Subgroups — C₁₃₉×#29304 #48023900

Order 35584.

770 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2084×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2083×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2058×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2057×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#1944×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1943×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1854×C₁₃₉	C₂	1	2	yes	maximal
10	#1854×C₁₃₉	C₂	1	2	yes	maximal
11	#1749×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₁₃₉	—	2	1	no	—
14	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#97×C₁₃₉	C₂²	1	2	yes	—
23	#391×C₁₃₉	—	2	1	no	—
24	#389×C₁₃₉	—	2	1	no	—
25	#389×C₁₃₉	C₂²	1	1	yes	characteristic
26	#389×C₁₃₉	C₂²	1	1	yes	characteristic
27	#389×C₁₃₉	C₂²	1	1	yes	characteristic
28	#389×C₁₃₉	C₂²	1	1	yes	characteristic
29	#389×C₁₃₉	C₂²	1	2	yes	—
30	#385×C₁₃₉	—	2	1	no	—
31	#385×C₁₃₉	—	2	1	no	—
32	#384×C₁₃₉	C₂²	1	1	yes	characteristic
33	#380×C₁₃₉	—	2	1	no	—
34	#380×C₁₃₉	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
36	C₄×C₄⋊C₄×C₁₃₉	—	2	1	no	—
37	#340×C₁₃₉	C₂²	1	2	yes	—
38	#340×C₁₃₉	C₂²	1	2	yes	—
39	#340×C₁₃₉	C₂²	1	2	yes	—
40	#340×C₁₃₉	C₂²	1	2	yes	—
41	#336×C₁₃₉	C₂²	1	1	yes	characteristic
42	#336×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃₉	—	2	1	no	—
44	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₉	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
50	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
51	#117×C₁₃₉	—	2	2	no	—
52	#117×C₁₃₉	—	2	2	no	—
53	#117×C₁₃₉	—	4	2	no	—
54	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
71	C₂×C₄²×C₁₃₉	—	2	1	no	—
72	C₂×C₄²×C₁₃₉	—	2	1	no	—
73	C₂×C₄²×C₁₃₉	—	4	2	no	—
74	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
78	#107×C₁₃₉	—	2	4	no	—
79	#107×C₁₃₉	—	4	2	no	—
80	#106×C₁₃₉	—	2	4	no	—
81	#106×C₁₃₉	—	4	2	no	—
82	C₂²⋊C₈×C₁₃₉	Q₈	1	8	yes	complemented
83	#97×C₁₃₉	—	4	2	no	—
84	#95×C₁₃₉	—	2	1	no	—
85	#95×C₁₃₉	—	2	1	no	—
86	#95×C₁₃₉	—	2	1	no	—
87	#95×C₁₃₉	—	2	1	no	—
88	#95×C₁₃₉	—	2	2	no	—
89	#95×C₁₃₉	—	2	2	no	—
90	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
91	C₂×Q₈×C₁₃₉	—	4	2	no	—
92	C₂×Q₈×C₁₃₉	—	4	2	no	—
93	C₂×Q₈×C₁₃₉	—	4	2	no	—
94	C₂²×C₄×C₁₃₉	—	2	1	no	—
95	C₂²×C₄×C₁₃₉	—	2	1	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	—	2	1	no	—
98	C₂²×C₄×C₁₃₉	—	2	1	no	—
99	C₂²×C₄×C₁₃₉	—	2	2	no	—
100	C₂²×C₄×C₁₃₉	—	2	2	no	—
101	C₂²×C₄×C₁₃₉	—	2	1	no	—
102	C₂²×C₄×C₁₃₉	—	2	1	no	—
103	C₂²×C₄×C₁₃₉	—	2	2	no	—
104	C₂²×C₄×C₁₃₉	—	2	2	no	—
105	C₂²×C₄×C₁₃₉	—	4	1	no	—
106	C₂²×C₄×C₁₃₉	—	4	1	no	—
107	C₂²×C₄×C₁₃₉	—	4	1	no	—
108	C₂²×C₄×C₁₃₉	—	4	1	no	—
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	1	yes	characteristic
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
115	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₁₃₉	—	2	2	no	—
117	C₂×C₈×C₁₃₉	—	2	2	no	—
118	C₂×C₈×C₁₃₉	—	2	2	no	—
119	C₂×C₈×C₁₃₉	—	2	2	no	—
120	C₂×C₈×C₁₃₉	C₂×Q₈	1	4	yes	—
121	C₂×C₈×C₁₃₉	C₂×Q₈	1	4	yes	—
122	C₄⋊C₄×C₁₃₉	—	2	1	no	—
123	C₄⋊C₄×C₁₃₉	—	2	1	no	—
124	C₄⋊C₄×C₁₃₉	—	2	2	no	—
125	C₄⋊C₄×C₁₃₉	—	2	2	no	—
126	C₄⋊C₄×C₁₃₉	—	2	2	no	—
127	C₄⋊C₄×C₁₃₉	—	2	2	no	—
128	C₄⋊C₄×C₁₃₉	—	2	2	no	—
129	C₄⋊C₄×C₁₃₉	—	2	2	no	—
130	C₄⋊C₄×C₁₃₉	—	4	2	no	—
131	C₄⋊C₄×C₁₃₉	—	4	2	no	—
132	C₄⋊C₄×C₁₃₉	—	4	2	no	—
133	C₄⋊C₄×C₁₃₉	—	4	4	no	—
134	C₄⋊C₄×C₁₃₉	—	4	2	no	—
135	C₄⋊C₄×C₁₃₉	—	4	2	no	—
136	C₄⋊C₄×C₁₃₉	—	4	2	no	—
137	C₄⋊C₄×C₁₃₉	—	4	2	no	—
138	C₄⋊C₄×C₁₃₉	#41	1	2	yes	—
139	C₄⋊C₄×C₁₃₉	#41	1	2	yes	—
140	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
141	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
142	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
143	C₄²×C₁₃₉	—	2	4	no	—
144	C₄²×C₁₃₉	—	2	2	no	—
145	C₄²×C₁₃₉	—	2	2	no	—
146	C₄²×C₁₃₉	—	4	1	no	—
147	C₄²×C₁₃₉	—	4	1	no	—
148	C₄²×C₁₃₉	—	4	2	no	—
149	C₂³×C₁₃₉	—	2	1	no	—
150	C₂³×C₁₃₉	—	2	1	no	—
151	C₂³×C₁₃₉	—	2	1	no	—
152	C₂³×C₁₃₉	—	2	1	no	—
153	C₂³×C₁₃₉	—	2	1	no	—
154	C₂³×C₁₃₉	—	2	1	no	—
155	C₂³×C₁₃₉	C₄⋊Q₈	1	2	yes	—
156	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₃₉	—	8	4	no	—
158	C₂×C₄×C₁₃₉	—	2	1	no	—
159	C₂×C₄×C₁₃₉	—	2	1	no	—
160	C₂×C₄×C₁₃₉	—	2	1	no	—
161	C₂×C₄×C₁₃₉	—	2	1	no	—
162	C₂×C₄×C₁₃₉	—	2	1	no	—
163	C₂×C₄×C₁₃₉	—	2	1	no	—
164	C₂×C₄×C₁₃₉	—	2	4	no	—
165	C₂×C₄×C₁₃₉	—	2	4	no	—
166	C₂×C₄×C₁₃₉	—	2	2	no	—
167	C₂×C₄×C₁₃₉	—	2	2	no	—
168	C₂×C₄×C₁₃₉	—	2	1	no	—
169	C₂×C₄×C₁₃₉	—	2	1	no	—
170	C₂×C₄×C₁₃₉	—	2	1	no	—
171	C₂×C₄×C₁₃₉	—	2	1	no	—
172	C₂×C₄×C₁₃₉	—	2	1	no	—
173	C₂×C₄×C₁₃₉	—	2	1	no	—
174	C₂×C₄×C₁₃₉	—	4	4	no	—
175	C₂×C₄×C₁₃₉	—	4	4	no	—
176	C₂×C₄×C₁₃₉	—	4	1	no	—
177	C₂×C₄×C₁₃₉	—	4	1	no	—
178	C₂×C₄×C₁₃₉	—	4	1	no	—
179	C₂×C₄×C₁₃₉	—	4	1	no	—
180	C₂×C₄×C₁₃₉	—	4	2	no	—
181	C₂×C₄×C₁₃₉	—	4	1	no	—
182	C₂×C₄×C₁₃₉	—	4	1	no	—
183	C₂×C₄×C₁₃₉	—	4	2	no	—
184	C₂×C₄×C₁₃₉	—	4	2	no	—
185	C₂×C₄×C₁₃₉	—	4	2	no	—
186	C₂×C₄×C₁₃₉	—	4	1	no	—
187	C₂×C₄×C₁₃₉	—	4	1	no	—
188	C₂×C₄×C₁₃₉	—	4	2	no	—
189	C₂×C₄×C₁₃₉	—	4	1	no	—
190	C₂×C₄×C₁₃₉	—	4	1	no	—
191	C₂×C₄×C₁₃₉	—	4	2	no	—
192	C₂×C₄×C₁₃₉	C₄⋊Q₈	1	2	yes	—
193	C₂×C₄×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₁₃₉	#137	1	2	yes	—
195	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
196	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
199	C₈×C₁₃₉	—	2	4	no	—
200	C₈×C₁₃₉	—	2	4	no	—
201	C₂²×C₁₃₉	—	2	2	no	—
202	C₂²×C₁₃₉	—	2	2	no	—
203	C₂²×C₁₃₉	—	2	2	no	—
204	C₂²×C₁₃₉	—	4	1	no	—
205	C₂²×C₁₃₉	—	4	1	no	—
206	C₂²×C₁₃₉	—	4	1	no	—
207	C₂²×C₁₃₉	—	4	1	no	—
208	C₂²×C₁₃₉	#525	1	1	yes	characteristic
209	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
210	C₂²×C₁₃₉	#534	1	1	yes	characteristic
211	C₂²×C₁₃₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂²×C₁₃₉	C₂×#137	1	1	yes	characteristic
213	C₂²×C₁₃₉	#575	1	1	yes	characteristic
214	C₂²×C₁₃₉	#575	1	1	yes	characteristic
215	C₄×C₁₃₉	—	2	2	no	—
216	C₄×C₁₃₉	—	2	2	no	—
217	C₄×C₁₃₉	—	2	2	no	—
218	C₄×C₁₃₉	—	4	2	no	—
219	C₄×C₁₃₉	—	4	2	no	—
220	C₄×C₁₃₉	—	4	1	no	—
221	C₄×C₁₃₉	—	4	1	no	—
222	C₄×C₁₃₉	—	8	2	no	—
223	C₄×C₁₃₉	—	8	1	no	—
224	C₄×C₁₃₉	—	8	2	no	—
225	C₄×C₁₃₉	—	8	1	no	—
226	C₄×C₁₃₉	#554	1	2	yes	—
227	C₄×C₁₃₉	#554	1	2	yes	—
228	C₂×C₁₃₉	—	4	2	no	—
229	C₂×C₁₃₉	#2583	1	1	yes	characteristic
230	C₂×C₁₃₉	#3115	1	1	yes	characteristic
231	C₂×C₁₃₉	#3116	1	1	yes	characteristic
232	C₂×C₁₃₉	#3162	1	1	yes	characteristic
233	C₂×C₁₃₉	#3165	1	1	yes	characteristic
234	C₂×C₁₃₉	#3194	1	1	yes	characteristic
235	C₂×C₁₃₉	#3196	1	1	yes	characteristic
236	#29304	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₁₃₉	#29304	1	1	yes	characteristic, direct product factor, Sylow
238	#2857	C₂×C₁₃₉	1	1	yes	characteristic
239	#2296	C₂×C₁₃₉	1	1	yes	characteristic
240	#2084	C₂×C₁₃₉	1	1	yes	characteristic, complemented
241	#2083	C₂×C₁₃₉	1	1	yes	characteristic, complemented
242	#2058	C₂×C₁₃₉	1	1	yes	characteristic, complemented
243	#2057	C₂×C₁₃₉	1	1	yes	characteristic, complemented
244	#1944	C₂×C₁₃₉	1	2	yes	complemented
245	#1943	C₂×C₁₃₉	1	2	yes	complemented
246	#1854	C₂×C₁₃₉	1	2	yes	—
247	#1854	C₂×C₁₃₉	1	2	yes	—
248	#1749	C₂×C₁₃₉	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
250	C₂×C₂²⋊Q₈	—	2	1	no	—
251	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
252	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
253	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
254	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
255	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
256	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
257	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
259	C₂×#97	C₂²×C₁₃₉	1	2	yes	—
260	#391	—	2	1	no	—
261	#389	—	2	1	no	—
262	#389	C₂²×C₁₃₉	1	1	yes	characteristic
263	#389	C₂²×C₁₃₉	1	1	yes	characteristic
264	#389	C₂²×C₁₃₉	1	2	yes	—
265	#389	C₂²×C₁₃₉	1	1	yes	characteristic
266	#389	C₂²×C₁₃₉	1	1	yes	characteristic
267	#385	—	2	1	no	—
268	#385	—	2	1	no	—
269	#384	C₂²×C₁₃₉	1	1	yes	characteristic
270	#380	—	2	1	no	—
271	#380	C₂²×C₁₃₉	1	2	yes	—
272	C₄×C₄⋊C₄	—	2	1	no	—
273	C₄×C₄⋊C₄	—	2	1	no	—
274	#340	C₂²×C₁₃₉	1	2	yes	—
275	#340	C₂²×C₁₃₉	1	2	yes	—
276	#340	C₂²×C₁₃₉	1	2	yes	—
277	#340	C₂²×C₁₃₉	1	2	yes	—
278	#336	C₂²×C₁₃₉	1	1	yes	characteristic
279	#336	C₂²×C₁₃₉	1	1	yes	characteristic
280	C₂²×Q₈	—	2	1	no	—
281	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
282	C₂³×C₄	D₄×C₁₃₉	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
285	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
286	C₄⋊Q₈	—	4	2	no	—
287	C₂²⋊Q₈	—	4	4	no	—
288	#117	—	2	2	no	—
289	#117	—	2	2	no	—
290	#117	—	4	2	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	4	2	no	—
311	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
312	C₂×C₄²	D₄×C₁₃₉	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
315	#107	—	2	4	no	—
316	#107	—	4	2	no	—
317	#106	—	2	4	no	—
318	#106	—	4	2	no	—
319	C₂²⋊C₈	Q₈×C₁₃₉	1	8	yes	complemented
320	#97	—	4	2	no	—
321	#95	—	2	1	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
328	C₂×Q₈	—	4	2	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
352	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	C₂×Q₈×C₁₃₉	1	4	yes	—
358	C₂×C₈	C₂×Q₈×C₁₃₉	1	4	yes	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	#41×C₁₃₉	1	2	yes	—
376	C₄⋊C₄	#41×C₁₃₉	1	2	yes	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₄²	—	2	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	4	1	no	—
384	C₄²	—	4	1	no	—
385	C₄²	—	4	2	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	C₄⋊Q₈×C₁₃₉	1	2	yes	—
393	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
394	Q₈	—	8	4	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	C₄⋊Q₈×C₁₃₉	1	2	yes	—
430	C₂×C₄	AGL(1,ℤ/8)×C₁₃₉	1	2	yes	—
431	C₂×C₄	#137×C₁₃₉	1	2	yes	—
432	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
433	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
435	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
436	C₈	—	2	4	no	—
437	C₈	—	2	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	#525×C₁₃₉	1	1	yes	characteristic
446	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
447	C₂²	#534×C₁₃₉	1	1	yes	characteristic
448	C₂²	C₂×AGL(1,ℤ/8)×C₁₃₉	1	1	yes	characteristic
449	C₂²	C₂×#137×C₁₃₉	1	1	yes	characteristic
450	C₂²	#575×C₁₃₉	1	1	yes	characteristic
451	C₂²	#575×C₁₃₉	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	1	no	—
462	C₄	—	8	1	no	—
463	C₄	#554×C₁₃₉	1	2	yes	—
464	C₄	#554×C₁₃₉	1	2	yes	—
465	C₂	—	4	2	no	—
466	C₂	#2583×C₁₃₉	1	1	yes	characteristic
467	C₂	#3115×C₁₃₉	1	1	yes	characteristic
468	C₂	#3116×C₁₃₉	1	1	yes	characteristic
469	C₂	#3162×C₁₃₉	1	1	yes	characteristic
470	C₂	#3165×C₁₃₉	1	1	yes	characteristic
471	C₂	#3194×C₁₃₉	1	1	yes	characteristic
472	C₂	#3196×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂×D₄
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
3. #2084×C₁₃₉	C₂	semidirect
4. #2083×C₁₃₉	C₂	semidirect
5. #2058×C₁₃₉	C₂	semidirect
6. #2057×C₁₃₉	C₂	semidirect
7. #1944×C₁₃₉	C₂	semidirect
8. #1943×C₁₃₉	C₂	semidirect
82. C₂²⋊C₈×C₁₃₉	Q₈	semidirect
236. #29304	C₁₃₉	direct (N × H)
237. C₁₃₉	#29304	direct (N × H)
240. #2084	C₂×C₁₃₉	semidirect
241. #2083	C₂×C₁₃₉	semidirect
242. #2058	C₂×C₁₃₉	semidirect
243. #2057	C₂×C₁₃₉	semidirect
244. #1944	C₂×C₁₃₉	semidirect
245. #1943	C₂×C₁₃₉	semidirect
319. C₂²⋊C₈	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2857×C₁₃₉	2
#2296×C₁₃₉	2
#2084×C₁₃₉	2
#2083×C₁₃₉	2
#2058×C₁₃₉	2
#2057×C₁₃₉	2
#1944×C₁₃₉	2
#1943×C₁₃₉	2
#1854×C₁₃₉	2
#1749×C₁₃₉	2
#29304	139

Subgroups — C139×#29304 #48023900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#29304 #48023900