Subgroups — C₁₃₉×#21865 #48016461

Order 35584.

1394 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	C₂×#532×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#382×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1993×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1961×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1874×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#1804×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₃₉	—	2	1	no	—
9	#532×C₁₃₉	—	2	4	no	—
10	#532×C₁₃₉	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#124×C₁₃₉	—	2	1	no	—
14	C₂×#121×C₁₃₉	—	2	1	no	—
15	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
17	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
20	#432×C₁₃₉	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#102×C₁₃₉	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#97×C₁₃₉	C₂²	1	2	yes	—
25	#382×C₁₃₉	—	2	1	no	—
26	#382×C₁₃₉	—	2	1	no	—
27	#382×C₁₃₉	C₂²	1	2	yes	—
28	#382×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#95×C₁₃₉	—	2	1	no	—
30	C₂×#95×C₁₃₉	—	2	1	no	—
31	#340×C₁₃₉	C₂²	1	8	yes	—
32	C₂×#41×C₁₃₉	—	2	8	no	—
33	C₂×#41×C₁₃₉	—	4	8	no	—
34	C₂²×Q₈×C₁₃₉	—	2	1	no	—
35	C₂²×D₄×C₁₃₉	—	2	2	no	—
36	C₂²×D₄×C₁₃₉	—	2	1	no	—
37	C₂²×D₄×C₁₃₉	—	2	1	no	—
38	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃₉	—	2	2	no	—
40	C₂³×C₄×C₁₃₉	—	2	2	no	—
41	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
46	C₄⋊Q₈×C₁₃₉	C₂×C₄	1	4	yes	complemented
47	#127×C₁₃₉	—	2	2	no	—
48	#127×C₁₃₉	C₂×C₄	1	4	yes	complemented
49	#124×C₁₃₉	—	2	8	no	—
50	#121×C₁₃₉	—	2	8	no	—
51	#121×C₁₃₉	—	2	4	no	—
52	#121×C₁₃₉	C₂×C₄	1	8	yes	—
53	C₄×D₄×C₁₃₉	—	2	8	no	—
54	C₄×D₄×C₁₃₉	—	2	4	no	—
55	C₄×D₄×C₁₃₉	C₂×C₄	1	8	yes	complemented
56	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
63	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
67	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₁₃₉	—	2	4	no	—
70	#102×C₁₃₉	—	4	8	no	—
71	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
72	#97×C₁₃₉	—	2	4	no	—
73	#95×C₁₃₉	—	2	2	no	—
74	#95×C₁₃₉	—	2	2	no	—
75	#95×C₁₃₉	—	2	2	no	—
76	#95×C₁₃₉	—	2	2	no	—
77	C₂⁴×C₁₃₉	—	2	2	no	—
78	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
79	#41×C₁₃₉	—	4	32	no	—
80	C₂×Q₈×C₁₃₉	—	2	4	no	—
81	C₂×Q₈×C₁₃₉	—	4	4	no	—
82	C₂×D₄×C₁₃₉	—	2	8	no	—
83	C₂×D₄×C₁₃₉	—	2	4	no	—
84	C₂×D₄×C₁₃₉	—	2	4	no	—
85	C₂×D₄×C₁₃₉	—	2	2	no	—
86	C₂×D₄×C₁₃₉	—	2	4	no	—
87	C₂×D₄×C₁₃₉	—	2	4	no	—
88	C₂×D₄×C₁₃₉	—	4	4	no	—
89	C₂×D₄×C₁₃₉	—	4	4	no	—
90	C₂×D₄×C₁₃₉	—	4	8	no	—
91	C₂×D₄×C₁₃₉	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₁₃₉	—	2	4	no	—
93	C₂²×C₄×C₁₃₉	—	2	2	no	—
94	C₂²×C₄×C₁₃₉	—	2	2	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	2	8	no	—
97	C₂²×C₄×C₁₃₉	—	2	4	no	—
98	C₂²×C₄×C₁₃₉	—	4	2	no	—
99	C₂²×C₄×C₁₃₉	—	4	8	no	—
100	C₂²×C₄×C₁₃₉	—	4	4	no	—
101	C₂²×C₄×C₁₃₉	—	4	4	no	—
102	C₂²×C₄×C₁₃₉	—	4	4	no	—
103	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₁₃₉	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₁₃₉	—	2	4	no	—
114	C₂×C₈×C₁₃₉	—	2	4	no	—
115	C₂×C₈×C₁₃₉	—	2	4	no	—
116	C₄⋊C₄×C₁₃₉	—	2	4	no	—
117	C₄⋊C₄×C₁₃₉	—	2	2	no	—
118	C₄⋊C₄×C₁₃₉	—	2	8	no	—
119	C₄⋊C₄×C₁₃₉	—	4	4	no	—
120	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
122	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
123	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
124	C₄²×C₁₃₉	C₂²⋊C₄	1	4	yes	—
125	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
126	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
127	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
128	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
129	C₂³×C₁₃₉	—	2	1	no	—
130	C₂³×C₁₃₉	—	2	1	no	—
131	C₂³×C₁₃₉	—	2	2	no	—
132	C₂³×C₁₃₉	—	2	4	no	—
133	C₂³×C₁₃₉	—	4	2	no	—
134	C₂³×C₁₃₉	—	4	2	no	—
135	C₂³×C₁₃₉	—	4	4	no	—
136	C₂³×C₁₃₉	—	4	4	no	—
137	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂³×C₁₃₉	AGL(1,ℤ/8)	1	4	yes	—
139	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₁₃₉	—	4	8	no	—
141	D₄×C₁₃₉	—	2	8	no	—
142	D₄×C₁₃₉	—	4	8	no	—
143	D₄×C₁₃₉	—	4	8	no	—
144	D₄×C₁₃₉	—	4	16	no	—
145	D₄×C₁₃₉	—	4	4	no	—
146	C₂×C₄×C₁₃₉	—	2	1	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	—	2	8	no	—
153	C₂×C₄×C₁₃₉	—	2	4	no	—
154	C₂×C₄×C₁₃₉	—	2	4	no	—
155	C₂×C₄×C₁₃₉	—	2	4	no	—
156	C₂×C₄×C₁₃₉	—	4	4	no	—
157	C₂×C₄×C₁₃₉	—	4	16	no	—
158	C₂×C₄×C₁₃₉	—	4	4	no	—
159	C₂×C₄×C₁₃₉	—	4	4	no	—
160	C₂×C₄×C₁₃₉	—	4	4	no	—
161	C₂×C₄×C₁₃₉	—	4	4	no	—
162	C₂×C₄×C₁₃₉	—	8	8	no	—
163	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
172	C₈×C₁₃₉	—	4	4	no	—
173	C₂²×C₁₃₉	—	2	2	no	—
174	C₂²×C₁₃₉	—	2	2	no	—
175	C₂²×C₁₃₉	—	2	4	no	—
176	C₂²×C₁₃₉	—	2	4	no	—
177	C₂²×C₁₃₉	—	4	4	no	—
178	C₂²×C₁₃₉	—	4	4	no	—
179	C₂²×C₁₃₉	—	4	4	no	—
180	C₂²×C₁₃₉	—	8	4	no	—
181	C₂²×C₁₃₉	—	8	4	no	—
182	C₂²×C₁₃₉	#418	1	4	yes	—
183	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₁₃₉	#535	1	1	yes	characteristic
185	C₂²×C₁₃₉	#536	1	1	yes	characteristic
186	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
187	C₂²×C₁₃₉	#575	1	2	yes	—
188	C₄×C₁₃₉	—	2	2	no	—
189	C₄×C₁₃₉	—	2	2	no	—
190	C₄×C₁₃₉	—	2	2	no	—
191	C₄×C₁₃₉	—	2	2	no	—
192	C₄×C₁₃₉	—	2	2	no	—
193	C₄×C₁₃₉	—	4	4	no	—
194	C₄×C₁₃₉	—	8	4	no	—
195	C₄×C₁₃₉	#520	1	2	yes	—
196	C₄×C₁₃₉	#537	1	2	yes	—
197	C₂×C₁₃₉	—	2	4	no	—
198	C₂×C₁₃₉	—	8	4	no	—
199	C₂×C₁₃₉	#2311	1	1	yes	characteristic
200	C₂×C₁₃₉	C₂×#418	1	1	yes	characteristic
201	C₂×C₁₃₉	#2896	1	1	yes	characteristic
202	C₂×C₁₃₉	#3213	1	2	yes	—
203	C₂×C₁₃₉	#3234	1	2	yes	—
204	#21865	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₃₉	#21865	1	1	yes	characteristic, direct product factor, Sylow
206	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic
207	C₂×#432	C₂×C₁₃₉	1	1	yes	characteristic, complemented
208	C₂×#382	C₂×C₁₃₉	1	1	yes	characteristic, complemented
209	#1993	C₂×C₁₃₉	1	2	yes	complemented
210	#1961	C₂×C₁₃₉	1	2	yes	complemented
211	#1874	C₂×C₁₃₉	1	4	yes	complemented
212	#1804	C₂×C₁₃₉	1	4	yes	complemented
213	C₂²×#41	—	2	1	no	—
214	#532	—	2	4	no	—
215	#532	C₄×C₁₃₉	1	8	yes	complemented
216	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
217	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
218	C₂×#124	—	2	1	no	—
219	C₂×#121	—	2	1	no	—
220	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
224	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
225	#432	—	2	4	no	—
226	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
227	C₂×#102	C₂²×C₁₃₉	1	8	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
229	C₂×#97	C₂²×C₁₃₉	1	2	yes	—
230	#382	—	2	1	no	—
231	#382	—	2	1	no	—
232	#382	C₂²×C₁₃₉	1	2	yes	—
233	#382	C₂²×C₁₃₉	1	2	yes	—
234	C₂×#95	—	2	1	no	—
235	C₂×#95	—	2	1	no	—
236	#340	C₂²×C₁₃₉	1	8	yes	—
237	C₂×#41	—	2	8	no	—
238	C₂×#41	—	4	8	no	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
244	C₂³×C₄	—	2	2	no	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	C₂×C₄×C₁₃₉	1	4	yes	complemented
252	#127	—	2	2	no	—
253	#127	C₂×C₄×C₁₃₉	1	4	yes	complemented
254	#124	—	2	8	no	—
255	#121	—	2	8	no	—
256	#121	—	2	4	no	—
257	#121	C₂×C₄×C₁₃₉	1	8	yes	—
258	C₄×D₄	—	2	8	no	—
259	C₄×D₄	—	2	4	no	—
260	C₄×D₄	C₂×C₄×C₁₃₉	1	8	yes	complemented
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	4	4	no	—
264	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	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×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
269	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
271	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
272	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
274	C₄⋊C₈	—	2	4	no	—
275	#102	—	4	8	no	—
276	C₂²⋊C₈	—	2	4	no	—
277	#97	—	2	4	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	C₂⁴	—	2	2	no	—
283	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
284	#41	—	4	32	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	8	no	—
296	C₂×D₄	C₂²×C₄×C₁₃₉	1	4	yes	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	8	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
309	C₂²×C₄	C₂²⋊C₄×C₁₃₉	1	4	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
329	C₄²	C₂²⋊C₄×C₁₃₉	1	4	yes	—
330	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
331	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
332	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
333	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
343	C₂³	AGL(1,ℤ/8)×C₁₃₉	1	4	yes	—
344	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
345	Q₈	—	4	8	no	—
346	D₄	—	2	8	no	—
347	D₄	—	4	8	no	—
348	D₄	—	4	8	no	—
349	D₄	—	4	16	no	—
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	16	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	8	8	no	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	2	yes	—
373	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
375	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
376	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
377	C₈	—	4	4	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	4	no	—
386	C₂²	—	8	4	no	—
387	C₂²	#418×C₁₃₉	1	4	yes	—
388	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
389	C₂²	#535×C₁₃₉	1	1	yes	characteristic
390	C₂²	#536×C₁₃₉	1	1	yes	characteristic
391	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
392	C₂²	#575×C₁₃₉	1	2	yes	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	4	no	—
400	C₄	#520×C₁₃₉	1	2	yes	—
401	C₄	#537×C₁₃₉	1	2	yes	—
402	C₂	—	2	4	no	—
403	C₂	—	8	4	no	—
404	C₂	#2311×C₁₃₉	1	1	yes	characteristic
405	C₂	C₂×#418×C₁₃₉	1	1	yes	characteristic
406	C₂	#2896×C₁₃₉	1	1	yes	characteristic
407	C₂	#3213×C₁₃₉	1	2	yes	—
408	C₂	#3234×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#532×C₁₃₉	C₂
LCS	G ▷ C₂×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
2. C₂×#432×C₁₃₉	C₂	semidirect
3. C₂×#382×C₁₃₉	C₂	semidirect
4. #1993×C₁₃₉	C₂	semidirect
5. #1961×C₁₃₉	C₂	semidirect
6. #1874×C₁₃₉	C₂	semidirect
7. #1804×C₁₃₉	C₂	semidirect
10. #532×C₁₃₉	C₄	semidirect
46. C₄⋊Q₈×C₁₃₉	C₂×C₄	semidirect
48. #127×C₁₃₉	C₂×C₄	semidirect
55. C₄×D₄×C₁₃₉	C₂×C₄	semidirect
204. #21865	C₁₃₉	direct (N × H)
205. C₁₃₉	#21865	direct (N × H)
207. C₂×#432	C₂×C₁₃₉	semidirect
208. C₂×#382	C₂×C₁₃₉	semidirect
209. #1993	C₂×C₁₃₉	semidirect
210. #1961	C₂×C₁₃₉	semidirect
211. #1874	C₂×C₁₃₉	semidirect
212. #1804	C₂×C₁₃₉	semidirect
215. #532	C₄×C₁₃₉	semidirect
251. C₄⋊Q₈	C₂×C₄×C₁₃₉	semidirect
253. #127	C₂×C₄×C₁₃₉	semidirect
260. C₄×D₄	C₂×C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₃₉	2
C₂×#432×C₁₃₉	2
C₂×#382×C₁₃₉	2
#1993×C₁₃₉	2
#1961×C₁₃₉	2
#1874×C₁₃₉	2
#1804×C₁₃₉	2
#21865	139

Subgroups — C139×#21865 #48016461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21865 #48016461