Subgroups — C₁₃₉×#29254 #48023850

Order 35584.

936 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	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2093×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2023×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1982×C₁₃₉	C₂	1	2	yes	maximal
6	#1947×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1862×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#1831×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₃₉	—	2	1	no	—
12	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
13	C₂×C₄×D₄×C₁₃₉	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#107×C₁₃₉	C₂²	1	4	yes	—
16	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#102×C₁₃₉	C₂²	1	4	yes	—
18	C₂×#102×C₁₃₉	C₂²	1	4	yes	—
19	#391×C₁₃₉	—	2	1	no	—
20	#390×C₁₃₉	—	2	1	no	—
21	#390×C₁₃₉	—	2	1	no	—
22	#390×C₁₃₉	C₂²	1	2	yes	—
23	#389×C₁₃₉	—	2	1	no	—
24	#389×C₁₃₉	C₂²	1	2	yes	—
25	#384×C₁₃₉	C₂²	1	1	yes	characteristic
26	#384×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
28	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
29	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
30	#340×C₁₃₉	C₂²	1	4	yes	—
31	#336×C₁₃₉	C₂²	1	2	yes	—
32	#336×C₁₃₉	C₂²	1	2	yes	—
33	C₂²×Q₈×C₁₃₉	—	2	1	no	—
34	C₂²×D₄×C₁₃₉	—	2	1	no	—
35	C₂²×D₄×C₁₃₉	—	2	1	no	—
36	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₉	—	2	2	no	—
38	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
39	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
40	#127×C₁₃₉	—	2	2	no	—
41	#127×C₁₃₉	Q₈	1	4	yes	complemented
42	C₄×Q₈×C₁₃₉	—	4	4	no	—
43	C₄×D₄×C₁₃₉	—	4	4	no	—
44	C₄×D₄×C₁₃₉	—	4	4	no	—
45	C₄×D₄×C₁₃₉	—	4	4	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₃₉	—	2	1	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×C₄²×C₁₃₉	—	2	2	no	—
59	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
66	#107×C₁₃₉	—	4	4	no	—
67	C₄⋊C₈×C₁₃₉	—	2	4	no	—
68	#102×C₁₃₉	—	2	8	no	—
69	#102×C₁₃₉	—	4	4	no	—
70	#95×C₁₃₉	—	2	2	no	—
71	#95×C₁₃₉	—	2	2	no	—
72	C₂⁴×C₁₃₉	—	2	2	no	—
73	C₂×Q₈×C₁₃₉	—	2	4	no	—
74	C₂×Q₈×C₁₃₉	—	4	2	no	—
75	C₂×Q₈×C₁₃₉	—	4	2	no	—
76	C₂×D₄×C₁₃₉	—	2	4	no	—
77	C₂×D₄×C₁₃₉	—	2	4	no	—
78	C₂×D₄×C₁₃₉	—	2	4	no	—
79	C₂×D₄×C₁₃₉	—	2	2	no	—
80	C₂×D₄×C₁₃₉	—	2	4	no	—
81	C₂×D₄×C₁₃₉	—	4	2	no	—
82	C₂×D₄×C₁₃₉	—	4	2	no	—
83	C₂×D₄×C₁₃₉	—	4	2	no	—
84	C₂×D₄×C₁₃₉	—	4	2	no	—
85	C₂×D₄×C₁₃₉	C₂×Q₈	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	—	4	4	no	—
90	C₂²×C₄×C₁₃₉	—	4	4	no	—
91	C₂²×C₄×C₁₃₉	—	4	4	no	—
92	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₃₉	—	2	4	no	—
100	C₂×C₈×C₁₃₉	—	2	4	no	—
101	C₂×C₈×C₁₃₉	—	2	4	no	—
102	C₄⋊C₄×C₁₃₉	—	2	4	no	—
103	C₄⋊C₄×C₁₃₉	—	2	2	no	—
104	C₄⋊C₄×C₁₃₉	—	2	2	no	—
105	C₄⋊C₄×C₁₃₉	—	2	2	no	—
106	C₄⋊C₄×C₁₃₉	—	2	4	no	—
107	C₄⋊C₄×C₁₃₉	—	4	2	no	—
108	C₄⋊C₄×C₁₃₉	—	4	2	no	—
109	C₄⋊C₄×C₁₃₉	—	4	4	no	—
110	C₄⋊C₄×C₁₃₉	—	4	2	no	—
111	C₄⋊C₄×C₁₃₉	—	4	2	no	—
112	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
113	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
114	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
115	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
116	C₄²×C₁₃₉	—	2	2	no	—
117	C₄²×C₁₃₉	—	2	2	no	—
118	C₄²×C₁₃₉	—	2	2	no	—
119	C₄²×C₁₃₉	—	2	2	no	—
120	C₄²×C₁₃₉	—	4	1	no	—
121	C₄²×C₁₃₉	—	4	4	no	—
122	C₄²×C₁₃₉	D₈	1	4	yes	—
123	C₄²×C₁₃₉	C₂×Q₈	1	2	yes	—
124	C₄²×C₁₃₉	#41	1	2	yes	—
125	C₂³×C₁₃₉	—	2	4	no	—
126	C₂³×C₁₃₉	—	4	2	no	—
127	C₂³×C₁₃₉	—	4	2	no	—
128	C₂³×C₁₃₉	—	4	2	no	—
129	C₂³×C₁₃₉	—	4	2	no	—
130	C₂³×C₁₃₉	—	4	2	no	—
131	C₂³×C₁₃₉	—	4	2	no	—
132	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
133	Q₈×C₁₃₉	—	4	8	no	—
134	D₄×C₁₃₉	—	2	8	no	—
135	D₄×C₁₃₉	—	4	8	no	—
136	D₄×C₁₃₉	—	4	4	no	—
137	D₄×C₁₃₉	—	4	8	no	—
138	C₂×C₄×C₁₃₉	—	2	1	no	—
139	C₂×C₄×C₁₃₉	—	2	1	no	—
140	C₂×C₄×C₁₃₉	—	2	1	no	—
141	C₂×C₄×C₁₃₉	—	2	1	no	—
142	C₂×C₄×C₁₃₉	—	2	1	no	—
143	C₂×C₄×C₁₃₉	—	2	1	no	—
144	C₂×C₄×C₁₃₉	—	2	1	no	—
145	C₂×C₄×C₁₃₉	—	2	1	no	—
146	C₂×C₄×C₁₃₉	—	2	4	no	—
147	C₂×C₄×C₁₃₉	—	2	1	no	—
148	C₂×C₄×C₁₃₉	—	2	1	no	—
149	C₂×C₄×C₁₃₉	—	2	1	no	—
150	C₂×C₄×C₁₃₉	—	4	2	no	—
151	C₂×C₄×C₁₃₉	—	4	2	no	—
152	C₂×C₄×C₁₃₉	—	4	2	no	—
153	C₂×C₄×C₁₃₉	—	4	2	no	—
154	C₂×C₄×C₁₃₉	—	4	2	no	—
155	C₂×C₄×C₁₃₉	—	4	2	no	—
156	C₂×C₄×C₁₃₉	—	4	2	no	—
157	C₂×C₄×C₁₃₉	—	4	2	no	—
158	C₂×C₄×C₁₃₉	—	8	8	no	—
159	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
160	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
161	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
162	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₁₃₉	C₂×D₈	1	2	yes	—
164	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₁₃₉	#137	1	2	yes	—
166	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
168	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
170	C₈×C₁₃₉	—	4	4	no	—
171	C₂²×C₁₃₉	—	4	4	no	—
172	C₂²×C₁₃₉	—	4	4	no	—
173	C₂²×C₁₃₉	—	4	4	no	—
174	C₂²×C₁₃₉	—	8	2	no	—
175	C₂²×C₁₃₉	—	8	2	no	—
176	C₂²×C₁₃₉	—	8	2	no	—
177	C₂²×C₁₃₉	—	8	2	no	—
178	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
179	C₂²×C₁₃₉	#525	1	1	yes	characteristic
180	C₂²×C₁₃₉	#535	1	1	yes	characteristic
181	C₂²×C₁₃₉	C₂²×D₈	1	1	yes	characteristic
182	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
184	C₂²×C₁₃₉	#575	1	1	yes	characteristic
185	C₄×C₁₃₉	—	2	2	no	—
186	C₄×C₁₃₉	—	2	2	no	—
187	C₄×C₁₃₉	—	2	2	no	—
188	C₄×C₁₃₉	—	2	2	no	—
189	C₄×C₁₃₉	—	4	4	no	—
190	C₄×C₁₃₉	—	4	1	no	—
191	C₄×C₁₃₉	—	8	2	no	—
192	C₄×C₁₃₉	—	8	2	no	—
193	C₄×C₁₃₉	#474	1	4	yes	—
194	C₄×C₁₃₉	#554	1	2	yes	—
195	C₄×C₁₃₉	#559	1	2	yes	—
196	C₂×C₁₃₉	—	8	4	no	—
197	C₂×C₁₃₉	#2580	1	1	yes	characteristic
198	C₂×C₁₃₉	C₂×#474	1	1	yes	characteristic
199	C₂×C₁₃₉	#3077	1	1	yes	characteristic
200	C₂×C₁₃₉	#3100	1	1	yes	characteristic
201	C₂×C₁₃₉	#3112	1	1	yes	characteristic
202	C₂×C₁₃₉	#3205	1	1	yes	characteristic
203	C₂×C₁₃₉	#3216	1	1	yes	characteristic
204	#29254	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₃₉	#29254	1	1	yes	characteristic, direct product factor, Sylow
206	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
207	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic
208	#2093	C₂×C₁₃₉	1	2	yes	complemented
209	#2023	C₂×C₁₃₉	1	2	yes	complemented
210	#1982	C₂×C₁₃₉	1	2	yes	—
211	#1947	C₂×C₁₃₉	1	2	yes	complemented
212	#1862	C₂×C₁₃₉	1	4	yes	complemented
213	#1831	C₂×C₁₃₉	1	1	yes	characteristic, complemented
214	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
215	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
216	C₂×C₄×Q₈	—	2	1	no	—
217	C₂×C₄×D₄	—	2	1	no	—
218	C₂×C₄×D₄	—	2	1	no	—
219	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
220	C₂×#107	C₂²×C₁₃₉	1	4	yes	—
221	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	—
222	C₂×#102	C₂²×C₁₃₉	1	4	yes	—
223	C₂×#102	C₂²×C₁₃₉	1	4	yes	—
224	#391	—	2	1	no	—
225	#390	—	2	1	no	—
226	#390	—	2	1	no	—
227	#390	C₂²×C₁₃₉	1	2	yes	—
228	#389	—	2	1	no	—
229	#389	C₂²×C₁₃₉	1	2	yes	—
230	#384	C₂²×C₁₃₉	1	1	yes	characteristic
231	#384	C₂²×C₁₃₉	1	1	yes	characteristic
232	C₄×C₄⋊C₄	—	2	1	no	—
233	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
234	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
235	#340	C₂²×C₁₃₉	1	4	yes	—
236	#336	C₂²×C₁₃₉	1	2	yes	—
237	#336	C₂²×C₁₃₉	1	2	yes	—
238	C₂²×Q₈	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
242	C₂³×C₄	—	2	2	no	—
243	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
244	C₄⋊Q₈	—	2	4	no	—
245	#127	—	2	2	no	—
246	#127	Q₈×C₁₃₉	1	4	yes	complemented
247	C₄×Q₈	—	4	4	no	—
248	C₄×D₄	—	4	4	no	—
249	C₄×D₄	—	4	4	no	—
250	C₄×D₄	—	4	4	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
265	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
271	#107	—	4	4	no	—
272	C₄⋊C₈	—	2	4	no	—
273	#102	—	2	8	no	—
274	#102	—	4	4	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	C₂⁴	—	2	2	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	—	4	4	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
303	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	4	1	no	—
326	C₄²	—	4	4	no	—
327	C₄²	D₈×C₁₃₉	1	4	yes	—
328	C₄²	C₂×Q₈×C₁₃₉	1	2	yes	—
329	C₄²	#41×C₁₃₉	1	2	yes	—
330	C₂³	—	2	4	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
338	Q₈	—	4	8	no	—
339	D₄	—	2	8	no	—
340	D₄	—	4	8	no	—
341	D₄	—	4	8	no	—
342	D₄	—	4	4	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	8	no	—
364	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
365	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
366	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
367	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
368	C₂×C₄	C₂×D₈×C₁₃₉	1	2	yes	—
369	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
370	C₂×C₄	#137×C₁₃₉	1	2	yes	—
371	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
373	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
374	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
375	C₈	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
384	C₂²	#525×C₁₃₉	1	1	yes	characteristic
385	C₂²	#535×C₁₃₉	1	1	yes	characteristic
386	C₂²	C₂²×D₈×C₁₃₉	1	1	yes	characteristic
387	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
388	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
389	C₂²	#575×C₁₃₉	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	4	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	#474×C₁₃₉	1	4	yes	—
399	C₄	#554×C₁₃₉	1	2	yes	—
400	C₄	#559×C₁₃₉	1	2	yes	—
401	C₂	—	8	4	no	—
402	C₂	#2580×C₁₃₉	1	1	yes	characteristic
403	C₂	C₂×#474×C₁₃₉	1	1	yes	characteristic
404	C₂	#3077×C₁₃₉	1	1	yes	characteristic
405	C₂	#3100×C₁₃₉	1	1	yes	characteristic
406	C₂	#3112×C₁₃₉	1	1	yes	characteristic
407	C₂	#3205×C₁₃₉	1	1	yes	characteristic
408	C₂	#3216×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂×#127×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₄³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
3. #2093×C₁₃₉	C₂	semidirect
4. #2023×C₁₃₉	C₂	semidirect
6. #1947×C₁₃₉	C₂	semidirect
7. #1862×C₁₃₉	C₂	semidirect
8. #1831×C₁₃₉	C₂	semidirect
41. #127×C₁₃₉	Q₈	semidirect
204. #29254	C₁₃₉	direct (N × H)
205. C₁₃₉	#29254	direct (N × H)
206. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
208. #2093	C₂×C₁₃₉	semidirect
209. #2023	C₂×C₁₃₉	semidirect
211. #1947	C₂×C₁₃₉	semidirect
212. #1862	C₂×C₁₃₉	semidirect
213. #1831	C₂×C₁₃₉	semidirect
246. #127	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊Q₈×C₁₃₉	2
C₄×#127×C₁₃₉	2
#2093×C₁₃₉	2
#2023×C₁₃₉	2
#1982×C₁₃₉	2
#1947×C₁₃₉	2
#1862×C₁₃₉	2
#1831×C₁₃₉	2
#29254	139

Subgroups — C139×#29254 #48023850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29254 #48023850