Subgroups — C₁₃₉×#14441 #48009037

Order 35584.

1390 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#389×C₁₃₉	C₂	1	2	yes	maximal
2	C₂×#389×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#387×C₁₃₉	C₂	1	2	yes	maximal
4	#1444×C₁₃₉	C₂	1	2	yes	maximal
5	#1441×C₁₃₉	C₂	1	2	yes	maximal
6	#1441×C₁₃₉	C₂	1	2	yes	maximal
7	#1436×C₁₃₉	C₂	1	2	yes	maximal
8	C₄⋊#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	C₄⋊#95×C₁₃₉	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
21	#389×C₁₃₉	—	2	8	no	—
22	#389×C₁₃₉	C₄	1	8	yes	complemented
23	#387×C₁₃₉	—	2	8	no	—
24	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
32	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
34	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
48	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
51	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
52	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
53	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
54	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
59	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	4	1	no	—
61	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
62	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₃₉	Q₈	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	Q₈	1	4	yes	—
70	C₂×C₄²×C₁₃₉	—	2	4	no	—
71	C₂×C₄²×C₁₃₉	—	2	4	no	—
72	C₂×C₄²×C₁₃₉	—	4	1	no	—
73	C₂×C₄²×C₁₃₉	—	4	1	no	—
74	C₂×C₄²×C₁₃₉	—	4	2	no	—
75	C₂×C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
76	#95×C₁₃₉	—	2	4	no	—
77	#95×C₁₃₉	—	2	4	no	—
78	#95×C₁₃₉	—	2	4	no	—
79	#95×C₁₃₉	—	2	4	no	—
80	#95×C₁₃₉	—	2	4	no	—
81	#95×C₁₃₉	—	2	4	no	—
82	#95×C₁₃₉	—	2	4	no	—
83	#95×C₁₃₉	—	4	2	no	—
84	#95×C₁₃₉	—	4	2	no	—
85	#95×C₁₃₉	C₂×C₄	1	8	yes	—
86	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
87	C₂²×C₄×C₁₃₉	—	2	2	no	—
88	C₂²×C₄×C₁₃₉	—	2	2	no	—
89	C₂²×C₄×C₁₃₉	—	2	1	no	—
90	C₂²×C₄×C₁₃₉	—	2	1	no	—
91	C₂²×C₄×C₁₃₉	—	2	1	no	—
92	C₂²×C₄×C₁₃₉	—	2	1	no	—
93	C₂²×C₄×C₁₃₉	—	2	1	no	—
94	C₂²×C₄×C₁₃₉	—	2	1	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	2	1	no	—
97	C₂²×C₄×C₁₃₉	—	2	1	no	—
98	C₂²×C₄×C₁₃₉	—	2	1	no	—
99	C₂²×C₄×C₁₃₉	—	2	1	no	—
100	C₂²×C₄×C₁₃₉	—	2	1	no	—
101	C₂²×C₄×C₁₃₉	—	2	1	no	—
102	C₂²×C₄×C₁₃₉	—	2	2	no	—
103	C₂²×C₄×C₁₃₉	—	2	2	no	—
104	C₂²×C₄×C₁₃₉	—	2	2	no	—
105	C₂²×C₄×C₁₃₉	—	2	2	no	—
106	C₂²×C₄×C₁₃₉	—	2	2	no	—
107	C₂²×C₄×C₁₃₉	—	2	2	no	—
108	C₂²×C₄×C₁₃₉	—	2	2	no	—
109	C₂²×C₄×C₁₃₉	—	2	2	no	—
110	C₂²×C₄×C₁₃₉	—	2	2	no	—
111	C₂²×C₄×C₁₃₉	—	2	2	no	—
112	C₂²×C₄×C₁₃₉	—	2	2	no	—
113	C₂²×C₄×C₁₃₉	—	2	2	no	—
114	C₂²×C₄×C₁₃₉	—	2	2	no	—
115	C₂²×C₄×C₁₃₉	—	2	2	no	—
116	C₂²×C₄×C₁₃₉	—	2	2	no	—
117	C₂²×C₄×C₁₃₉	—	2	2	no	—
118	C₂²×C₄×C₁₃₉	—	2	2	no	—
119	C₂²×C₄×C₁₃₉	—	2	2	no	—
120	C₂²×C₄×C₁₃₉	—	2	2	no	—
121	C₂²×C₄×C₁₃₉	—	2	2	no	—
122	C₂²×C₄×C₁₃₉	—	2	2	no	—
123	C₂²×C₄×C₁₃₉	—	2	2	no	—
124	C₂²×C₄×C₁₃₉	—	2	2	no	—
125	C₂²×C₄×C₁₃₉	—	2	2	no	—
126	C₂²×C₄×C₁₃₉	—	2	2	no	—
127	C₂²×C₄×C₁₃₉	—	2	2	no	—
128	C₂²×C₄×C₁₃₉	—	2	2	no	—
129	C₂²×C₄×C₁₃₉	—	2	2	no	—
130	C₂²×C₄×C₁₃₉	—	2	2	no	—
131	C₂²×C₄×C₁₃₉	—	2	2	no	—
132	C₂²×C₄×C₁₃₉	—	2	2	no	—
133	C₂²×C₄×C₁₃₉	—	2	2	no	—
134	C₂²×C₄×C₁₃₉	—	2	2	no	—
135	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
136	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
145	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
146	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
147	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
148	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
149	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
150	C₄⋊C₄×C₁₃₉	—	2	16	no	—
151	C₄⋊C₄×C₁₃₉	—	4	4	no	—
152	C₄⋊C₄×C₁₃₉	—	4	4	no	—
153	C₄⋊C₄×C₁₃₉	—	4	4	no	—
154	C₄⋊C₄×C₁₃₉	—	4	8	no	—
155	C₄⋊C₄×C₁₃₉	—	4	4	no	—
156	C₄⋊C₄×C₁₃₉	—	4	4	no	—
157	C₄⋊C₄×C₁₃₉	—	4	8	no	—
158	C₄⋊C₄×C₁₃₉	C₄⋊C₄	1	16	yes	complemented
159	C₄²×C₁₃₉	—	4	4	no	—
160	C₄²×C₁₃₉	—	4	8	no	—
161	C₂³×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
162	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
163	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
164	C₂³×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
165	C₂³×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
166	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
167	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
168	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂³×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂³×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂³×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂³×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
175	C₂³×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
176	C₂×C₄×C₁₃₉	—	2	4	no	—
177	C₂×C₄×C₁₃₉	—	2	2	no	—
178	C₂×C₄×C₁₃₉	—	2	2	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	2	no	—
181	C₂×C₄×C₁₃₉	—	2	2	no	—
182	C₂×C₄×C₁₃₉	—	2	2	no	—
183	C₂×C₄×C₁₃₉	—	2	4	no	—
184	C₂×C₄×C₁₃₉	—	2	2	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	2	no	—
187	C₂×C₄×C₁₃₉	—	2	2	no	—
188	C₂×C₄×C₁₃₉	—	2	2	no	—
189	C₂×C₄×C₁₃₉	—	2	2	no	—
190	C₂×C₄×C₁₃₉	—	2	2	no	—
191	C₂×C₄×C₁₃₉	—	2	2	no	—
192	C₂×C₄×C₁₃₉	—	2	2	no	—
193	C₂×C₄×C₁₃₉	—	2	2	no	—
194	C₂×C₄×C₁₃₉	—	2	2	no	—
195	C₂×C₄×C₁₃₉	—	2	2	no	—
196	C₂×C₄×C₁₃₉	—	2	4	no	—
197	C₂×C₄×C₁₃₉	—	2	4	no	—
198	C₂×C₄×C₁₃₉	—	2	4	no	—
199	C₂×C₄×C₁₃₉	—	2	4	no	—
200	C₂×C₄×C₁₃₉	—	2	4	no	—
201	C₂×C₄×C₁₃₉	—	2	4	no	—
202	C₂×C₄×C₁₃₉	—	2	4	no	—
203	C₂×C₄×C₁₃₉	—	2	4	no	—
204	C₂×C₄×C₁₃₉	—	2	4	no	—
205	C₂×C₄×C₁₃₉	—	2	4	no	—
206	C₂×C₄×C₁₃₉	—	2	4	no	—
207	C₂×C₄×C₁₃₉	—	2	4	no	—
208	C₂×C₄×C₁₃₉	—	2	4	no	—
209	C₂×C₄×C₁₃₉	—	4	2	no	—
210	C₂×C₄×C₁₃₉	—	4	2	no	—
211	C₂×C₄×C₁₃₉	—	4	2	no	—
212	C₂×C₄×C₁₃₉	—	4	2	no	—
213	C₂×C₄×C₁₃₉	—	4	2	no	—
214	C₂×C₄×C₁₃₉	—	4	2	no	—
215	C₂×C₄×C₁₃₉	—	4	2	no	—
216	C₂×C₄×C₁₃₉	—	4	2	no	—
217	C₂×C₄×C₁₃₉	—	4	2	no	—
218	C₂×C₄×C₁₃₉	—	4	2	no	—
219	C₂×C₄×C₁₃₉	—	4	2	no	—
220	C₂×C₄×C₁₃₉	—	4	2	no	—
221	C₂×C₄×C₁₃₉	—	4	2	no	—
222	C₂×C₄×C₁₃₉	—	4	2	no	—
223	C₂×C₄×C₁₃₉	—	4	2	no	—
224	C₂×C₄×C₁₃₉	—	4	2	no	—
225	C₂×C₄×C₁₃₉	—	4	2	no	—
226	C₂×C₄×C₁₃₉	—	4	2	no	—
227	C₂×C₄×C₁₃₉	—	4	2	no	—
228	C₂×C₄×C₁₃₉	—	4	2	no	—
229	C₂×C₄×C₁₃₉	—	4	2	no	—
230	C₂×C₄×C₁₃₉	—	4	2	no	—
231	C₂×C₄×C₁₃₉	—	4	2	no	—
232	C₂×C₄×C₁₃₉	—	4	2	no	—
233	C₂×C₄×C₁₃₉	—	4	2	no	—
234	C₂×C₄×C₁₃₉	—	4	2	no	—
235	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
236	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	8	yes	—
237	C₂×C₄×C₁₃₉	C₄×D₄	1	4	yes	—
238	C₂×C₄×C₁₃₉	C₄×Q₈	1	4	yes	—
239	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₂²×C₁₃₉	C₂×C₄×D₄	1	1	yes	characteristic
241	C₂²×C₁₃₉	C₂×C₄×Q₈	1	1	yes	characteristic
242	C₂²×C₁₃₉	#518	1	1	yes	characteristic
243	C₂²×C₁₃₉	#519	1	1	yes	characteristic
244	C₂²×C₁₃₉	#520	1	1	yes	characteristic
245	C₂²×C₁₃₉	#520	1	1	yes	characteristic
246	C₂²×C₁₃₉	#534	1	1	yes	characteristic
247	C₂²×C₁₃₉	#537	1	1	yes	characteristic
248	C₂²×C₁₃₉	#537	1	1	yes	characteristic
249	C₂²×C₁₃₉	#537	1	1	yes	characteristic
250	C₂²×C₁₃₉	#538	1	1	yes	characteristic
251	C₂²×C₁₃₉	#538	1	1	yes	characteristic
252	C₂²×C₁₃₉	#539	1	1	yes	characteristic
253	C₂²×C₁₃₉	#539	1	1	yes	characteristic
254	C₂²×C₁₃₉	#543	1	1	yes	characteristic
255	C₂²×C₁₃₉	#544	1	1	yes	characteristic
256	C₂²×C₁₃₉	#544	1	1	yes	characteristic
257	C₂²×C₁₃₉	#544	1	1	yes	characteristic
258	C₂²×C₁₃₉	D₄²	1	1	yes	characteristic
259	C₂²×C₁₃₉	#547	1	1	yes	characteristic
260	C₂²×C₁₃₉	#547	1	1	yes	characteristic
261	C₂²×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
262	C₂²×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
263	C₂²×C₁₃₉	D₄×Q₈	1	1	yes	characteristic
264	C₂²×C₁₃₉	#550	1	1	yes	characteristic
265	C₂²×C₁₃₉	#554	1	1	yes	characteristic
266	C₂²×C₁₃₉	#556	1	1	yes	characteristic
267	C₂²×C₁₃₉	#557	1	1	yes	characteristic
268	C₂²×C₁₃₉	#557	1	1	yes	characteristic
269	C₂²×C₁₃₉	Q₈²	1	1	yes	characteristic
270	C₂²×C₁₃₉	#562	1	1	yes	characteristic
271	C₂²×C₁₃₉	#563	1	1	yes	characteristic
272	C₂²×C₁₃₉	#563	1	1	yes	characteristic
273	C₂²×C₁₃₉	#564	1	1	yes	characteristic
274	C₄×C₁₃₉	—	2	4	no	—
275	C₄×C₁₃₉	—	2	4	no	—
276	C₄×C₁₃₉	—	2	4	no	—
277	C₄×C₁₃₉	—	2	8	no	—
278	C₄×C₁₃₉	—	4	4	no	—
279	C₄×C₁₃₉	—	4	4	no	—
280	C₄×C₁₃₉	—	4	4	no	—
281	C₄×C₁₃₉	—	8	2	no	—
282	C₄×C₁₃₉	—	8	2	no	—
283	C₂×C₁₃₉	#2316	1	1	yes	characteristic
284	C₂×C₁₃₉	#2325	1	1	yes	characteristic
285	C₂×C₁₃₉	#2329	1	1	yes	characteristic
286	C₂×C₁₃₉	D₄×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₁₃₉	Q₈×C₄⋊C₄	1	1	yes	characteristic
288	C₂×C₁₃₉	#2365	1	1	yes	characteristic
289	C₂×C₁₃₉	#2382	1	1	yes	characteristic
290	C₂×C₁₃₉	#2682	1	1	yes	characteristic
291	C₂×C₁₃₉	#2683	1	1	yes	characteristic
292	C₂×C₁₃₉	#2726	1	1	yes	characteristic
293	C₂×C₁₃₉	#2726	1	1	yes	characteristic
294	C₂×C₁₃₉	#2727	1	1	yes	characteristic
295	C₂×C₁₃₉	#2734	1	1	yes	characteristic
296	C₂×C₁₃₉	#2805	1	1	yes	characteristic
297	C₂×C₁₃₉	#2806	1	1	yes	characteristic
298	#14441	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₁₃₉	#14441	1	1	yes	characteristic, direct product factor, Sylow
300	C₂×#389	C₂×C₁₃₉	1	2	yes	—
301	C₂×#389	C₂×C₁₃₉	1	1	yes	characteristic
302	C₂×#387	C₂×C₁₃₉	1	2	yes	—
303	#1444	C₂×C₁₃₉	1	2	yes	—
304	#1441	C₂×C₁₃₉	1	2	yes	—
305	#1441	C₂×C₁₃₉	1	2	yes	—
306	#1436	C₂×C₁₃₉	1	2	yes	—
307	C₄⋊#95	C₂×C₁₃₉	1	1	yes	characteristic
308	C₄⋊#95	C₂×C₁₃₉	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
310	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
311	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
312	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
313	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
314	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
315	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
316	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
317	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
318	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
319	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
320	#389	—	2	8	no	—
321	#389	C₄×C₁₃₉	1	8	yes	complemented
322	#387	—	2	8	no	—
323	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
324	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
325	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
326	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
327	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
328	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
329	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
330	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
331	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
332	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
333	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
334	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
335	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
336	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
337	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
338	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
339	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
342	C₂×C₄⋊C₄	—	2	4	no	—
343	C₂×C₄⋊C₄	—	2	4	no	—
344	C₂×C₄⋊C₄	—	2	4	no	—
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	4	1	no	—
350	C₂×C₄⋊C₄	—	4	1	no	—
351	C₂×C₄⋊C₄	—	4	1	no	—
352	C₂×C₄⋊C₄	—	4	1	no	—
353	C₂×C₄⋊C₄	—	4	1	no	—
354	C₂×C₄⋊C₄	—	4	1	no	—
355	C₂×C₄⋊C₄	—	4	2	no	—
356	C₂×C₄⋊C₄	—	4	1	no	—
357	C₂×C₄⋊C₄	—	4	1	no	—
358	C₂×C₄⋊C₄	—	4	1	no	—
359	C₂×C₄⋊C₄	—	4	1	no	—
360	C₂×C₄⋊C₄	—	4	2	no	—
361	C₂×C₄⋊C₄	—	4	2	no	—
362	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	—
363	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
364	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	4	yes	—
365	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
366	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
367	C₂×C₄⋊C₄	Q₈×C₁₃₉	1	4	yes	—
368	C₂×C₄⋊C₄	Q₈×C₁₃₉	1	4	yes	—
369	C₂×C₄²	—	2	4	no	—
370	C₂×C₄²	—	2	4	no	—
371	C₂×C₄²	—	4	1	no	—
372	C₂×C₄²	—	4	1	no	—
373	C₂×C₄²	—	4	2	no	—
374	C₂×C₄²	C₂×C₄×C₁₃₉	1	4	yes	—
375	#95	—	2	4	no	—
376	#95	—	2	4	no	—
377	#95	—	2	4	no	—
378	#95	—	2	4	no	—
379	#95	—	2	4	no	—
380	#95	—	2	4	no	—
381	#95	—	2	4	no	—
382	#95	—	4	2	no	—
383	#95	—	4	2	no	—
384	#95	C₂×C₄×C₁₃₉	1	8	yes	—
385	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
435	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
436	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
437	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
438	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
440	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
441	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
442	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
443	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
444	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
445	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
446	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
447	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
448	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
449	C₄⋊C₄	—	2	16	no	—
450	C₄⋊C₄	—	4	4	no	—
451	C₄⋊C₄	—	4	4	no	—
452	C₄⋊C₄	—	4	4	no	—
453	C₄⋊C₄	—	4	8	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₄⋊C₄	—	4	4	no	—
456	C₄⋊C₄	—	4	8	no	—
457	C₄⋊C₄	C₄⋊C₄×C₁₃₉	1	16	yes	complemented
458	C₄²	—	4	4	no	—
459	C₄²	—	4	8	no	—
460	C₂³	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
461	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
462	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
463	C₂³	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
464	C₂³	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
465	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
466	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
467	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
468	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
469	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
470	C₂³	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
471	C₂³	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
472	C₂³	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
473	C₂³	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
474	C₂³	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
535	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	8	yes	—
536	C₂×C₄	C₄×D₄×C₁₃₉	1	4	yes	—
537	C₂×C₄	C₄×Q₈×C₁₃₉	1	4	yes	—
538	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
539	C₂²	C₂×C₄×D₄×C₁₃₉	1	1	yes	characteristic
540	C₂²	C₂×C₄×Q₈×C₁₃₉	1	1	yes	characteristic
541	C₂²	#518×C₁₃₉	1	1	yes	characteristic
542	C₂²	#519×C₁₃₉	1	1	yes	characteristic
543	C₂²	#520×C₁₃₉	1	1	yes	characteristic
544	C₂²	#520×C₁₃₉	1	1	yes	characteristic
545	C₂²	#534×C₁₃₉	1	1	yes	characteristic
546	C₂²	#537×C₁₃₉	1	1	yes	characteristic
547	C₂²	#537×C₁₃₉	1	1	yes	characteristic
548	C₂²	#537×C₁₃₉	1	1	yes	characteristic
549	C₂²	#538×C₁₃₉	1	1	yes	characteristic
550	C₂²	#538×C₁₃₉	1	1	yes	characteristic
551	C₂²	#539×C₁₃₉	1	1	yes	characteristic
552	C₂²	#539×C₁₃₉	1	1	yes	characteristic
553	C₂²	#543×C₁₃₉	1	1	yes	characteristic
554	C₂²	#544×C₁₃₉	1	1	yes	characteristic
555	C₂²	#544×C₁₃₉	1	1	yes	characteristic
556	C₂²	#544×C₁₃₉	1	1	yes	characteristic
557	C₂²	D₄²×C₁₃₉	1	1	yes	characteristic
558	C₂²	#547×C₁₃₉	1	1	yes	characteristic
559	C₂²	#547×C₁₃₉	1	1	yes	characteristic
560	C₂²	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
561	C₂²	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
562	C₂²	D₄×Q₈×C₁₃₉	1	1	yes	characteristic
563	C₂²	#550×C₁₃₉	1	1	yes	characteristic
564	C₂²	#554×C₁₃₉	1	1	yes	characteristic
565	C₂²	#556×C₁₃₉	1	1	yes	characteristic
566	C₂²	#557×C₁₃₉	1	1	yes	characteristic
567	C₂²	#557×C₁₃₉	1	1	yes	characteristic
568	C₂²	Q₈²×C₁₃₉	1	1	yes	characteristic
569	C₂²	#562×C₁₃₉	1	1	yes	characteristic
570	C₂²	#563×C₁₃₉	1	1	yes	characteristic
571	C₂²	#563×C₁₃₉	1	1	yes	characteristic
572	C₂²	#564×C₁₃₉	1	1	yes	characteristic
573	C₄	—	2	4	no	—
574	C₄	—	2	4	no	—
575	C₄	—	2	4	no	—
576	C₄	—	2	8	no	—
577	C₄	—	4	4	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	4	no	—
580	C₄	—	8	2	no	—
581	C₄	—	8	2	no	—
582	C₂	#2316×C₁₃₉	1	1	yes	characteristic
583	C₂	#2325×C₁₃₉	1	1	yes	characteristic
584	C₂	#2329×C₁₃₉	1	1	yes	characteristic
585	C₂	D₄×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
586	C₂	Q₈×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
587	C₂	#2365×C₁₃₉	1	1	yes	characteristic
588	C₂	#2382×C₁₃₉	1	1	yes	characteristic
589	C₂	#2682×C₁₃₉	1	1	yes	characteristic
590	C₂	#2683×C₁₃₉	1	1	yes	characteristic
591	C₂	#2726×C₁₃₉	1	1	yes	characteristic
592	C₂	#2726×C₁₃₉	1	1	yes	characteristic
593	C₂	#2727×C₁₃₉	1	1	yes	characteristic
594	C₂	#2734×C₁₃₉	1	1	yes	characteristic
595	C₂	#2805×C₁₃₉	1	1	yes	characteristic
596	C₂	#2806×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₉
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
22. #389×C₁₃₉	C₄	semidirect
158. C₄⋊C₄×C₁₃₉	C₄⋊C₄	semidirect
298. #14441	C₁₃₉	direct (N × H)
299. C₁₃₉	#14441	direct (N × H)
321. #389	C₄×C₁₃₉	semidirect
457. C₄⋊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×#389×C₁₃₉	2
C₂×#387×C₁₃₉	2
#1444×C₁₃₉	2
#1441×C₁₃₉	2
#1436×C₁₃₉	2
C₄⋊#95×C₁₃₉	2
#14441	139

Subgroups — C139×#14441 #48009037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#14441 #48009037