Subgroups — C₁₃₉×#36966 #48031562

Order 35584.

2406 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#543×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2855×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2700×C₁₃₉	C₂	1	8	yes	maximal, complemented
5	#2674×C₁₃₉	C₂	1	8	yes	maximal, complemented
6	#2626×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2561×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2483×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2434×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2405×C₁₃₉	C₂	1	2	yes	maximal
11	#2312×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	#543×C₁₃₉	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
16	C₂×#124×C₁₃₉	—	2	8	no	—
17	C₂×#124×C₁₃₉	C₂²	1	8	yes	—
18	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
22	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
23	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
29	#399×C₁₃₉	C₂²	1	4	yes	complemented
30	#397×C₁₃₉	C₂²	1	4	yes	complemented
31	#397×C₁₃₉	C₂²	1	8	yes	complemented
32	#396×C₁₃₉	C₂²	1	8	yes	complemented
33	#395×C₁₃₉	C₂²	1	8	yes	complemented
34	#394×C₁₃₉	C₂²	1	8	yes	—
35	#393×C₁₃₉	C₂²	1	4	yes	complemented
36	#393×C₁₃₉	C₂²	1	4	yes	complemented
37	#391×C₁₃₉	C₂²	1	4	yes	complemented
38	#391×C₁₃₉	C₂²	1	4	yes	complemented
39	#389×C₁₃₉	C₂²	1	4	yes	complemented
40	#388×C₁₃₉	C₂²	1	8	yes	complemented
41	#388×C₁₃₉	C₂²	1	8	yes	complemented
42	#387×C₁₃₉	C₂²	1	8	yes	complemented
43	#386×C₁₃₉	C₂²	1	4	yes	—
44	#385×C₁₃₉	C₂²	1	4	yes	—
45	#385×C₁₃₉	C₂²	1	4	yes	—
46	#385×C₁₃₉	C₂²	1	4	yes	complemented
47	#381×C₁₃₉	C₂²	1	4	yes	—
48	#381×C₁₃₉	C₂²	1	4	yes	complemented
49	#380×C₁₃₉	C₂²	1	2	yes	—
50	#379×C₁₃₉	C₂²	1	4	yes	—
51	#379×C₁₃₉	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
53	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃₉	—	2	4	no	—
56	C₂²×Q₈×C₁₃₉	—	4	4	no	—
57	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
58	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
59	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃₉	—	2	4	no	—
61	C₂²×D₄×C₁₃₉	—	4	4	no	—
62	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₁₃₉	—	4	8	no	—
71	#124×C₁₃₉	—	2	32	no	—
72	#123×C₁₃₉	—	4	8	no	—
73	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
74	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
75	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
76	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
88	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	8	yes	—
89	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₄²×C₁₃₉	—	2	4	no	—
101	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
103	#95×C₁₃₉	C₂³	1	4	yes	—
104	#95×C₁₃₉	C₂³	1	8	yes	—
105	#95×C₁₃₉	C₂³	1	8	yes	—
106	#95×C₁₃₉	C₂³	1	8	yes	—
107	#95×C₁₃₉	C₂³	1	8	yes	—
108	#95×C₁₃₉	C₂³	1	4	yes	—
109	C₂⁴×C₁₃₉	—	2	4	no	—
110	C₂⁴×C₁₃₉	—	2	2	no	—
111	C₂⁴×C₁₃₉	—	2	4	no	—
112	C₂⁴×C₁₃₉	—	4	2	no	—
113	C₂⁴×C₁₃₉	—	4	2	no	—
114	C₂⁴×C₁₃₉	—	4	2	no	—
115	C₂⁴×C₁₃₉	—	4	2	no	—
116	C₂⁴×C₁₃₉	C₂×D₄	1	4	yes	—
117	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
118	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
119	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
120	C₂×Q₈×C₁₃₉	—	2	8	no	—
121	C₂×Q₈×C₁₃₉	—	2	4	no	—
122	C₂×Q₈×C₁₃₉	—	2	4	no	—
123	C₂×Q₈×C₁₃₉	—	2	8	no	—
124	C₂×Q₈×C₁₃₉	—	4	4	no	—
125	C₂×Q₈×C₁₃₉	—	4	4	no	—
126	C₂×Q₈×C₁₃₉	—	4	4	no	—
127	C₂×Q₈×C₁₃₉	—	4	16	no	—
128	C₂×D₄×C₁₃₉	—	2	8	no	—
129	C₂×D₄×C₁₃₉	—	2	8	no	—
130	C₂×D₄×C₁₃₉	—	4	4	no	—
131	C₂×D₄×C₁₃₉	—	4	16	no	—
132	C₂²×C₄×C₁₃₉	—	2	2	no	—
133	C₂²×C₄×C₁₃₉	—	2	4	no	—
134	C₂²×C₄×C₁₃₉	—	2	2	no	—
135	C₂²×C₄×C₁₃₉	—	2	2	no	—
136	C₂²×C₄×C₁₃₉	—	2	4	no	—
137	C₂²×C₄×C₁₃₉	—	2	4	no	—
138	C₂²×C₄×C₁₃₉	—	2	4	no	—
139	C₂²×C₄×C₁₃₉	—	4	2	no	—
140	C₂²×C₄×C₁₃₉	—	4	2	no	—
141	C₂²×C₄×C₁₃₉	—	4	2	no	—
142	C₂²×C₄×C₁₃₉	—	4	4	no	—
143	C₂²×C₄×C₁₃₉	—	4	4	no	—
144	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
148	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
154	C₄⋊C₄×C₁₃₉	—	2	8	no	—
155	C₄⋊C₄×C₁₃₉	—	2	4	no	—
156	C₄⋊C₄×C₁₃₉	—	2	8	no	—
157	C₄⋊C₄×C₁₃₉	—	2	4	no	—
158	C₄⋊C₄×C₁₃₉	—	2	16	no	—
159	C₄⋊C₄×C₁₃₉	—	4	4	no	—
160	C₄⋊C₄×C₁₃₉	—	4	8	no	—
161	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
162	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
163	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
164	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
165	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
166	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
167	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
168	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
169	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
170	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
171	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	—
172	C₄²×C₁₃₉	—	2	8	no	—
173	C₄²×C₁₃₉	—	4	4	no	—
174	C₂³×C₁₃₉	—	2	2	no	—
175	C₂³×C₁₃₉	—	2	2	no	—
176	C₂³×C₁₃₉	—	2	4	no	—
177	C₂³×C₁₃₉	—	2	4	no	—
178	C₂³×C₁₃₉	—	2	4	no	—
179	C₂³×C₁₃₉	—	2	8	no	—
180	C₂³×C₁₃₉	—	2	2	no	—
181	C₂³×C₁₃₉	—	2	4	no	—
182	C₂³×C₁₃₉	—	2	4	no	—
183	C₂³×C₁₃₉	—	2	4	no	—
184	C₂³×C₁₃₉	—	4	4	no	—
185	C₂³×C₁₃₉	—	4	4	no	—
186	C₂³×C₁₃₉	—	4	4	no	—
187	C₂³×C₁₃₉	—	4	4	no	—
188	C₂³×C₁₃₉	—	4	4	no	—
189	C₂³×C₁₃₉	—	8	8	no	—
190	C₂³×C₁₃₉	—	8	8	no	—
191	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
192	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
193	C₂³×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
194	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
195	Q₈×C₁₃₉	—	4	16	no	—
196	Q₈×C₁₃₉	—	8	4	no	—
197	Q₈×C₁₃₉	—	8	4	no	—
198	D₄×C₁₃₉	—	4	16	no	—
199	C₂×C₄×C₁₃₉	—	2	8	no	—
200	C₂×C₄×C₁₃₉	—	2	2	no	—
201	C₂×C₄×C₁₃₉	—	2	4	no	—
202	C₂×C₄×C₁₃₉	—	2	2	no	—
203	C₂×C₄×C₁₃₉	—	2	4	no	—
204	C₂×C₄×C₁₃₉	—	2	2	no	—
205	C₂×C₄×C₁₃₉	—	2	2	no	—
206	C₂×C₄×C₁₃₉	—	2	4	no	—
207	C₂×C₄×C₁₃₉	—	2	4	no	—
208	C₂×C₄×C₁₃₉	—	2	8	no	—
209	C₂×C₄×C₁₃₉	—	2	8	no	—
210	C₂×C₄×C₁₃₉	—	2	4	no	—
211	C₂×C₄×C₁₃₉	—	2	8	no	—
212	C₂×C₄×C₁₃₉	—	2	4	no	—
213	C₂×C₄×C₁₃₉	—	2	8	no	—
214	C₂×C₄×C₁₃₉	—	2	8	no	—
215	C₂×C₄×C₁₃₉	—	4	4	no	—
216	C₂×C₄×C₁₃₉	—	4	4	no	—
217	C₂×C₄×C₁₃₉	—	4	4	no	—
218	C₂×C₄×C₁₃₉	—	4	4	no	—
219	C₂×C₄×C₁₃₉	—	8	4	no	—
220	C₂×C₄×C₁₃₉	—	8	4	no	—
221	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
222	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
224	C₂²×C₁₃₉	—	2	2	no	—
225	C₂²×C₁₃₉	—	2	2	no	—
226	C₂²×C₁₃₉	—	2	8	no	—
227	C₂²×C₁₃₉	—	2	4	no	—
228	C₂²×C₁₃₉	—	2	4	no	—
229	C₂²×C₁₃₉	—	2	4	no	—
230	C₂²×C₁₃₉	—	4	8	no	—
231	C₂²×C₁₃₉	—	4	2	no	—
232	C₂²×C₁₃₉	—	4	2	no	—
233	C₂²×C₁₃₉	—	4	2	no	—
234	C₂²×C₁₃₉	—	4	8	no	—
235	C₂²×C₁₃₉	—	8	8	no	—
236	C₂²×C₁₃₉	—	8	8	no	—
237	C₂²×C₁₃₉	#536	1	4	yes	—
238	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
239	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
240	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
241	C₂²×C₁₃₉	#585	1	2	yes	—
242	C₄×C₁₃₉	—	2	4	no	—
243	C₄×C₁₃₉	—	2	4	no	—
244	C₄×C₁₃₉	—	2	4	no	—
245	C₄×C₁₃₉	—	4	2	no	—
246	C₄×C₁₃₉	—	4	2	no	—
247	C₄×C₁₃₉	—	4	4	no	—
248	C₄×C₁₃₉	—	4	4	no	—
249	C₄×C₁₃₉	—	4	8	no	—
250	C₂×C₁₃₉	—	2	4	no	—
251	C₂×C₁₃₉	—	4	4	no	—
252	C₂×C₁₃₉	—	8	2	no	—
253	C₂×C₁₃₉	C₂×#536	1	1	yes	characteristic
254	C₂×C₁₃₉	#3484	1	1	yes	characteristic
255	C₂×C₁₃₉	#3485	1	1	yes	characteristic
256	C₂×C₁₃₉	#3561	1	4	yes	—
257	#36966	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₁₃₉	#36966	1	1	yes	characteristic, direct product factor, Sylow
259	C₂×#543	C₂×C₁₃₉	1	1	yes	characteristic, complemented
260	C₂²×#124	C₂×C₁₃₉	1	1	yes	characteristic
261	#2855	C₂×C₁₃₉	1	2	yes	complemented
262	#2700	C₂×C₁₃₉	1	8	yes	complemented
263	#2674	C₂×C₁₃₉	1	8	yes	complemented
264	#2626	C₂×C₁₃₉	1	2	yes	complemented
265	#2561	C₂×C₁₃₉	1	2	yes	complemented
266	#2483	C₂×C₁₃₉	1	2	yes	complemented
267	#2434	C₂×C₁₃₉	1	2	yes	complemented
268	#2405	C₂×C₁₃₉	1	2	yes	—
269	#2312	C₂×C₁₃₉	1	1	yes	characteristic, complemented
270	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
271	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
272	#543	—	2	8	no	—
273	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
274	C₂×#124	—	2	8	no	—
275	C₂×#124	C₂²×C₁₃₉	1	8	yes	—
276	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
277	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
278	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
279	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
280	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
281	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
282	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
283	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
284	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
285	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
286	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
287	#399	C₂²×C₁₃₉	1	4	yes	complemented
288	#397	C₂²×C₁₃₉	1	4	yes	complemented
289	#397	C₂²×C₁₃₉	1	8	yes	complemented
290	#396	C₂²×C₁₃₉	1	8	yes	complemented
291	#395	C₂²×C₁₃₉	1	8	yes	complemented
292	#394	C₂²×C₁₃₉	1	8	yes	—
293	#393	C₂²×C₁₃₉	1	4	yes	complemented
294	#393	C₂²×C₁₃₉	1	4	yes	complemented
295	#391	C₂²×C₁₃₉	1	4	yes	complemented
296	#391	C₂²×C₁₃₉	1	4	yes	complemented
297	#389	C₂²×C₁₃₉	1	4	yes	complemented
298	#388	C₂²×C₁₃₉	1	8	yes	complemented
299	#388	C₂²×C₁₃₉	1	8	yes	complemented
300	#387	C₂²×C₁₃₉	1	8	yes	complemented
301	#386	C₂²×C₁₃₉	1	4	yes	—
302	#385	C₂²×C₁₃₉	1	4	yes	—
303	#385	C₂²×C₁₃₉	1	4	yes	—
304	#385	C₂²×C₁₃₉	1	4	yes	complemented
305	#381	C₂²×C₁₃₉	1	4	yes	—
306	#381	C₂²×C₁₃₉	1	4	yes	complemented
307	#380	C₂²×C₁₃₉	1	2	yes	—
308	#379	C₂²×C₁₃₉	1	4	yes	—
309	#379	C₂²×C₁₃₉	1	2	yes	—
310	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
311	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
312	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
313	C₂²×Q₈	—	2	4	no	—
314	C₂²×Q₈	—	4	4	no	—
315	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
316	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
317	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
318	C₂²×D₄	—	2	4	no	—
319	C₂²×D₄	—	4	4	no	—
320	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
321	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
325	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
326	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
328	C₄⋊Q₈	—	4	8	no	—
329	#124	—	2	32	no	—
330	#123	—	4	8	no	—
331	C₂²⋊Q₈	—	2	8	no	—
332	C₂²⋊Q₈	—	2	8	no	—
333	C₂²⋊Q₈	—	2	16	no	—
334	C₂²⋊Q₈	—	2	16	no	—
335	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₂²⋊C₄	—	2	8	no	—
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
358	C₂×C₄²	—	2	4	no	—
359	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
360	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
361	#95	C₂³×C₁₃₉	1	4	yes	—
362	#95	C₂³×C₁₃₉	1	4	yes	—
363	#95	C₂³×C₁₃₉	1	8	yes	—
364	#95	C₂³×C₁₃₉	1	8	yes	—
365	#95	C₂³×C₁₃₉	1	8	yes	—
366	#95	C₂³×C₁₃₉	1	8	yes	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	2	no	—
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	4	2	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	—	4	2	no	—
373	C₂⁴	—	4	2	no	—
374	C₂⁴	C₂×D₄×C₁₃₉	1	4	yes	—
375	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
376	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
377	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
378	C₂×Q₈	—	2	8	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	8	no	—
382	C₂×Q₈	—	4	4	no	—
383	C₂×Q₈	—	4	4	no	—
384	C₂×Q₈	—	4	4	no	—
385	C₂×Q₈	—	4	16	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	8	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	16	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	4	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
403	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
406	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	16	no	—
417	C₄⋊C₄	—	4	4	no	—
418	C₄⋊C₄	—	4	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	4	4	no	—
426	C₂²⋊C₄	—	4	8	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	8	no	—
429	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	—
430	C₄²	—	2	8	no	—
431	C₄²	—	4	4	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	8	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	8	8	no	—
448	C₂³	—	8	8	no	—
449	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
450	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
451	C₂³	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
452	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
453	Q₈	—	4	16	no	—
454	Q₈	—	8	4	no	—
455	Q₈	—	8	4	no	—
456	D₄	—	4	16	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	—	4	4	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	8	4	no	—
478	C₂×C₄	—	8	4	no	—
479	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
481	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
482	C₂²	—	2	8	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	4	8	no	—
489	C₂²	—	4	8	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	8	8	no	—
494	C₂²	—	8	8	no	—
495	C₂²	#536×C₁₃₉	1	4	yes	—
496	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
497	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
498	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
499	C₂²	#585×C₁₃₉	1	2	yes	—
500	C₄	—	2	4	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	4	no	—
503	C₄	—	4	8	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	4	no	—
508	C₂	—	2	4	no	—
509	C₂	—	4	4	no	—
510	C₂	—	8	2	no	—
511	C₂	C₂×#536×C₁₃₉	1	1	yes	characteristic
512	C₂	#3484×C₁₃₉	1	1	yes	characteristic
513	C₂	#3485×C₁₃₉	1	1	yes	characteristic
514	C₂	#3561×C₁₃₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂³×D₄×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
1. C₂×#543×C₁₃₉	C₂	semidirect
3. #2855×C₁₃₉	C₂	semidirect
4. #2700×C₁₃₉	C₂	semidirect
5. #2674×C₁₃₉	C₂	semidirect
6. #2626×C₁₃₉	C₂	semidirect
7. #2561×C₁₃₉	C₂	semidirect
8. #2483×C₁₃₉	C₂	semidirect
9. #2434×C₁₃₉	C₂	semidirect
11. #2312×C₁₃₉	C₂	semidirect
15. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
21. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
22. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
29. #399×C₁₃₉	C₂²	semidirect
30. #397×C₁₃₉	C₂²	semidirect
31. #397×C₁₃₉	C₂²	semidirect
32. #396×C₁₃₉	C₂²	semidirect
33. #395×C₁₃₉	C₂²	semidirect
35. #393×C₁₃₉	C₂²	semidirect
36. #393×C₁₃₉	C₂²	semidirect
37. #391×C₁₃₉	C₂²	semidirect
38. #391×C₁₃₉	C₂²	semidirect
39. #389×C₁₃₉	C₂²	semidirect
40. #388×C₁₃₉	C₂²	semidirect
41. #388×C₁₃₉	C₂²	semidirect
42. #387×C₁₃₉	C₂²	semidirect
46. #385×C₁₃₉	C₂²	semidirect
48. #381×C₁₃₉	C₂²	semidirect
257. #36966	C₁₃₉	direct (N × H)
258. C₁₃₉	#36966	direct (N × H)
259. C₂×#543	C₂×C₁₃₉	semidirect
261. #2855	C₂×C₁₃₉	semidirect
262. #2700	C₂×C₁₃₉	semidirect
263. #2674	C₂×C₁₃₉	semidirect
264. #2626	C₂×C₁₃₉	semidirect
265. #2561	C₂×C₁₃₉	semidirect
266. #2483	C₂×C₁₃₉	semidirect
267. #2434	C₂×C₁₃₉	semidirect
269. #2312	C₂×C₁₃₉	semidirect
273. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
279. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
280. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
287. #399	C₂²×C₁₃₉	semidirect
288. #397	C₂²×C₁₃₉	semidirect
289. #397	C₂²×C₁₃₉	semidirect
290. #396	C₂²×C₁₃₉	semidirect
291. #395	C₂²×C₁₃₉	semidirect
293. #393	C₂²×C₁₃₉	semidirect
294. #393	C₂²×C₁₃₉	semidirect
295. #391	C₂²×C₁₃₉	semidirect
296. #391	C₂²×C₁₃₉	semidirect
297. #389	C₂²×C₁₃₉	semidirect
298. #388	C₂²×C₁₃₉	semidirect
299. #388	C₂²×C₁₃₉	semidirect
300. #387	C₂²×C₁₃₉	semidirect
304. #385	C₂²×C₁₃₉	semidirect
306. #381	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#543×C₁₃₉	2
C₂²×#124×C₁₃₉	2
#2855×C₁₃₉	2
#2700×C₁₃₉	2
#2674×C₁₃₉	2
#2626×C₁₃₉	2
#2561×C₁₃₉	2
#2483×C₁₃₉	2
#2434×C₁₃₉	2
#2405×C₁₃₉	2
#2312×C₁₃₉	2
#36966	139

Subgroups — C139×#36966 #48031562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36966 #48031562