Subgroups — C₁₃₉×#14355 #48008951

Order 35584.

1566 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#381×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#380×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1444×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1442×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1439×C₁₃₉	C₂	1	4	yes	maximal
7	C₄⋊#95×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1434×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
12	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
16	#381×C₁₃₉	—	2	4	no	—
17	#380×C₁₃₉	—	2	4	no	—
18	C₄×C₂²⋊C₄×C₁₃₉	C₄	1	8	yes	complemented
19	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
26	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#95×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
29	C₂³×C₄×C₁₃₉	—	4	4	no	—
30	C₂³×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
31	C₂³×C₄×C₁₃₉	D₄	1	4	yes	—
32	C₂³×C₄×C₁₃₉	Q₈	1	4	yes	—
33	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
34	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
35	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
40	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
45	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
46	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
47	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₁₃₉	—	4	2	no	—
49	C₂×C₂²⋊C₄×C₁₃₉	—	4	4	no	—
50	C₂×C₂²⋊C₄×C₁₃₉	—	4	2	no	—
51	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
52	C₂×C₄²×C₁₃₉	—	4	4	no	—
53	C₂×C₄²×C₁₃₉	C₂×C₄	1	8	yes	—
54	#95×C₁₃₉	—	2	4	no	—
55	#95×C₁₃₉	—	2	2	no	—
56	#95×C₁₃₉	—	2	2	no	—
57	#95×C₁₃₉	—	2	4	no	—
58	#95×C₁₃₉	—	2	8	no	—
59	#95×C₁₃₉	—	4	4	no	—
60	#95×C₁₃₉	—	4	4	no	—
61	#95×C₁₃₉	C₂×C₄	1	4	yes	—
62	#95×C₁₃₉	C₂×C₄	1	4	yes	—
63	C₂⁴×C₁₃₉	—	2	4	no	—
64	C₂⁴×C₁₃₉	—	2	1	no	—
65	C₂⁴×C₁₃₉	—	2	1	no	—
66	C₂⁴×C₁₃₉	—	2	4	no	—
67	C₂⁴×C₁₃₉	—	2	1	no	—
68	C₂⁴×C₁₃₉	—	2	1	no	—
69	C₂⁴×C₁₃₉	C₂²×C₄	1	2	yes	—
70	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
71	C₂⁴×C₁₃₉	C₂×Q₈	1	2	yes	—
72	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
73	C₂²×C₄×C₁₃₉	—	2	4	no	—
74	C₂²×C₄×C₁₃₉	—	2	4	no	—
75	C₂²×C₄×C₁₃₉	—	2	2	no	—
76	C₂²×C₄×C₁₃₉	—	2	4	no	—
77	C₂²×C₄×C₁₃₉	—	2	2	no	—
78	C₂²×C₄×C₁₃₉	—	2	4	no	—
79	C₂²×C₄×C₁₃₉	—	2	2	no	—
80	C₂²×C₄×C₁₃₉	—	2	4	no	—
81	C₂²×C₄×C₁₃₉	—	2	2	no	—
82	C₂²×C₄×C₁₃₉	—	2	2	no	—
83	C₂²×C₄×C₁₃₉	—	2	2	no	—
84	C₂²×C₄×C₁₃₉	—	2	4	no	—
85	C₂²×C₄×C₁₃₉	—	2	4	no	—
86	C₂²×C₄×C₁₃₉	—	2	4	no	—
87	C₂²×C₄×C₁₃₉	—	2	4	no	—
88	C₂²×C₄×C₁₃₉	—	2	4	no	—
89	C₂²×C₄×C₁₃₉	—	2	2	no	—
90	C₂²×C₄×C₁₃₉	—	2	4	no	—
91	C₂²×C₄×C₁₃₉	—	2	4	no	—
92	C₂²×C₄×C₁₃₉	—	2	4	no	—
93	C₂²×C₄×C₁₃₉	—	2	4	no	—
94	C₂²×C₄×C₁₃₉	—	2	4	no	—
95	C₂²×C₄×C₁₃₉	—	2	4	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	—	2	2	no	—
98	C₂²×C₄×C₁₃₉	—	2	2	no	—
99	C₂²×C₄×C₁₃₉	—	4	8	no	—
100	C₂²×C₄×C₁₃₉	—	4	8	no	—
101	C₂²×C₄×C₁₃₉	—	4	8	no	—
102	C₂²×C₄×C₁₃₉	C₄⋊C₄	1	16	yes	complemented
103	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₁₃₉	#41	1	8	yes	—
112	C₄⋊C₄×C₁₃₉	—	4	8	no	—
113	C₄⋊C₄×C₁₃₉	—	4	16	no	—
114	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
115	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
116	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
117	C₄²×C₁₃₉	—	4	8	no	—
118	C₂³×C₁₃₉	—	2	4	no	—
119	C₂³×C₁₃₉	—	2	4	no	—
120	C₂³×C₁₃₉	—	2	2	no	—
121	C₂³×C₁₃₉	—	2	2	no	—
122	C₂³×C₁₃₉	—	2	4	no	—
123	C₂³×C₁₃₉	—	2	4	no	—
124	C₂³×C₁₃₉	—	2	4	no	—
125	C₂³×C₁₃₉	—	2	2	no	—
126	C₂³×C₁₃₉	—	2	2	no	—
127	C₂³×C₁₃₉	—	2	4	no	—
128	C₂³×C₁₃₉	—	2	2	no	—
129	C₂³×C₁₃₉	—	2	2	no	—
130	C₂³×C₁₃₉	—	4	4	no	—
131	C₂³×C₁₃₉	—	4	4	no	—
132	C₂³×C₁₃₉	—	4	4	no	—
133	C₂³×C₁₃₉	—	4	4	no	—
134	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
135	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
136	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
137	C₂³×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
138	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
139	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
140	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
141	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂³×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
143	C₂³×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
144	C₂×C₄×C₁₃₉	—	2	4	no	—
145	C₂×C₄×C₁₃₉	—	2	4	no	—
146	C₂×C₄×C₁₃₉	—	2	4	no	—
147	C₂×C₄×C₁₃₉	—	2	4	no	—
148	C₂×C₄×C₁₃₉	—	2	4	no	—
149	C₂×C₄×C₁₃₉	—	2	4	no	—
150	C₂×C₄×C₁₃₉	—	2	8	no	—
151	C₂×C₄×C₁₃₉	—	2	8	no	—
152	C₂×C₄×C₁₃₉	—	2	4	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	—	2	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	2	no	—
161	C₂×C₄×C₁₃₉	—	4	4	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	4	no	—
166	C₂×C₄×C₁₃₉	—	4	4	no	—
167	C₂×C₄×C₁₃₉	—	4	2	no	—
168	C₂×C₄×C₁₃₉	—	4	2	no	—
169	C₂×C₄×C₁₃₉	—	4	4	no	—
170	C₂×C₄×C₁₃₉	—	4	4	no	—
171	C₂×C₄×C₁₃₉	—	4	4	no	—
172	C₂×C₄×C₁₃₉	—	4	4	no	—
173	C₂×C₄×C₁₃₉	—	4	4	no	—
174	C₂×C₄×C₁₃₉	—	4	4	no	—
175	C₂×C₄×C₁₃₉	—	4	4	no	—
176	C₂×C₄×C₁₃₉	—	4	4	no	—
177	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
178	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
179	C₂×C₄×C₁₃₉	#117	1	8	yes	—
180	C₂²×C₁₃₉	—	2	4	no	—
181	C₂²×C₁₃₉	—	2	4	no	—
182	C₂²×C₁₃₉	—	2	4	no	—
183	C₂²×C₁₃₉	—	4	4	no	—
184	C₂²×C₁₃₉	—	4	4	no	—
185	C₂²×C₁₃₉	—	4	4	no	—
186	C₂²×C₁₃₉	—	4	4	no	—
187	C₂²×C₁₃₉	—	4	4	no	—
188	C₂²×C₁₃₉	—	4	4	no	—
189	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
190	C₂²×C₁₃₉	C₂×#117	1	2	yes	—
191	C₂²×C₁₃₉	#518	1	2	yes	—
192	C₂²×C₁₃₉	#520	1	1	yes	characteristic
193	C₂²×C₁₃₉	#520	1	1	yes	characteristic
194	C₂²×C₁₃₉	#532	1	2	yes	—
195	C₂²×C₁₃₉	#533	1	2	yes	—
196	C₂²×C₁₃₉	#534	1	2	yes	—
197	C₂²×C₁₃₉	#535	1	1	yes	characteristic
198	C₂²×C₁₃₉	#536	1	1	yes	characteristic
199	C₂²×C₁₃₉	#538	1	4	yes	—
200	C₂²×C₁₃₉	#539	1	4	yes	—
201	C₂²×C₁₃₉	#540	1	4	yes	—
202	C₂²×C₁₃₉	#542	1	4	yes	—
203	C₂²×C₁₃₉	#543	1	2	yes	—
204	C₂²×C₁₃₉	#544	1	1	yes	characteristic
205	C₂²×C₁₃₉	#544	1	1	yes	characteristic
206	C₄×C₁₃₉	—	2	4	no	—
207	C₄×C₁₃₉	—	2	4	no	—
208	C₄×C₁₃₉	—	2	8	no	—
209	C₄×C₁₃₉	—	4	4	no	—
210	C₄×C₁₃₉	—	8	2	no	—
211	C₄×C₁₃₉	—	8	4	no	—
212	C₄×C₁₃₉	—	8	2	no	—
213	C₂×C₁₃₉	—	4	4	no	—
214	C₂×C₁₃₉	#2285	1	1	yes	characteristic
215	C₂×C₁₃₉	#2315	1	1	yes	characteristic
216	C₂×C₁₃₉	#2317	1	1	yes	characteristic
217	C₂×C₁₃₉	#2318	1	2	yes	—
218	C₂×C₁₃₉	#2319	1	2	yes	—
219	C₂×C₁₃₉	#2661	1	2	yes	—
220	C₂×C₁₃₉	#2663	1	2	yes	—
221	C₂×C₁₃₉	#2665	1	2	yes	—
222	C₂×C₁₃₉	#2667	1	2	yes	—
223	#14355	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₁₃₉	#14355	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×#381	C₂×C₁₃₉	1	1	yes	characteristic
226	C₂×#380	C₂×C₁₃₉	1	1	yes	characteristic
227	C₂×C₄×C₂²⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
228	#1444	C₂×C₁₃₉	1	2	yes	complemented
229	#1442	C₂×C₁₃₉	1	2	yes	complemented
230	#1439	C₂×C₁₃₉	1	4	yes	—
231	C₄⋊#95	C₂×C₁₃₉	1	2	yes	complemented
232	#1434	C₂×C₁₃₉	1	2	yes	complemented
233	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
238	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
239	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
240	#381	—	2	4	no	—
241	#380	—	2	4	no	—
242	C₄×C₂²⋊C₄	C₄×C₁₃₉	1	8	yes	complemented
243	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
244	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
245	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
246	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
247	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
248	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
249	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
250	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
251	C₂×#95	C₂²×C₁₃₉	1	1	yes	characteristic
252	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
253	C₂³×C₄	—	4	4	no	—
254	C₂³×C₄	C₂×C₄×C₁₃₉	1	4	yes	—
255	C₂³×C₄	D₄×C₁₃₉	1	4	yes	—
256	C₂³×C₄	Q₈×C₁₃₉	1	4	yes	—
257	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
258	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
259	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
260	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
261	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	8	no	—
266	C₂×C₄⋊C₄	—	4	4	no	—
267	C₂×C₄⋊C₄	—	4	4	no	—
268	C₂×C₄⋊C₄	—	4	4	no	—
269	C₂×C₂²⋊C₄	—	2	8	no	—
270	C₂×C₂²⋊C₄	—	2	4	no	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₂²⋊C₄	—	4	2	no	—
273	C₂×C₂²⋊C₄	—	4	4	no	—
274	C₂×C₂²⋊C₄	—	4	2	no	—
275	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
276	C₂×C₄²	—	4	4	no	—
277	C₂×C₄²	C₂×C₄×C₁₃₉	1	8	yes	—
278	#95	—	2	4	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	4	no	—
282	#95	—	2	8	no	—
283	#95	—	4	4	no	—
284	#95	—	4	4	no	—
285	#95	C₂×C₄×C₁₃₉	1	4	yes	—
286	#95	C₂×C₄×C₁₃₉	1	4	yes	—
287	C₂⁴	—	2	4	no	—
288	C₂⁴	—	2	1	no	—
289	C₂⁴	—	2	1	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	1	no	—
292	C₂⁴	—	2	1	no	—
293	C₂⁴	C₂²×C₄×C₁₃₉	1	2	yes	—
294	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
295	C₂⁴	C₂×Q₈×C₁₃₉	1	2	yes	—
296	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	8	no	—
324	C₂²×C₄	—	4	8	no	—
325	C₂²×C₄	—	4	8	no	—
326	C₂²×C₄	C₄⋊C₄×C₁₃₉	1	16	yes	complemented
327	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
328	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
329	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
331	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
333	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
334	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
335	C₂²×C₄	#41×C₁₃₉	1	8	yes	—
336	C₄⋊C₄	—	4	8	no	—
337	C₄⋊C₄	—	4	16	no	—
338	C₂²⋊C₄	—	2	16	no	—
339	C₂²⋊C₄	—	4	8	no	—
340	C₂²⋊C₄	—	4	8	no	—
341	C₄²	—	4	8	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	4	4	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
359	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
360	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
361	C₂³	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
362	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
363	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
364	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
365	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
366	C₂³	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
367	C₂³	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	16	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
402	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
403	C₂×C₄	#117×C₁₃₉	1	8	yes	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	4	no	—
413	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
414	C₂²	C₂×#117×C₁₃₉	1	2	yes	—
415	C₂²	#518×C₁₃₉	1	2	yes	—
416	C₂²	#520×C₁₃₉	1	1	yes	characteristic
417	C₂²	#520×C₁₃₉	1	1	yes	characteristic
418	C₂²	#532×C₁₃₉	1	2	yes	—
419	C₂²	#533×C₁₃₉	1	2	yes	—
420	C₂²	#534×C₁₃₉	1	2	yes	—
421	C₂²	#535×C₁₃₉	1	1	yes	characteristic
422	C₂²	#536×C₁₃₉	1	1	yes	characteristic
423	C₂²	#538×C₁₃₉	1	4	yes	—
424	C₂²	#539×C₁₃₉	1	4	yes	—
425	C₂²	#540×C₁₃₉	1	4	yes	—
426	C₂²	#542×C₁₃₉	1	4	yes	—
427	C₂²	#543×C₁₃₉	1	2	yes	—
428	C₂²	#544×C₁₃₉	1	1	yes	characteristic
429	C₂²	#544×C₁₃₉	1	1	yes	characteristic
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	2	8	no	—
433	C₄	—	4	4	no	—
434	C₄	—	8	2	no	—
435	C₄	—	8	4	no	—
436	C₄	—	8	2	no	—
437	C₂	—	4	4	no	—
438	C₂	#2285×C₁₃₉	1	1	yes	characteristic
439	C₂	#2315×C₁₃₉	1	1	yes	characteristic
440	C₂	#2317×C₁₃₉	1	1	yes	characteristic
441	C₂	#2318×C₁₃₉	1	2	yes	—
442	C₂	#2319×C₁₃₉	1	2	yes	—
443	C₂	#2661×C₁₃₉	1	2	yes	—
444	C₂	#2663×C₁₃₉	1	2	yes	—
445	C₂	#2665×C₁₃₉	1	2	yes	—
446	C₂	#2667×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₉
prime radical	C₂⁵×C₁₃₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1444×C₁₃₉	C₂	semidirect
5. #1442×C₁₃₉	C₂	semidirect
7. C₄⋊#95×C₁₃₉	C₂	semidirect
8. #1434×C₁₃₉	C₂	semidirect
18. C₄×C₂²⋊C₄×C₁₃₉	C₄	semidirect
102. C₂²×C₄×C₁₃₉	C₄⋊C₄	semidirect
223. #14355	C₁₃₉	direct (N × H)
224. C₁₃₉	#14355	direct (N × H)
228. #1444	C₂×C₁₃₉	semidirect
229. #1442	C₂×C₁₃₉	semidirect
231. C₄⋊#95	C₂×C₁₃₉	semidirect
232. #1434	C₂×C₁₃₉	semidirect
242. C₄×C₂²⋊C₄	C₄×C₁₃₉	semidirect
326. C₂²×C₄	C₄⋊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×#381×C₁₃₉	2
C₂×#380×C₁₃₉	2
C₂×C₄×C₂²⋊C₄×C₁₃₉	2
#1444×C₁₃₉	2
#1442×C₁₃₉	2
#1439×C₁₃₉	2
C₄⋊#95×C₁₃₉	2
#1434×C₁₃₉	2
#14355	139

Subgroups — C139×#14355 #48008951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#14355 #48008951