Subgroups — C₁₃₉×#36538 #48031134

Order 35584.

2238 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#557×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2861×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2568×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2566×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2558×C₁₃₉	C₂	1	8	yes	maximal, complemented
8	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#2545×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2545×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2367×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#124×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₄²×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#559×C₁₃₉	—	2	8	no	—
16	#557×C₁₃₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
26	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
28	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	#400×C₁₃₉	C₂²	1	4	yes	—
37	#396×C₁₃₉	C₂²	1	8	yes	—
38	#396×C₁₃₉	C₂²	1	8	yes	—
39	#394×C₁₃₉	C₂²	1	4	yes	—
40	#391×C₁₃₉	C₂²	1	2	yes	—
41	#391×C₁₃₉	C₂²	1	4	yes	—
42	#391×C₁₃₉	C₂²	1	1	yes	characteristic
43	#391×C₁₃₉	C₂²	1	1	yes	characteristic
44	#390×C₁₃₉	C₂²	1	4	yes	—
45	#390×C₁₃₉	C₂²	1	2	yes	—
46	#390×C₁₃₉	C₂²	1	2	yes	—
47	#390×C₁₃₉	C₂²	1	4	yes	—
48	#390×C₁₃₉	C₂²	1	2	yes	—
49	#389×C₁₃₉	C₂²	1	4	yes	—
50	#388×C₁₃₉	C₂²	1	8	yes	—
51	#388×C₁₃₉	C₂²	1	8	yes	—
52	#388×C₁₃₉	C₂²	1	8	yes	—
53	#388×C₁₃₉	C₂²	1	8	yes	—
54	#385×C₁₃₉	C₂²	1	8	yes	—
55	#384×C₁₃₉	C₂²	1	1	yes	characteristic
56	#382×C₁₃₉	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
61	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	—
63	C₄³×C₁₃₉	C₂²	1	2	yes	—
64	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
73	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
74	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
75	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
76	#127×C₁₃₉	—	2	4	no	—
77	#125×C₁₃₉	—	2	16	no	—
78	#125×C₁₃₉	—	2	8	no	—
79	#124×C₁₃₉	—	2	8	no	—
80	#124×C₁₃₉	—	2	8	no	—
81	#124×C₁₃₉	—	2	8	no	—
82	#124×C₁₃₉	—	2	16	no	—
83	#123×C₁₃₉	—	2	16	no	—
84	C₄×Q₈×C₁₃₉	—	2	8	no	—
85	C₄×Q₈×C₁₃₉	—	2	8	no	—
86	C₄×Q₈×C₁₃₉	—	2	4	no	—
87	C₄×Q₈×C₁₃₉	—	2	4	no	—
88	C₄×Q₈×C₁₃₉	—	2	8	no	—
89	C₄×Q₈×C₁₃₉	D₄	1	8	yes	—
90	C₄×D₄×C₁₃₉	—	2	8	no	—
91	C₄×D₄×C₁₃₉	—	2	8	no	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
114	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
126	#95×C₁₃₉	C₂³	1	8	yes	—
127	#95×C₁₃₉	C₂³	1	8	yes	—
128	#95×C₁₃₉	C₂³	1	2	yes	—
129	#95×C₁₃₉	C₂³	1	4	yes	—
130	#95×C₁₃₉	C₂³	1	4	yes	—
131	#95×C₁₃₉	C₂³	1	4	yes	—
132	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
133	C₂×Q₈×C₁₃₉	—	2	2	no	—
134	C₂×Q₈×C₁₃₉	—	2	2	no	—
135	C₂×Q₈×C₁₃₉	—	2	4	no	—
136	C₂×Q₈×C₁₃₉	—	2	4	no	—
137	C₂×Q₈×C₁₃₉	—	2	8	no	—
138	C₂×Q₈×C₁₃₉	—	2	2	no	—
139	C₂×Q₈×C₁₃₉	—	2	2	no	—
140	C₂×Q₈×C₁₃₉	—	2	2	no	—
141	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
142	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
143	C₂×D₄×C₁₃₉	—	2	4	no	—
144	C₂×D₄×C₁₃₉	—	2	4	no	—
145	C₂×D₄×C₁₃₉	—	2	4	no	—
146	C₂×D₄×C₁₃₉	—	2	8	no	—
147	C₂×D₄×C₁₃₉	—	2	4	no	—
148	C₂×D₄×C₁₃₉	—	2	4	no	—
149	C₂×D₄×C₁₃₉	—	4	4	no	—
150	C₂²×C₄×C₁₃₉	—	2	8	no	—
151	C₂²×C₄×C₁₃₉	—	4	8	no	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
165	C₄⋊C₄×C₁₃₉	—	2	2	no	—
166	C₄⋊C₄×C₁₃₉	—	2	4	no	—
167	C₄⋊C₄×C₁₃₉	—	2	4	no	—
168	C₄⋊C₄×C₁₃₉	—	2	2	no	—
169	C₄⋊C₄×C₁₃₉	—	2	8	no	—
170	C₄⋊C₄×C₁₃₉	—	2	8	no	—
171	C₄⋊C₄×C₁₃₉	—	2	4	no	—
172	C₄⋊C₄×C₁₃₉	—	2	8	no	—
173	C₄⋊C₄×C₁₃₉	—	2	4	no	—
174	C₄⋊C₄×C₁₃₉	—	2	8	no	—
175	C₄⋊C₄×C₁₃₉	—	2	4	no	—
176	C₄⋊C₄×C₁₃₉	—	2	8	no	—
177	C₄⋊C₄×C₁₃₉	—	4	4	no	—
178	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
179	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
180	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
181	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
182	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
183	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
184	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
185	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
186	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
187	C₄²×C₁₃₉	—	2	4	no	—
188	C₄²×C₁₃₉	—	2	8	no	—
189	C₄²×C₁₃₉	—	2	4	no	—
190	C₄²×C₁₃₉	—	2	8	no	—
191	C₄²×C₁₃₉	—	2	4	no	—
192	C₄²×C₁₃₉	—	2	2	no	—
193	C₄²×C₁₃₉	—	2	2	no	—
194	C₄²×C₁₃₉	—	4	2	no	—
195	C₄²×C₁₃₉	—	4	4	no	—
196	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
197	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
198	C₄²×C₁₃₉	#41	1	8	yes	—
199	C₂³×C₁₃₉	—	2	4	no	—
200	C₂³×C₁₃₉	—	2	8	no	—
201	C₂³×C₁₃₉	—	2	4	no	—
202	C₂³×C₁₃₉	—	2	4	no	—
203	C₂³×C₁₃₉	—	2	8	no	—
204	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
205	Q₈×C₁₃₉	—	2	8	no	—
206	Q₈×C₁₃₉	—	2	8	no	—
207	Q₈×C₁₃₉	—	4	8	no	—
208	Q₈×C₁₃₉	—	4	4	no	—
209	D₄×C₁₃₉	—	4	8	no	—
210	D₄×C₁₃₉	—	4	8	no	—
211	D₄×C₁₃₉	—	8	4	no	—
212	C₂×C₄×C₁₃₉	—	2	2	no	—
213	C₂×C₄×C₁₃₉	—	2	2	no	—
214	C₂×C₄×C₁₃₉	—	2	4	no	—
215	C₂×C₄×C₁₃₉	—	2	2	no	—
216	C₂×C₄×C₁₃₉	—	2	2	no	—
217	C₂×C₄×C₁₃₉	—	2	2	no	—
218	C₂×C₄×C₁₃₉	—	2	2	no	—
219	C₂×C₄×C₁₃₉	—	2	4	no	—
220	C₂×C₄×C₁₃₉	—	2	2	no	—
221	C₂×C₄×C₁₃₉	—	2	2	no	—
222	C₂×C₄×C₁₃₉	—	2	2	no	—
223	C₂×C₄×C₁₃₉	—	2	2	no	—
224	C₂×C₄×C₁₃₉	—	2	4	no	—
225	C₂×C₄×C₁₃₉	—	2	4	no	—
226	C₂×C₄×C₁₃₉	—	2	4	no	—
227	C₂×C₄×C₁₃₉	—	2	8	no	—
228	C₂×C₄×C₁₃₉	—	2	2	no	—
229	C₂×C₄×C₁₃₉	—	2	2	no	—
230	C₂×C₄×C₁₃₉	—	2	4	no	—
231	C₂×C₄×C₁₃₉	—	2	4	no	—
232	C₂×C₄×C₁₃₉	—	2	4	no	—
233	C₂×C₄×C₁₃₉	—	8	8	no	—
234	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
235	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
236	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
238	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
240	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
241	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
242	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
243	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
245	C₂²×C₁₃₉	—	4	4	no	—
246	C₂²×C₁₃₉	—	4	4	no	—
247	C₂²×C₁₃₉	—	4	8	no	—
248	C₂²×C₁₃₉	—	4	4	no	—
249	C₂²×C₁₃₉	—	4	8	no	—
250	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
251	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
252	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
253	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
254	C₂²×C₁₃₉	#585	1	2	yes	—
255	C₄×C₁₃₉	—	2	4	no	—
256	C₄×C₁₃₉	—	2	4	no	—
257	C₄×C₁₃₉	—	2	4	no	—
258	C₄×C₁₃₉	—	2	4	no	—
259	C₄×C₁₃₉	—	2	2	no	—
260	C₄×C₁₃₉	—	2	4	no	—
261	C₄×C₁₃₉	—	4	4	no	—
262	C₄×C₁₃₉	—	4	2	no	—
263	C₄×C₁₃₉	—	4	4	no	—
264	C₄×C₁₃₉	—	4	2	no	—
265	C₄×C₁₃₉	—	4	2	no	—
266	C₄×C₁₃₉	#532	1	4	yes	—
267	C₄×C₁₃₉	#548	1	4	yes	—
268	C₂×C₁₃₉	—	8	4	no	—
269	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
270	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
271	C₂×C₁₃₉	#3480	1	2	yes	—
272	C₂×C₁₃₉	#3500	1	1	yes	characteristic
273	C₂×C₁₃₉	#3507	1	2	yes	—
274	#36538	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₁₃₉	#36538	1	1	yes	characteristic, direct product factor, Sylow
276	C₂×#559	C₂×C₁₃₉	1	1	yes	characteristic
277	C₂×#557	C₂×C₁₃₉	1	1	yes	characteristic, complemented
278	#2861	C₂×C₁₃₉	1	2	yes	complemented
279	#2858	C₂×C₁₃₉	1	1	yes	characteristic
280	#2568	C₂×C₁₃₉	1	1	yes	characteristic, complemented
281	#2566	C₂×C₁₃₉	1	2	yes	complemented
282	#2558	C₂×C₁₃₉	1	8	yes	complemented
283	#2548	C₂×C₁₃₉	1	1	yes	characteristic
284	#2545	C₂×C₁₃₉	1	2	yes	complemented
285	#2545	C₂×C₁₃₉	1	4	yes	complemented
286	#2367	C₂×C₁₃₉	1	4	yes	complemented
287	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
288	C₄×#124	C₂×C₁₃₉	1	2	yes	complemented
289	C₄²×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
290	#559	—	2	8	no	—
291	#557	—	2	8	no	—
292	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
293	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
294	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
295	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
296	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
297	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
298	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
299	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
300	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
301	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
302	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
303	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
304	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
305	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
306	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
307	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
308	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
310	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
311	#400	C₂²×C₁₃₉	1	4	yes	—
312	#396	C₂²×C₁₃₉	1	8	yes	—
313	#396	C₂²×C₁₃₉	1	8	yes	—
314	#394	C₂²×C₁₃₉	1	4	yes	—
315	#391	C₂²×C₁₃₉	1	1	yes	characteristic
316	#391	C₂²×C₁₃₉	1	1	yes	characteristic
317	#391	C₂²×C₁₃₉	1	2	yes	—
318	#391	C₂²×C₁₃₉	1	4	yes	—
319	#390	C₂²×C₁₃₉	1	2	yes	—
320	#390	C₂²×C₁₃₉	1	2	yes	—
321	#390	C₂²×C₁₃₉	1	2	yes	—
322	#390	C₂²×C₁₃₉	1	4	yes	—
323	#390	C₂²×C₁₃₉	1	4	yes	—
324	#389	C₂²×C₁₃₉	1	4	yes	—
325	#388	C₂²×C₁₃₉	1	8	yes	—
326	#388	C₂²×C₁₃₉	1	8	yes	—
327	#388	C₂²×C₁₃₉	1	8	yes	—
328	#388	C₂²×C₁₃₉	1	8	yes	—
329	#385	C₂²×C₁₃₉	1	8	yes	—
330	#384	C₂²×C₁₃₉	1	1	yes	characteristic
331	#382	C₂²×C₁₃₉	1	2	yes	—
332	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
333	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
334	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
335	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
336	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
337	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	—
338	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
339	C₄³	C₂²×C₁₃₉	1	2	yes	—
340	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
341	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
342	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
343	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
344	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
345	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
346	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
347	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
348	C₄⋊Q₈	—	2	8	no	—
349	C₄⋊Q₈	—	2	4	no	—
350	C₄⋊Q₈	—	2	4	no	—
351	#127	—	2	4	no	—
352	#125	—	2	16	no	—
353	#125	—	2	8	no	—
354	#124	—	2	8	no	—
355	#124	—	2	8	no	—
356	#124	—	2	8	no	—
357	#124	—	2	16	no	—
358	#123	—	2	16	no	—
359	C₄×Q₈	—	2	8	no	—
360	C₄×Q₈	—	2	8	no	—
361	C₄×Q₈	—	2	4	no	—
362	C₄×Q₈	—	2	4	no	—
363	C₄×Q₈	—	2	8	no	—
364	C₄×Q₈	D₄×C₁₃₉	1	8	yes	—
365	C₄×D₄	—	2	8	no	—
366	C₄×D₄	—	2	8	no	—
367	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
382	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
389	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
390	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
391	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
392	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
393	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
394	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
398	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
399	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
401	#95	C₂³×C₁₃₉	1	4	yes	—
402	#95	C₂³×C₁₃₉	1	8	yes	—
403	#95	C₂³×C₁₃₉	1	4	yes	—
404	#95	C₂³×C₁₃₉	1	2	yes	—
405	#95	C₂³×C₁₃₉	1	4	yes	—
406	#95	C₂³×C₁₃₉	1	8	yes	—
407	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	—	2	8	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
417	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	4	8	no	—
427	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
428	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
429	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	4	4	no	—
453	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
454	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	—	2	16	no	—
459	C₂²⋊C₄	—	2	16	no	—
460	C₂²⋊C₄	—	2	16	no	—
461	C₂²⋊C₄	—	4	8	no	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	8	no	—
464	C₄²	—	2	4	no	—
465	C₄²	—	2	8	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	4	2	no	—
470	C₄²	—	4	4	no	—
471	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
472	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
473	C₄²	#41×C₁₃₉	1	8	yes	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	8	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	8	no	—
479	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
480	Q₈	—	2	8	no	—
481	Q₈	—	2	8	no	—
482	Q₈	—	4	8	no	—
483	Q₈	—	4	4	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	8	no	—
486	D₄	—	8	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	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	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	8	8	no	—
509	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
510	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
511	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
514	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
515	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
516	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
517	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
518	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
519	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	8	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	8	no	—
525	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
526	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
527	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
528	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
529	C₂²	#585×C₁₃₉	1	2	yes	—
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	4	no	—
533	C₄	—	2	4	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	4	no	—
536	C₄	—	4	4	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	#532×C₁₃₉	1	4	yes	—
542	C₄	#548×C₁₃₉	1	4	yes	—
543	C₂	—	8	4	no	—
544	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
545	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
546	C₂	#3480×C₁₃₉	1	2	yes	—
547	C₂	#3500×C₁₃₉	1	1	yes	characteristic
548	C₂	#3507×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×#127×C₁₃₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#557×C₁₃₉	C₂	semidirect
3. #2861×C₁₃₉	C₂	semidirect
5. #2568×C₁₃₉	C₂	semidirect
6. #2566×C₁₃₉	C₂	semidirect
7. #2558×C₁₃₉	C₂	semidirect
9. #2545×C₁₃₉	C₂	semidirect
10. #2545×C₁₃₉	C₂	semidirect
11. #2367×C₁₃₉	C₂	semidirect
12. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
13. C₄×#124×C₁₃₉	C₂	semidirect
14. C₄²×Q₈×C₁₃₉	C₂	semidirect
274. #36538	C₁₃₉	direct (N × H)
275. C₁₃₉	#36538	direct (N × H)
277. C₂×#557	C₂×C₁₃₉	semidirect
278. #2861	C₂×C₁₃₉	semidirect
280. #2568	C₂×C₁₃₉	semidirect
281. #2566	C₂×C₁₃₉	semidirect
282. #2558	C₂×C₁₃₉	semidirect
284. #2545	C₂×C₁₃₉	semidirect
285. #2545	C₂×C₁₃₉	semidirect
286. #2367	C₂×C₁₃₉	semidirect
287. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
288. C₄×#124	C₂×C₁₃₉	semidirect
289. C₄²×Q₈	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₁₃₉	2
C₂×#557×C₁₃₉	2
#2861×C₁₃₉	2
#2858×C₁₃₉	2
#2568×C₁₃₉	2
#2566×C₁₃₉	2
#2558×C₁₃₉	2
#2548×C₁₃₉	2
#2545×C₁₃₉	2
#2367×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₄²×Q₈×C₁₃₉	2
#36538	139

Subgroups — C139×#36538 #48031134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36538 #48031134