂²	1	2	yes	—
42	#397×C₁₃₉	C₂²	1	2	yes	—
43	#397×C₁₃₉	C₂²	1	2	yes	—
44	#397×C₁₃₉	C₂²	1	2	yes	—
45	#397×C₁₃₉	C₂²	1	2	yes	—
46	#396×C₁₃₉	C₂²	1	2	yes	—
47	#396×C₁₃₉	C₂²	1	2	yes	—
48	#396×C₁₃₉	C₂²	1	2	yes	—
49	#395×C₁₃₉	C₂²	1	1	yes	characteristic
50	#395×C₁₃₉	C₂²	1	1	yes	characteristic
51	#394×C₁₃₉	C₂²	1	1	yes	characteristic
52	#394×C₁₃₉	C₂²	1	2	yes	—
53	#394×C₁₃₉	C₂²	1	1	yes	characteristic
54	#393×C₁₃₉	C₂²	1	2	yes	—
55	#391×C₁₃₉	C₂²	1	2	yes	—
56	#389×C₁₃₉	C₂²	1	2	yes	—
57	#389×C₁₃₉	C₂²	1	2	yes	—
58	#389×C₁₃₉	C₂²	1	2	yes	—
59	#388×C₁₃₉	C₂²	1	2	yes	—
60	#388×C₁₃₉	C₂²	1	2	yes	—
61	#388×C₁₃₉	C₂²	1	2	yes	—
62	#388×C₁₃₉	C₂²	1	2	yes	—
63	#388×C₁₃₉	C₂²	1	2	yes	—
64	#388×C₁₃₉	C₂²	1	2	yes	—
65	#388×C₁₃₉	C₂²	1	2	yes	—
66	#388×C₁₃₉	C₂²	1	2	yes	—
67	#388×C₁₃₉	C₂²	1	2	yes	—
68	#387×C₁₃₉	C₂²	1	2	yes	—
69	#387×C₁₃₉	C₂²	1	2	yes	—
70	#387×C₁₃₉	C₂²	1	2	yes	—
71	#387×C₁₃₉	C₂²	1	2	yes	—
72	#387×C₁₃₉	C₂²	1	2	yes	—
73	#387×C₁₃₉	C₂²	1	2	yes	—
74	#387×C₁₃₉	C₂²	1	2	yes	—
75	#387×C₁₃₉	C₂²	1	2	yes	—
76	#387×C₁₃₉	C₂²	1	2	yes	—
77	#387×C₁₃₉	C₂²	1	2	yes	—
78	#387×C₁₃₉	C₂²	1	2	yes	—
79	#386×C₁₃₉	C₂²	1	2	yes	—
80	#386×C₁₃₉	C₂²	1	2	yes	—
81	#386×C₁₃₉	C₂²	1	2	yes	—
82	#386×C₁₃₉	C₂²	1	2	yes	—
83	#386×C₁₃₉	C₂²	1	2	yes	—
84	#385×C₁₃₉	C₂²	1	2	yes	—
85	#385×C₁₃₉	C₂²	1	2	yes	—
86	#385×C₁₃₉	C₂²	1	2	yes	—
87	#385×C₁₃₉	C₂²	1	2	yes	—
88	#385×C₁₃₉	C₂²	1	2	yes	—
89	#385×C₁₃₉	C₂²	1	2	yes	—
90	#385×C₁₃₉	C₂²	1	2	yes	—
91	#383×C₁₃₉	C₂²	1	2	yes	—
92	#382×C₁₃₉	C₂²	1	2	yes	—
93	#382×C₁₃₉	C₂²	1	2	yes	—
94	#382×C₁₃₉	C₂²	1	1	yes	characteristic
95	#382×C₁₃₉	C₂²	1	2	yes	—
96	#382×C₁₃₉	C₂²	1	1	yes	characteristic
97	#382×C₁₃₉	C₂²	1	1	yes	characteristic
98	#382×C₁₃₉	C₂²	1	1	yes	characteristic
99	#381×C₁₃₉	C₂²	1	2	yes	—
100	#381×C₁₃₉	C₂²	1	2	yes	—
101	#380×C₁₃₉	C₂²	1	1	yes	characteristic
102	#380×C₁₃₉	C₂²	1	2	yes	—
103	#380×C₁₃₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
105	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
106	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
116	#123×C₁₃₉	—	2	8	no	—
117	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
118	#121×C₁₃₉	—	4	2	no	—
119	C₄×D₄×C₁₃₉	—	4	4	no	—
120	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
121	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	yes	—
136	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	2	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×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₁₃₉	—	2	4	no	—
161	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
167	#95×C₁₃₉	C₂³	1	1	yes	characteristic
168	#95×C₁₃₉	C₂³	1	2	yes	—
169	#95×C₁₃₉	C₂³	1	2	yes	—
170	#95×C₁₃₉	C₂³	1	1	yes	characteristic
171	#95×C₁₃₉	C₂³	1	2	yes	—
172	#95×C₁₃₉	C₂³	1	2	yes	—
173	#95×C₁₃₉	C₂³	1	2	yes	—
174	#95×C₁₃₉	C₂³	1	2	yes	—
175	#95×C₁₃₉	C₂³	1	2	yes	—
176	#95×C₁₃₉	C₂³	1	2	yes	—
177	#95×C₁₃₉	C₂³	1	2	yes	—
178	#95×C₁₃₉	C₂³	1	2	yes	—
179	#95×C₁₃₉	C₂³	1	2	yes	—
180	#95×C₁₃₉	C₂³	1	2	yes	—
181	#95×C₁₃₉	C₂³	1	2	yes	—
182	#95×C₁₃₉	C₂³	1	2	yes	—
183	#95×C₁₃₉	C₂³	1	2	yes	—
184	#95×C₁₃₉	C₂³	1	2	yes	—
185	#95×C₁₃₉	C₂³	1	1	yes	characteristic
186	#95×C₁₃₉	C₂³	1	1	yes	characteristic
187	#95×C₁₃₉	C₂³	1	2	yes	—
188	#95×C₁₃₉	C₂³	1	2	yes	—
189	#95×C₁₃₉	C₂³	1	2	yes	—
190	#95×C₁₃₉	C₂³	1	2	yes	—
191	#95×C₁₃₉	C₂³	1	2	yes	—
192	#95×C₁₃₉	C₂³	1	2	yes	—
193	#95×C₁₃₉	C₂³	1	2	yes	—
194	#95×C₁₃₉	C₂³	1	2	yes	—
195	#95×C₁₃₉	C₂³	1	2	yes	—
196	#95×C₁₃₉	C₂³	1	2	yes	—
197	#95×C₁₃₉	C₂³	1	2	yes	—
198	#95×C₁₃₉	C₂³	1	2	yes	—
199	#95×C₁₃₉	C₂³	1	2	yes	—
200	#95×C₁₃₉	C₂³	1	2	yes	—
201	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
203	C₂×Q₈×C₁₃₉	—	4	1	no	—
204	C₂×Q₈×C₁₃₉	—	4	2	no	—
205	C₂×D₄×C₁₃₉	—	2	4	no	—
206	C₂×D₄×C₁₃₉	—	2	4	no	—
207	C₂×D₄×C₁₃₉	—	2	4	no	—
208	C₂×D₄×C₁₃₉	—	4	1	no	—
209	C₂×D₄×C₁₃₉	—	4	2	no	—
210	C₂²×C₄×C₁₃₉	—	2	2	no	—
211	C₂²×C₄×C₁₃₉	—	2	2	no	—
212	C₂²×C₄×C₁₃₉	—	2	4	no	—
213	C₂²×C₄×C₁₃₉	—	2	4	no	—
214	C₂²×C₄×C₁₃₉	—	2	2	no	—
215	C₂²×C₄×C₁₃₉	—	2	2	no	—
216	C₂²×C₄×C₁₃₉	—	4	2	no	—
217	C₂²×C₄×C₁₃₉	—	4	2	no	—
218	C₂²×C₄×C₁₃₉	—	4	2	no	—
219	C₂²×C₄×C₁₃₉	—	4	2	no	—
220	C₂²×C₄×C₁₃₉	—	4	2	no	—
221	C₂²×C₄×C₁₃₉	—	4	2	no	—
222	C₂²×C₄×C₁₃₉	—	4	2	no	—
223	C₂²×C₄×C₁₃₉	—	4	2	no	—
224	C₂²×C₄×C₁₃₉	—	4	2	no	—
225	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
226	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
243	C₄⋊C₄×C₁₃₉	—	2	4	no	—
244	C₄⋊C₄×C₁₃₉	—	2	4	no	—
245	C₄⋊C₄×C₁₃₉	—	4	1	no	—
246	C₄⋊C₄×C₁₃₉	—	4	2	no	—
247	C₄⋊C₄×C₁₃₉	—	4	1	no	—
248	C₄⋊C₄×C₁₃₉	—	4	1	no	—
249	C₄⋊C₄×C₁₃₉	—	4	1	no	—
250	C₄⋊C₄×C₁₃₉	—	4	1	no	—
251	C₄⋊C₄×C₁₃₉	—	4	1	no	—
252	C₄⋊C₄×C₁₃₉	—	4	2	no	—
253	C₄⋊C₄×C₁₃₉	—	4	2	no	—
254	C₄⋊C₄×C₁₃₉	—	4	2	no	—
255	C₄⋊C₄×C₁₃₉	—	4	2	no	—
256	C₄⋊C₄×C₁₃₉	—	4	2	no	—
257	C₄⋊C₄×C₁₃₉	—	4	2	no	—
258	C₄⋊C₄×C₁₃₉	—	4	2	no	—
259	C₄⋊C₄×C₁₃₉	—	4	2	no	—
260	C₄⋊C₄×C₁₃₉	—	4	2	no	—
261	C₄⋊C₄×C₁₃₉	—	4	2	no	—
262	C₄⋊C₄×C₁₃₉	—	4	2	no	—
263	C₄⋊C₄×C₁₃₉	—	4	1	no	—
264	C₄⋊C₄×C₁₃₉	—	4	2	no	—
265	C₄⋊C₄×C₁₃₉	—	4	1	no	—
266	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
267	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
268	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
269	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
270	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
271	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
272	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
273	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
274	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
275	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
276	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
277	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
278	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
279	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
280	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
281	C₄²×C₁₃₉	—	2	4	no	—
282	C₄²×C₁₃₉	—	2	2	no	—
283	C₄²×C₁₃₉	—	2	2	no	—
284	C₄²×C₁₃₉	—	4	2	no	—
285	C₄²×C₁₃₉	—	4	2	no	—
286	C₄²×C₁₃₉	—	4	2	no	—
287	C₂³×C₁₃₉	—	2	2	no	—
288	C₂³×C₁₃₉	—	2	2	no	—
289	C₂³×C₁₃₉	—	2	2	no	—
290	C₂³×C₁₃₉	—	2	2	no	—
291	C₂³×C₁₃₉	—	2	2	no	—
292	C₂³×C₁₃₉	—	2	2	no	—
293	C₂³×C₁₃₉	—	2	2	no	—
294	C₂³×C₁₃₉	—	2	2	no	—
295	C₂³×C₁₃₉	—	2	2	no	—
296	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
297	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
298	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
299	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
300	Q₈×C₁₃₉	—	8	2	no	—
301	D₄×C₁₃₉	—	4	8	no	—
302	D₄×C₁₃₉	—	8	2	no	—
303	C₂×C₄×C₁₃₉	—	2	8	no	—
304	C₂×C₄×C₁₃₉	—	2	1	no	—
305	C₂×C₄×C₁₃₉	—	2	1	no	—
306	C₂×C₄×C₁₃₉	—	2	1	no	—
307	C₂×C₄×C₁₃₉	—	2	1	no	—
308	C₂×C₄×C₁₃₉	—	2	2	no	—
309	C₂×C₄×C₁₃₉	—	2	2	no	—
310	C₂×C₄×C₁₃₉	—	2	2	no	—
311	C₂×C₄×C₁₃₉	—	2	2	no	—
312	C₂×C₄×C₁₃₉	—	2	2	no	—
313	C₂×C₄×C₁₃₉	—	2	2	no	—
314	C₂×C₄×C₁₃₉	—	2	2	no	—
315	C₂×C₄×C₁₃₉	—	2	2	no	—
316	C₂×C₄×C₁₃₉	—	2	2	no	—
317	C₂×C₄×C₁₃₉	—	2	1	no	—
318	C₂×C₄×C₁₃₉	—	2	2	no	—
319	C₂×C₄×C₁₃₉	—	2	1	no	—
320	C₂×C₄×C₁₃₉	—	2	1	no	—
321	C₂×C₄×C₁₃₉	—	2	1	no	—
322	C₂×C₄×C₁₃₉	—	2	2	no	—
323	C₂×C₄×C₁₃₉	—	2	2	no	—
324	C₂×C₄×C₁₃₉	—	2	2	no	—
325	C₂×C₄×C₁₃₉	—	2	2	no	—
326	C₂×C₄×C₁₃₉	—	2	2	no	—
327	C₂×C₄×C₁₃₉	—	2	2	no	—
328	C₂×C₄×C₁₃₉	—	2	2	no	—
329	C₂×C₄×C₁₃₉	—	2	2	no	—
330	C₂×C₄×C₁₃₉	—	2	2	no	—
331	C₂×C₄×C₁₃₉	—	2	2	no	—
332	C₂×C₄×C₁₃₉	—	2	2	no	—
333	C₂×C₄×C₁₃₉	—	2	2	no	—
334	C₂×C₄×C₁₃₉	—	2	2	no	—
335	C₂×C₄×C₁₃₉	—	2	2	no	—
336	C₂×C₄×C₁₃₉	—	2	2	no	—
337	C₂×C₄×C₁₃₉	—	2	2	no	—
338	C₂×C₄×C₁₃₉	—	2	2	no	—
339	C₂×C₄×C₁₃₉	—	2	2	no	—
340	C₂×C₄×C₁₃₉	—	2	2	no	—
341	C₂×C₄×C₁₃₉	—	2	2	no	—
342	C₂×C₄×C₁₃₉	—	2	2	no	—
343	C₂×C₄×C₁₃₉	—	2	2	no	—
344	C₂×C₄×C₁₃₉	—	2	2	no	—
345	C₂×C₄×C₁₃₉	—	2	2	no	—
346	C₂×C₄×C₁₃₉	—	2	2	no	—
347	C₂×C₄×C₁₃₉	—	2	2	no	—
348	C₂×C₄×C₁₃₉	—	2	2	no	—
349	C₂×C₄×C₁₃₉	—	4	8	no	—
350	C₂×C₄×C₁₃₉	—	8	4	no	—
351	C₂×C₄×C₁₃₉	—	8	2	no	—
352	C₂×C₄×C₁₃₉	—	8	2	no	—
353	C₂×C₄×C₁₃₉	—	8	4	no	—
354	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
355	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
356	C₂²×C₁₃₉	—	2	4	no	—
357	C₂²×C₁₃₉	—	2	2	no	—
358	C₂²×C₁₃₉	—	2	2	no	—
359	C₂²×C₁₃₉	—	2	4	no	—
360	C₂²×C₁₃₉	—	4	2	no	—
361	C₂²×C₁₃₉	—	4	2	no	—
362	C₂²×C₁₃₉	—	4	2	no	—
363	C₂²×C₁₃₉	—	4	2	no	—
364	C₂²×C₁₃₉	—	4	2	no	—
365	C₂²×C₁₃₉	—	4	2	no	—
366	C₂²×C₁₃₉	—	4	2	no	—
367	C₂²×C₁₃₉	#539	1	4	yes	—
368	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
369	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
370	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
371	C₂²×C₁₃₉	#585	1	2	yes	—
372	C₂²×C₁₃₉	#585	1	2	yes	—
373	C₄×C₁₃₉	—	2	2	no	—
374	C₄×C₁₃₉	—	2	2	no	—
375	C₄×C₁₃₉	—	4	2	no	—
376	C₄×C₁₃₉	—	4	2	no	—
377	C₄×C₁₃₉	—	4	2	no	—
378	C₄×C₁₃₉	—	4	2	no	—
379	C₄×C₁₃₉	—	4	2	no	—
380	C₄×C₁₃₉	—	4	2	no	—
381	C₄×C₁₃₉	—	4	1	no	—
382	C₄×C₁₃₉	—	4	2	no	—
383	C₄×C₁₃₉	—	4	1	no	—
384	C₄×C₁₃₉	—	4	2	no	—
385	C₄×C₁₃₉	—	4	1	no	—
386	C₄×C₁₃₉	—	4	1	no	—
387	C₄×C₁₃₉	—	4	2	no	—
388	C₄×C₁₃₉	—	4	2	no	—
389	C₄×C₁₃₉	—	4	2	no	—
390	C₂×C₁₃₉	—	2	4	no	—
391	C₂×C₁₃₉	—	8	2	no	—
392	C₂×C₁₃₉	C₂×#539	1	1	yes	characteristic
393	C₂×C₁₃₉	#3493	1	2	yes	—
394	C₂×C₁₃₉	#3545	1	1	yes	characteristic
395	C₂×C₁₃₉	#3545	1	1	yes	characteristic
396	C₂×C₁₃₉	#3553	1	2	yes	—
397	#37124	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
398	C₁₃₉	#37124	1	1	yes	characteristic, direct product factor, Sylow
399	#2853	C₂×C₁₃₉	1	2	yes	complemented
400	#2789	C₂×C₁₃₉	1	1	yes	characteristic, complemented
401	#2785	C₂×C₁₃₉	1	1	yes	characteristic, complemented
402	#2783	C₂×C₁₃₉	1	2	yes	complemented
403	#2782	C₂×C₁₃₉	1	1	yes	characteristic, complemented
404	#2781	C₂×C₁₃₉	1	2	yes	complemented
405	#2775	C₂×C₁₃₉	1	2	yes	complemented
406	#2769	C₂×C₁₃₉	1	1	yes	characteristic, complemented
407	#2767	C₂×C₁₃₉	1	2	yes	complemented
408	#2765	C₂×C₁₃₉	1	2	yes	complemented
409	#2744	C₂×C₁₃₉	1	2	yes	complemented
410	#2627	C₂×C₁₃₉	1	1	yes	characteristic, complemented
411	#2618	C₂×C₁₃₉	1	1	yes	characteristic
412	#2510	C₂×C₁₃₉	1	2	yes	complemented
413	#2505	C₂×C₁₃₉	1	2	yes	complemented
414	#2450	C₂×C₁₃₉	1	2	yes	complemented
415	#2444	C₂×C₁₃₉	1	2	yes	—
416	#2322	C₂×C₁₃₉	1	2	yes	complemented
417	C₂×#382	C₂×C₁₃₉	1	1	yes	characteristic, complemented
418	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
419	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
420	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
422	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
423	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
424	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
425	#401	C₂²×C₁₃₉	1	2	yes	—
426	#400	C₂²×C₁₃₉	1	1	yes	characteristic
427	#400	C₂²×C₁₃₉	1	1	yes	characteristic
428	#400	C₂²×C₁₃₉	1	2	yes	—
429	#400	C₂²×C₁₃₉	1	2	yes	—
430	#400	C₂²×C₁₃₉	1	2	yes	—
431	#400	C₂²×C₁₃₉	1	2	yes	—
432	#400	C₂²×C₁₃₉	1	2	yes	—
433	#400	C₂²×C₁₃₉	1	2	yes	—
434	#398	C₂²×C₁₃₉	1	1	yes	characteristic
435	#398	C₂²×C₁₃₉	1	1	yes	characteristic
436	#398	C₂²×C₁₃₉	1	2	yes	—
437	#398	C₂²×C₁₃₉	1	2	yes	—
438	#398	C₂²×C₁₃₉	1	2	yes	—
439	#398	C₂²×C₁₃₉	1	2	yes	—
440	#397	C₂²×C₁₃₉	1	2	yes	—
441	#397	C₂²×C₁₃₉	1	2	yes	—
442	#397	C₂²×C₁₃₉	1	2	yes	—
443	#397	C₂²×C₁₃₉	1	2	yes	—
444	#396	C₂²×C₁₃₉	1	2	yes	—
445	#396	C₂²×C₁₃₉	1	2	yes	—
446	#396	C₂²×C₁₃₉	1	2	yes	—
447	#395	C₂²×C₁₃₉	1	1	yes	characteristic
448	#395	C₂²×C₁₃₉	1	1	yes	characteristic
449	#394	C₂²×C₁₃₉	1	1	yes	characteristic
450	#394	C₂²×C₁₃₉	1	1	yes	characteristic
451	#394	C₂²×C₁₃₉	1	2	yes	—
452	#393	C₂²×C₁₃₉	1	2	yes	—
453	#391	C₂²×C₁₃₉	1	2	yes	—
454	#389	C₂²×C₁₃₉	1	2	yes	—
455	#389	C₂²×C₁₃₉	1	2	yes	—
456	#389	C₂²×C₁₃₉	1	2	yes	—
457	#388	C₂²×C₁₃₉	1	2	yes	—
458	#388	C₂²×C₁₃₉	1	2	yes	—
459	#388	C₂²×C₁₃₉	1	2	yes	—
460	#388	C₂²×C₁₃₉	1	2	yes	—
461	#388	C₂²×C₁₃₉	1	2	yes	—
462	#388	C₂²×C₁₃₉	1	2	yes	—
463	#388	C₂²×C₁₃₉	1	2	yes	—
464	#388	C₂²×C₁₃₉	1	2	yes	—
465	#388	C₂²×C₁₃₉	1	2	yes	—
466	#387	C₂²×C₁₃₉	1	2	yes	—
467	#387	C₂²×C₁₃₉	1	2	yes	—
468	#387	C₂²×C₁₃₉	1	2	yes	—
469	#387	C₂²×C₁₃₉	1	2	yes	—
470	#387	C₂²×C₁₃₉	1	2	yes	—
471	#387	C₂²×C₁₃₉	1	2	yes	—
472	#387	C₂²×C₁₃₉	1	2	yes	—
473	#387	C₂²×C₁₃₉	1	2	yes	—
474	#387	C₂²×C₁₃₉	1	2	yes	—
475	#387	C₂²×C₁₃₉	1	2	yes	—
476	#387	C₂²×C₁₃₉	1	2	yes	—
477	#386	C₂²×C₁₃₉	1	2	yes	—
478	#386	C₂²×C₁₃₉	1	2	yes	—
479	#386	C₂²×C₁₃₉	1	2	yes	—
480	#386	C₂²×C₁₃₉	1	2	yes	—
481	#386	C₂²×C₁₃₉	1	2	yes	—
482	#385	C₂²×C₁₃₉	1	2	yes	—
483	#385	C₂²×C₁₃₉	1	2	yes	—
484	#385	C₂²×C₁₃₉	1	2	yes	—
485	#385	C₂²×C₁₃₉	1	2	yes	—
486	#385	C₂²×C₁₃₉	1	2	yes	—
487	#385	C₂²×C₁₃₉	1	2	yes	—
488	#385	C₂²×C₁₃₉	1	2	yes	—
489	#383	C₂²×C₁₃₉	1	2	yes	—
490	#382	C₂²×C₁₃₉	1	1	yes	characteristic
491	#382	C₂²×C₁₃₉	1	2	yes	—
492	#382	C₂²×C₁₃₉	1	2	yes	—
493	#382	C₂²×C₁₃₉	1	2	yes	—
494	#382	C₂²×C₁₃₉	1	1	yes	characteristic
495	#382	C₂²×C₁₃₉	1	1	yes	characteristic
496	#382	C₂²×C₁₃₉	1	1	yes	characteristic
497	#381	C₂²×C₁₃₉	1	2	yes	—
498	#381	C₂²×C₁₃₉	1	2	yes	—
499	#380	C₂²×C₁₃₉	1	1	yes	characteristic
500	#380	C₂²×C₁₃₉	1	1	yes	characteristic
501	#380	C₂²×C₁₃₉	1	2	yes	—
502	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
503	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
504	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
505	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
506	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
507	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
510	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
513	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
514	#123	—	2	8	no	—
515	C₂²⋊Q₈	—	4	2	no	—
516	#121	—	4	2	no	—
517	C₄×D₄	—	4	4	no	—
518	C₂×C₄⋊C₄	—	4	2	no	—
519	C₂×C₄⋊C₄	—	4	2	no	—
520	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
526	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
527	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
528	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
558	C₂×C₄²	—	2	4	no	—
559	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
561	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
563	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
564	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
565	#95	C₂³×C₁₃₉	1	2	yes	—
566	#95	C₂³×C₁₃₉	1	2	yes	—
567	#95	C₂³×C₁₃₉	1	2	yes	—
568	#95	C₂³×C₁₃₉	1	2	yes	—
569	#95	C₂³×C₁₃₉	1	2	yes	—
570	#95	C₂³×C₁₃₉	1	2	yes	—
571	#95	C₂³×C₁₃₉	1	2	yes	—
572	#95	C₂³×C₁₃₉	1	2	yes	—
573	#95	C₂³×C₁₃₉	1	2	yes	—
574	#95	C₂³×C₁₃₉	1	2	yes	—
575	#95	C₂³×C₁₃₉	1	1	yes	characteristic
576	#95	C₂³×C₁₃₉	1	1	yes	characteristic
577	#95	C₂³×C₁₃₉	1	2	yes	—
578	#95	C₂³×C₁₃₉	1	1	yes	characteristic
579	#95	C₂³×C₁₃₉	1	1	yes	characteristic
580	#95	C₂³×C₁₃₉	1	2	yes	—
581	#95	C₂³×C₁₃₉	1	2	yes	—
582	#95	C₂³×C₁₃₉	1	2	yes	—
583	#95	C₂³×C₁₃₉	1	2	yes	—
584	#95	C₂³×C₁₃₉	1	2	yes	—
585	#95	C₂³×C₁₃₉	1	2	yes	—
586	#95	C₂³×C₁₃₉	1	2	yes	—
587	#95	C₂³×C₁₃₉	1	2	yes	—
588	#95	C₂³×C₁₃₉	1	2	yes	—
589	#95	C₂³×C₁₃₉	1	2	yes	—
590	#95	C₂³×C₁₃₉	1	2	yes	—
591	#95	C₂³×C₁₃₉	1	2	yes	—
592	#95	C₂³×C₁₃₉	1	2	yes	—
593	#95	C₂³×C₁₃₉	1	2	yes	—
594	#95	C₂³×C₁₃₉	1	2	yes	—
595	#95	C₂³×C₁₃₉	1	2	yes	—
596	#95	C₂³×C₁₃₉	1	2	yes	—
597	#95	C₂³×C₁₃₉	1	2	yes	—
598	#95	C₂³×C₁₃₉	1	2	yes	—
599	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
600	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
601	C₂×Q₈	—	4	1	no	—
602	C₂×Q₈	—	4	2	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	4	1	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	4	2	no	—
615	C₂²×C₄	—	4	2	no	—
616	C₂²×C₄	—	4	2	no	—
617	C₂²×C₄	—	4	2	no	—
618	C₂²×C₄	—	4	2	no	—
619	C₂²×C₄	—	4	2	no	—
620	C₂²×C₄	—	4	2	no	—
621	C₂²×C₄	—	4	2	no	—
622	C₂²×C₄	—	4	2	no	—
623	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
624	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
630	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
631	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
632	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
633	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	4	1	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	1	no	—
646	C₄⋊C₄	—	4	1	no	—
647	C₄⋊C₄	—	4	1	no	—
648	C₄⋊C₄	—	4	1	no	—
649	C₄⋊C₄	—	4	1	no	—
650	C₄⋊C₄	—	4	2	no	—
651	C₄⋊C₄	—	4	2	no	—
652	C₄⋊C₄	—	4	2	no	—
653	C₄⋊C₄	—	4	2	no	—
654	C₄⋊C₄	—	4	2	no	—
655	C₄⋊C₄	—	4	2	no	—
656	C₄⋊C₄	—	4	2	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	1	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	1	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	4	2	no	—
670	C₂²⋊C₄	—	4	2	no	—
671	C₂²⋊C₄	—	4	2	no	—
672	C₂²⋊C₄	—	4	2	no	—
673	C₂²⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₄²	—	2	2	no	—
680	C₄²	—	2	4	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	4	2	no	—
683	C₄²	—	4	2	no	—
684	C₄²	—	4	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	2	no	—
691	C₂³	—	2	2	no	—
692	C₂³	—	2	2	no	—
693	C₂³	—	2	2	no	—
694	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
695	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
696	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
697	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
698	Q₈	—	8	2	no	—
699	D₄	—	4	8	no	—
700	D₄	—	8	2	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	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	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	4	8	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	—	8	2	no	—
750	C₂×C₄	—	8	2	no	—
751	C₂×C₄	—	8	4	no	—
752	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
753	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	#539×C₁₃₉	1	4	yes	—
766	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
767	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
768	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
769	C₂²	#585×C₁₃₉	1	2	yes	—
770	C₂²	#585×C₁₃₉	1	2	yes	—
771	C₄	—	2	2	no	—
772	C₄	—	2	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	1	no	—
778	C₄	—	4	2	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₂	—	2	4	no	—
789	C₂	—	8	2	no	—
790	C₂	C₂×#539×C₁₃₉	1	1	yes	characteristic
791	C₂	#3493×C₁₃₉	1	2	yes	—
792	C₂	#3545×C₁₃₉	1	1	yes	characteristic
793	C₂	#3545×C₁₃₉	1	1	yes	characteristic
794	C₂	#3553×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#121×C₁₃₉	C₂²
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. #2853×C₁₃₉	C₂	semidirect
2. #2789×C₁₃₉	C₂	semidirect
3. #2785×C₁₃₉	C₂	semidirect
4. #2783×C₁₃₉	C₂	semidirect
5. #2782×C₁₃₉	C₂	semidirect
6. #2781×C₁₃₉	C₂	semidirect
7. #2775×C₁₃₉	C₂	semidirect
8. #2769×C₁₃₉	C₂	semidirect
9. #2767×C₁₃₉	C₂	semidirect
10. #2765×C₁₃₉	C₂	semidirect
11. #2744×C₁₃₉	C₂	semidirect
12. #2627×C₁₃₉	C₂	semidirect
14. #2510×C₁₃₉	C₂	semidirect
15. #2505×C₁₃₉	C₂	semidirect
16. #2450×C₁₃₉	C₂	semidirect
18. #2322×C₁₃₉	C₂	semidirect
19. C₂×#382×C₁₃₉	C₂	semidirect
397. #37124	C₁₃₉	direct (N × H)
398. C₁₃₉	#37124	direct (N × H)
399. #2853	C₂×C₁₃₉	semidirect
400. #2789	C₂×C₁₃₉	semidirect
401. #2785	C₂×C₁₃₉	semidirect
402. #2783	C₂×C₁₃₉	semidirect
403. #2782	C₂×C₁₃₉	semidirect
404. #2781	C₂×C₁₃₉	semidirect
405. #2775	C₂×C₁₃₉	semidirect
406. #2769	C₂×C₁₃₉	semidirect
407. #2767	C₂×C₁₃₉	semidirect
408. #2765	C₂×C₁₃₉	semidirect
409. #2744	C₂×C₁₃₉	semidirect
410. #2627	C₂×C₁₃₉	semidirect
412. #2510	C₂×C₁₃₉	semidirect
413. #2505	C₂×C₁₃₉	semidirect
414. #2450	C₂×C₁₃₉	semidirect
416. #2322	C₂×C₁₃₉	semidirect
417. C₂×#382	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2853×C₁₃₉	2
#2789×C₁₃₉	2
#2785×C₁₃₉	2
#2783×C₁₃₉	2
#2782×C₁₃₉	2
#2781×C₁₃₉	2
#2775×C₁₃₉	2
#2769×C₁₃₉	2
#2767×C₁₃₉	2
#2765×C₁₃₉	2
#2744×C₁₃₉	2
#2627×C₁₃₉	2
#2618×C₁₃₉	2
#2510×C₁₃₉	2
#2505×C₁₃₉	2
#2450×C₁₃₉	2
#2444×C₁₃₉	2
#2322×C₁₃₉	2
C₂×#382×C₁₃₉	2
#37124	139

Subgroups — C139×#37124 #48031720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37124 #48031720