Subgroups — C₁₃₉×#29340 #48023936

Order 35584.

830 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2619×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2316×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2101×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2041×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1936×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1934×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1875×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1874×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1750×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
12	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
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	2	yes	—
20	C₂×#97×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	#394×C₁₃₉	—	2	2	no	—
23	#392×C₁₃₉	—	2	2	no	—
24	#390×C₁₃₉	C₂²	1	2	yes	—
25	#389×C₁₃₉	—	2	2	no	—
26	#389×C₁₃₉	C₂²	1	2	yes	—
27	#389×C₁₃₉	C₂²	1	2	yes	—
28	#382×C₁₃₉	C₂²	1	1	yes	characteristic
29	#380×C₁₃₉	—	2	2	no	—
30	#340×C₁₃₉	C₂²	1	2	yes	—
31	#340×C₁₃₉	C₂²	1	2	yes	—
32	#340×C₁₃₉	C₂²	1	2	yes	—
33	#340×C₁₃₉	C₂²	1	2	yes	—
34	#336×C₁₃₉	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₃₉	—	2	2	no	—
36	C₂²×D₄×C₁₃₉	—	2	2	no	—
37	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃₉	—	2	1	no	—
39	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
42	#127×C₁₃₉	—	4	1	no	—
43	#127×C₁₃₉	—	4	1	no	—
44	#121×C₁₃₉	—	2	4	no	—
45	#121×C₁₃₉	—	2	4	no	—
46	#117×C₁₃₉	—	4	1	no	—
47	#117×C₁₃₉	—	4	1	no	—
48	#117×C₁₃₉	—	4	1	no	—
49	#117×C₁₃₉	—	4	1	no	—
50	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	2	yes	—
63	C₂×C₄²×C₁₃₉	—	2	1	no	—
64	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
66	#102×C₁₃₉	—	2	4	no	—
67	#102×C₁₃₉	—	2	4	no	—
68	#102×C₁₃₉	—	4	2	no	—
69	#102×C₁₃₉	—	4	2	no	—
70	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
71	#97×C₁₃₉	—	4	1	no	—
72	C₄×C₈×C₁₃₉	—	4	1	no	—
73	#95×C₁₃₉	—	2	2	no	—
74	#95×C₁₃₉	—	2	2	no	—
75	#95×C₁₃₉	—	2	2	no	—
76	C₂⁴×C₁₃₉	—	2	2	no	—
77	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
84	C₂×D₄×C₁₃₉	—	4	4	no	—
85	C₂×D₄×C₁₃₉	—	4	4	no	—
86	C₂×D₄×C₁₃₉	—	8	2	no	—
87	C₂×D₄×C₁₃₉	—	8	2	no	—
88	C₂×D₄×C₁₃₉	—	8	2	no	—
89	C₂×D₄×C₁₃₉	—	8	2	no	—
90	C₂²×C₄×C₁₃₉	—	2	2	no	—
91	C₂²×C₄×C₁₃₉	—	2	1	no	—
92	C₂²×C₄×C₁₃₉	—	2	1	no	—
93	C₂²×C₄×C₁₃₉	—	2	2	no	—
94	C₂²×C₄×C₁₃₉	—	2	4	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	—	8	2	no	—
98	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
102	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₁₃₉	—	2	2	no	—
104	C₂×C₈×C₁₃₉	—	2	2	no	—
105	C₂×C₈×C₁₃₉	—	2	2	no	—
106	C₂×C₈×C₁₃₉	—	2	2	no	—
107	C₂×C₈×C₁₃₉	—	2	2	no	—
108	C₂×C₈×C₁₃₉	—	2	2	no	—
109	C₄⋊C₄×C₁₃₉	—	2	4	no	—
110	C₄⋊C₄×C₁₃₉	—	2	2	no	—
111	C₄⋊C₄×C₁₃₉	—	2	2	no	—
112	C₄⋊C₄×C₁₃₉	—	2	2	no	—
113	C₄⋊C₄×C₁₃₉	—	2	2	no	—
114	C₄⋊C₄×C₁₃₉	—	2	2	no	—
115	C₄⋊C₄×C₁₃₉	—	4	2	no	—
116	C₄⋊C₄×C₁₃₉	—	8	2	no	—
117	C₄⋊C₄×C₁₃₉	—	8	2	no	—
118	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
119	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
120	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
121	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
122	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
123	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
124	C₄²×C₁₃₉	—	2	1	no	—
125	C₄²×C₁₃₉	—	2	1	no	—
126	C₄²×C₁₃₉	—	2	1	no	—
127	C₄²×C₁₃₉	—	2	1	no	—
128	C₄²×C₁₃₉	—	4	2	no	—
129	C₂³×C₁₃₉	—	2	1	no	—
130	C₂³×C₁₃₉	—	2	1	no	—
131	C₂³×C₁₃₉	—	2	2	no	—
132	C₂³×C₁₃₉	—	2	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	—	4	2	no	—
138	C₂³×C₁₃₉	—	4	2	no	—
139	C₂³×C₁₃₉	—	4	2	no	—
140	C₂³×C₁₃₉	#124	1	2	yes	—
141	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
142	D₄×C₁₃₉	—	4	2	no	—
143	D₄×C₁₃₉	—	4	2	no	—
144	D₄×C₁₃₉	—	4	2	no	—
145	D₄×C₁₃₉	—	4	2	no	—
146	D₄×C₁₃₉	—	8	8	no	—
147	D₄×C₁₃₉	—	8	8	no	—
148	C₂×C₄×C₁₃₉	—	2	1	no	—
149	C₂×C₄×C₁₃₉	—	2	1	no	—
150	C₂×C₄×C₁₃₉	—	2	4	no	—
151	C₂×C₄×C₁₃₉	—	2	4	no	—
152	C₂×C₄×C₁₃₉	—	2	4	no	—
153	C₂×C₄×C₁₃₉	—	2	2	no	—
154	C₂×C₄×C₁₃₉	—	2	2	no	—
155	C₂×C₄×C₁₃₉	—	2	2	no	—
156	C₂×C₄×C₁₃₉	—	2	2	no	—
157	C₂×C₄×C₁₃₉	—	2	2	no	—
158	C₂×C₄×C₁₃₉	—	2	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	—	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	—	8	4	no	—
168	C₂×C₄×C₁₃₉	#124	1	2	yes	—
169	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
170	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
171	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
173	C₈×C₁₃₉	—	4	2	no	—
174	C₈×C₁₃₉	—	4	2	no	—
175	C₂²×C₁₃₉	—	2	2	no	—
176	C₂²×C₁₃₉	—	2	4	no	—
177	C₂²×C₁₃₉	—	4	1	no	—
178	C₂²×C₁₃₉	—	4	1	no	—
179	C₂²×C₁₃₉	—	4	2	no	—
180	C₂²×C₁₃₉	—	8	2	no	—
181	C₂²×C₁₃₉	—	8	2	no	—
182	C₂²×C₁₃₉	—	8	2	no	—
183	C₂²×C₁₃₉	—	8	2	no	—
184	C₂²×C₁₃₉	—	8	2	no	—
185	C₂²×C₁₃₉	—	8	2	no	—
186	C₂²×C₁₃₉	—	8	2	no	—
187	C₂²×C₁₃₉	#525	1	1	yes	characteristic
188	C₂²×C₁₃₉	C₂×#124	1	1	yes	characteristic
189	C₂²×C₁₃₉	#534	1	1	yes	characteristic
190	C₂²×C₁₃₉	#576	1	2	yes	—
191	C₂²×C₁₃₉	#577	1	2	yes	—
192	C₄×C₁₃₉	—	2	2	no	—
193	C₄×C₁₃₉	—	4	4	no	—
194	C₄×C₁₃₉	—	4	2	no	—
195	C₄×C₁₃₉	—	4	2	no	—
196	C₄×C₁₃₉	—	8	2	no	—
197	C₄×C₁₃₉	—	8	2	no	—
198	C₄×C₁₃₉	#553	1	2	yes	—
199	C₄×C₁₃₉	#553	1	2	yes	—
200	C₂×C₁₃₉	—	4	2	no	—
201	C₂×C₁₃₉	—	16	2	no	—
202	C₂×C₁₃₉	#2591	1	1	yes	characteristic
203	C₂×C₁₃₉	#3122	1	1	yes	characteristic
204	C₂×C₁₃₉	#3126	1	1	yes	characteristic
205	C₂×C₁₃₉	#3136	1	2	yes	—
206	C₂×C₁₃₉	#3198	1	2	yes	—
207	#29340	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₁₃₉	#29340	1	1	yes	characteristic, direct product factor, Sylow
209	#2619	C₂×C₁₃₉	1	1	yes	characteristic
210	#2316	C₂×C₁₃₉	1	1	yes	characteristic, complemented
211	#2101	C₂×C₁₃₉	1	2	yes	complemented
212	#2041	C₂×C₁₃₉	1	2	yes	complemented
213	#1936	C₂×C₁₃₉	1	2	yes	complemented
214	#1934	C₂×C₁₃₉	1	2	yes	complemented
215	#1875	C₂×C₁₃₉	1	2	yes	complemented
216	#1874	C₂×C₁₃₉	1	2	yes	complemented
217	#1750	C₂×C₁₃₉	1	1	yes	characteristic, complemented
218	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
219	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
220	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
221	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
222	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
223	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
224	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
225	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
226	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
228	C₂×#97	C₂²×C₁₃₉	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
230	#394	—	2	2	no	—
231	#392	—	2	2	no	—
232	#390	C₂²×C₁₃₉	1	2	yes	—
233	#389	—	2	2	no	—
234	#389	C₂²×C₁₃₉	1	2	yes	—
235	#389	C₂²×C₁₃₉	1	2	yes	—
236	#382	C₂²×C₁₃₉	1	1	yes	characteristic
237	#380	—	2	2	no	—
238	#340	C₂²×C₁₃₉	1	2	yes	—
239	#340	C₂²×C₁₃₉	1	2	yes	—
240	#340	C₂²×C₁₃₉	1	2	yes	—
241	#340	C₂²×C₁₃₉	1	2	yes	—
242	#336	C₂²×C₁₃₉	1	2	yes	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
249	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
250	#127	—	4	1	no	—
251	#127	—	4	1	no	—
252	#121	—	2	4	no	—
253	#121	—	2	4	no	—
254	#117	—	4	1	no	—
255	#117	—	4	1	no	—
256	#117	—	4	1	no	—
257	#117	—	4	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	4	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
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	1	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	D₄×C₁₃₉	1	2	yes	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
274	#102	—	2	4	no	—
275	#102	—	2	4	no	—
276	#102	—	4	2	no	—
277	#102	—	4	2	no	—
278	C₂²⋊C₈	—	2	4	no	—
279	#97	—	4	1	no	—
280	C₄×C₈	—	4	1	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	C₂⁴	—	2	2	no	—
285	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	8	2	no	—
295	C₂×D₄	—	8	2	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂×D₄	—	8	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	8	2	no	—
306	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
309	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
310	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	8	2	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₂²⋊C₄	—	8	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	4	2	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	#124×C₁₃₉	1	2	yes	—
349	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	8	8	no	—
355	D₄	—	8	8	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	8	4	no	—
376	C₂×C₄	#124×C₁₃₉	1	2	yes	—
377	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
378	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
379	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
380	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	#525×C₁₃₉	1	1	yes	characteristic
396	C₂²	C₂×#124×C₁₃₉	1	1	yes	characteristic
397	C₂²	#534×C₁₃₉	1	1	yes	characteristic
398	C₂²	#576×C₁₃₉	1	2	yes	—
399	C₂²	#577×C₁₃₉	1	2	yes	—
400	C₄	—	2	2	no	—
401	C₄	—	4	4	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	8	2	no	—
405	C₄	—	8	2	no	—
406	C₄	#553×C₁₃₉	1	2	yes	—
407	C₄	#553×C₁₃₉	1	2	yes	—
408	C₂	—	4	2	no	—
409	C₂	—	16	2	no	—
410	C₂	#2591×C₁₃₉	1	1	yes	characteristic
411	C₂	#3122×C₁₃₉	1	1	yes	characteristic
412	C₂	#3126×C₁₃₉	1	1	yes	characteristic
413	C₂	#3136×C₁₃₉	1	2	yes	—
414	C₂	#3198×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	#2619×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
2. #2316×C₁₃₉	C₂	semidirect
3. #2101×C₁₃₉	C₂	semidirect
4. #2041×C₁₃₉	C₂	semidirect
5. #1936×C₁₃₉	C₂	semidirect
6. #1934×C₁₃₉	C₂	semidirect
7. #1875×C₁₃₉	C₂	semidirect
8. #1874×C₁₃₉	C₂	semidirect
9. #1750×C₁₃₉	C₂	semidirect
207. #29340	C₁₃₉	direct (N × H)
208. C₁₃₉	#29340	direct (N × H)
210. #2316	C₂×C₁₃₉	semidirect
211. #2101	C₂×C₁₃₉	semidirect
212. #2041	C₂×C₁₃₉	semidirect
213. #1936	C₂×C₁₃₉	semidirect
214. #1934	C₂×C₁₃₉	semidirect
215. #1875	C₂×C₁₃₉	semidirect
216. #1874	C₂×C₁₃₉	semidirect
217. #1750	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2619×C₁₃₉	2
#2316×C₁₃₉	2
#2101×C₁₃₉	2
#2041×C₁₃₉	2
#1936×C₁₃₉	2
#1934×C₁₃₉	2
#1875×C₁₃₉	2
#1874×C₁₃₉	2
#1750×C₁₃₉	2
#29340	139

Subgroups — C139×#29340 #48023936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29340 #48023936