Subgroups — C₁₃₉×#36534 #48031130

Order 35584.

2282 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#554×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2861×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2565×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2563×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2560×C₁₃₉	C₂	1	8	yes	maximal, complemented
8	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2544×C₁₃₉	C₂	1	2	yes	maximal
10	#2536×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2352×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic
13	C₄×#124×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₄²×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#556×C₁₃₉	—	2	8	no	—
16	#554×C₁₃₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
27	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
36	#398×C₁₃₉	C₂²	1	8	yes	—
37	#397×C₁₃₉	C₂²	1	4	yes	—
38	#394×C₁₃₉	C₂²	1	8	yes	—
39	#393×C₁₃₉	C₂²	1	4	yes	—
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#391×C₁₃₉	C₂²	1	2	yes	—
42	#391×C₁₃₉	C₂²	1	2	yes	—
43	#391×C₁₃₉	C₂²	1	4	yes	—
44	#390×C₁₃₉	C₂²	1	2	yes	—
45	#390×C₁₃₉	C₂²	1	1	yes	characteristic
46	#390×C₁₃₉	C₂²	1	4	yes	—
47	#390×C₁₃₉	C₂²	1	1	yes	characteristic
48	#388×C₁₃₉	C₂²	1	8	yes	—
49	#388×C₁₃₉	C₂²	1	8	yes	—
50	#388×C₁₃₉	C₂²	1	8	yes	—
51	#387×C₁₃₉	C₂²	1	8	yes	—
52	#386×C₁₃₉	C₂²	1	8	yes	—
53	#384×C₁₃₉	C₂²	1	1	yes	characteristic
54	#382×C₁₃₉	C₂²	1	4	yes	—
55	#382×C₁₃₉	C₂²	1	2	yes	—
56	#380×C₁₃₉	C₂²	1	4	yes	—
57	#380×C₁₃₉	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
61	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	—
63	C₄³×C₁₃₉	C₂²	1	2	yes	—
64	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
74	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
75	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
76	#127×C₁₃₉	—	2	4	no	—
77	#126×C₁₃₉	—	2	16	no	—
78	#125×C₁₃₉	—	2	8	no	—
79	#124×C₁₃₉	—	2	8	no	—
80	#124×C₁₃₉	—	2	8	no	—
81	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
82	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
83	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
84	C₄×Q₈×C₁₃₉	—	2	8	no	—
85	C₄×Q₈×C₁₃₉	—	2	8	no	—
86	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
87	C₄×D₄×C₁₃₉	—	2	4	no	—
88	C₄×D₄×C₁₃₉	—	2	8	no	—
89	C₄×D₄×C₁₃₉	—	2	4	no	—
90	C₄×D₄×C₁₃₉	—	2	16	no	—
91	#117×C₁₃₉	—	2	8	no	—
92	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
126	#95×C₁₃₉	C₂³	1	2	yes	—
127	#95×C₁₃₉	C₂³	1	8	yes	—
128	#95×C₁₃₉	C₂³	1	8	yes	—
129	#95×C₁₃₉	C₂³	1	8	yes	—
130	#95×C₁₃₉	C₂³	1	8	yes	—
131	#95×C₁₃₉	C₂³	1	4	yes	—
132	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
133	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
134	C₂×Q₈×C₁₃₉	—	2	4	no	—
135	C₂×Q₈×C₁₃₉	—	2	4	no	—
136	C₂×Q₈×C₁₃₉	—	2	4	no	—
137	C₂×Q₈×C₁₃₉	—	2	4	no	—
138	C₂×Q₈×C₁₃₉	—	2	4	no	—
139	C₂×Q₈×C₁₃₉	—	4	4	no	—
140	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
141	C₂×D₄×C₁₃₉	—	2	8	no	—
142	C₂×D₄×C₁₃₉	—	2	2	no	—
143	C₂×D₄×C₁₃₉	—	2	2	no	—
144	C₂×D₄×C₁₃₉	—	2	8	no	—
145	C₂×D₄×C₁₃₉	—	2	2	no	—
146	C₂×D₄×C₁₃₉	—	2	2	no	—
147	C₂×D₄×C₁₃₉	—	2	2	no	—
148	C₂×D₄×C₁₃₉	—	4	4	no	—
149	C₂×D₄×C₁₃₉	#41	1	4	yes	—
150	C₂²×C₄×C₁₃₉	—	2	4	no	—
151	C₂²×C₄×C₁₃₉	—	2	4	no	—
152	C₂²×C₄×C₁₃₉	—	2	8	no	—
153	C₂²×C₄×C₁₃₉	—	2	8	no	—
154	C₂²×C₄×C₁₃₉	—	2	8	no	—
155	C₂²×C₄×C₁₃₉	—	4	8	no	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
168	C₄⋊C₄×C₁₃₉	—	2	8	no	—
169	C₄⋊C₄×C₁₃₉	—	2	4	no	—
170	C₄⋊C₄×C₁₃₉	—	2	4	no	—
171	C₄⋊C₄×C₁₃₉	—	2	2	no	—
172	C₄⋊C₄×C₁₃₉	—	2	2	no	—
173	C₄⋊C₄×C₁₃₉	—	2	4	no	—
174	C₄⋊C₄×C₁₃₉	—	2	8	no	—
175	C₄⋊C₄×C₁₃₉	—	2	8	no	—
176	C₄⋊C₄×C₁₃₉	—	2	4	no	—
177	C₄⋊C₄×C₁₃₉	—	2	8	no	—
178	C₄⋊C₄×C₁₃₉	—	2	8	no	—
179	C₄⋊C₄×C₁₃₉	—	2	4	no	—
180	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
181	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
182	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
183	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
184	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
185	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
186	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
187	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
188	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
189	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
190	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
191	C₄²×C₁₃₉	—	2	8	no	—
192	C₄²×C₁₃₉	—	2	8	no	—
193	C₄²×C₁₃₉	—	2	4	no	—
194	C₄²×C₁₃₉	—	2	2	no	—
195	C₄²×C₁₃₉	—	2	2	no	—
196	C₄²×C₁₃₉	—	4	4	no	—
197	C₄²×C₁₃₉	—	4	2	no	—
198	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
199	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
200	C₄²×C₁₃₉	#41	1	8	yes	—
201	C₂³×C₁₃₉	—	2	2	no	—
202	C₂³×C₁₃₉	—	2	4	no	—
203	C₂³×C₁₃₉	—	2	2	no	—
204	C₂³×C₁₃₉	—	2	4	no	—
205	C₂³×C₁₃₉	—	2	2	no	—
206	C₂³×C₁₃₉	—	2	4	no	—
207	C₂³×C₁₃₉	—	2	2	no	—
208	C₂³×C₁₃₉	—	2	2	no	—
209	C₂³×C₁₃₉	—	2	4	no	—
210	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
211	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
212	Q₈×C₁₃₉	—	2	8	no	—
213	Q₈×C₁₃₉	—	4	8	no	—
214	Q₈×C₁₃₉	—	8	4	no	—
215	D₄×C₁₃₉	—	2	8	no	—
216	D₄×C₁₃₉	—	4	16	no	—
217	D₄×C₁₃₉	—	4	4	no	—
218	C₂×C₄×C₁₃₉	—	2	4	no	—
219	C₂×C₄×C₁₃₉	—	2	2	no	—
220	C₂×C₄×C₁₃₉	—	2	2	no	—
221	C₂×C₄×C₁₃₉	—	2	2	no	—
222	C₂×C₄×C₁₃₉	—	2	4	no	—
223	C₂×C₄×C₁₃₉	—	2	2	no	—
224	C₂×C₄×C₁₃₉	—	2	2	no	—
225	C₂×C₄×C₁₃₉	—	2	2	no	—
226	C₂×C₄×C₁₃₉	—	2	4	no	—
227	C₂×C₄×C₁₃₉	—	2	2	no	—
228	C₂×C₄×C₁₃₉	—	2	4	no	—
229	C₂×C₄×C₁₃₉	—	2	4	no	—
230	C₂×C₄×C₁₃₉	—	2	4	no	—
231	C₂×C₄×C₁₃₉	—	2	4	no	—
232	C₂×C₄×C₁₃₉	—	2	4	no	—
233	C₂×C₄×C₁₃₉	—	2	4	no	—
234	C₂×C₄×C₁₃₉	—	2	4	no	—
235	C₂×C₄×C₁₃₉	—	2	4	no	—
236	C₂×C₄×C₁₃₉	—	2	8	no	—
237	C₂×C₄×C₁₃₉	—	4	8	no	—
238	C₂×C₄×C₁₃₉	—	4	8	no	—
239	C₂×C₄×C₁₃₉	—	8	8	no	—
240	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
241	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
242	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
246	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
247	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
248	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
249	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
250	C₂²×C₁₃₉	—	2	4	no	—
251	C₂²×C₁₃₉	—	2	8	no	—
252	C₂²×C₁₃₉	—	4	2	no	—
253	C₂²×C₁₃₉	—	4	2	no	—
254	C₂²×C₁₃₉	—	4	4	no	—
255	C₂²×C₁₃₉	—	4	2	no	—
256	C₂²×C₁₃₉	—	4	2	no	—
257	C₂²×C₁₃₉	—	4	4	no	—
258	C₂²×C₁₃₉	—	4	2	no	—
259	C₂²×C₁₃₉	—	4	4	no	—
260	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
261	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
262	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
263	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
264	C₂²×C₁₃₉	#585	1	2	yes	—
265	C₄×C₁₃₉	—	2	4	no	—
266	C₄×C₁₃₉	—	2	4	no	—
267	C₄×C₁₃₉	—	2	4	no	—
268	C₄×C₁₃₉	—	2	2	no	—
269	C₄×C₁₃₉	—	2	4	no	—
270	C₄×C₁₃₉	—	4	2	no	—
271	C₄×C₁₃₉	—	4	2	no	—
272	C₄×C₁₃₉	—	4	4	no	—
273	C₄×C₁₃₉	—	4	4	no	—
274	C₄×C₁₃₉	—	4	4	no	—
275	C₄×C₁₃₉	#532	1	4	yes	—
276	C₄×C₁₃₉	#548	1	4	yes	—
277	C₂×C₁₃₉	—	4	4	no	—
278	C₂×C₁₃₉	—	8	2	no	—
279	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
280	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
281	C₂×C₁₃₉	#3475	1	2	yes	—
282	C₂×C₁₃₉	#3500	1	1	yes	characteristic
283	C₂×C₁₃₉	#3507	1	2	yes	—
284	#36534	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₁₃₉	#36534	1	1	yes	characteristic, direct product factor, Sylow
286	C₂×#556	C₂×C₁₃₉	1	1	yes	characteristic, complemented
287	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
288	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
289	#2861	C₂×C₁₃₉	1	2	yes	complemented
290	#2565	C₂×C₁₃₉	1	2	yes	complemented
291	#2563	C₂×C₁₃₉	1	1	yes	characteristic, complemented
292	#2560	C₂×C₁₃₉	1	8	yes	complemented
293	#2547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
294	#2544	C₂×C₁₃₉	1	2	yes	—
295	#2536	C₂×C₁₃₉	1	4	yes	complemented
296	#2352	C₂×C₁₃₉	1	4	yes	complemented
297	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic
298	C₄×#124	C₂×C₁₃₉	1	2	yes	complemented
299	C₄²×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
300	#556	—	2	8	no	—
301	#554	—	2	8	no	—
302	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
303	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
304	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
305	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
306	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
307	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
308	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
309	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
310	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
311	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
312	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
313	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
314	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
315	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
317	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
318	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
319	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
320	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
321	#398	C₂²×C₁₃₉	1	8	yes	—
322	#397	C₂²×C₁₃₉	1	4	yes	—
323	#394	C₂²×C₁₃₉	1	8	yes	—
324	#393	C₂²×C₁₃₉	1	4	yes	—
325	#391	C₂²×C₁₃₉	1	4	yes	—
326	#391	C₂²×C₁₃₉	1	2	yes	—
327	#391	C₂²×C₁₃₉	1	2	yes	—
328	#391	C₂²×C₁₃₉	1	2	yes	—
329	#390	C₂²×C₁₃₉	1	4	yes	—
330	#390	C₂²×C₁₃₉	1	1	yes	characteristic
331	#390	C₂²×C₁₃₉	1	1	yes	characteristic
332	#390	C₂²×C₁₃₉	1	2	yes	—
333	#388	C₂²×C₁₃₉	1	8	yes	—
334	#388	C₂²×C₁₃₉	1	8	yes	—
335	#388	C₂²×C₁₃₉	1	8	yes	—
336	#387	C₂²×C₁₃₉	1	8	yes	—
337	#386	C₂²×C₁₃₉	1	8	yes	—
338	#384	C₂²×C₁₃₉	1	1	yes	characteristic
339	#382	C₂²×C₁₃₉	1	2	yes	—
340	#382	C₂²×C₁₃₉	1	4	yes	—
341	#380	C₂²×C₁₃₉	1	4	yes	—
342	#380	C₂²×C₁₃₉	1	4	yes	—
343	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
344	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
345	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
346	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
347	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	—
348	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
349	C₄³	C₂²×C₁₃₉	1	2	yes	—
350	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
351	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
352	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
353	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
354	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
355	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
357	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
359	C₄⋊Q₈	—	2	4	no	—
360	C₄⋊Q₈	—	2	4	no	—
361	#127	—	2	4	no	—
362	#126	—	2	16	no	—
363	#125	—	2	8	no	—
364	#124	—	2	8	no	—
365	#124	—	2	8	no	—
366	C₂²⋊Q₈	—	2	8	no	—
367	C₂²⋊Q₈	—	2	8	no	—
368	C₂²⋊Q₈	—	2	16	no	—
369	C₄×Q₈	—	2	8	no	—
370	C₄×Q₈	—	2	8	no	—
371	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
372	C₄×D₄	—	2	4	no	—
373	C₄×D₄	—	2	8	no	—
374	C₄×D₄	—	2	4	no	—
375	C₄×D₄	—	2	16	no	—
376	#117	—	2	8	no	—
377	C₂×C₄⋊C₄	—	2	8	no	—
378	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
401	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
402	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
403	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
404	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
407	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
408	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
410	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
411	#95	C₂³×C₁₃₉	1	8	yes	—
412	#95	C₂³×C₁₃₉	1	8	yes	—
413	#95	C₂³×C₁₃₉	1	4	yes	—
414	#95	C₂³×C₁₃₉	1	2	yes	—
415	#95	C₂³×C₁₃₉	1	8	yes	—
416	#95	C₂³×C₁₃₉	1	8	yes	—
417	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
418	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
419	C₂×Q₈	—	2	4	no	—
420	C₂×Q₈	—	2	4	no	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	2	4	no	—
423	C₂×Q₈	—	2	4	no	—
424	C₂×Q₈	—	4	4	no	—
425	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
426	C₂×D₄	—	2	8	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	8	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	#41×C₁₃₉	1	4	yes	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	8	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	—	4	8	no	—
441	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
445	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
452	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
466	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
467	C₂²⋊C₄	—	2	16	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	4	8	no	—
476	C₄²	—	2	8	no	—
477	C₄²	—	2	8	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	4	4	no	—
482	C₄²	—	4	2	no	—
483	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
484	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
485	C₄²	#41×C₁₃₉	1	8	yes	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	4	no	—
495	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
496	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
497	Q₈	—	2	8	no	—
498	Q₈	—	4	8	no	—
499	Q₈	—	8	4	no	—
500	D₄	—	2	8	no	—
501	D₄	—	4	16	no	—
502	D₄	—	4	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	4	8	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	—	8	8	no	—
525	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
526	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
527	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
528	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
530	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
531	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
532	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
533	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
534	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
535	C₂²	—	2	4	no	—
536	C₂²	—	2	8	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	4	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	4	no	—
545	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
546	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
547	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
548	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
549	C₂²	#585×C₁₃₉	1	2	yes	—
550	C₄	—	2	4	no	—
551	C₄	—	2	4	no	—
552	C₄	—	2	4	no	—
553	C₄	—	2	2	no	—
554	C₄	—	2	4	no	—
555	C₄	—	4	2	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	4	no	—
558	C₄	—	4	4	no	—
559	C₄	—	4	4	no	—
560	C₄	#532×C₁₃₉	1	4	yes	—
561	C₄	#548×C₁₃₉	1	4	yes	—
562	C₂	—	4	4	no	—
563	C₂	—	8	2	no	—
564	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
565	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
566	C₂	#3475×C₁₃₉	1	2	yes	—
567	C₂	#3500×C₁₃₉	1	1	yes	characteristic
568	C₂	#3507×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#127×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. C₂×#556×C₁₃₉	C₂	semidirect
2. C₂×#554×C₁₃₉	C₂	semidirect
3. #2862×C₁₃₉	C₂	semidirect
4. #2861×C₁₃₉	C₂	semidirect
5. #2565×C₁₃₉	C₂	semidirect
6. #2563×C₁₃₉	C₂	semidirect
7. #2560×C₁₃₉	C₂	semidirect
8. #2547×C₁₃₉	C₂	semidirect
10. #2536×C₁₃₉	C₂	semidirect
11. #2352×C₁₃₉	C₂	semidirect
13. C₄×#124×C₁₃₉	C₂	semidirect
14. C₄²×Q₈×C₁₃₉	C₂	semidirect
86. C₄×Q₈×C₁₃₉	D₄	semidirect
284. #36534	C₁₃₉	direct (N × H)
285. C₁₃₉	#36534	direct (N × H)
286. C₂×#556	C₂×C₁₃₉	semidirect
287. C₂×#554	C₂×C₁₃₉	semidirect
288. #2862	C₂×C₁₃₉	semidirect
289. #2861	C₂×C₁₃₉	semidirect
290. #2565	C₂×C₁₃₉	semidirect
291. #2563	C₂×C₁₃₉	semidirect
292. #2560	C₂×C₁₃₉	semidirect
293. #2547	C₂×C₁₃₉	semidirect
295. #2536	C₂×C₁₃₉	semidirect
296. #2352	C₂×C₁₃₉	semidirect
298. C₄×#124	C₂×C₁₃₉	semidirect
299. C₄²×Q₈	C₂×C₁₃₉	semidirect
371. C₄×Q₈	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×#556×C₁₃₉	2
C₂×#554×C₁₃₉	2
#2862×C₁₃₉	2
#2861×C₁₃₉	2
#2565×C₁₃₉	2
#2563×C₁₃₉	2
#2560×C₁₃₉	2
#2547×C₁₃₉	2
#2544×C₁₃₉	2
#2536×C₁₃₉	2
#2352×C₁₃₉	2
C₄×#127×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₄²×Q₈×C₁₃₉	2
#36534	139

Subgroups — C139×#36534 #48031130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36534 #48031130