Subgroups — C₁₃₉×#29422 #48024018

Order 35584.

836 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2324×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2076×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2033×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#1999×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#1925×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1921×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1879×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1862×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1818×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#107×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	#390×C₁₃₉	—	2	2	no	—
22	#390×C₁₃₉	C₂²	1	2	yes	—
23	#389×C₁₃₉	C₂²	1	2	yes	—
24	#388×C₁₃₉	—	2	2	no	—
25	#386×C₁₃₉	—	2	2	no	—
26	#385×C₁₃₉	—	2	2	no	—
27	#380×C₁₃₉	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
29	#340×C₁₃₉	C₂²	1	1	yes	characteristic
30	#340×C₁₃₉	C₂²	1	2	yes	—
31	#340×C₁₃₉	C₂²	1	2	yes	—
32	#340×C₁₃₉	C₂²	1	1	yes	characteristic
33	#336×C₁₃₉	C₂²	1	2	yes	—
34	#336×C₁₃₉	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₃₉	—	2	2	no	—
36	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₉	—	2	2	no	—
38	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂×D₈×C₁₃₉	—	2	4	no	—
40	C₂×D₈×C₁₃₉	—	4	1	no	—
41	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
44	#121×C₁₃₉	—	2	4	no	—
45	#121×C₁₃₉	—	2	4	no	—
46	C₄×D₄×C₁₃₉	—	4	2	no	—
47	C₄×D₄×C₁₃₉	—	4	2	no	—
48	#117×C₁₃₉	—	4	1	no	—
49	#117×C₁₃₉	—	4	1	no	—
50	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	2	yes	—
62	C₂×C₄²×C₁₃₉	—	2	2	no	—
63	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
64	#107×C₁₃₉	—	2	4	no	—
65	#107×C₁₃₉	—	4	1	no	—
66	#102×C₁₃₉	—	2	4	no	—
67	#102×C₁₃₉	—	2	4	no	—
68	#102×C₁₃₉	—	4	2	no	—
69	C₂²⋊C₈×C₁₃₉	—	4	1	no	—
70	C₂²⋊C₈×C₁₃₉	—	4	1	no	—
71	#95×C₁₃₉	—	2	2	no	—
72	#95×C₁₃₉	—	2	2	no	—
73	#95×C₁₃₉	—	2	2	no	—
74	C₂⁴×C₁₃₉	—	2	2	no	—
75	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
76	C₂×D₄×C₁₃₉	—	2	8	no	—
77	C₂×D₄×C₁₃₉	—	2	2	no	—
78	C₂×D₄×C₁₃₉	—	2	2	no	—
79	C₂×D₄×C₁₃₉	—	2	2	no	—
80	C₂×D₄×C₁₃₉	—	2	2	no	—
81	C₂×D₄×C₁₃₉	—	2	2	no	—
82	C₂×D₄×C₁₃₉	—	8	2	no	—
83	C₂×D₄×C₁₃₉	—	8	2	no	—
84	C₂×D₄×C₁₃₉	#41	1	4	yes	—
85	C₂²×C₄×C₁₃₉	—	2	2	no	—
86	C₂²×C₄×C₁₃₉	—	2	2	no	—
87	C₂²×C₄×C₁₃₉	—	2	2	no	—
88	C₂²×C₄×C₁₃₉	—	2	1	no	—
89	C₂²×C₄×C₁₃₉	—	2	1	no	—
90	C₂²×C₄×C₁₃₉	—	2	2	no	—
91	C₂²×C₄×C₁₃₉	—	2	2	no	—
92	C₂²×C₄×C₁₃₉	—	4	4	no	—
93	C₂²×C₄×C₁₃₉	—	8	2	no	—
94	C₂²×C₄×C₁₃₉	—	8	2	no	—
95	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
99	D₈×C₁₃₉	—	4	4	no	—
100	C₂×C₈×C₁₃₉	—	2	2	no	—
101	C₂×C₈×C₁₃₉	—	2	2	no	—
102	C₂×C₈×C₁₃₉	—	2	2	no	—
103	C₂×C₈×C₁₃₉	—	2	2	no	—
104	C₂×C₈×C₁₃₉	—	2	2	no	—
105	C₂×C₈×C₁₃₉	—	2	1	no	—
106	C₂×C₈×C₁₃₉	—	2	1	no	—
107	C₄⋊C₄×C₁₃₉	—	2	2	no	—
108	C₄⋊C₄×C₁₃₉	—	2	2	no	—
109	C₄⋊C₄×C₁₃₉	—	2	2	no	—
110	C₄⋊C₄×C₁₃₉	—	2	2	no	—
111	C₄⋊C₄×C₁₃₉	—	2	2	no	—
112	C₄⋊C₄×C₁₃₉	—	4	1	no	—
113	C₄⋊C₄×C₁₃₉	—	4	1	no	—
114	C₄⋊C₄×C₁₃₉	—	8	2	no	—
115	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
116	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
117	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
119	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
120	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
121	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
122	C₄²×C₁₃₉	—	2	2	no	—
123	C₄²×C₁₃₉	—	2	2	no	—
124	C₄²×C₁₃₉	—	8	2	no	—
125	C₂³×C₁₃₉	—	2	4	no	—
126	C₂³×C₁₃₉	—	2	2	no	—
127	C₂³×C₁₃₉	—	2	1	no	—
128	C₂³×C₁₃₉	—	2	2	no	—
129	C₂³×C₁₃₉	—	2	1	no	—
130	C₂³×C₁₃₉	—	2	1	no	—
131	C₂³×C₁₃₉	—	4	2	no	—
132	C₂³×C₁₃₉	—	4	2	no	—
133	C₂³×C₁₃₉	—	4	2	no	—
134	C₂³×C₁₃₉	—	4	2	no	—
135	C₂³×C₁₃₉	—	4	2	no	—
136	C₂³×C₁₃₉	—	4	2	no	—
137	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
138	D₄×C₁₃₉	—	2	4	no	—
139	D₄×C₁₃₉	—	2	4	no	—
140	D₄×C₁₃₉	—	4	2	no	—
141	D₄×C₁₃₉	—	4	2	no	—
142	D₄×C₁₃₉	—	8	8	no	—
143	C₂×C₄×C₁₃₉	—	2	2	no	—
144	C₂×C₄×C₁₃₉	—	2	4	no	—
145	C₂×C₄×C₁₃₉	—	2	2	no	—
146	C₂×C₄×C₁₃₉	—	2	2	no	—
147	C₂×C₄×C₁₃₉	—	2	1	no	—
148	C₂×C₄×C₁₃₉	—	2	2	no	—
149	C₂×C₄×C₁₃₉	—	2	2	no	—
150	C₂×C₄×C₁₃₉	—	2	2	no	—
151	C₂×C₄×C₁₃₉	—	2	2	no	—
152	C₂×C₄×C₁₃₉	—	4	2	no	—
153	C₂×C₄×C₁₃₉	—	4	2	no	—
154	C₂×C₄×C₁₃₉	—	4	1	no	—
155	C₂×C₄×C₁₃₉	—	4	2	no	—
156	C₂×C₄×C₁₃₉	—	4	1	no	—
157	C₂×C₄×C₁₃₉	—	4	2	no	—
158	C₂×C₄×C₁₃₉	—	4	2	no	—
159	C₂×C₄×C₁₃₉	—	4	2	no	—
160	C₂×C₄×C₁₃₉	—	4	2	no	—
161	C₂×C₄×C₁₃₉	—	4	2	no	—
162	C₂×C₄×C₁₃₉	—	4	2	no	—
163	C₂×C₄×C₁₃₉	—	8	8	no	—
164	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
165	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
166	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
168	C₈×C₁₃₉	—	4	1	no	—
169	C₈×C₁₃₉	—	4	2	no	—
170	C₈×C₁₃₉	—	4	1	no	—
171	C₂²×C₁₃₉	—	4	1	no	—
172	C₂²×C₁₃₉	—	4	4	no	—
173	C₂²×C₁₃₉	—	4	2	no	—
174	C₂²×C₁₃₉	—	4	4	no	—
175	C₂²×C₁₃₉	—	4	2	no	—
176	C₂²×C₁₃₉	—	4	4	no	—
177	C₂²×C₁₃₉	—	4	1	no	—
178	C₂²×C₁₃₉	—	4	1	no	—
179	C₂²×C₁₃₉	—	8	2	no	—
180	C₂²×C₁₃₉	—	8	2	no	—
181	C₂²×C₁₃₉	—	8	2	no	—
182	C₂²×C₁₃₉	—	8	2	no	—
183	C₂²×C₁₃₉	#525	1	2	yes	—
184	C₂²×C₁₃₉	#534	1	1	yes	characteristic
185	C₂²×C₁₃₉	#576	1	1	yes	characteristic
186	C₂²×C₁₃₉	#576	1	2	yes	—
187	C₂²×C₁₃₉	#578	1	1	yes	characteristic
188	C₄×C₁₃₉	—	4	1	no	—
189	C₄×C₁₃₉	—	4	4	no	—
190	C₄×C₁₃₉	—	4	2	no	—
191	C₄×C₁₃₉	—	4	2	no	—
192	C₄×C₁₃₉	—	8	2	no	—
193	C₄×C₁₃₉	—	8	2	no	—
194	C₄×C₁₃₉	#551	1	1	yes	characteristic
195	C₄×C₁₃₉	#553	1	2	yes	—
196	C₄×C₁₃₉	#559	1	1	yes	characteristic
197	C₂×C₁₃₉	—	8	1	no	—
198	C₂×C₁₃₉	—	8	4	no	—
199	C₂×C₁₃₉	#2600	1	1	yes	characteristic
200	C₂×C₁₃₉	#3122	1	2	yes	—
201	C₂×C₁₃₉	#3124	1	2	yes	—
202	C₂×C₁₃₉	#3199	1	1	yes	characteristic
203	C₂×C₁₃₉	#3203	1	1	yes	characteristic
204	#29422	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₃₉	#29422	1	1	yes	characteristic, direct product factor, Sylow
206	#2324	C₂×C₁₃₉	1	2	yes	complemented
207	#2076	C₂×C₁₃₉	1	1	yes	characteristic, complemented
208	#2033	C₂×C₁₃₉	1	2	yes	complemented
209	#1999	C₂×C₁₃₉	1	1	yes	characteristic
210	#1925	C₂×C₁₃₉	1	2	yes	complemented
211	#1921	C₂×C₁₃₉	1	2	yes	complemented
212	#1879	C₂×C₁₃₉	1	2	yes	complemented
213	#1862	C₂×C₁₃₉	1	2	yes	complemented
214	#1818	C₂×C₁₃₉	1	1	yes	characteristic, complemented
215	C₂²×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
216	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
217	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
218	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
219	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
220	C₂×#107	C₂²×C₁₃₉	1	1	yes	characteristic
221	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
222	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
223	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
225	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
226	#390	—	2	2	no	—
227	#390	C₂²×C₁₃₉	1	2	yes	—
228	#389	C₂²×C₁₃₉	1	2	yes	—
229	#388	—	2	2	no	—
230	#386	—	2	2	no	—
231	#385	—	2	2	no	—
232	#380	C₂²×C₁₃₉	1	2	yes	—
233	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
234	#340	C₂²×C₁₃₉	1	2	yes	—
235	#340	C₂²×C₁₃₉	1	1	yes	characteristic
236	#340	C₂²×C₁₃₉	1	2	yes	—
237	#340	C₂²×C₁₃₉	1	1	yes	characteristic
238	#336	C₂²×C₁₃₉	1	2	yes	—
239	#336	C₂²×C₁₃₉	1	2	yes	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
244	C₂×D₈	—	2	4	no	—
245	C₂×D₈	—	4	1	no	—
246	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
249	#121	—	2	4	no	—
250	#121	—	2	4	no	—
251	C₄×D₄	—	4	2	no	—
252	C₄×D₄	—	4	2	no	—
253	#117	—	4	1	no	—
254	#117	—	4	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
257	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	2	yes	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
269	#107	—	2	4	no	—
270	#107	—	4	1	no	—
271	#102	—	2	4	no	—
272	#102	—	2	4	no	—
273	#102	—	4	2	no	—
274	C₂²⋊C₈	—	4	1	no	—
275	C₂²⋊C₈	—	4	1	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	C₂⁴	—	2	2	no	—
280	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
281	C₂×D₄	—	2	8	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	8	2	no	—
288	C₂×D₄	—	8	2	no	—
289	C₂×D₄	#41×C₁₃₉	1	4	yes	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	8	2	no	—
299	C₂²×C₄	—	8	2	no	—
300	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
304	D₈	—	4	4	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	8	2	no	—
320	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
321	C₂²⋊C₄	—	2	8	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	4	no	—
324	C₂²⋊C₄	—	8	2	no	—
325	C₂²⋊C₄	—	8	2	no	—
326	C₂²⋊C₄	—	8	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	8	2	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
343	D₄	—	2	4	no	—
344	D₄	—	2	4	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	8	8	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	8	no	—
369	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
370	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
371	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
372	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
373	C₈	—	4	1	no	—
374	C₈	—	4	2	no	—
375	C₈	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	#525×C₁₃₉	1	2	yes	—
389	C₂²	#534×C₁₃₉	1	1	yes	characteristic
390	C₂²	#576×C₁₃₉	1	1	yes	characteristic
391	C₂²	#576×C₁₃₉	1	2	yes	—
392	C₂²	#578×C₁₃₉	1	1	yes	characteristic
393	C₄	—	4	1	no	—
394	C₄	—	4	4	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	#551×C₁₃₉	1	1	yes	characteristic
400	C₄	#553×C₁₃₉	1	2	yes	—
401	C₄	#559×C₁₃₉	1	1	yes	characteristic
402	C₂	—	8	1	no	—
403	C₂	—	8	4	no	—
404	C₂	#2600×C₁₃₉	1	1	yes	characteristic
405	C₂	#3122×C₁₃₉	1	2	yes	—
406	C₂	#3124×C₁₃₉	1	2	yes	—
407	C₂	#3199×C₁₃₉	1	1	yes	characteristic
408	C₂	#3203×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	#1999×C₁₃₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×#117×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2324×C₁₃₉	C₂	semidirect
2. #2076×C₁₃₉	C₂	semidirect
3. #2033×C₁₃₉	C₂	semidirect
5. #1925×C₁₃₉	C₂	semidirect
6. #1921×C₁₃₉	C₂	semidirect
7. #1879×C₁₃₉	C₂	semidirect
8. #1862×C₁₃₉	C₂	semidirect
9. #1818×C₁₃₉	C₂	semidirect
204. #29422	C₁₃₉	direct (N × H)
205. C₁₃₉	#29422	direct (N × H)
206. #2324	C₂×C₁₃₉	semidirect
207. #2076	C₂×C₁₃₉	semidirect
208. #2033	C₂×C₁₃₉	semidirect
210. #1925	C₂×C₁₃₉	semidirect
211. #1921	C₂×C₁₃₉	semidirect
212. #1879	C₂×C₁₃₉	semidirect
213. #1862	C₂×C₁₃₉	semidirect
214. #1818	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2324×C₁₃₉	2
#2076×C₁₃₉	2
#2033×C₁₃₉	2
#1999×C₁₃₉	2
#1925×C₁₃₉	2
#1921×C₁₃₉	2
#1879×C₁₃₉	2
#1862×C₁₃₉	2
#1818×C₁₃₉	2
#29422	139

Subgroups — C139×#29422 #48024018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29422 #48024018