Subgroups — C₁₃₉×#36956 #48031552

Order 35584.

2518 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#123×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2849×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2718×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2710×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2706×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2703×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2613×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2561×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2539×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#2534×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2503×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2501×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2486×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2312×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	#538×C₁₃₉	—	2	8	no	—
19	C₂×#126×C₁₃₉	C₂²	1	2	yes	complemented
20	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
21	C₂×#123×C₁₃₉	—	2	8	no	—
22	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
23	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#123×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#123×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#120×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
39	#400×C₁₃₉	C₂²	1	4	yes	complemented
40	#399×C₁₃₉	C₂²	1	2	yes	complemented
41	#399×C₁₃₉	C₂²	1	4	yes	complemented
42	#398×C₁₃₉	C₂²	1	4	yes	complemented
43	#397×C₁₃₉	C₂²	1	2	yes	complemented
44	#397×C₁₃₉	C₂²	1	4	yes	complemented
45	#396×C₁₃₉	C₂²	1	4	yes	complemented
46	#394×C₁₃₉	C₂²	1	4	yes	—
47	#394×C₁₃₉	C₂²	1	4	yes	—
48	#394×C₁₃₉	C₂²	1	4	yes	complemented
49	#393×C₁₃₉	C₂²	1	2	yes	complemented
50	#392×C₁₃₉	C₂²	1	4	yes	—
51	#392×C₁₃₉	C₂²	1	4	yes	—
52	#392×C₁₃₉	C₂²	1	2	yes	complemented
53	#391×C₁₃₉	C₂²	1	2	yes	complemented
54	#390×C₁₃₉	C₂²	1	4	yes	complemented
55	#390×C₁₃₉	C₂²	1	2	yes	complemented
56	#389×C₁₃₉	C₂²	1	4	yes	complemented
57	#388×C₁₃₉	C₂²	1	4	yes	complemented
58	#388×C₁₃₉	C₂²	1	4	yes	complemented
59	#388×C₁₃₉	C₂²	1	4	yes	complemented
60	#388×C₁₃₉	C₂²	1	4	yes	complemented
61	#386×C₁₃₉	C₂²	1	4	yes	complemented
62	#386×C₁₃₉	C₂²	1	4	yes	complemented
63	#386×C₁₃₉	C₂²	1	4	yes	complemented
64	#385×C₁₃₉	C₂²	1	4	yes	complemented
65	#385×C₁₃₉	C₂²	1	4	yes	complemented
66	#384×C₁₃₉	C₂²	1	2	yes	complemented
67	#382×C₁₃₉	C₂²	1	2	yes	complemented
68	#381×C₁₃₉	C₂²	1	2	yes	—
69	#381×C₁₃₉	C₂²	1	2	yes	—
70	#381×C₁₃₉	C₂²	1	2	yes	—
71	#380×C₁₃₉	C₂²	1	2	yes	—
72	#380×C₁₃₉	C₂²	1	4	yes	complemented
73	#379×C₁₃₉	C₂²	1	2	yes	—
74	#379×C₁₃₉	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
77	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃₉	—	2	4	no	—
81	C₂²×D₄×C₁₃₉	—	4	4	no	—
82	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂³×C₄×C₁₃₉	—	2	4	no	—
89	C₂³×C₄×C₁₃₉	—	4	4	no	—
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	4	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	#126×C₁₃₉	—	2	8	no	—
98	#124×C₁₃₉	—	2	8	no	—
99	#123×C₁₃₉	—	2	16	no	—
100	#123×C₁₃₉	—	2	16	no	—
101	#123×C₁₃₉	—	2	8	no	—
102	#123×C₁₃₉	—	4	4	no	—
103	#123×C₁₃₉	—	4	4	no	—
104	#123×C₁₃₉	—	4	4	no	—
105	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
106	#121×C₁₃₉	—	2	4	no	—
107	#121×C₁₃₉	—	2	8	no	—
108	#120×C₁₃₉	—	2	8	no	—
109	#120×C₁₃₉	—	4	4	no	—
110	C₄×D₄×C₁₃₉	—	2	8	no	—
111	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
112	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
126	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	8	yes	complemented
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
150	#95×C₁₃₉	C₂³	1	4	yes	—
151	#95×C₁₃₉	C₂³	1	4	yes	—
152	#95×C₁₃₉	C₂³	1	4	yes	—
153	#95×C₁₃₉	C₂³	1	2	yes	—
154	#95×C₁₃₉	C₂³	1	4	yes	—
155	#95×C₁₃₉	C₂³	1	4	yes	—
156	#95×C₁₃₉	C₂³	1	4	yes	—
157	#95×C₁₃₉	C₂³	1	2	yes	—
158	#95×C₁₃₉	C₂³	1	4	yes	—
159	C₂⁴×C₁₃₉	—	2	4	no	—
160	C₂⁴×C₁₃₉	—	2	2	no	—
161	C₂⁴×C₁₃₉	—	2	4	no	—
162	C₂⁴×C₁₃₉	—	4	2	no	—
163	C₂⁴×C₁₃₉	—	4	2	no	—
164	C₂⁴×C₁₃₉	—	4	2	no	—
165	C₂⁴×C₁₃₉	—	4	2	no	—
166	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
167	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
168	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
169	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
170	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
171	C₂×Q₈×C₁₃₉	—	2	2	no	—
172	C₂×Q₈×C₁₃₉	—	4	2	no	—
173	C₂×D₄×C₁₃₉	—	2	4	no	—
174	C₂×D₄×C₁₃₉	—	2	8	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	4	no	—
179	C₂×D₄×C₁₃₉	—	2	2	no	—
180	C₂×D₄×C₁₃₉	—	4	8	no	—
181	C₂×D₄×C₁₃₉	—	4	4	no	—
182	C₂×D₄×C₁₃₉	—	4	2	no	—
183	C₂×D₄×C₁₃₉	—	4	4	no	—
184	C₂×D₄×C₁₃₉	—	4	4	no	—
185	C₂×D₄×C₁₃₉	—	4	4	no	—
186	C₂×D₄×C₁₃₉	—	4	4	no	—
187	C₂×D₄×C₁₃₉	—	4	16	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	8	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	8	no	—
197	C₂²×C₄×C₁₃₉	—	4	2	no	—
198	C₂²×C₄×C₁₃₉	—	4	2	no	—
199	C₂²×C₄×C₁₃₉	—	4	4	no	—
200	C₂²×C₄×C₁₃₉	—	4	16	no	—
201	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₄⋊C₄×C₁₃₉	—	2	8	no	—
215	C₄⋊C₄×C₁₃₉	—	2	4	no	—
216	C₄⋊C₄×C₁₃₉	—	2	4	no	—
217	C₄⋊C₄×C₁₃₉	—	2	4	no	—
218	C₄⋊C₄×C₁₃₉	—	2	4	no	—
219	C₄⋊C₄×C₁₃₉	—	2	2	no	—
220	C₄⋊C₄×C₁₃₉	—	2	2	no	—
221	C₄⋊C₄×C₁₃₉	—	4	4	no	—
222	C₄⋊C₄×C₁₃₉	—	4	4	no	—
223	C₄⋊C₄×C₁₃₉	—	4	4	no	—
224	C₄⋊C₄×C₁₃₉	—	4	4	no	—
225	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
226	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
227	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
228	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
229	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
230	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
231	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
232	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
233	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
234	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
235	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
236	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
237	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
238	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
239	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
240	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
241	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
242	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
243	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
244	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
245	C₄²×C₁₃₉	—	2	4	no	—
246	C₄²×C₁₃₉	—	4	2	no	—
247	C₄²×C₁₃₉	—	4	2	no	—
248	C₂³×C₁₃₉	—	2	2	no	—
249	C₂³×C₁₃₉	—	2	2	no	—
250	C₂³×C₁₃₉	—	2	8	no	—
251	C₂³×C₁₃₉	—	2	4	no	—
252	C₂³×C₁₃₉	—	2	4	no	—
253	C₂³×C₁₃₉	—	2	4	no	—
254	C₂³×C₁₃₉	—	2	2	no	—
255	C₂³×C₁₃₉	—	2	2	no	—
256	C₂³×C₁₃₉	—	2	2	no	—
257	C₂³×C₁₃₉	—	2	2	no	—
258	C₂³×C₁₃₉	—	2	4	no	—
259	C₂³×C₁₃₉	—	2	2	no	—
260	C₂³×C₁₃₉	—	2	4	no	—
261	C₂³×C₁₃₉	—	2	4	no	—
262	C₂³×C₁₃₉	—	2	4	no	—
263	C₂³×C₁₃₉	—	2	2	no	—
264	C₂³×C₁₃₉	—	4	4	no	—
265	C₂³×C₁₃₉	—	4	4	no	—
266	C₂³×C₁₃₉	—	4	16	no	—
267	C₂³×C₁₃₉	—	4	4	no	—
268	C₂³×C₁₃₉	—	4	4	no	—
269	C₂³×C₁₃₉	—	4	4	no	—
270	C₂³×C₁₃₉	—	8	8	no	—
271	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
272	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
273	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
274	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
275	Q₈×C₁₃₉	—	8	2	no	—
276	D₄×C₁₃₉	—	4	16	no	—
277	D₄×C₁₃₉	—	4	8	no	—
278	D₄×C₁₃₉	—	8	2	no	—
279	D₄×C₁₃₉	—	8	4	no	—
280	D₄×C₁₃₉	—	8	4	no	—
281	D₄×C₁₃₉	—	8	8	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	4	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	2	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	4	no	—
292	C₂×C₄×C₁₃₉	—	2	4	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	4	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	4	no	—
297	C₂×C₄×C₁₃₉	—	2	2	no	—
298	C₂×C₄×C₁₃₉	—	2	4	no	—
299	C₂×C₄×C₁₃₉	—	2	4	no	—
300	C₂×C₄×C₁₃₉	—	2	4	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	—	4	4	no	—
305	C₂×C₄×C₁₃₉	—	4	4	no	—
306	C₂×C₄×C₁₃₉	—	4	16	no	—
307	C₂×C₄×C₁₃₉	—	4	4	no	—
308	C₂×C₄×C₁₃₉	—	4	4	no	—
309	C₂×C₄×C₁₃₉	—	4	4	no	—
310	C₂×C₄×C₁₃₉	—	8	4	no	—
311	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
312	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
314	C₂²×C₁₃₉	—	2	2	no	—
315	C₂²×C₁₃₉	—	2	2	no	—
316	C₂²×C₁₃₉	—	2	8	no	—
317	C₂²×C₁₃₉	—	2	4	no	—
318	C₂²×C₁₃₉	—	2	4	no	—
319	C₂²×C₁₃₉	—	2	4	no	—
320	C₂²×C₁₃₉	—	4	16	no	—
321	C₂²×C₁₃₉	—	4	8	no	—
322	C₂²×C₁₃₉	—	4	2	no	—
323	C₂²×C₁₃₉	—	4	2	no	—
324	C₂²×C₁₃₉	—	4	2	no	—
325	C₂²×C₁₃₉	—	4	2	no	—
326	C₂²×C₁₃₉	—	4	2	no	—
327	C₂²×C₁₃₉	—	4	2	no	—
328	C₂²×C₁₃₉	—	4	4	no	—
329	C₂²×C₁₃₉	—	4	4	no	—
330	C₂²×C₁₃₉	—	4	4	no	—
331	C₂²×C₁₃₉	—	4	4	no	—
332	C₂²×C₁₃₉	—	8	8	no	—
333	C₂²×C₁₃₉	#535	1	4	yes	—
334	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
335	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
336	C₂²×C₁₃₉	#585	1	2	yes	—
337	C₂²×C₁₃₉	#585	1	2	yes	—
338	C₄×C₁₃₉	—	2	4	no	—
339	C₄×C₁₃₉	—	2	2	no	—
340	C₄×C₁₃₉	—	2	2	no	—
341	C₄×C₁₃₉	—	4	2	no	—
342	C₄×C₁₃₉	—	4	2	no	—
343	C₄×C₁₃₉	—	4	2	no	—
344	C₄×C₁₃₉	—	4	2	no	—
345	C₄×C₁₃₉	—	4	2	no	—
346	C₄×C₁₃₉	—	4	2	no	—
347	C₄×C₁₃₉	—	4	4	no	—
348	C₄×C₁₃₉	—	4	4	no	—
349	C₂×C₁₃₉	—	2	4	no	—
350	C₂×C₁₃₉	—	4	4	no	—
351	C₂×C₁₃₉	—	8	2	no	—
352	C₂×C₁₃₉	—	8	2	no	—
353	C₂×C₁₃₉	C₂×#535	1	1	yes	characteristic
354	C₂×C₁₃₉	#3485	1	1	yes	characteristic
355	C₂×C₁₃₉	#3485	1	1	yes	characteristic
356	C₂×C₁₃₉	#3533	1	4	yes	—
357	#36956	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
358	C₁₃₉	#36956	1	1	yes	characteristic, direct product factor, Sylow
359	C₂×#538	C₂×C₁₃₉	1	1	yes	characteristic, complemented
360	C₂²×#123	C₂×C₁₃₉	1	1	yes	characteristic, complemented
361	#2849	C₂×C₁₃₉	1	2	yes	complemented
362	#2718	C₂×C₁₃₉	1	4	yes	complemented
363	#2710	C₂×C₁₃₉	1	4	yes	complemented
364	#2706	C₂×C₁₃₉	1	4	yes	complemented
365	#2703	C₂×C₁₃₉	1	4	yes	complemented
366	#2613	C₂×C₁₃₉	1	2	yes	complemented
367	#2561	C₂×C₁₃₉	1	1	yes	characteristic, complemented
368	#2539	C₂×C₁₃₉	1	1	yes	characteristic, complemented
369	#2534	C₂×C₁₃₉	1	2	yes	complemented
370	#2503	C₂×C₁₃₉	1	1	yes	characteristic, complemented
371	#2501	C₂×C₁₃₉	1	1	yes	characteristic, complemented
372	#2486	C₂×C₁₃₉	1	2	yes	complemented
373	#2312	C₂×C₁₃₉	1	1	yes	characteristic, complemented
374	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
375	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
376	#538	—	2	8	no	—
377	C₂×#126	C₂²×C₁₃₉	1	2	yes	complemented
378	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
379	C₂×#123	—	2	8	no	—
380	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
381	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
382	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
383	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
384	C₂×#123	C₂²×C₁₃₉	1	2	yes	—
385	C₂×#123	C₂²×C₁₃₉	1	2	yes	complemented
386	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
387	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
388	C₂×#121	C₂²×C₁₃₉	1	2	yes	complemented
389	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
390	C₂×#120	C₂²×C₁₃₉	1	2	yes	—
391	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
392	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
393	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
394	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
395	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
396	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
397	#400	C₂²×C₁₃₉	1	4	yes	complemented
398	#399	C₂²×C₁₃₉	1	4	yes	complemented
399	#399	C₂²×C₁₃₉	1	2	yes	complemented
400	#398	C₂²×C₁₃₉	1	4	yes	complemented
401	#397	C₂²×C₁₃₉	1	2	yes	complemented
402	#397	C₂²×C₁₃₉	1	4	yes	complemented
403	#396	C₂²×C₁₃₉	1	4	yes	complemented
404	#394	C₂²×C₁₃₉	1	4	yes	—
405	#394	C₂²×C₁₃₉	1	4	yes	—
406	#394	C₂²×C₁₃₉	1	4	yes	complemented
407	#393	C₂²×C₁₃₉	1	2	yes	complemented
408	#392	C₂²×C₁₃₉	1	4	yes	—
409	#392	C₂²×C₁₃₉	1	4	yes	—
410	#392	C₂²×C₁₃₉	1	2	yes	complemented
411	#391	C₂²×C₁₃₉	1	2	yes	complemented
412	#390	C₂²×C₁₃₉	1	2	yes	complemented
413	#390	C₂²×C₁₃₉	1	4	yes	complemented
414	#389	C₂²×C₁₃₉	1	4	yes	complemented
415	#388	C₂²×C₁₃₉	1	4	yes	complemented
416	#388	C₂²×C₁₃₉	1	4	yes	complemented
417	#388	C₂²×C₁₃₉	1	4	yes	complemented
418	#388	C₂²×C₁₃₉	1	4	yes	complemented
419	#386	C₂²×C₁₃₉	1	4	yes	complemented
420	#386	C₂²×C₁₃₉	1	4	yes	complemented
421	#386	C₂²×C₁₃₉	1	4	yes	complemented
422	#385	C₂²×C₁₃₉	1	4	yes	complemented
423	#385	C₂²×C₁₃₉	1	4	yes	complemented
424	#384	C₂²×C₁₃₉	1	2	yes	complemented
425	#382	C₂²×C₁₃₉	1	2	yes	complemented
426	#381	C₂²×C₁₃₉	1	2	yes	—
427	#381	C₂²×C₁₃₉	1	2	yes	—
428	#381	C₂²×C₁₃₉	1	2	yes	—
429	#380	C₂²×C₁₃₉	1	2	yes	—
430	#380	C₂²×C₁₃₉	1	4	yes	complemented
431	#379	C₂²×C₁₃₉	1	2	yes	—
432	#379	C₂²×C₁₃₉	1	2	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
434	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
435	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
436	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
437	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
438	C₂²×D₄	—	2	4	no	—
439	C₂²×D₄	—	4	4	no	—
440	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
441	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
442	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
443	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
445	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
446	C₂³×C₄	—	2	4	no	—
447	C₂³×C₄	—	4	4	no	—
448	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
449	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
453	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
454	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
455	#126	—	2	8	no	—
456	#124	—	2	8	no	—
457	#123	—	2	16	no	—
458	#123	—	2	16	no	—
459	#123	—	2	8	no	—
460	#123	—	4	4	no	—
461	#123	—	4	4	no	—
462	#123	—	4	4	no	—
463	C₂²⋊Q₈	—	2	4	no	—
464	#121	—	2	4	no	—
465	#121	—	2	8	no	—
466	#120	—	2	8	no	—
467	#120	—	4	4	no	—
468	C₄×D₄	—	2	8	no	—
469	C₂×C₄⋊C₄	—	2	4	no	—
470	C₂×C₄⋊C₄	—	2	4	no	—
471	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
482	C₂×C₂²⋊C₄	—	2	4	no	—
483	C₂×C₂²⋊C₄	—	2	4	no	—
484	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	8	yes	complemented
485	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
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	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
505	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
507	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
508	#95	C₂³×C₁₃₉	1	2	yes	—
509	#95	C₂³×C₁₃₉	1	2	yes	—
510	#95	C₂³×C₁₃₉	1	4	yes	—
511	#95	C₂³×C₁₃₉	1	4	yes	—
512	#95	C₂³×C₁₃₉	1	4	yes	—
513	#95	C₂³×C₁₃₉	1	4	yes	—
514	#95	C₂³×C₁₃₉	1	4	yes	—
515	#95	C₂³×C₁₃₉	1	4	yes	—
516	#95	C₂³×C₁₃₉	1	4	yes	—
517	C₂⁴	—	2	4	no	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	4	no	—
520	C₂⁴	—	4	2	no	—
521	C₂⁴	—	4	2	no	—
522	C₂⁴	—	4	2	no	—
523	C₂⁴	—	4	2	no	—
524	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
525	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
526	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
527	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
528	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	4	2	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	4	8	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	4	4	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂×D₄	—	4	16	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	8	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	4	8	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	16	no	—
559	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
560	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
561	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
565	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
566	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
571	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
572	C₄⋊C₄	—	2	8	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	4	4	no	—
580	C₄⋊C₄	—	4	4	no	—
581	C₄⋊C₄	—	4	4	no	—
582	C₄⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	4	no	—
593	C₂²⋊C₄	—	4	4	no	—
594	C₂²⋊C₄	—	4	4	no	—
595	C₂²⋊C₄	—	4	4	no	—
596	C₂²⋊C₄	—	4	4	no	—
597	C₂²⋊C₄	—	4	4	no	—
598	C₂²⋊C₄	—	4	4	no	—
599	C₂²⋊C₄	—	4	4	no	—
600	C₂²⋊C₄	—	4	4	no	—
601	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
602	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
603	C₄²	—	2	4	no	—
604	C₄²	—	4	2	no	—
605	C₄²	—	4	2	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	2	4	no	—
610	C₂³	—	2	4	no	—
611	C₂³	—	2	4	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	4	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	4	4	no	—
623	C₂³	—	4	4	no	—
624	C₂³	—	4	16	no	—
625	C₂³	—	4	4	no	—
626	C₂³	—	4	4	no	—
627	C₂³	—	4	4	no	—
628	C₂³	—	8	8	no	—
629	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
630	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
631	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
632	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
633	Q₈	—	8	2	no	—
634	D₄	—	4	16	no	—
635	D₄	—	4	8	no	—
636	D₄	—	8	2	no	—
637	D₄	—	8	4	no	—
638	D₄	—	8	4	no	—
639	D₄	—	8	8	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	16	no	—
665	C₂×C₄	—	4	4	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	8	4	no	—
669	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
670	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	8	no	—
675	C₂²	—	2	4	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	4	no	—
678	C₂²	—	4	16	no	—
679	C₂²	—	4	8	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	4	2	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	4	2	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	4	4	no	—
688	C₂²	—	4	4	no	—
689	C₂²	—	4	4	no	—
690	C₂²	—	8	8	no	—
691	C₂²	#535×C₁₃₉	1	4	yes	—
692	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
693	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
694	C₂²	#585×C₁₃₉	1	2	yes	—
695	C₂²	#585×C₁₃₉	1	2	yes	—
696	C₄	—	2	4	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	2	no	—
699	C₄	—	4	2	no	—
700	C₄	—	4	2	no	—
701	C₄	—	4	2	no	—
702	C₄	—	4	2	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	4	no	—
706	C₄	—	4	4	no	—
707	C₂	—	2	4	no	—
708	C₂	—	4	4	no	—
709	C₂	—	8	2	no	—
710	C₂	—	8	2	no	—
711	C₂	C₂×#535×C₁₃₉	1	1	yes	characteristic
712	C₂	#3485×C₁₃₉	1	1	yes	characteristic
713	C₂	#3485×C₁₃₉	1	1	yes	characteristic
714	C₂	#3533×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
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×#538×C₁₃₉	C₂	semidirect
2. C₂²×#123×C₁₃₉	C₂	semidirect
3. #2849×C₁₃₉	C₂	semidirect
4. #2718×C₁₃₉	C₂	semidirect
5. #2710×C₁₃₉	C₂	semidirect
6. #2706×C₁₃₉	C₂	semidirect
7. #2703×C₁₃₉	C₂	semidirect
8. #2613×C₁₃₉	C₂	semidirect
9. #2561×C₁₃₉	C₂	semidirect
10. #2539×C₁₃₉	C₂	semidirect
11. #2534×C₁₃₉	C₂	semidirect
12. #2503×C₁₃₉	C₂	semidirect
13. #2501×C₁₃₉	C₂	semidirect
14. #2486×C₁₃₉	C₂	semidirect
15. #2312×C₁₃₉	C₂	semidirect
19. C₂×#126×C₁₃₉	C₂²	semidirect
20. C₂×#124×C₁₃₉	C₂²	semidirect
27. C₂×#123×C₁₃₉	C₂²	semidirect
30. C₂×#121×C₁₃₉	C₂²	semidirect
39. #400×C₁₃₉	C₂²	semidirect
40. #399×C₁₃₉	C₂²	semidirect
41. #399×C₁₃₉	C₂²	semidirect
42. #398×C₁₃₉	C₂²	semidirect
43. #397×C₁₃₉	C₂²	semidirect
44. #397×C₁₃₉	C₂²	semidirect
45. #396×C₁₃₉	C₂²	semidirect
48. #394×C₁₃₉	C₂²	semidirect
49. #393×C₁₃₉	C₂²	semidirect
52. #392×C₁₃₉	C₂²	semidirect
53. #391×C₁₃₉	C₂²	semidirect
54. #390×C₁₃₉	C₂²	semidirect
55. #390×C₁₃₉	C₂²	semidirect
56. #389×C₁₃₉	C₂²	semidirect
57. #388×C₁₃₉	C₂²	semidirect
58. #388×C₁₃₉	C₂²	semidirect
59. #388×C₁₃₉	C₂²	semidirect
60. #388×C₁₃₉	C₂²	semidirect
61. #386×C₁₃₉	C₂²	semidirect
62. #386×C₁₃₉	C₂²	semidirect
63. #386×C₁₃₉	C₂²	semidirect
64. #385×C₁₃₉	C₂²	semidirect
65. #385×C₁₃₉	C₂²	semidirect
66. #384×C₁₃₉	C₂²	semidirect
67. #382×C₁₃₉	C₂²	semidirect
72. #380×C₁₃₉	C₂²	semidirect
126. C₂×C₂²⋊C₄×C₁₃₉	D₄	semidirect
357. #36956	C₁₃₉	direct (N × H)
358. C₁₃₉	#36956	direct (N × H)
359. C₂×#538	C₂×C₁₃₉	semidirect
360. C₂²×#123	C₂×C₁₃₉	semidirect
361. #2849	C₂×C₁₃₉	semidirect
362. #2718	C₂×C₁₃₉	semidirect
363. #2710	C₂×C₁₃₉	semidirect
364. #2706	C₂×C₁₃₉	semidirect
365. #2703	C₂×C₁₃₉	semidirect
366. #2613	C₂×C₁₃₉	semidirect
367. #2561	C₂×C₁₃₉	semidirect
368. #2539	C₂×C₁₃₉	semidirect
369. #2534	C₂×C₁₃₉	semidirect
370. #2503	C₂×C₁₃₉	semidirect
371. #2501	C₂×C₁₃₉	semidirect
372. #2486	C₂×C₁₃₉	semidirect
373. #2312	C₂×C₁₃₉	semidirect
377. C₂×#126	C₂²×C₁₃₉	semidirect
378. C₂×#124	C₂²×C₁₃₉	semidirect
385. C₂×#123	C₂²×C₁₃₉	semidirect
388. C₂×#121	C₂²×C₁₃₉	semidirect
397. #400	C₂²×C₁₃₉	semidirect
398. #399	C₂²×C₁₃₉	semidirect
399. #399	C₂²×C₁₃₉	semidirect
400. #398	C₂²×C₁₃₉	semidirect
401. #397	C₂²×C₁₃₉	semidirect
402. #397	C₂²×C₁₃₉	semidirect
403. #396	C₂²×C₁₃₉	semidirect
406. #394	C₂²×C₁₃₉	semidirect
407. #393	C₂²×C₁₃₉	semidirect
410. #392	C₂²×C₁₃₉	semidirect
411. #391	C₂²×C₁₃₉	semidirect
412. #390	C₂²×C₁₃₉	semidirect
413. #390	C₂²×C₁₃₉	semidirect
414. #389	C₂²×C₁₃₉	semidirect
415. #388	C₂²×C₁₃₉	semidirect
416. #388	C₂²×C₁₃₉	semidirect
417. #388	C₂²×C₁₃₉	semidirect
418. #388	C₂²×C₁₃₉	semidirect
419. #386	C₂²×C₁₃₉	semidirect
420. #386	C₂²×C₁₃₉	semidirect
421. #386	C₂²×C₁₃₉	semidirect
422. #385	C₂²×C₁₃₉	semidirect
423. #385	C₂²×C₁₃₉	semidirect
424. #384	C₂²×C₁₃₉	semidirect
425. #382	C₂²×C₁₃₉	semidirect
430. #380	C₂²×C₁₃₉	semidirect
484. C₂×C₂²⋊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×#538×C₁₃₉	2
C₂²×#123×C₁₃₉	2
#2849×C₁₃₉	2
#2718×C₁₃₉	2
#2710×C₁₃₉	2
#2706×C₁₃₉	2
#2703×C₁₃₉	2
#2613×C₁₃₉	2
#2561×C₁₃₉	2
#2539×C₁₃₉	2
#2534×C₁₃₉	2
#2503×C₁₃₉	2
#2501×C₁₃₉	2
#2486×C₁₃₉	2
#2312×C₁₃₉	2
#36956	139

Subgroups — C139×#36956 #48031552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36956 #48031552