Subgroups — C₁₃₉×#29408 #48024004

Order 35584.

952 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#121×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2075×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	#1918×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	#1817×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	—	2	2	no	—
13	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#107×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
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	#380×C₁₃₉	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
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	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	C₂×D₈×C₁₃₉	—	2	4	no	—
42	C₂×D₈×C₁₃₉	—	4	1	no	—
43	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
46	#121×C₁₃₉	—	2	4	no	—
47	#121×C₁₃₉	—	2	4	no	—
48	C₄×D₄×C₁₃₉	—	4	2	no	—
49	C₄×D₄×C₁₃₉	—	4	2	no	—
50	C₄×D₄×C₁₃₉	—	4	8	no	—
51	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
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×C₄²×C₁₃₉	—	2	2	no	—
61	C₂×C₄²×C₁₃₉	—	4	1	no	—
62	C₂×C₄²×C₁₃₉	—	4	1	no	—
63	C₂×C₄²×C₁₃₉	D₄	1	2	yes	—
64	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
65	#107×C₁₃₉	—	2	4	no	—
66	#107×C₁₃₉	—	4	1	no	—
67	#102×C₁₃₉	—	2	4	no	—
68	#102×C₁₃₉	—	2	4	no	—
69	#102×C₁₃₉	—	4	2	no	—
70	C₂²⋊C₈×C₁₃₉	—	4	1	no	—
71	C₂²⋊C₈×C₁₃₉	—	4	1	no	—
72	#95×C₁₃₉	—	2	2	no	—
73	#95×C₁₃₉	—	2	2	no	—
74	#95×C₁₃₉	—	2	2	no	—
75	C₂⁴×C₁₃₉	—	2	2	no	—
76	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
77	C₂×D₄×C₁₃₉	—	2	8	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	—	2	2	no	—
83	C₂×D₄×C₁₃₉	—	4	4	no	—
84	C₂×D₄×C₁₃₉	—	4	4	no	—
85	C₂×D₄×C₁₃₉	#41	1	4	yes	—
86	C₂²×C₄×C₁₃₉	—	2	2	no	—
87	C₂²×C₄×C₁₃₉	—	2	2	no	—
88	C₂²×C₄×C₁₃₉	—	2	2	no	—
89	C₂²×C₄×C₁₃₉	—	2	1	no	—
90	C₂²×C₄×C₁₃₉	—	2	1	no	—
91	C₂²×C₄×C₁₃₉	—	2	2	no	—
92	C₂²×C₄×C₁₃₉	—	2	2	no	—
93	C₂²×C₄×C₁₃₉	—	4	1	no	—
94	C₂²×C₄×C₁₃₉	—	4	1	no	—
95	C₂²×C₄×C₁₃₉	—	4	1	no	—
96	C₂²×C₄×C₁₃₉	—	4	2	no	—
97	C₂²×C₄×C₁₃₉	—	4	4	no	—
98	C₂²×C₄×C₁₃₉	—	4	4	no	—
99	C₂²×C₄×C₁₃₉	—	4	4	no	—
100	C₂²×C₄×C₁₃₉	D₈	1	4	yes	complemented
101	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
105	D₈×C₁₃₉	—	4	4	no	—
106	C₂×C₈×C₁₃₉	—	2	2	no	—
107	C₂×C₈×C₁₃₉	—	2	2	no	—
108	C₂×C₈×C₁₃₉	—	2	2	no	—
109	C₂×C₈×C₁₃₉	—	2	2	no	—
110	C₂×C₈×C₁₃₉	—	2	2	no	—
111	C₂×C₈×C₁₃₉	—	2	1	no	—
112	C₂×C₈×C₁₃₉	—	2	1	no	—
113	C₄⋊C₄×C₁₃₉	—	2	2	no	—
114	C₄⋊C₄×C₁₃₉	—	2	2	no	—
115	C₄⋊C₄×C₁₃₉	—	2	2	no	—
116	C₄⋊C₄×C₁₃₉	—	2	2	no	—
117	C₄⋊C₄×C₁₃₉	—	2	2	no	—
118	C₄⋊C₄×C₁₃₉	—	4	4	no	—
119	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
120	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
121	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
122	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
123	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
124	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
125	C₄²×C₁₃₉	—	2	2	no	—
126	C₄²×C₁₃₉	—	2	2	no	—
127	C₄²×C₁₃₉	—	4	2	no	—
128	C₄²×C₁₃₉	—	4	4	no	—
129	C₂³×C₁₃₉	—	2	2	no	—
130	C₂³×C₁₃₉	—	2	1	no	—
131	C₂³×C₁₃₉	—	2	2	no	—
132	C₂³×C₁₃₉	—	2	1	no	—
133	C₂³×C₁₃₉	—	2	4	no	—
134	C₂³×C₁₃₉	—	4	2	no	—
135	C₂³×C₁₃₉	—	4	2	no	—
136	C₂³×C₁₃₉	—	4	2	no	—
137	C₂³×C₁₃₉	—	4	2	no	—
138	C₂³×C₁₃₉	—	4	2	no	—
139	C₂³×C₁₃₉	—	4	2	no	—
140	C₂³×C₁₃₉	C₂×D₈	1	2	yes	—
141	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
142	D₄×C₁₃₉	—	2	4	no	—
143	D₄×C₁₃₉	—	2	4	no	—
144	D₄×C₁₃₉	—	4	16	no	—
145	D₄×C₁₃₉	—	4	2	no	—
146	D₄×C₁₃₉	—	4	2	no	—
147	C₂×C₄×C₁₃₉	—	2	2	no	—
148	C₂×C₄×C₁₃₉	—	2	2	no	—
149	C₂×C₄×C₁₃₉	—	2	2	no	—
150	C₂×C₄×C₁₃₉	—	2	4	no	—
151	C₂×C₄×C₁₃₉	—	2	2	no	—
152	C₂×C₄×C₁₃₉	—	2	1	no	—
153	C₂×C₄×C₁₃₉	—	2	2	no	—
154	C₂×C₄×C₁₃₉	—	2	2	no	—
155	C₂×C₄×C₁₃₉	—	4	4	no	—
156	C₂×C₄×C₁₃₉	—	4	4	no	—
157	C₂×C₄×C₁₃₉	—	4	2	no	—
158	C₂×C₄×C₁₃₉	—	4	2	no	—
159	C₂×C₄×C₁₃₉	—	4	1	no	—
160	C₂×C₄×C₁₃₉	—	4	2	no	—
161	C₂×C₄×C₁₃₉	—	4	1	no	—
162	C₂×C₄×C₁₃₉	—	4	2	no	—
163	C₂×C₄×C₁₃₉	—	4	2	no	—
164	C₂×C₄×C₁₃₉	—	4	2	no	—
165	C₂×C₄×C₁₃₉	—	4	2	no	—
166	C₂×C₄×C₁₃₉	—	4	2	no	—
167	C₂×C₄×C₁₃₉	—	4	2	no	—
168	C₂×C₄×C₁₃₉	—	8	8	no	—
169	C₂×C₄×C₁₃₉	C₂×D₈	1	4	yes	—
170	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
171	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
174	C₈×C₁₃₉	—	4	1	no	—
175	C₈×C₁₃₉	—	4	2	no	—
176	C₈×C₁₃₉	—	4	1	no	—
177	C₂²×C₁₃₉	—	2	4	no	—
178	C₂²×C₁₃₉	—	2	2	no	—
179	C₂²×C₁₃₉	—	4	2	no	—
180	C₂²×C₁₃₉	—	4	1	no	—
181	C₂²×C₁₃₉	—	4	1	no	—
182	C₂²×C₁₃₉	—	4	4	no	—
183	C₂²×C₁₃₉	—	4	4	no	—
184	C₂²×C₁₃₉	—	4	4	no	—
185	C₂²×C₁₃₉	—	8	2	no	—
186	C₂²×C₁₃₉	—	8	2	no	—
187	C₂²×C₁₃₉	—	8	2	no	—
188	C₂²×C₁₃₉	—	8	2	no	—
189	C₂²×C₁₃₉	#525	1	2	yes	—
190	C₂²×C₁₃₉	#534	1	1	yes	characteristic
191	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
192	C₂²×C₁₃₉	#575	1	2	yes	—
193	C₂²×C₁₃₉	#575	1	1	yes	characteristic
194	C₄×C₁₃₉	—	2	4	no	—
195	C₄×C₁₃₉	—	4	4	no	—
196	C₄×C₁₃₉	—	4	1	no	—
197	C₄×C₁₃₉	—	4	2	no	—
198	C₄×C₁₃₉	—	8	2	no	—
199	C₄×C₁₃₉	—	8	2	no	—
200	C₄×C₁₃₉	#551	1	1	yes	characteristic
201	C₄×C₁₃₉	#553	1	2	yes	—
202	C₄×C₁₃₉	#559	1	1	yes	characteristic
203	C₂×C₁₃₉	—	4	2	no	—
204	C₂×C₁₃₉	—	8	4	no	—
205	C₂×C₁₃₉	#2600	1	1	yes	characteristic
206	C₂×C₁₃₉	#3100	1	2	yes	—
207	C₂×C₁₃₉	#3111	1	2	yes	—
208	C₂×C₁₃₉	#3186	1	1	yes	characteristic
209	C₂×C₁₃₉	#3197	1	1	yes	characteristic
210	#29408	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₁₃₉	#29408	1	1	yes	characteristic, direct product factor, Sylow
212	C₄×#121	C₂×C₁₃₉	1	2	yes	complemented
213	#2075	C₂×C₁₃₉	1	1	yes	characteristic, complemented
214	#2033	C₂×C₁₃₉	1	2	yes	complemented
215	#1999	C₂×C₁₃₉	1	1	yes	characteristic
216	#1925	C₂×C₁₃₉	1	2	yes	complemented
217	#1918	C₂×C₁₃₉	1	2	yes	complemented
218	#1879	C₂×C₁₃₉	1	2	yes	complemented
219	#1862	C₂×C₁₃₉	1	2	yes	complemented
220	#1817	C₂×C₁₃₉	1	1	yes	characteristic, complemented
221	C₂²×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
222	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
223	C₂×C₄×D₄	—	2	2	no	—
224	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
225	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
226	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
227	C₂×#107	C₂²×C₁₃₉	1	1	yes	characteristic
228	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
229	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
230	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
231	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
232	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
233	#390	C₂²×C₁₃₉	1	2	yes	—
234	#389	C₂²×C₁₃₉	1	2	yes	—
235	#388	—	2	2	no	—
236	#386	—	2	2	no	—
237	#380	C₂²×C₁₃₉	1	2	yes	—
238	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
239	C₄×C₂²⋊C₄	—	2	2	no	—
240	#340	C₂²×C₁₃₉	1	2	yes	—
241	#340	C₂²×C₁₃₉	1	1	yes	characteristic
242	#340	C₂²×C₁₃₉	1	2	yes	—
243	#340	C₂²×C₁₃₉	1	1	yes	characteristic
244	#336	C₂²×C₁₃₉	1	2	yes	—
245	#336	C₂²×C₁₃₉	1	2	yes	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
250	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
252	C₂×D₈	—	2	4	no	—
253	C₂×D₈	—	4	1	no	—
254	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
257	#121	—	2	4	no	—
258	#121	—	2	4	no	—
259	C₄×D₄	—	4	2	no	—
260	C₄×D₄	—	4	2	no	—
261	C₄×D₄	—	4	8	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	4	1	no	—
273	C₂×C₄²	—	4	1	no	—
274	C₂×C₄²	D₄×C₁₃₉	1	2	yes	—
275	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
276	#107	—	2	4	no	—
277	#107	—	4	1	no	—
278	#102	—	2	4	no	—
279	#102	—	2	4	no	—
280	#102	—	4	2	no	—
281	C₂²⋊C₈	—	4	1	no	—
282	C₂²⋊C₈	—	4	1	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	C₂⁴	—	2	2	no	—
287	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
288	C₂×D₄	—	2	8	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	#41×C₁₃₉	1	4	yes	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	D₈×C₁₃₉	1	4	yes	complemented
312	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
316	D₈	—	4	4	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	4	2	no	—
339	C₄²	—	4	4	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	C₂×D₈×C₁₃₉	1	2	yes	—
352	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
353	D₄	—	2	4	no	—
354	D₄	—	2	4	no	—
355	D₄	—	4	16	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	8	no	—
380	C₂×C₄	C₂×D₈×C₁₃₉	1	4	yes	—
381	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
382	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
383	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
384	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	1	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	#525×C₁₃₉	1	2	yes	—
401	C₂²	#534×C₁₃₉	1	1	yes	characteristic
402	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
403	C₂²	#575×C₁₃₉	1	2	yes	—
404	C₂²	#575×C₁₃₉	1	1	yes	characteristic
405	C₄	—	2	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	#551×C₁₃₉	1	1	yes	characteristic
412	C₄	#553×C₁₃₉	1	2	yes	—
413	C₄	#559×C₁₃₉	1	1	yes	characteristic
414	C₂	—	4	2	no	—
415	C₂	—	8	4	no	—
416	C₂	#2600×C₁₃₉	1	1	yes	characteristic
417	C₂	#3100×C₁₃₉	1	2	yes	—
418	C₂	#3111×C₁₃₉	1	2	yes	—
419	C₂	#3186×C₁₃₉	1	1	yes	characteristic
420	C₂	#3197×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 ◁ C₂²×C₄²×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×#121×C₁₃₉	C₂	semidirect
2. #2075×C₁₃₉	C₂	semidirect
3. #2033×C₁₃₉	C₂	semidirect
5. #1925×C₁₃₉	C₂	semidirect
6. #1918×C₁₃₉	C₂	semidirect
7. #1879×C₁₃₉	C₂	semidirect
8. #1862×C₁₃₉	C₂	semidirect
9. #1817×C₁₃₉	C₂	semidirect
100. C₂²×C₄×C₁₃₉	D₈	semidirect
210. #29408	C₁₃₉	direct (N × H)
211. C₁₃₉	#29408	direct (N × H)
212. C₄×#121	C₂×C₁₃₉	semidirect
213. #2075	C₂×C₁₃₉	semidirect
214. #2033	C₂×C₁₃₉	semidirect
216. #1925	C₂×C₁₃₉	semidirect
217. #1918	C₂×C₁₃₉	semidirect
218. #1879	C₂×C₁₃₉	semidirect
219. #1862	C₂×C₁₃₉	semidirect
220. #1817	C₂×C₁₃₉	semidirect
311. C₂²×C₄	D₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×#121×C₁₃₉	2
#2075×C₁₃₉	2
#2033×C₁₃₉	2
#1999×C₁₃₉	2
#1925×C₁₃₉	2
#1918×C₁₃₉	2
#1879×C₁₃₉	2
#1862×C₁₃₉	2
#1817×C₁₃₉	2
#29408	139

Subgroups — C139×#29408 #48024004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29408 #48024004