Subgroups — C₁₃₉×#22962 #48017558

Order 35584.

926 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#474×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2365×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1990×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1947×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#1942×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1918×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1862×C₁₃₉	C₂	1	2	yes	maximal
9	C₈×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#102×C₁₃₉	C₂	1	1	yes	maximal, characteristic
11	C₄×#102×C₁₃₉	C₂	1	2	yes	maximal
12	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃₉	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₃₉	—	2	1	no	—
17	#474×C₁₃₉	C₄	1	8	yes	complemented
18	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃₉	C₂²	1	2	yes	—
26	#391×C₁₃₉	—	2	1	no	—
27	#389×C₁₃₉	C₂²	1	2	yes	—
28	#389×C₁₃₉	C₂²	1	2	yes	—
29	#387×C₁₃₉	—	2	2	no	—
30	#385×C₁₃₉	—	2	2	no	—
31	#384×C₁₃₉	C₂²	1	1	yes	characteristic
32	#380×C₁₃₉	—	2	1	no	—
33	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
36	#340×C₁₃₉	C₂²	1	1	yes	characteristic
37	#340×C₁₃₉	C₂²	1	2	yes	—
38	#340×C₁₃₉	C₂²	1	1	yes	characteristic
39	#340×C₁₃₉	C₂²	1	2	yes	—
40	#340×C₁₃₉	C₂²	1	2	yes	—
41	#336×C₁₃₉	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃₉	—	2	1	no	—
43	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₉	—	2	1	no	—
45	C₂³×C₄×C₁₃₉	—	2	2	no	—
46	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
50	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	4	yes	complemented
51	C₄×Q₈×C₁₃₉	—	4	4	no	—
52	C₄×D₄×C₁₃₉	—	2	4	no	—
53	C₄×D₄×C₁₃₉	—	2	2	no	—
54	C₄×D₄×C₁₃₉	—	4	2	no	—
55	C₄×D₄×C₁₃₉	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
62	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
71	C₂×C₄²×C₁₃₉	—	2	2	no	—
72	C₂×C₄²×C₁₃₉	—	2	1	no	—
73	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
75	#107×C₁₃₉	—	4	2	no	—
76	#107×C₁₃₉	C₂×C₄	1	8	yes	complemented
77	C₄⋊C₈×C₁₃₉	C₂×C₄	1	4	yes	complemented
78	#102×C₁₃₉	—	2	2	no	—
79	#102×C₁₃₉	C₂×C₄	1	8	yes	—
80	#102×C₁₃₉	Q₈	1	4	yes	complemented
81	C₄×C₈×C₁₃₉	—	2	2	no	—
82	C₄×C₈×C₁₃₉	—	4	2	no	—
83	#95×C₁₃₉	—	2	1	no	—
84	#95×C₁₃₉	—	2	2	no	—
85	#95×C₁₃₉	—	2	2	no	—
86	#95×C₁₃₉	—	2	2	no	—
87	#95×C₁₃₉	D₄	1	2	yes	—
88	C₂⁴×C₁₃₉	—	2	1	no	—
89	C₂×Q₈×C₁₃₉	—	2	4	no	—
90	C₂×Q₈×C₁₃₉	—	4	2	no	—
91	C₂×Q₈×C₁₃₉	—	4	2	no	—
92	C₂×D₄×C₁₃₉	—	2	1	no	—
93	C₂×D₄×C₁₃₉	—	2	1	no	—
94	C₂×D₄×C₁₃₉	—	2	1	no	—
95	C₂×D₄×C₁₃₉	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₁₃₉	C₂×Q₈	1	2	yes	—
97	C₂×D₄×C₁₃₉	#41	1	2	yes	—
98	C₂²×C₄×C₁₃₉	—	2	1	no	—
99	C₂²×C₄×C₁₃₉	—	2	2	no	—
100	C₂²×C₄×C₁₃₉	—	2	1	no	—
101	C₂²×C₄×C₁₃₉	—	2	4	no	—
102	C₂²×C₄×C₁₃₉	—	2	1	no	—
103	C₂²×C₄×C₁₃₉	—	2	2	no	—
104	C₂²×C₄×C₁₃₉	—	4	4	no	—
105	C₂²×C₄×C₁₃₉	—	4	2	no	—
106	C₂²×C₄×C₁₃₉	—	4	2	no	—
107	C₂²×C₄×C₁₃₉	—	4	4	no	—
108	C₂²×C₄×C₁₃₉	—	8	2	no	—
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₁₃₉	—	2	1	no	—
115	C₂×C₈×C₁₃₉	—	2	1	no	—
116	C₂×C₈×C₁₃₉	—	2	2	no	—
117	C₂×C₈×C₁₃₉	—	2	2	no	—
118	C₂×C₈×C₁₃₉	—	2	1	no	—
119	C₂×C₈×C₁₃₉	—	2	1	no	—
120	C₂×C₈×C₁₃₉	—	2	1	no	—
121	C₂×C₈×C₁₃₉	C₂²×C₄	1	4	yes	—
122	C₂×C₈×C₁₃₉	C₂×Q₈	1	2	yes	—
123	C₄⋊C₄×C₁₃₉	—	2	4	no	—
124	C₄⋊C₄×C₁₃₉	—	2	2	no	—
125	C₄⋊C₄×C₁₃₉	—	2	1	no	—
126	C₄⋊C₄×C₁₃₉	—	2	2	no	—
127	C₄⋊C₄×C₁₃₉	—	2	1	no	—
128	C₄⋊C₄×C₁₃₉	—	2	1	no	—
129	C₄⋊C₄×C₁₃₉	—	2	2	no	—
130	C₄⋊C₄×C₁₃₉	—	2	1	no	—
131	C₄⋊C₄×C₁₃₉	—	2	2	no	—
132	C₄⋊C₄×C₁₃₉	—	4	4	no	—
133	C₄⋊C₄×C₁₃₉	—	4	2	no	—
134	C₄⋊C₄×C₁₃₉	—	4	4	no	—
135	C₄⋊C₄×C₁₃₉	—	8	1	no	—
136	C₄⋊C₄×C₁₃₉	D₈	1	4	yes	—
137	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
138	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
140	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
141	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
142	C₄²×C₁₃₉	—	2	2	no	—
143	C₄²×C₁₃₉	—	2	2	no	—
144	C₄²×C₁₃₉	—	4	4	no	—
145	C₄²×C₁₃₉	—	4	2	no	—
146	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
147	C₄²×C₁₃₉	#41	1	2	yes	—
148	C₂³×C₁₃₉	—	2	2	no	—
149	C₂³×C₁₃₉	—	2	2	no	—
150	C₂³×C₁₃₉	—	2	2	no	—
151	C₂³×C₁₃₉	—	4	1	no	—
152	C₂³×C₁₃₉	—	4	1	no	—
153	C₂³×C₁₃₉	—	4	1	no	—
154	C₂³×C₁₃₉	—	4	1	no	—
155	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₃₉	—	4	8	no	—
157	D₄×C₁₃₉	—	2	2	no	—
158	D₄×C₁₃₉	—	2	2	no	—
159	D₄×C₁₃₉	—	2	2	no	—
160	D₄×C₁₃₉	C₄×Q₈	1	4	yes	complemented
161	C₂×C₄×C₁₃₉	—	2	2	no	—
162	C₂×C₄×C₁₃₉	—	2	1	no	—
163	C₂×C₄×C₁₃₉	—	2	2	no	—
164	C₂×C₄×C₁₃₉	—	2	1	no	—
165	C₂×C₄×C₁₃₉	—	2	2	no	—
166	C₂×C₄×C₁₃₉	—	2	4	no	—
167	C₂×C₄×C₁₃₉	—	2	2	no	—
168	C₂×C₄×C₁₃₉	—	2	2	no	—
169	C₂×C₄×C₁₃₉	—	2	2	no	—
170	C₂×C₄×C₁₃₉	—	2	2	no	—
171	C₂×C₄×C₁₃₉	—	4	1	no	—
172	C₂×C₄×C₁₃₉	—	4	2	no	—
173	C₂×C₄×C₁₃₉	—	4	1	no	—
174	C₂×C₄×C₁₃₉	—	4	1	no	—
175	C₂×C₄×C₁₃₉	—	4	2	no	—
176	C₂×C₄×C₁₃₉	—	4	1	no	—
177	C₂×C₄×C₁₃₉	—	4	8	no	—
178	C₂×C₄×C₁₃₉	—	4	2	no	—
179	C₂×C₄×C₁₃₉	—	4	1	no	—
180	C₂×C₄×C₁₃₉	—	4	1	no	—
181	C₂×C₄×C₁₃₉	—	4	2	no	—
182	C₂×C₄×C₁₃₉	—	4	2	no	—
183	C₂×C₄×C₁₃₉	—	4	1	no	—
184	C₂×C₄×C₁₃₉	—	8	8	no	—
185	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₃₉	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₁₃₉	C₂×D₈	1	4	yes	—
188	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
189	C₂×C₄×C₁₃₉	#135	1	2	yes	—
190	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
196	C₈×C₁₃₉	—	2	4	no	—
197	C₈×C₁₃₉	—	2	2	no	—
198	C₈×C₁₃₉	—	4	1	no	—
199	C₂²×C₁₃₉	—	2	4	no	—
200	C₂²×C₁₃₉	—	4	2	no	—
201	C₂²×C₁₃₉	—	4	2	no	—
202	C₂²×C₁₃₉	—	4	2	no	—
203	C₂²×C₁₃₉	—	4	2	no	—
204	C₂²×C₁₃₉	—	4	2	no	—
205	C₂²×C₁₃₉	—	4	2	no	—
206	C₂²×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂²×C₁₃₉	#546	1	1	yes	characteristic
208	C₂²×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
209	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
210	C₂²×C₁₃₉	C₂×#135	1	1	yes	characteristic
211	C₂²×C₁₃₉	#577	1	1	yes	characteristic
212	C₂²×C₁₃₉	#578	1	1	yes	characteristic
213	C₄×C₁₃₉	—	2	2	no	—
214	C₄×C₁₃₉	—	2	4	no	—
215	C₄×C₁₃₉	—	4	2	no	—
216	C₄×C₁₃₉	—	4	2	no	—
217	C₄×C₁₃₉	—	4	4	no	—
218	C₄×C₁₃₉	—	4	2	no	—
219	C₄×C₁₃₉	—	8	1	no	—
220	C₄×C₁₃₉	—	8	2	no	—
221	C₄×C₁₃₉	C₄×D₈	1	4	yes	—
222	C₄×C₁₃₉	C₂×C₄×Q₈	1	1	yes	characteristic
223	C₄×C₁₃₉	#520	1	1	yes	characteristic
224	C₄×C₁₃₉	#552	1	1	yes	characteristic
225	C₄×C₁₃₉	#554	1	1	yes	characteristic
226	C₂×C₁₃₉	—	4	4	no	—
227	C₂×C₁₃₉	#2360	1	1	yes	characteristic
228	C₂×C₁₃₉	C₂×C₄×D₈	1	1	yes	characteristic
229	C₂×C₁₃₉	#2947	1	1	yes	characteristic
230	C₂×C₁₃₉	#3294	1	1	yes	characteristic
231	C₂×C₁₃₉	#3302	1	1	yes	characteristic
232	C₂×C₁₃₉	Q₈×D₈	1	1	yes	characteristic
233	C₂×C₁₃₉	#3381	1	1	yes	characteristic
234	#22962	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₁₃₉	#22962	1	1	yes	characteristic, direct product factor, Sylow
236	C₂×#474	C₂×C₁₃₉	1	1	yes	characteristic
237	#2365	C₂×C₁₃₉	1	1	yes	characteristic, complemented
238	D₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
239	#1990	C₂×C₁₃₉	1	1	yes	characteristic, complemented
240	#1947	C₂×C₁₃₉	1	1	yes	characteristic, complemented
241	#1942	C₂×C₁₃₉	1	2	yes	complemented
242	#1918	C₂×C₁₃₉	1	2	yes	complemented
243	#1862	C₂×C₁₃₉	1	2	yes	—
244	C₈×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
245	C₄×#102	C₂×C₁₃₉	1	2	yes	—
246	C₄×#102	C₂×C₁₃₉	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
248	C₂×C₄×Q₈	—	2	1	no	—
249	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
250	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	—	2	1	no	—
252	#474	C₄×C₁₃₉	1	8	yes	complemented
253	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
254	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
255	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
256	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
257	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
258	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂²×C₁₃₉	1	2	yes	—
261	#391	—	2	1	no	—
262	#389	C₂²×C₁₃₉	1	2	yes	—
263	#389	C₂²×C₁₃₉	1	2	yes	—
264	#387	—	2	2	no	—
265	#385	—	2	2	no	—
266	#384	C₂²×C₁₃₉	1	1	yes	characteristic
267	#380	—	2	1	no	—
268	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
269	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
270	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
271	#340	C₂²×C₁₃₉	1	2	yes	—
272	#340	C₂²×C₁₃₉	1	1	yes	characteristic
273	#340	C₂²×C₁₃₉	1	2	yes	—
274	#340	C₂²×C₁₃₉	1	1	yes	characteristic
275	#340	C₂²×C₁₃₉	1	2	yes	—
276	#336	C₂²×C₁₃₉	1	2	yes	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	—	2	2	no	—
281	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
283	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	4	yes	complemented
286	C₄×Q₈	—	4	4	no	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	4	2	no	—
290	C₄×D₄	C₂×C₄×C₁₃₉	1	4	yes	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	4	4	no	—
297	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
298	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
309	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
310	#107	—	4	2	no	—
311	#107	C₂×C₄×C₁₃₉	1	8	yes	complemented
312	C₄⋊C₈	C₂×C₄×C₁₃₉	1	4	yes	complemented
313	#102	—	2	2	no	—
314	#102	C₂×C₄×C₁₃₉	1	8	yes	—
315	#102	Q₈×C₁₃₉	1	4	yes	complemented
316	C₄×C₈	—	2	2	no	—
317	C₄×C₈	—	4	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	D₄×C₁₃₉	1	2	yes	—
323	C₂⁴	—	2	1	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	—	4	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	C₂²×C₄×C₁₃₉	1	2	yes	—
331	C₂×D₄	C₂×Q₈×C₁₃₉	1	2	yes	—
332	C₂×D₄	#41×C₁₃₉	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	4	4	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	—	8	2	no	—
344	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
348	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	C₂²×C₄×C₁₃₉	1	4	yes	—
357	C₂×C₈	C₂×Q₈×C₁₃₉	1	2	yes	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	8	1	no	—
371	C₄⋊C₄	D₈×C₁₃₉	1	4	yes	—
372	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
373	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
374	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	4	4	no	—
380	C₄²	—	4	2	no	—
381	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
382	C₄²	#41×C₁₃₉	1	2	yes	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
391	Q₈	—	4	8	no	—
392	D₄	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	2	no	—
395	D₄	C₄×Q₈×C₁₃₉	1	4	yes	complemented
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	8	8	no	—
420	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
421	C₂×C₄	C₄×D₄×C₁₃₉	1	2	yes	—
422	C₂×C₄	C₂×D₈×C₁₃₉	1	4	yes	—
423	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
424	C₂×C₄	#135×C₁₃₉	1	2	yes	—
425	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
426	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
429	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
430	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
431	C₈	—	2	4	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	1	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
442	C₂²	#546×C₁₃₉	1	1	yes	characteristic
443	C₂²	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
444	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
445	C₂²	C₂×#135×C₁₃₉	1	1	yes	characteristic
446	C₂²	#577×C₁₃₉	1	1	yes	characteristic
447	C₂²	#578×C₁₃₉	1	1	yes	characteristic
448	C₄	—	2	4	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	4	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	1	no	—
456	C₄	C₄×D₈×C₁₃₉	1	4	yes	—
457	C₄	C₂×C₄×Q₈×C₁₃₉	1	1	yes	characteristic
458	C₄	#520×C₁₃₉	1	1	yes	characteristic
459	C₄	#552×C₁₃₉	1	1	yes	characteristic
460	C₄	#554×C₁₃₉	1	1	yes	characteristic
461	C₂	—	4	4	no	—
462	C₂	#2360×C₁₃₉	1	1	yes	characteristic
463	C₂	C₂×C₄×D₈×C₁₃₉	1	1	yes	characteristic
464	C₂	#2947×C₁₃₉	1	1	yes	characteristic
465	C₂	#3294×C₁₃₉	1	1	yes	characteristic
466	C₂	#3302×C₁₃₉	1	1	yes	characteristic
467	C₂	Q₈×D₈×C₁₃₉	1	1	yes	characteristic
468	C₂	#3381×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₄×C₄⋊C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2365×C₁₃₉	C₂	semidirect
4. #1990×C₁₃₉	C₂	semidirect
5. #1947×C₁₃₉	C₂	semidirect
6. #1942×C₁₃₉	C₂	semidirect
7. #1918×C₁₃₉	C₂	semidirect
9. C₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
17. #474×C₁₃₉	C₄	semidirect
50. C₄⋊Q₈×C₁₃₉	C₂×C₄	semidirect
76. #107×C₁₃₉	C₂×C₄	semidirect
77. C₄⋊C₈×C₁₃₉	C₂×C₄	semidirect
80. #102×C₁₃₉	Q₈	semidirect
160. D₄×C₁₃₉	C₄×Q₈	semidirect
234. #22962	C₁₃₉	direct (N × H)
235. C₁₃₉	#22962	direct (N × H)
237. #2365	C₂×C₁₃₉	semidirect
239. #1990	C₂×C₁₃₉	semidirect
240. #1947	C₂×C₁₃₉	semidirect
241. #1942	C₂×C₁₃₉	semidirect
242. #1918	C₂×C₁₃₉	semidirect
244. C₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
252. #474	C₄×C₁₃₉	semidirect
285. C₄⋊Q₈	C₂×C₄×C₁₃₉	semidirect
311. #107	C₂×C₄×C₁₃₉	semidirect
312. C₄⋊C₈	C₂×C₄×C₁₃₉	semidirect
315. #102	Q₈×C₁₃₉	semidirect
395. D₄	C₄×Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#474×C₁₃₉	2
#2365×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
#1990×C₁₃₉	2
#1947×C₁₃₉	2
#1942×C₁₃₉	2
#1918×C₁₃₉	2
#1862×C₁₃₉	2
C₈×C₄⋊C₄×C₁₃₉	2
C₄×#102×C₁₃₉	2
#22962	139

Subgroups — C139×#22962 #48017558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#22962 #48017558