Subgroups — C₁₃₉×#35914 #48030510

Order 35584.

2174 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2644×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2643×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2512×C₁₃₉	C₂	1	3	yes	maximal, complemented
4	#2497×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2481×C₁₃₉	C₂	1	6	yes	maximal, complemented
6	#2480×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2401×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#396×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	D₄×C₄⋊C₄×C₁₃₉	C₂	1	3	yes	maximal, complemented
10	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	3	yes	maximal
11	#2275×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#126×C₁₃₉	C₂²	1	6	yes	complemented
14	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
15	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
16	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
17	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
18	#401×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
19	#400×C₁₃₉	C₂²	1	6	yes	complemented
20	#400×C₁₃₉	C₂²	1	3	yes	complemented
21	#397×C₁₃₉	C₂²	1	3	yes	—
22	#397×C₁₃₉	C₂²	1	6	yes	complemented
23	#397×C₁₃₉	C₂²	1	6	yes	complemented
24	#396×C₁₃₉	C₂²	1	1	yes	characteristic
25	#396×C₁₃₉	C₂²	1	6	yes	—
26	#396×C₁₃₉	C₂²	1	6	yes	complemented
27	#396×C₁₃₉	C₂²	1	2	yes	complemented
28	#390×C₁₃₉	C₂²	1	3	yes	—
29	#390×C₁₃₉	C₂²	1	3	yes	—
30	#389×C₁₃₉	C₂²	1	3	yes	complemented
31	#389×C₁₃₉	C₂²	1	3	yes	complemented
32	#388×C₁₃₉	C₂²	1	6	yes	—
33	#388×C₁₃₉	C₂²	1	6	yes	complemented
34	#387×C₁₃₉	C₂²	1	6	yes	complemented
35	#386×C₁₃₉	C₂²	1	6	yes	—
36	#386×C₁₃₉	C₂²	1	6	yes	—
37	#385×C₁₃₉	C₂²	1	6	yes	complemented
38	#385×C₁₃₉	C₂²	1	6	yes	complemented
39	#384×C₁₃₉	C₂²	1	3	yes	complemented
40	#380×C₁₃₉	C₂²	1	3	yes	—
41	#380×C₁₃₉	C₂²	1	6	yes	complemented
42	#379×C₁₃₉	C₂²	1	6	yes	—
43	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	complemented
44	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	complemented
45	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
46	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
47	#376×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×#95×C₁₃₉	C₂²	1	2	yes	complemented
49	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
50	C₂²×D₄×C₁₃₉	—	2	12	no	—
51	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
56	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
57	#126×C₁₃₉	—	4	12	no	—
58	C₄×D₄×C₁₃₉	—	2	12	no	—
59	C₄×D₄×C₁₃₉	—	2	12	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	4	12	no	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
69	C₂×C₂²⋊C₄×C₁₃₉	—	4	12	no	—
70	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
71	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
72	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
73	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
74	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
75	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
76	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
77	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
78	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
79	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
80	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
81	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
82	#95×C₁₃₉	C₂³	1	1	yes	characteristic
83	#95×C₁₃₉	C₂³	1	6	yes	—
84	#95×C₁₃₉	C₂³	1	3	yes	—
85	#95×C₁₃₉	C₂³	1	3	yes	—
86	#95×C₁₃₉	C₂³	1	3	yes	—
87	#95×C₁₃₉	C₂³	1	6	yes	—
88	#95×C₁₃₉	C₂³	1	6	yes	—
89	#95×C₁₃₉	C₂³	1	3	yes	—
90	#95×C₁₃₉	C₂³	1	3	yes	—
91	#95×C₁₃₉	C₂³	1	6	yes	—
92	C₂⁴×C₁₃₉	—	2	4	no	—
93	C₂⁴×C₁₃₉	—	2	12	no	—
94	C₂⁴×C₁₃₉	—	4	6	no	—
95	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
96	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
97	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
98	C₂×D₄×C₁₃₉	—	2	12	no	—
99	C₂×D₄×C₁₃₉	—	2	6	no	—
100	C₂×D₄×C₁₃₉	—	4	16	no	—
101	C₂×D₄×C₁₃₉	#41	1	12	yes	—
102	C₂²×C₄×C₁₃₉	—	2	12	no	—
103	C₂²×C₄×C₁₃₉	—	2	12	no	—
104	C₂²×C₄×C₁₃₉	—	2	6	no	—
105	C₂²×C₄×C₁₃₉	—	2	12	no	—
106	C₂²×C₄×C₁₃₉	—	4	6	no	—
107	C₂²×C₄×C₁₃₉	—	4	6	no	—
108	C₂²×C₄×C₁₃₉	—	4	6	no	—
109	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
111	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
112	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
113	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
114	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
115	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
116	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
117	C₄⋊C₄×C₁₃₉	—	2	6	no	—
118	C₄⋊C₄×C₁₃₉	—	2	6	no	—
119	C₄⋊C₄×C₁₃₉	—	2	6	no	—
120	C₄⋊C₄×C₁₃₉	—	2	12	no	—
121	C₄⋊C₄×C₁₃₉	—	2	6	no	—
122	C₄⋊C₄×C₁₃₉	—	4	6	no	—
123	C₄⋊C₄×C₁₃₉	—	4	6	no	—
124	C₄⋊C₄×C₁₃₉	—	4	6	no	—
125	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
126	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
127	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
128	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
129	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
130	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
131	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
132	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
133	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
134	C₄²×C₁₃₉	—	2	6	no	—
135	C₄²×C₁₃₉	—	2	6	no	—
136	C₄²×C₁₃₉	—	4	6	no	—
137	C₂³×C₁₃₉	—	2	6	no	—
138	C₂³×C₁₃₉	—	2	2	no	—
139	C₂³×C₁₃₉	—	2	3	no	—
140	C₂³×C₁₃₉	—	2	3	no	—
141	C₂³×C₁₃₉	—	2	6	no	—
142	C₂³×C₁₃₉	—	2	6	no	—
143	C₂³×C₁₃₉	—	2	2	no	—
144	C₂³×C₁₃₉	—	4	24	no	—
145	C₂³×C₁₃₉	—	4	8	no	—
146	C₂³×C₁₃₉	—	8	12	no	—
147	C₂³×C₁₃₉	C₂×#41	1	12	yes	—
148	C₂³×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
149	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
150	D₄×C₁₃₉	—	4	8	no	—
151	D₄×C₁₃₉	—	4	4	no	—
152	D₄×C₁₃₉	#126	1	16	yes	complemented
153	C₂×C₄×C₁₃₉	—	2	3	no	—
154	C₂×C₄×C₁₃₉	—	2	3	no	—
155	C₂×C₄×C₁₃₉	—	2	3	no	—
156	C₂×C₄×C₁₃₉	—	2	3	no	—
157	C₂×C₄×C₁₃₉	—	2	3	no	—
158	C₂×C₄×C₁₃₉	—	2	6	no	—
159	C₂×C₄×C₁₃₉	—	2	6	no	—
160	C₂×C₄×C₁₃₉	—	2	3	no	—
161	C₂×C₄×C₁₃₉	—	2	3	no	—
162	C₂×C₄×C₁₃₉	—	2	6	no	—
163	C₂×C₄×C₁₃₉	—	2	6	no	—
164	C₂×C₄×C₁₃₉	—	2	3	no	—
165	C₂×C₄×C₁₃₉	—	2	3	no	—
166	C₂×C₄×C₁₃₉	—	2	6	no	—
167	C₂×C₄×C₁₃₉	—	2	6	no	—
168	C₂×C₄×C₁₃₉	—	2	3	no	—
169	C₂×C₄×C₁₃₉	—	2	3	no	—
170	C₂×C₄×C₁₃₉	—	2	3	no	—
171	C₂×C₄×C₁₃₉	—	4	24	no	—
172	C₂×C₄×C₁₃₉	—	4	4	no	—
173	C₂×C₄×C₁₃₉	—	8	12	no	—
174	C₂×C₄×C₁₃₉	C₂×#41	1	6	yes	—
175	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	6	yes	—
176	C₂²×C₁₃₉	—	2	12	no	—
177	C₂²×C₁₃₉	—	2	12	no	—
178	C₂²×C₁₃₉	—	2	6	no	—
179	C₂²×C₁₃₉	—	4	1	no	—
180	C₂²×C₁₃₉	—	4	3	no	—
181	C₂²×C₁₃₉	—	4	2	no	—
182	C₂²×C₁₃₉	—	4	6	no	—
183	C₂²×C₁₃₉	—	4	6	no	—
184	C₂²×C₁₃₉	—	8	16	no	—
185	C₂²×C₁₃₉	C₂×#126	1	8	yes	—
186	C₂²×C₁₃₉	C₂²×#41	1	3	yes	—
187	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	3	yes	—
188	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
189	C₄×C₁₃₉	—	2	6	no	—
190	C₄×C₁₃₉	—	4	1	no	—
191	C₄×C₁₃₉	—	4	6	no	—
192	C₄×C₁₃₉	—	4	6	no	—
193	C₄×C₁₃₉	—	4	3	no	—
194	C₄×C₁₃₉	—	4	3	no	—
195	C₄×C₁₃₉	—	4	3	no	—
196	C₄×C₁₃₉	C₂×#126	1	4	yes	—
197	C₂×C₁₃₉	—	2	8	no	—
198	C₂×C₁₃₉	—	4	2	no	—
199	C₂×C₁₃₉	—	8	2	no	—
200	C₂×C₁₃₉	C₂²×#126	1	1	yes	characteristic
201	C₂×C₁₃₉	#3519	1	3	yes	—
202	C₂×C₁₃₉	#3520	1	3	yes	—
203	#35914	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₁₃₉	#35914	1	1	yes	characteristic, direct product factor, Sylow
205	#2644	C₂×C₁₃₉	1	1	yes	characteristic, complemented
206	#2643	C₂×C₁₃₉	1	2	yes	complemented
207	#2512	C₂×C₁₃₉	1	3	yes	complemented
208	#2497	C₂×C₁₃₉	1	3	yes	complemented
209	#2481	C₂×C₁₃₉	1	6	yes	complemented
210	#2480	C₂×C₁₃₉	1	6	yes	complemented
211	#2401	C₂×C₁₃₉	1	1	yes	characteristic, complemented
212	C₂×#396	C₂×C₁₃₉	1	2	yes	complemented
213	D₄×C₄⋊C₄	C₂×C₁₃₉	1	3	yes	complemented
214	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	3	yes	—
215	#2275	C₂×C₁₃₉	1	1	yes	characteristic, complemented
216	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
217	C₂×#126	C₂²×C₁₃₉	1	6	yes	complemented
218	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
219	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
220	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
221	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
222	#401	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
223	#400	C₂²×C₁₃₉	1	6	yes	complemented
224	#400	C₂²×C₁₃₉	1	3	yes	complemented
225	#397	C₂²×C₁₃₉	1	3	yes	—
226	#397	C₂²×C₁₃₉	1	6	yes	complemented
227	#397	C₂²×C₁₃₉	1	6	yes	complemented
228	#396	C₂²×C₁₃₉	1	1	yes	characteristic
229	#396	C₂²×C₁₃₉	1	6	yes	—
230	#396	C₂²×C₁₃₉	1	2	yes	complemented
231	#396	C₂²×C₁₃₉	1	6	yes	complemented
232	#390	C₂²×C₁₃₉	1	3	yes	—
233	#390	C₂²×C₁₃₉	1	3	yes	—
234	#389	C₂²×C₁₃₉	1	3	yes	complemented
235	#389	C₂²×C₁₃₉	1	3	yes	complemented
236	#388	C₂²×C₁₃₉	1	6	yes	—
237	#388	C₂²×C₁₃₉	1	6	yes	complemented
238	#387	C₂²×C₁₃₉	1	6	yes	complemented
239	#386	C₂²×C₁₃₉	1	6	yes	—
240	#386	C₂²×C₁₃₉	1	6	yes	—
241	#385	C₂²×C₁₃₉	1	6	yes	complemented
242	#385	C₂²×C₁₃₉	1	6	yes	complemented
243	#384	C₂²×C₁₃₉	1	3	yes	complemented
244	#380	C₂²×C₁₃₉	1	3	yes	—
245	#380	C₂²×C₁₃₉	1	6	yes	complemented
246	#379	C₂²×C₁₃₉	1	6	yes	—
247	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	complemented
248	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	complemented
249	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
250	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
251	#376	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
252	C₂×#95	C₂²×C₁₃₉	1	2	yes	complemented
253	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
254	C₂²×D₄	—	2	12	no	—
255	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
256	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
257	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
260	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
261	#126	—	4	12	no	—
262	C₄×D₄	—	2	12	no	—
263	C₄×D₄	—	2	12	no	—
264	C₂×C₄⋊C₄	—	4	12	no	—
265	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
273	C₂×C₂²⋊C₄	—	4	12	no	—
274	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
283	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
284	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
285	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
286	#95	C₂³×C₁₃₉	1	1	yes	characteristic
287	#95	C₂³×C₁₃₉	1	6	yes	—
288	#95	C₂³×C₁₃₉	1	3	yes	—
289	#95	C₂³×C₁₃₉	1	3	yes	—
290	#95	C₂³×C₁₃₉	1	3	yes	—
291	#95	C₂³×C₁₃₉	1	3	yes	—
292	#95	C₂³×C₁₃₉	1	3	yes	—
293	#95	C₂³×C₁₃₉	1	6	yes	—
294	#95	C₂³×C₁₃₉	1	6	yes	—
295	#95	C₂³×C₁₃₉	1	6	yes	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	—	2	12	no	—
298	C₂⁴	—	4	6	no	—
299	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
300	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
301	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
302	C₂×D₄	—	2	12	no	—
303	C₂×D₄	—	2	6	no	—
304	C₂×D₄	—	4	16	no	—
305	C₂×D₄	#41×C₁₃₉	1	12	yes	—
306	C₂²×C₄	—	2	12	no	—
307	C₂²×C₄	—	2	12	no	—
308	C₂²×C₄	—	2	6	no	—
309	C₂²×C₄	—	2	12	no	—
310	C₂²×C₄	—	4	6	no	—
311	C₂²×C₄	—	4	6	no	—
312	C₂²×C₄	—	4	6	no	—
313	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
315	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
316	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
317	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
318	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
319	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
320	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
321	C₄⋊C₄	—	2	6	no	—
322	C₄⋊C₄	—	2	6	no	—
323	C₄⋊C₄	—	2	6	no	—
324	C₄⋊C₄	—	2	12	no	—
325	C₄⋊C₄	—	2	6	no	—
326	C₄⋊C₄	—	4	6	no	—
327	C₄⋊C₄	—	4	6	no	—
328	C₄⋊C₄	—	4	6	no	—
329	C₂²⋊C₄	—	2	12	no	—
330	C₂²⋊C₄	—	2	12	no	—
331	C₂²⋊C₄	—	2	6	no	—
332	C₂²⋊C₄	—	2	6	no	—
333	C₂²⋊C₄	—	2	12	no	—
334	C₂²⋊C₄	—	4	6	no	—
335	C₂²⋊C₄	—	4	6	no	—
336	C₂²⋊C₄	—	4	6	no	—
337	C₂²⋊C₄	—	4	6	no	—
338	C₄²	—	2	6	no	—
339	C₄²	—	2	6	no	—
340	C₄²	—	4	6	no	—
341	C₂³	—	2	6	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	3	no	—
344	C₂³	—	2	3	no	—
345	C₂³	—	2	6	no	—
346	C₂³	—	2	6	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	4	24	no	—
349	C₂³	—	4	8	no	—
350	C₂³	—	8	12	no	—
351	C₂³	C₂×#41×C₁₃₉	1	12	yes	—
352	C₂³	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
353	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
354	D₄	—	4	8	no	—
355	D₄	—	4	4	no	—
356	D₄	#126×C₁₃₉	1	16	yes	complemented
357	C₂×C₄	—	2	3	no	—
358	C₂×C₄	—	2	3	no	—
359	C₂×C₄	—	2	3	no	—
360	C₂×C₄	—	2	3	no	—
361	C₂×C₄	—	2	3	no	—
362	C₂×C₄	—	2	6	no	—
363	C₂×C₄	—	2	6	no	—
364	C₂×C₄	—	2	3	no	—
365	C₂×C₄	—	2	3	no	—
366	C₂×C₄	—	2	6	no	—
367	C₂×C₄	—	2	6	no	—
368	C₂×C₄	—	2	3	no	—
369	C₂×C₄	—	2	3	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	2	3	no	—
373	C₂×C₄	—	2	3	no	—
374	C₂×C₄	—	2	3	no	—
375	C₂×C₄	—	4	24	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	8	12	no	—
378	C₂×C₄	C₂×#41×C₁₃₉	1	6	yes	—
379	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	6	yes	—
380	C₂²	—	2	12	no	—
381	C₂²	—	2	12	no	—
382	C₂²	—	2	6	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	3	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	6	no	—
387	C₂²	—	4	6	no	—
388	C₂²	—	8	16	no	—
389	C₂²	C₂×#126×C₁₃₉	1	8	yes	—
390	C₂²	C₂²×#41×C₁₃₉	1	3	yes	—
391	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	3	yes	—
392	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
393	C₄	—	2	6	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	6	no	—
396	C₄	—	4	3	no	—
397	C₄	—	4	6	no	—
398	C₄	—	4	3	no	—
399	C₄	—	4	3	no	—
400	C₄	C₂×#126×C₁₃₉	1	4	yes	—
401	C₂	—	2	8	no	—
402	C₂	—	4	2	no	—
403	C₂	—	8	2	no	—
404	C₂	C₂²×#126×C₁₃₉	1	1	yes	characteristic
405	C₂	#3519×C₁₃₉	1	3	yes	—
406	C₂	#3520×C₁₃₉	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×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. #2644×C₁₃₉	C₂	semidirect
2. #2643×C₁₃₉	C₂	semidirect
3. #2512×C₁₃₉	C₂	semidirect
4. #2497×C₁₃₉	C₂	semidirect
5. #2481×C₁₃₉	C₂	semidirect
6. #2480×C₁₃₉	C₂	semidirect
7. #2401×C₁₃₉	C₂	semidirect
8. C₂×#396×C₁₃₉	C₂	semidirect
9. D₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
11. #2275×C₁₃₉	C₂	semidirect
13. C₂×#126×C₁₃₉	C₂²	semidirect
16. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
18. #401×C₁₃₉	C₂²	semidirect
19. #400×C₁₃₉	C₂²	semidirect
20. #400×C₁₃₉	C₂²	semidirect
22. #397×C₁₃₉	C₂²	semidirect
23. #397×C₁₃₉	C₂²	semidirect
26. #396×C₁₃₉	C₂²	semidirect
27. #396×C₁₃₉	C₂²	semidirect
30. #389×C₁₃₉	C₂²	semidirect
31. #389×C₁₃₉	C₂²	semidirect
33. #388×C₁₃₉	C₂²	semidirect
34. #387×C₁₃₉	C₂²	semidirect
37. #385×C₁₃₉	C₂²	semidirect
38. #385×C₁₃₉	C₂²	semidirect
39. #384×C₁₃₉	C₂²	semidirect
41. #380×C₁₃₉	C₂²	semidirect
43. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
44. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
46. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
47. #376×C₁₃₉	C₂²	semidirect
48. C₂×#95×C₁₃₉	C₂²	semidirect
152. D₄×C₁₃₉	#126	semidirect
203. #35914	C₁₃₉	direct (N × H)
204. C₁₃₉	#35914	direct (N × H)
205. #2644	C₂×C₁₃₉	semidirect
206. #2643	C₂×C₁₃₉	semidirect
207. #2512	C₂×C₁₃₉	semidirect
208. #2497	C₂×C₁₃₉	semidirect
209. #2481	C₂×C₁₃₉	semidirect
210. #2480	C₂×C₁₃₉	semidirect
211. #2401	C₂×C₁₃₉	semidirect
212. C₂×#396	C₂×C₁₃₉	semidirect
213. D₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
215. #2275	C₂×C₁₃₉	semidirect
217. C₂×#126	C₂²×C₁₃₉	semidirect
220. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
222. #401	C₂²×C₁₃₉	semidirect
223. #400	C₂²×C₁₃₉	semidirect
224. #400	C₂²×C₁₃₉	semidirect
226. #397	C₂²×C₁₃₉	semidirect
227. #397	C₂²×C₁₃₉	semidirect
230. #396	C₂²×C₁₃₉	semidirect
231. #396	C₂²×C₁₃₉	semidirect
234. #389	C₂²×C₁₃₉	semidirect
235. #389	C₂²×C₁₃₉	semidirect
237. #388	C₂²×C₁₃₉	semidirect
238. #387	C₂²×C₁₃₉	semidirect
241. #385	C₂²×C₁₃₉	semidirect
242. #385	C₂²×C₁₃₉	semidirect
243. #384	C₂²×C₁₃₉	semidirect
245. #380	C₂²×C₁₃₉	semidirect
247. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
248. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
250. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
251. #376	C₂²×C₁₃₉	semidirect
252. C₂×#95	C₂²×C₁₃₉	semidirect
356. D₄	#126×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2644×C₁₃₉	2
#2643×C₁₃₉	2
#2512×C₁₃₉	2
#2497×C₁₃₉	2
#2481×C₁₃₉	2
#2480×C₁₃₉	2
#2401×C₁₃₉	2
C₂×#396×C₁₃₉	2
D₄×C₄⋊C₄×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
#2275×C₁₃₉	2
#35914	139

Subgroups — C139×#35914 #48030510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#35914 #48030510