Subgroups — C₁₃₉×#36496 #48031092

Order 35584.

2546 conjugacy classes of subgroups.

The subgroup lattice has 584 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, complemented
2	C₂×#554×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, complemented
5	#2567×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2566×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2544×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2541×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#2461×C₁₃₉	C₂	1	8	yes	maximal, complemented
10	#2426×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2361×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	C₄×#127×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#559×C₁₃₉	—	2	8	no	—
16	#554×C₁₃₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#127×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#125×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
28	C₂×#121×C₁₃₉	C₂²	1	4	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×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	8	yes	—
37	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
38	#396×C₁₃₉	C₂²	1	8	yes	—
39	#395×C₁₃₉	C₂²	1	4	yes	—
40	#394×C₁₃₉	C₂²	1	8	yes	—
41	#392×C₁₃₉	C₂²	1	4	yes	—
42	#391×C₁₃₉	C₂²	1	2	yes	—
43	#391×C₁₃₉	C₂²	1	1	yes	characteristic
44	#390×C₁₃₉	C₂²	1	2	yes	—
45	#390×C₁₃₉	C₂²	1	2	yes	—
46	#390×C₁₃₉	C₂²	1	1	yes	characteristic
47	#390×C₁₃₉	C₂²	1	2	yes	—
48	#390×C₁₃₉	C₂²	1	8	yes	—
49	#390×C₁₃₉	C₂²	1	4	yes	—
50	#389×C₁₃₉	C₂²	1	4	yes	—
51	#388×C₁₃₉	C₂²	1	4	yes	—
52	#388×C₁₃₉	C₂²	1	8	yes	—
53	#388×C₁₃₉	C₂²	1	8	yes	—
54	#386×C₁₃₉	C₂²	1	8	yes	—
55	#385×C₁₃₉	C₂²	1	8	yes	—
56	#384×C₁₃₉	C₂²	1	2	yes	—
57	#382×C₁₃₉	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
59	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	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	4	yes	—
63	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
64	C₄³×C₁₃₉	C₂²	1	2	yes	—
65	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
71	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
76	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
77	#127×C₁₃₉	—	2	8	no	—
78	#127×C₁₃₉	—	2	4	no	—
79	#125×C₁₃₉	—	2	8	no	—
80	#124×C₁₃₉	—	2	8	no	—
81	#124×C₁₃₉	—	2	4	no	—
82	#124×C₁₃₉	—	2	8	no	—
83	#124×C₁₃₉	—	4	8	no	—
84	#123×C₁₃₉	—	2	16	no	—
85	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
86	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
87	#121×C₁₃₉	—	2	16	no	—
88	C₄×Q₈×C₁₃₉	—	2	8	no	—
89	C₄×Q₈×C₁₃₉	—	2	4	no	—
90	C₄×Q₈×C₁₃₉	D₄	1	8	yes	complemented
91	C₄×D₄×C₁₃₉	—	2	8	no	—
92	C₄×D₄×C₁₃₉	—	2	8	no	—
93	C₄×D₄×C₁₃₉	—	2	4	no	—
94	C₄×D₄×C₁₃₉	—	2	8	no	—
95	C₄×D₄×C₁₃₉	—	4	16	no	—
96	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
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	1	yes	characteristic
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	2	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
119	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃₉	C₂³	1	4	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	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
129	#95×C₁₃₉	C₂³	1	2	yes	—
130	#95×C₁₃₉	C₂³	1	8	yes	—
131	#95×C₁₃₉	C₂³	1	4	yes	—
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
135	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
136	C₂×Q₈×C₁₃₉	—	2	2	no	—
137	C₂×Q₈×C₁₃₉	—	2	4	no	—
138	C₂×Q₈×C₁₃₉	—	2	4	no	—
139	C₂×Q₈×C₁₃₉	—	2	2	no	—
140	C₂×Q₈×C₁₃₉	—	2	2	no	—
141	C₂×Q₈×C₁₃₉	—	4	4	no	—
142	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
143	C₂×D₄×C₁₃₉	—	2	16	no	—
144	C₂×D₄×C₁₃₉	—	2	2	no	—
145	C₂×D₄×C₁₃₉	—	2	4	no	—
146	C₂×D₄×C₁₃₉	—	2	4	no	—
147	C₂×D₄×C₁₃₉	—	2	4	no	—
148	C₂×D₄×C₁₃₉	—	2	16	no	—
149	C₂×D₄×C₁₃₉	—	2	8	no	—
150	C₂×D₄×C₁₃₉	—	2	4	no	—
151	C₂×D₄×C₁₃₉	—	2	2	no	—
152	C₂×D₄×C₁₃₉	—	2	4	no	—
153	C₂×D₄×C₁₃₉	—	4	8	no	—
154	C₂×D₄×C₁₃₉	—	4	4	no	—
155	C₂×D₄×C₁₃₉	#41	1	4	yes	—
156	C₂²×C₄×C₁₃₉	—	2	4	no	—
157	C₂²×C₄×C₁₃₉	—	2	8	no	—
158	C₂²×C₄×C₁₃₉	—	2	8	no	—
159	C₂²×C₄×C₁₃₉	—	2	8	no	—
160	C₂²×C₄×C₁₃₉	—	4	8	no	—
161	C₂²×C₄×C₁₃₉	—	4	8	no	—
162	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
174	C₄⋊C₄×C₁₃₉	—	2	8	no	—
175	C₄⋊C₄×C₁₃₉	—	2	4	no	—
176	C₄⋊C₄×C₁₃₉	—	2	2	no	—
177	C₄⋊C₄×C₁₃₉	—	2	2	no	—
178	C₄⋊C₄×C₁₃₉	—	2	4	no	—
179	C₄⋊C₄×C₁₃₉	—	2	4	no	—
180	C₄⋊C₄×C₁₃₉	—	2	8	no	—
181	C₄⋊C₄×C₁₃₉	—	2	8	no	—
182	C₄⋊C₄×C₁₃₉	—	4	8	no	—
183	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
184	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
185	C₄⋊C₄×C₁₃₉	#41	1	8	yes	—
186	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
187	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
188	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
189	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
190	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
191	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
192	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
193	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
194	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
195	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
196	C₄²×C₁₃₉	—	2	4	no	—
197	C₄²×C₁₃₉	—	2	8	no	—
198	C₄²×C₁₃₉	—	2	4	no	—
199	C₄²×C₁₃₉	—	2	2	no	—
200	C₄²×C₁₃₉	—	2	4	no	—
201	C₄²×C₁₃₉	—	2	8	no	—
202	C₄²×C₁₃₉	—	2	4	no	—
203	C₄²×C₁₃₉	—	2	2	no	—
204	C₄²×C₁₃₉	C₂×D₄	1	8	yes	—
205	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
206	C₂³×C₁₃₉	—	2	2	no	—
207	C₂³×C₁₃₉	—	2	4	no	—
208	C₂³×C₁₃₉	—	2	4	no	—
209	C₂³×C₁₃₉	—	2	2	no	—
210	C₂³×C₁₃₉	—	2	4	no	—
211	C₂³×C₁₃₉	—	2	8	no	—
212	C₂³×C₁₃₉	—	2	4	no	—
213	C₂³×C₁₃₉	—	2	8	no	—
214	C₂³×C₁₃₉	—	2	4	no	—
215	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
216	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
217	Q₈×C₁₃₉	—	2	8	no	—
218	Q₈×C₁₃₉	—	4	4	no	—
219	Q₈×C₁₃₉	—	8	4	no	—
220	D₄×C₁₃₉	—	2	8	no	—
221	D₄×C₁₃₉	—	4	32	no	—
222	D₄×C₁₃₉	—	4	8	no	—
223	D₄×C₁₃₉	—	4	8	no	—
224	D₄×C₁₃₉	—	8	4	no	—
225	C₂×C₄×C₁₃₉	—	2	2	no	—
226	C₂×C₄×C₁₃₉	—	2	4	no	—
227	C₂×C₄×C₁₃₉	—	2	4	no	—
228	C₂×C₄×C₁₃₉	—	2	4	no	—
229	C₂×C₄×C₁₃₉	—	2	4	no	—
230	C₂×C₄×C₁₃₉	—	2	2	no	—
231	C₂×C₄×C₁₃₉	—	2	2	no	—
232	C₂×C₄×C₁₃₉	—	2	2	no	—
233	C₂×C₄×C₁₃₉	—	2	2	no	—
234	C₂×C₄×C₁₃₉	—	2	2	no	—
235	C₂×C₄×C₁₃₉	—	2	4	no	—
236	C₂×C₄×C₁₃₉	—	2	2	no	—
237	C₂×C₄×C₁₃₉	—	2	2	no	—
238	C₂×C₄×C₁₃₉	—	2	4	no	—
239	C₂×C₄×C₁₃₉	—	2	2	no	—
240	C₂×C₄×C₁₃₉	—	2	2	no	—
241	C₂×C₄×C₁₃₉	—	2	8	no	—
242	C₂×C₄×C₁₃₉	—	2	4	no	—
243	C₂×C₄×C₁₃₉	—	2	2	no	—
244	C₂×C₄×C₁₃₉	—	4	8	no	—
245	C₂×C₄×C₁₃₉	—	8	8	no	—
246	C₂×C₄×C₁₃₉	—	8	8	no	—
247	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
249	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₁₃₉	C₂×#41	1	8	yes	—
253	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
254	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
255	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
256	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
257	C₂²×C₁₃₉	—	2	4	no	—
258	C₂²×C₁₃₉	—	2	8	no	—
259	C₂²×C₁₃₉	—	4	2	no	—
260	C₂²×C₁₃₉	—	4	2	no	—
261	C₂²×C₁₃₉	—	4	4	no	—
262	C₂²×C₁₃₉	—	4	4	no	—
263	C₂²×C₁₃₉	—	4	4	no	—
264	C₂²×C₁₃₉	—	4	8	no	—
265	C₂²×C₁₃₉	—	4	4	no	—
266	C₂²×C₁₃₉	—	4	8	no	—
267	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
268	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
269	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
270	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
271	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
272	C₄×C₁₃₉	—	2	4	no	—
273	C₄×C₁₃₉	—	2	8	no	—
274	C₄×C₁₃₉	—	2	4	no	—
275	C₄×C₁₃₉	—	2	2	no	—
276	C₄×C₁₃₉	—	2	4	no	—
277	C₄×C₁₃₉	—	4	2	no	—
278	C₄×C₁₃₉	—	4	2	no	—
279	C₄×C₁₃₉	—	4	2	no	—
280	C₄×C₁₃₉	—	4	2	no	—
281	C₄×C₁₃₉	—	4	4	no	—
282	C₄×C₁₃₉	#532	1	4	yes	—
283	C₄×C₁₃₉	#548	1	4	yes	—
284	C₂×C₁₃₉	—	4	4	no	—
285	C₂×C₁₃₉	—	8	4	no	—
286	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
287	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
288	C₂×C₁₃₉	#3481	1	2	yes	—
289	C₂×C₁₃₉	#3498	1	1	yes	characteristic
290	C₂×C₁₃₉	#3522	1	2	yes	—
291	#36496	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₁₃₉	#36496	1	1	yes	characteristic, direct product factor, Sylow
293	C₂×#559	C₂×C₁₃₉	1	1	yes	characteristic, complemented
294	C₂×#554	C₂×C₁₃₉	1	1	yes	characteristic, complemented
295	#2861	C₂×C₁₃₉	1	2	yes	complemented
296	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
297	#2567	C₂×C₁₃₉	1	1	yes	characteristic, complemented
298	#2566	C₂×C₁₃₉	1	2	yes	complemented
299	#2544	C₂×C₁₃₉	1	2	yes	complemented
300	#2541	C₂×C₁₃₉	1	1	yes	characteristic
301	#2461	C₂×C₁₃₉	1	8	yes	complemented
302	#2426	C₂×C₁₃₉	1	4	yes	complemented
303	#2361	C₂×C₁₃₉	1	4	yes	complemented
304	C₄×#127	C₂×C₁₃₉	1	2	yes	complemented
305	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
306	C₄²×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
307	#559	—	2	8	no	—
308	#554	—	2	8	no	—
309	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
310	C₂×#127	C₂²×C₁₃₉	1	2	yes	—
311	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
312	C₂×#125	C₂²×C₁₃₉	1	2	yes	—
313	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
314	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
315	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
316	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
317	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
318	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
319	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
320	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
321	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
323	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
325	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
326	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
327	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
328	C₂×C₄×D₄	C₂²×C₁₃₉	1	8	yes	—
329	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
330	#396	C₂²×C₁₃₉	1	8	yes	—
331	#395	C₂²×C₁₃₉	1	4	yes	—
332	#394	C₂²×C₁₃₉	1	8	yes	—
333	#392	C₂²×C₁₃₉	1	4	yes	—
334	#391	C₂²×C₁₃₉	1	2	yes	—
335	#391	C₂²×C₁₃₉	1	1	yes	characteristic
336	#390	C₂²×C₁₃₉	1	1	yes	characteristic
337	#390	C₂²×C₁₃₉	1	2	yes	—
338	#390	C₂²×C₁₃₉	1	8	yes	—
339	#390	C₂²×C₁₃₉	1	2	yes	—
340	#390	C₂²×C₁₃₉	1	2	yes	—
341	#390	C₂²×C₁₃₉	1	4	yes	—
342	#389	C₂²×C₁₃₉	1	4	yes	—
343	#388	C₂²×C₁₃₉	1	8	yes	—
344	#388	C₂²×C₁₃₉	1	8	yes	—
345	#388	C₂²×C₁₃₉	1	4	yes	—
346	#386	C₂²×C₁₃₉	1	8	yes	—
347	#385	C₂²×C₁₃₉	1	8	yes	—
348	#384	C₂²×C₁₃₉	1	2	yes	—
349	#382	C₂²×C₁₃₉	1	1	yes	characteristic
350	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
351	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
353	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
354	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
355	C₄³	C₂²×C₁₃₉	1	2	yes	—
356	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
357	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
358	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
360	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
361	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
362	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
363	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
364	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
365	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
366	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
367	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
368	C₄⋊Q₈	—	2	4	no	—
369	#127	—	2	8	no	—
370	#127	—	2	4	no	—
371	#125	—	2	8	no	—
372	#124	—	2	8	no	—
373	#124	—	2	4	no	—
374	#124	—	2	8	no	—
375	#124	—	4	8	no	—
376	#123	—	2	16	no	—
377	C₂²⋊Q₈	—	2	8	no	—
378	C₂²⋊Q₈	—	2	16	no	—
379	#121	—	2	16	no	—
380	C₄×Q₈	—	2	8	no	—
381	C₄×Q₈	—	2	4	no	—
382	C₄×Q₈	D₄×C₁₃₉	1	8	yes	complemented
383	C₄×D₄	—	2	8	no	—
384	C₄×D₄	—	2	8	no	—
385	C₄×D₄	—	2	4	no	—
386	C₄×D₄	—	2	8	no	—
387	C₄×D₄	—	4	16	no	—
388	C₂×C₄⋊C₄	—	2	8	no	—
389	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
397	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
411	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
412	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
413	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
414	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
415	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
416	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
418	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
420	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
421	#95	C₂³×C₁₃₉	1	4	yes	—
422	#95	C₂³×C₁₃₉	1	4	yes	—
423	#95	C₂³×C₁₃₉	1	4	yes	—
424	#95	C₂³×C₁₃₉	1	2	yes	—
425	#95	C₂³×C₁₃₉	1	8	yes	—
426	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
427	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	4	no	—
430	C₂×Q₈	—	2	4	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	4	4	no	—
434	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
435	C₂×D₄	—	2	16	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	16	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	4	8	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	#41×C₁₃₉	1	4	yes	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	8	no	—
450	C₂²×C₄	—	2	8	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	4	8	no	—
453	C₂²×C₄	—	4	8	no	—
454	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
455	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
463	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	8	no	—
473	C₄⋊C₄	—	2	8	no	—
474	C₄⋊C₄	—	4	8	no	—
475	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
476	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
477	C₄⋊C₄	#41×C₁₃₉	1	8	yes	—
478	C₂²⋊C₄	—	2	8	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	2	8	no	—
482	C₂²⋊C₄	—	2	8	no	—
483	C₂²⋊C₄	—	2	8	no	—
484	C₂²⋊C₄	—	2	16	no	—
485	C₂²⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	—	2	16	no	—
487	C₂²⋊C₄	—	4	8	no	—
488	C₄²	—	2	4	no	—
489	C₄²	—	2	8	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	2	8	no	—
494	C₄²	—	2	4	no	—
495	C₄²	—	2	2	no	—
496	C₄²	C₂×D₄×C₁₃₉	1	8	yes	—
497	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	8	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	8	no	—
506	C₂³	—	2	4	no	—
507	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
508	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
509	Q₈	—	2	8	no	—
510	Q₈	—	4	4	no	—
511	Q₈	—	8	4	no	—
512	D₄	—	2	8	no	—
513	D₄	—	4	32	no	—
514	D₄	—	4	8	no	—
515	D₄	—	4	8	no	—
516	D₄	—	8	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	—	8	8	no	—
538	C₂×C₄	—	8	8	no	—
539	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
540	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
541	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
544	C₂×C₄	C₂×#41×C₁₃₉	1	8	yes	—
545	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
546	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
547	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
548	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	8	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	4	no	—
554	C₂²	—	4	4	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	8	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	8	no	—
559	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
560	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
561	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
562	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
563	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
564	C₄	—	2	4	no	—
565	C₄	—	2	8	no	—
566	C₄	—	2	4	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	4	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	4	no	—
574	C₄	#532×C₁₃₉	1	4	yes	—
575	C₄	#548×C₁₃₉	1	4	yes	—
576	C₂	—	4	4	no	—
577	C₂	—	8	4	no	—
578	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
579	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
580	C₂	#3481×C₁₃₉	1	2	yes	—
581	C₂	#3498×C₁₃₉	1	1	yes	characteristic
582	C₂	#3522×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2541×C₁₃₉	C₂
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
1. C₂×#559×C₁₃₉	C₂	semidirect
2. C₂×#554×C₁₃₉	C₂	semidirect
3. #2861×C₁₃₉	C₂	semidirect
4. #2858×C₁₃₉	C₂	semidirect
5. #2567×C₁₃₉	C₂	semidirect
6. #2566×C₁₃₉	C₂	semidirect
7. #2544×C₁₃₉	C₂	semidirect
9. #2461×C₁₃₉	C₂	semidirect
10. #2426×C₁₃₉	C₂	semidirect
11. #2361×C₁₃₉	C₂	semidirect
12. C₄×#127×C₁₃₉	C₂	semidirect
13. C₄×#124×C₁₃₉	C₂	semidirect
14. C₄²×Q₈×C₁₃₉	C₂	semidirect
90. C₄×Q₈×C₁₃₉	D₄	semidirect
291. #36496	C₁₃₉	direct (N × H)
292. C₁₃₉	#36496	direct (N × H)
293. C₂×#559	C₂×C₁₃₉	semidirect
294. C₂×#554	C₂×C₁₃₉	semidirect
295. #2861	C₂×C₁₃₉	semidirect
296. #2858	C₂×C₁₃₉	semidirect
297. #2567	C₂×C₁₃₉	semidirect
298. #2566	C₂×C₁₃₉	semidirect
299. #2544	C₂×C₁₃₉	semidirect
301. #2461	C₂×C₁₃₉	semidirect
302. #2426	C₂×C₁₃₉	semidirect
303. #2361	C₂×C₁₃₉	semidirect
304. C₄×#127	C₂×C₁₃₉	semidirect
305. C₄×#124	C₂×C₁₃₉	semidirect
306. C₄²×Q₈	C₂×C₁₃₉	semidirect
382. C₄×Q₈	D₄×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×#554×C₁₃₉	2
#2861×C₁₃₉	2
#2858×C₁₃₉	2
#2567×C₁₃₉	2
#2566×C₁₃₉	2
#2544×C₁₃₉	2
#2541×C₁₃₉	2
#2461×C₁₃₉	2
#2426×C₁₃₉	2
#2361×C₁₃₉	2
C₄×#127×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₄²×Q₈×C₁₃₉	2
#36496	139

Subgroups — C139×#36496 #48031092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36496 #48031092