Subgroups — C₁₃₉×#36719 #48031315

Order 35584.

2490 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#539×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2848×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2847×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2704×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2702×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2683×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2681×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2627×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2618×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2534×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2413×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2411×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2409×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2316×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	#539×C₁₃₉	—	2	8	no	—
19	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
20	C₂×#125×C₁₃₉	C₂²	1	2	yes	complemented
21	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
31	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	#400×C₁₃₉	C₂²	1	2	yes	complemented
42	#398×C₁₃₉	C₂²	1	2	yes	complemented
43	#398×C₁₃₉	C₂²	1	4	yes	complemented
44	#398×C₁₃₉	C₂²	1	4	yes	complemented
45	#396×C₁₃₉	C₂²	1	4	yes	—
46	#396×C₁₃₉	C₂²	1	4	yes	—
47	#396×C₁₃₉	C₂²	1	4	yes	complemented
48	#396×C₁₃₉	C₂²	1	4	yes	complemented
49	#395×C₁₃₉	C₂²	1	2	yes	complemented
50	#395×C₁₃₉	C₂²	1	4	yes	complemented
51	#394×C₁₃₉	C₂²	1	4	yes	—
52	#394×C₁₃₉	C₂²	1	4	yes	—
53	#394×C₁₃₉	C₂²	1	2	yes	complemented
54	#393×C₁₃₉	C₂²	1	4	yes	complemented
55	#391×C₁₃₉	C₂²	1	4	yes	complemented
56	#390×C₁₃₉	C₂²	1	4	yes	—
57	#389×C₁₃₉	C₂²	1	4	yes	complemented
58	#389×C₁₃₉	C₂²	1	4	yes	complemented
59	#389×C₁₃₉	C₂²	1	4	yes	complemented
60	#388×C₁₃₉	C₂²	1	4	yes	—
61	#388×C₁₃₉	C₂²	1	4	yes	—
62	#388×C₁₃₉	C₂²	1	4	yes	complemented
63	#386×C₁₃₉	C₂²	1	4	yes	—
64	#386×C₁₃₉	C₂²	1	2	yes	—
65	#386×C₁₃₉	C₂²	1	4	yes	—
66	#386×C₁₃₉	C₂²	1	2	yes	—
67	#385×C₁₃₉	C₂²	1	2	yes	—
68	#385×C₁₃₉	C₂²	1	4	yes	—
69	#385×C₁₃₉	C₂²	1	2	yes	—
70	#381×C₁₃₉	C₂²	1	2	yes	—
71	#380×C₁₃₉	C₂²	1	2	yes	—
72	#380×C₁₃₉	C₂²	1	1	yes	characteristic
73	#380×C₁₃₉	C₂²	1	1	yes	characteristic
74	#380×C₁₃₉	C₂²	1	2	yes	—
75	#380×C₁₃₉	C₂²	1	2	yes	—
76	#379×C₁₃₉	C₂²	1	2	yes	—
77	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃₉	—	2	4	no	—
79	C₂²×Q₈×C₁₃₉	—	4	4	no	—
80	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
81	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃₉	—	2	4	no	—
86	C₂³×C₄×C₁₃₉	—	4	4	no	—
87	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	#126×C₁₃₉	—	2	8	no	—
97	#125×C₁₃₉	—	2	8	no	—
98	#123×C₁₃₉	—	2	8	no	—
99	#123×C₁₃₉	—	2	8	no	—
100	#123×C₁₃₉	—	4	4	no	—
101	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
102	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
103	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
104	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
105	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
106	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
107	#121×C₁₃₉	—	2	4	no	—
108	#121×C₁₃₉	—	4	4	no	—
109	#120×C₁₃₉	—	4	4	no	—
110	C₄×D₄×C₁₃₉	—	2	8	no	—
111	#117×C₁₃₉	—	4	4	no	—
112	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
113	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
114	C₂×C₄⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	2	yes	—
124	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
150	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
152	#95×C₁₃₉	C₂³	1	4	yes	—
153	#95×C₁₃₉	C₂³	1	4	yes	—
154	#95×C₁₃₉	C₂³	1	4	yes	—
155	#95×C₁₃₉	C₂³	1	2	yes	—
156	#95×C₁₃₉	C₂³	1	4	yes	—
157	#95×C₁₃₉	C₂³	1	4	yes	—
158	#95×C₁₃₉	C₂³	1	4	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	#95×C₁₃₉	C₂³	1	2	yes	—
161	C₂⁴×C₁₃₉	—	2	2	no	—
162	C₂⁴×C₁₃₉	—	2	4	no	—
163	C₂⁴×C₁₃₉	—	2	2	no	—
164	C₂⁴×C₁₃₉	—	2	2	no	—
165	C₂⁴×C₁₃₉	—	4	2	no	—
166	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
167	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
168	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
169	C₂×Q₈×C₁₃₉	—	2	8	no	—
170	C₂×Q₈×C₁₃₉	—	2	2	no	—
171	C₂×Q₈×C₁₃₉	—	2	8	no	—
172	C₂×Q₈×C₁₃₉	—	4	4	no	—
173	C₂×Q₈×C₁₃₉	—	4	2	no	—
174	C₂×Q₈×C₁₃₉	—	4	16	no	—
175	C₂×D₄×C₁₃₉	—	2	4	no	—
176	C₂×D₄×C₁₃₉	—	2	4	no	—
177	C₂×D₄×C₁₃₉	—	2	4	no	—
178	C₂×D₄×C₁₃₉	—	2	8	no	—
179	C₂×D₄×C₁₃₉	—	2	2	no	—
180	C₂×D₄×C₁₃₉	—	4	4	no	—
181	C₂×D₄×C₁₃₉	—	4	2	no	—
182	C₂×D₄×C₁₃₉	—	4	4	no	—
183	C₂²×C₄×C₁₃₉	—	2	2	no	—
184	C₂²×C₄×C₁₃₉	—	2	2	no	—
185	C₂²×C₄×C₁₃₉	—	2	2	no	—
186	C₂²×C₄×C₁₃₉	—	2	4	no	—
187	C₂²×C₄×C₁₃₉	—	2	2	no	—
188	C₂²×C₄×C₁₃₉	—	2	2	no	—
189	C₂²×C₄×C₁₃₉	—	2	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	2	no	—
191	C₂²×C₄×C₁₃₉	—	2	4	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	—	4	2	no	—
197	C₂²×C₄×C₁₃₉	—	4	2	no	—
198	C₂²×C₄×C₁₃₉	—	4	2	no	—
199	C₂²×C₄×C₁₃₉	—	4	2	no	—
200	C₂²×C₄×C₁₃₉	—	4	2	no	—
201	C₂²×C₄×C₁₃₉	—	4	4	no	—
202	C₂²×C₄×C₁₃₉	—	4	16	no	—
203	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₄⋊C₄×C₁₃₉	—	2	8	no	—
219	C₄⋊C₄×C₁₃₉	—	2	4	no	—
220	C₄⋊C₄×C₁₃₉	—	2	4	no	—
221	C₄⋊C₄×C₁₃₉	—	2	4	no	—
222	C₄⋊C₄×C₁₃₉	—	2	2	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	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	8	no	—
228	C₄⋊C₄×C₁₃₉	—	4	4	no	—
229	C₄⋊C₄×C₁₃₉	—	4	2	no	—
230	C₄⋊C₄×C₁₃₉	—	4	2	no	—
231	C₄⋊C₄×C₁₃₉	—	4	4	no	—
232	C₄⋊C₄×C₁₃₉	—	4	4	no	—
233	C₄⋊C₄×C₁₃₉	—	4	4	no	—
234	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
235	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
236	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
237	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
239	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
240	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
241	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
242	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
243	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
246	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
247	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
248	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
249	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
250	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
251	C₄²×C₁₃₉	—	2	4	no	—
252	C₄²×C₁₃₉	—	4	4	no	—
253	C₂³×C₁₃₉	—	2	2	no	—
254	C₂³×C₁₃₉	—	2	2	no	—
255	C₂³×C₁₃₉	—	2	8	no	—
256	C₂³×C₁₃₉	—	2	2	no	—
257	C₂³×C₁₃₉	—	2	2	no	—
258	C₂³×C₁₃₉	—	2	2	no	—
259	C₂³×C₁₃₉	—	2	2	no	—
260	C₂³×C₁₃₉	—	2	2	no	—
261	C₂³×C₁₃₉	—	2	2	no	—
262	C₂³×C₁₃₉	—	2	2	no	—
263	C₂³×C₁₃₉	—	2	4	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	2	no	—
266	C₂³×C₁₃₉	—	2	4	no	—
267	C₂³×C₁₃₉	—	4	8	no	—
268	C₂³×C₁₃₉	—	4	8	no	—
269	C₂³×C₁₃₉	—	4	4	no	—
270	C₂³×C₁₃₉	—	4	4	no	—
271	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
272	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
273	C₂³×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
274	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
275	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
276	Q₈×C₁₃₉	—	4	16	no	—
277	Q₈×C₁₃₉	—	8	2	no	—
278	D₄×C₁₃₉	—	4	8	no	—
279	D₄×C₁₃₉	—	8	2	no	—
280	D₄×C₁₃₉	—	8	8	no	—
281	C₂×C₄×C₁₃₉	—	2	8	no	—
282	C₂×C₄×C₁₃₉	—	2	8	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	2	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	4	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	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	4	no	—
297	C₂×C₄×C₁₃₉	—	2	4	no	—
298	C₂×C₄×C₁₃₉	—	2	4	no	—
299	C₂×C₄×C₁₃₉	—	2	2	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	4	no	—
302	C₂×C₄×C₁₃₉	—	2	4	no	—
303	C₂×C₄×C₁₃₉	—	2	4	no	—
304	C₂×C₄×C₁₃₉	—	2	4	no	—
305	C₂×C₄×C₁₃₉	—	2	2	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	2	4	no	—
308	C₂×C₄×C₁₃₉	—	4	4	no	—
309	C₂×C₄×C₁₃₉	—	4	4	no	—
310	C₂×C₄×C₁₃₉	—	4	8	no	—
311	C₂×C₄×C₁₃₉	—	4	8	no	—
312	C₂×C₄×C₁₃₉	—	4	4	no	—
313	C₂×C₄×C₁₃₉	—	4	4	no	—
314	C₂×C₄×C₁₃₉	—	8	4	no	—
315	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
320	C₂²×C₁₃₉	—	2	2	no	—
321	C₂²×C₁₃₉	—	2	2	no	—
322	C₂²×C₁₃₉	—	2	4	no	—
323	C₂²×C₁₃₉	—	2	4	no	—
324	C₂²×C₁₃₉	—	2	4	no	—
325	C₂²×C₁₃₉	—	2	4	no	—
326	C₂²×C₁₃₉	—	2	4	no	—
327	C₂²×C₁₃₉	—	4	16	no	—
328	C₂²×C₁₃₉	—	4	2	no	—
329	C₂²×C₁₃₉	—	4	2	no	—
330	C₂²×C₁₃₉	—	4	2	no	—
331	C₂²×C₁₃₉	—	4	2	no	—
332	C₂²×C₁₃₉	—	4	2	no	—
333	C₂²×C₁₃₉	—	4	2	no	—
334	C₂²×C₁₃₉	—	4	2	no	—
335	C₂²×C₁₃₉	—	4	4	no	—
336	C₂²×C₁₃₉	—	4	4	no	—
337	C₂²×C₁₃₉	#537	1	4	yes	—
338	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
339	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
340	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
341	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
342	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
343	C₄×C₁₃₉	—	2	4	no	—
344	C₄×C₁₃₉	—	2	4	no	—
345	C₄×C₁₃₉	—	2	2	no	—
346	C₄×C₁₃₉	—	2	2	no	—
347	C₄×C₁₃₉	—	2	4	no	—
348	C₄×C₁₃₉	—	4	2	no	—
349	C₄×C₁₃₉	—	4	2	no	—
350	C₄×C₁₃₉	—	4	2	no	—
351	C₄×C₁₃₉	—	4	2	no	—
352	C₄×C₁₃₉	—	4	2	no	—
353	C₄×C₁₃₉	—	4	4	no	—
354	C₄×C₁₃₉	—	4	4	no	—
355	C₂×C₁₃₉	—	2	4	no	—
356	C₂×C₁₃₉	—	4	4	no	—
357	C₂×C₁₃₉	—	8	2	no	—
358	C₂×C₁₃₉	C₂×#537	1	1	yes	characteristic
359	C₂×C₁₃₉	#3484	1	1	yes	characteristic
360	C₂×C₁₃₉	#3486	1	1	yes	characteristic
361	C₂×C₁₃₉	#3536	1	2	yes	—
362	C₂×C₁₃₉	#3538	1	2	yes	—
363	#36719	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
364	C₁₃₉	#36719	1	1	yes	characteristic, direct product factor, Sylow
365	C₂×#539	C₂×C₁₃₉	1	1	yes	characteristic, complemented
366	C₂²×C₂²⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
367	#2848	C₂×C₁₃₉	1	1	yes	characteristic, complemented
368	#2847	C₂×C₁₃₉	1	1	yes	characteristic
369	#2704	C₂×C₁₃₉	1	4	yes	complemented
370	#2702	C₂×C₁₃₉	1	4	yes	complemented
371	#2683	C₂×C₁₃₉	1	4	yes	complemented
372	#2681	C₂×C₁₃₉	1	4	yes	complemented
373	#2627	C₂×C₁₃₉	1	1	yes	characteristic, complemented
374	#2618	C₂×C₁₃₉	1	1	yes	characteristic, complemented
375	#2534	C₂×C₁₃₉	1	2	yes	complemented
376	#2413	C₂×C₁₃₉	1	2	yes	complemented
377	#2411	C₂×C₁₃₉	1	2	yes	complemented
378	#2409	C₂×C₁₃₉	1	2	yes	complemented
379	#2316	C₂×C₁₃₉	1	1	yes	characteristic, complemented
380	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
381	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
382	#539	—	2	8	no	—
383	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
384	C₂×#125	C₂²×C₁₃₉	1	2	yes	complemented
385	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
386	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
387	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
388	C₂×C₂²⋊Q₈	—	2	8	no	—
389	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
390	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
392	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
393	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
394	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
395	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
396	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
397	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
398	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
399	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
400	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
401	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
402	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
405	#400	C₂²×C₁₃₉	1	2	yes	complemented
406	#398	C₂²×C₁₃₉	1	2	yes	complemented
407	#398	C₂²×C₁₃₉	1	4	yes	complemented
408	#398	C₂²×C₁₃₉	1	4	yes	complemented
409	#396	C₂²×C₁₃₉	1	4	yes	—
410	#396	C₂²×C₁₃₉	1	4	yes	—
411	#396	C₂²×C₁₃₉	1	4	yes	complemented
412	#396	C₂²×C₁₃₉	1	4	yes	complemented
413	#395	C₂²×C₁₃₉	1	2	yes	complemented
414	#395	C₂²×C₁₃₉	1	4	yes	complemented
415	#394	C₂²×C₁₃₉	1	4	yes	—
416	#394	C₂²×C₁₃₉	1	4	yes	—
417	#394	C₂²×C₁₃₉	1	2	yes	complemented
418	#393	C₂²×C₁₃₉	1	4	yes	complemented
419	#391	C₂²×C₁₃₉	1	4	yes	complemented
420	#390	C₂²×C₁₃₉	1	4	yes	—
421	#389	C₂²×C₁₃₉	1	4	yes	complemented
422	#389	C₂²×C₁₃₉	1	4	yes	complemented
423	#389	C₂²×C₁₃₉	1	4	yes	complemented
424	#388	C₂²×C₁₃₉	1	4	yes	—
425	#388	C₂²×C₁₃₉	1	4	yes	—
426	#388	C₂²×C₁₃₉	1	4	yes	complemented
427	#386	C₂²×C₁₃₉	1	2	yes	—
428	#386	C₂²×C₁₃₉	1	4	yes	—
429	#386	C₂²×C₁₃₉	1	2	yes	—
430	#386	C₂²×C₁₃₉	1	4	yes	—
431	#385	C₂²×C₁₃₉	1	2	yes	—
432	#385	C₂²×C₁₃₉	1	4	yes	—
433	#385	C₂²×C₁₃₉	1	2	yes	—
434	#381	C₂²×C₁₃₉	1	2	yes	—
435	#380	C₂²×C₁₃₉	1	1	yes	characteristic
436	#380	C₂²×C₁₃₉	1	1	yes	characteristic
437	#380	C₂²×C₁₃₉	1	2	yes	—
438	#380	C₂²×C₁₃₉	1	2	yes	—
439	#380	C₂²×C₁₃₉	1	2	yes	—
440	#379	C₂²×C₁₃₉	1	2	yes	—
441	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
442	C₂²×Q₈	—	2	4	no	—
443	C₂²×Q₈	—	4	4	no	—
444	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
445	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
446	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
447	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
448	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
449	C₂³×C₄	—	2	4	no	—
450	C₂³×C₄	—	4	4	no	—
451	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
454	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
455	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
456	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
458	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
460	#126	—	2	8	no	—
461	#125	—	2	8	no	—
462	#123	—	2	8	no	—
463	#123	—	2	8	no	—
464	#123	—	4	4	no	—
465	C₂²⋊Q₈	—	2	4	no	—
466	C₂²⋊Q₈	—	2	16	no	—
467	C₂²⋊Q₈	—	2	16	no	—
468	C₂²⋊Q₈	—	2	8	no	—
469	C₂²⋊Q₈	—	4	8	no	—
470	C₂²⋊Q₈	—	4	4	no	—
471	#121	—	2	4	no	—
472	#121	—	4	4	no	—
473	#120	—	4	4	no	—
474	C₄×D₄	—	2	8	no	—
475	#117	—	4	4	no	—
476	C₂×C₄⋊C₄	—	2	4	no	—
477	C₂×C₄⋊C₄	—	2	4	no	—
478	C₂×C₄⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
493	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
497	C₂×C₂²⋊C₄	—	2	4	no	—
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
514	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
515	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
516	#95	C₂³×C₁₃₉	1	4	yes	—
517	#95	C₂³×C₁₃₉	1	2	yes	—
518	#95	C₂³×C₁₃₉	1	2	yes	—
519	#95	C₂³×C₁₃₉	1	4	yes	—
520	#95	C₂³×C₁₃₉	1	4	yes	—
521	#95	C₂³×C₁₃₉	1	4	yes	—
522	#95	C₂³×C₁₃₉	1	4	yes	—
523	#95	C₂³×C₁₃₉	1	4	yes	—
524	#95	C₂³×C₁₃₉	1	4	yes	—
525	C₂⁴	—	2	2	no	—
526	C₂⁴	—	2	4	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	4	2	no	—
530	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
531	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
532	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
533	C₂×Q₈	—	2	8	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	8	no	—
536	C₂×Q₈	—	4	4	no	—
537	C₂×Q₈	—	4	2	no	—
538	C₂×Q₈	—	4	16	no	—
539	C₂×D₄	—	2	4	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	—	4	2	no	—
565	C₂²×C₄	—	4	4	no	—
566	C₂²×C₄	—	4	16	no	—
567	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
568	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
569	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
582	C₄⋊C₄	—	2	8	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	4	4	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₄⋊C₄	—	4	2	no	—
595	C₄⋊C₄	—	4	4	no	—
596	C₄⋊C₄	—	4	4	no	—
597	C₄⋊C₄	—	4	4	no	—
598	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
599	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	8	no	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	4	4	no	—
612	C₂²⋊C₄	—	4	4	no	—
613	C₂²⋊C₄	—	4	4	no	—
614	C₂²⋊C₄	—	4	4	no	—
615	C₄²	—	2	4	no	—
616	C₄²	—	4	4	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	8	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	4	8	no	—
632	C₂³	—	4	8	no	—
633	C₂³	—	4	4	no	—
634	C₂³	—	4	4	no	—
635	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
636	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
637	C₂³	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
638	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
639	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
640	Q₈	—	4	16	no	—
641	Q₈	—	8	2	no	—
642	D₄	—	4	8	no	—
643	D₄	—	8	2	no	—
644	D₄	—	8	8	no	—
645	C₂×C₄	—	2	8	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	—	4	8	no	—
675	C₂×C₄	—	4	8	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	8	4	no	—
679	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
680	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
681	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
683	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
684	C₂²	—	2	4	no	—
685	C₂²	—	2	4	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	4	16	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	#537×C₁₃₉	1	4	yes	—
702	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
703	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
704	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
705	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
706	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	4	no	—
712	C₄	—	4	4	no	—
713	C₄	—	4	4	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₂	—	2	4	no	—
720	C₂	—	4	4	no	—
721	C₂	—	8	2	no	—
722	C₂	C₂×#537×C₁₃₉	1	1	yes	characteristic
723	C₂	#3484×C₁₃₉	1	1	yes	characteristic
724	C₂	#3486×C₁₃₉	1	1	yes	characteristic
725	C₂	#3536×C₁₃₉	1	2	yes	—
726	C₂	#3538×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2847×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×#539×C₁₃₉	C₂	semidirect
2. C₂²×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
3. #2848×C₁₃₉	C₂	semidirect
5. #2704×C₁₃₉	C₂	semidirect
6. #2702×C₁₃₉	C₂	semidirect
7. #2683×C₁₃₉	C₂	semidirect
8. #2681×C₁₃₉	C₂	semidirect
9. #2627×C₁₃₉	C₂	semidirect
10. #2618×C₁₃₉	C₂	semidirect
11. #2534×C₁₃₉	C₂	semidirect
12. #2413×C₁₃₉	C₂	semidirect
13. #2411×C₁₃₉	C₂	semidirect
14. #2409×C₁₃₉	C₂	semidirect
15. #2316×C₁₃₉	C₂	semidirect
19. C₂×#126×C₁₃₉	C₂²	semidirect
20. C₂×#125×C₁₃₉	C₂²	semidirect
23. C₂×#123×C₁₃₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
41. #400×C₁₃₉	C₂²	semidirect
42. #398×C₁₃₉	C₂²	semidirect
43. #398×C₁₃₉	C₂²	semidirect
44. #398×C₁₃₉	C₂²	semidirect
47. #396×C₁₃₉	C₂²	semidirect
48. #396×C₁₃₉	C₂²	semidirect
49. #395×C₁₃₉	C₂²	semidirect
50. #395×C₁₃₉	C₂²	semidirect
53. #394×C₁₃₉	C₂²	semidirect
54. #393×C₁₃₉	C₂²	semidirect
55. #391×C₁₃₉	C₂²	semidirect
57. #389×C₁₃₉	C₂²	semidirect
58. #389×C₁₃₉	C₂²	semidirect
59. #389×C₁₃₉	C₂²	semidirect
62. #388×C₁₃₉	C₂²	semidirect
114. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
363. #36719	C₁₃₉	direct (N × H)
364. C₁₃₉	#36719	direct (N × H)
365. C₂×#539	C₂×C₁₃₉	semidirect
366. C₂²×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
367. #2848	C₂×C₁₃₉	semidirect
369. #2704	C₂×C₁₃₉	semidirect
370. #2702	C₂×C₁₃₉	semidirect
371. #2683	C₂×C₁₃₉	semidirect
372. #2681	C₂×C₁₃₉	semidirect
373. #2627	C₂×C₁₃₉	semidirect
374. #2618	C₂×C₁₃₉	semidirect
375. #2534	C₂×C₁₃₉	semidirect
376. #2413	C₂×C₁₃₉	semidirect
377. #2411	C₂×C₁₃₉	semidirect
378. #2409	C₂×C₁₃₉	semidirect
379. #2316	C₂×C₁₃₉	semidirect
383. C₂×#126	C₂²×C₁₃₉	semidirect
384. C₂×#125	C₂²×C₁₃₉	semidirect
387. C₂×#123	C₂²×C₁₃₉	semidirect
393. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
394. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
405. #400	C₂²×C₁₃₉	semidirect
406. #398	C₂²×C₁₃₉	semidirect
407. #398	C₂²×C₁₃₉	semidirect
408. #398	C₂²×C₁₃₉	semidirect
411. #396	C₂²×C₁₃₉	semidirect
412. #396	C₂²×C₁₃₉	semidirect
413. #395	C₂²×C₁₃₉	semidirect
414. #395	C₂²×C₁₃₉	semidirect
417. #394	C₂²×C₁₃₉	semidirect
418. #393	C₂²×C₁₃₉	semidirect
419. #391	C₂²×C₁₃₉	semidirect
421. #389	C₂²×C₁₃₉	semidirect
422. #389	C₂²×C₁₃₉	semidirect
423. #389	C₂²×C₁₃₉	semidirect
426. #388	C₂²×C₁₃₉	semidirect
478. C₂×C₄⋊C₄	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×#539×C₁₃₉	2
C₂²×C₂²⋊Q₈×C₁₃₉	2
#2848×C₁₃₉	2
#2847×C₁₃₉	2
#2704×C₁₃₉	2
#2702×C₁₃₉	2
#2683×C₁₃₉	2
#2681×C₁₃₉	2
#2627×C₁₃₉	2
#2618×C₁₃₉	2
#2534×C₁₃₉	2
#2413×C₁₃₉	2
#2411×C₁₃₉	2
#2409×C₁₃₉	2
#2316×C₁₃₉	2
#36719	139

Subgroups — C139×#36719 #48031315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36719 #48031315