Subgroups — C₁₃₉×#37194 #48031790

Order 35584.

1650 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2855×C₁₃₉	C₂	1	2	yes	maximal
2	#2811×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2809×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2809×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2806×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2806×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2799×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2799×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#2627×C₁₃₉	C₂	1	2	yes	maximal
10	#2438×C₁₃₉	C₂	1	4	yes	maximal
11	#2438×C₁₃₉	C₂	1	4	yes	maximal
12	#2310×C₁₃₉	C₂	1	2	yes	maximal
13	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic
14	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
21	#400×C₁₃₉	C₂²	1	2	yes	—
22	#400×C₁₃₉	C₂²	1	4	yes	—
23	#400×C₁₃₉	C₂²	1	2	yes	—
24	#400×C₁₃₉	C₂²	1	4	yes	—
25	#398×C₁₃₉	C₂²	1	4	yes	—
26	#398×C₁₃₉	C₂²	1	4	yes	—
27	#398×C₁₃₉	C₂²	1	4	yes	—
28	#398×C₁₃₉	C₂²	1	4	yes	—
29	#398×C₁₃₉	C₂²	1	4	yes	—
30	#398×C₁₃₉	C₂²	1	4	yes	—
31	#395×C₁₃₉	C₂²	1	4	yes	—
32	#395×C₁₃₉	C₂²	1	2	yes	—
33	#395×C₁₃₉	C₂²	1	2	yes	—
34	#395×C₁₃₉	C₂²	1	4	yes	—
35	#391×C₁₃₉	C₂²	1	1	yes	characteristic
36	#391×C₁₃₉	C₂²	1	2	yes	—
37	#391×C₁₃₉	C₂²	1	2	yes	—
38	#391×C₁₃₉	C₂²	1	4	yes	—
39	#391×C₁₃₉	C₂²	1	4	yes	—
40	#391×C₁₃₉	C₂²	1	4	yes	—
41	#391×C₁₃₉	C₂²	1	4	yes	—
42	#391×C₁₃₉	C₂²	1	4	yes	—
43	#391×C₁₃₉	C₂²	1	1	yes	characteristic
44	#391×C₁₃₉	C₂²	1	1	yes	characteristic
45	#391×C₁₃₉	C₂²	1	1	yes	characteristic
46	#391×C₁₃₉	C₂²	1	2	yes	—
47	#391×C₁₃₉	C₂²	1	2	yes	—
48	#391×C₁₃₉	C₂²	1	2	yes	—
49	#391×C₁₃₉	C₂²	1	2	yes	—
50	#389×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	4	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	4	yes	—
54	#387×C₁₃₉	C₂²	1	4	yes	—
55	#387×C₁₃₉	C₂²	1	4	yes	—
56	#387×C₁₃₉	C₂²	1	4	yes	—
57	#387×C₁₃₉	C₂²	1	4	yes	—
58	#387×C₁₃₉	C₂²	1	4	yes	—
59	#387×C₁₃₉	C₂²	1	4	yes	—
60	#385×C₁₃₉	C₂²	1	4	yes	—
61	#385×C₁₃₉	C₂²	1	4	yes	—
62	#381×C₁₃₉	C₂²	1	4	yes	—
63	#381×C₁₃₉	C₂²	1	4	yes	—
64	#380×C₁₃₉	C₂²	1	2	yes	—
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
67	C₂²×Q₈×C₁₃₉	—	4	2	no	—
68	C₂²×Q₈×C₁₃₉	—	4	2	no	—
69	C₂²×Q₈×C₁₃₉	Q₈	1	8	yes	complemented
70	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
71	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
72	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
74	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
80	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
81	#117×C₁₃₉	—	4	4	no	—
82	#117×C₁₃₉	—	4	4	no	—
83	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
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	2	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₄²×C₁₃₉	—	4	2	no	—
104	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
110	#95×C₁₃₉	C₂³	1	2	yes	—
111	#95×C₁₃₉	C₂³	1	4	yes	—
112	#95×C₁₃₉	C₂³	1	4	yes	—
113	#95×C₁₃₉	C₂³	1	4	yes	—
114	#95×C₁₃₉	C₂³	1	4	yes	—
115	#95×C₁₃₉	C₂³	1	4	yes	—
116	#95×C₁₃₉	C₂³	1	4	yes	—
117	#95×C₁₃₉	C₂³	1	2	yes	—
118	#95×C₁₃₉	C₂³	1	4	yes	—
119	#95×C₁₃₉	C₂³	1	4	yes	—
120	#95×C₁₃₉	C₂³	1	4	yes	—
121	#95×C₁₃₉	C₂³	1	4	yes	—
122	#95×C₁₃₉	C₂³	1	4	yes	—
123	#95×C₁₃₉	C₂³	1	4	yes	—
124	#95×C₁₃₉	C₂³	1	4	yes	—
125	#95×C₁₃₉	C₂³	1	4	yes	—
126	#95×C₁₃₉	C₂³	1	4	yes	—
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	4	yes	—
129	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
130	C₂×Q₈×C₁₃₉	—	2	4	no	—
131	C₂×Q₈×C₁₃₉	—	4	16	no	—
132	C₂×Q₈×C₁₃₉	—	4	1	no	—
133	C₂×Q₈×C₁₃₉	—	4	2	no	—
134	C₂×Q₈×C₁₃₉	—	4	1	no	—
135	C₂×Q₈×C₁₃₉	—	4	1	no	—
136	C₂×Q₈×C₁₃₉	—	4	2	no	—
137	C₂×Q₈×C₁₃₉	—	4	1	no	—
138	C₂×Q₈×C₁₃₉	—	4	2	no	—
139	C₂×Q₈×C₁₃₉	—	4	2	no	—
140	C₂×Q₈×C₁₃₉	—	4	2	no	—
141	C₂×Q₈×C₁₃₉	—	4	4	no	—
142	C₂×Q₈×C₁₃₉	C₂×Q₈	1	4	yes	—
143	C₂×Q₈×C₁₃₉	C₂×Q₈	1	8	yes	—
144	C₂×Q₈×C₁₃₉	C₂×Q₈	1	4	yes	—
145	C₂²×C₄×C₁₃₉	—	2	2	no	—
146	C₂²×C₄×C₁₃₉	—	2	2	no	—
147	C₂²×C₄×C₁₃₉	—	2	4	no	—
148	C₂²×C₄×C₁₃₉	—	2	4	no	—
149	C₂²×C₄×C₁₃₉	—	2	4	no	—
150	C₂²×C₄×C₁₃₉	—	2	4	no	—
151	C₂²×C₄×C₁₃₉	—	2	4	no	—
152	C₂²×C₄×C₁₃₉	—	4	2	no	—
153	C₂²×C₄×C₁₃₉	—	4	4	no	—
154	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
155	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
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	1	yes	characteristic
166	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
168	C₄⋊C₄×C₁₃₉	—	2	8	no	—
169	C₄⋊C₄×C₁₃₉	—	2	4	no	—
170	C₄⋊C₄×C₁₃₉	—	4	1	no	—
171	C₄⋊C₄×C₁₃₉	—	4	2	no	—
172	C₄⋊C₄×C₁₃₉	—	4	1	no	—
173	C₄⋊C₄×C₁₃₉	—	4	2	no	—
174	C₄⋊C₄×C₁₃₉	—	4	4	no	—
175	C₄⋊C₄×C₁₃₉	—	4	4	no	—
176	C₄⋊C₄×C₁₃₉	—	4	4	no	—
177	C₄⋊C₄×C₁₃₉	—	4	4	no	—
178	C₄⋊C₄×C₁₃₉	—	4	2	no	—
179	C₄⋊C₄×C₁₃₉	—	4	4	no	—
180	C₄⋊C₄×C₁₃₉	—	4	2	no	—
181	C₄⋊C₄×C₁₃₉	—	4	2	no	—
182	C₄⋊C₄×C₁₃₉	—	4	4	no	—
183	C₄⋊C₄×C₁₃₉	—	4	2	no	—
184	C₄⋊C₄×C₁₃₉	—	4	4	no	—
185	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
186	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
187	C₄²×C₁₃₉	—	4	1	no	—
188	C₄²×C₁₃₉	—	4	2	no	—
189	C₄²×C₁₃₉	—	4	1	no	—
190	C₄²×C₁₃₉	—	4	2	no	—
191	C₄²×C₁₃₉	—	4	4	no	—
192	C₄²×C₁₃₉	—	4	2	no	—
193	C₂³×C₁₃₉	—	2	2	no	—
194	C₂³×C₁₃₉	—	2	2	no	—
195	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
196	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
197	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
198	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
199	Q₈×C₁₃₉	—	4	4	no	—
200	Q₈×C₁₃₉	—	4	8	no	—
201	Q₈×C₁₃₉	—	4	4	no	—
202	Q₈×C₁₃₉	—	8	4	no	—
203	Q₈×C₁₃₉	—	8	4	no	—
204	C₂×C₄×C₁₃₉	—	2	8	no	—
205	C₂×C₄×C₁₃₉	—	2	16	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	1	no	—
208	C₂×C₄×C₁₃₉	—	2	1	no	—
209	C₂×C₄×C₁₃₉	—	2	2	no	—
210	C₂×C₄×C₁₃₉	—	2	2	no	—
211	C₂×C₄×C₁₃₉	—	2	2	no	—
212	C₂×C₄×C₁₃₉	—	2	1	no	—
213	C₂×C₄×C₁₃₉	—	2	1	no	—
214	C₂×C₄×C₁₃₉	—	2	2	no	—
215	C₂×C₄×C₁₃₉	—	2	2	no	—
216	C₂×C₄×C₁₃₉	—	2	2	no	—
217	C₂×C₄×C₁₃₉	—	2	4	no	—
218	C₂×C₄×C₁₃₉	—	2	4	no	—
219	C₂×C₄×C₁₃₉	—	2	4	no	—
220	C₂×C₄×C₁₃₉	—	2	4	no	—
221	C₂×C₄×C₁₃₉	—	2	2	no	—
222	C₂×C₄×C₁₃₉	—	2	2	no	—
223	C₂×C₄×C₁₃₉	—	2	4	no	—
224	C₂×C₄×C₁₃₉	—	2	4	no	—
225	C₂×C₄×C₁₃₉	—	2	4	no	—
226	C₂×C₄×C₁₃₉	—	2	2	no	—
227	C₂×C₄×C₁₃₉	—	2	4	no	—
228	C₂×C₄×C₁₃₉	—	2	4	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	—	2	4	no	—
234	C₂×C₄×C₁₃₉	—	2	4	no	—
235	C₂×C₄×C₁₃₉	—	4	8	no	—
236	C₂×C₄×C₁₃₉	—	8	4	no	—
237	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
238	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
239	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
240	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
241	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
242	C₂²×C₁₃₉	—	2	4	no	—
243	C₂²×C₁₃₉	—	2	4	no	—
244	C₂²×C₁₃₉	—	2	2	no	—
245	C₂²×C₁₃₉	—	2	2	no	—
246	C₂²×C₁₃₉	#543	1	4	yes	—
247	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
248	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
249	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
250	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
251	C₂²×C₁₃₉	#585	1	2	yes	—
252	C₄×C₁₃₉	—	2	2	no	—
253	C₄×C₁₃₉	—	2	2	no	—
254	C₄×C₁₃₉	—	2	4	no	—
255	C₄×C₁₃₉	—	2	4	no	—
256	C₄×C₁₃₉	—	2	4	no	—
257	C₄×C₁₃₉	—	4	4	no	—
258	C₄×C₁₃₉	—	4	2	no	—
259	C₄×C₁₃₉	—	4	4	no	—
260	C₄×C₁₃₉	—	4	4	no	—
261	C₄×C₁₃₉	—	4	2	no	—
262	C₄×C₁₃₉	—	4	2	no	—
263	C₄×C₁₃₉	—	4	4	no	—
264	C₂×C₁₃₉	—	2	4	no	—
265	C₂×C₁₃₉	C₂×#543	1	1	yes	characteristic
266	C₂×C₁₃₉	#3502	1	2	yes	—
267	C₂×C₁₃₉	#3535	1	2	yes	—
268	C₂×C₁₃₉	#3544	1	1	yes	characteristic
269	C₂×C₁₃₉	#3545	1	1	yes	characteristic
270	#37194	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₁₃₉	#37194	1	1	yes	characteristic, direct product factor, Sylow
272	#2855	C₂×C₁₃₉	1	2	yes	—
273	#2811	C₂×C₁₃₉	1	1	yes	characteristic, complemented
274	#2809	C₂×C₁₃₉	1	2	yes	complemented
275	#2809	C₂×C₁₃₉	1	1	yes	characteristic, complemented
276	#2806	C₂×C₁₃₉	1	4	yes	complemented
277	#2806	C₂×C₁₃₉	1	2	yes	complemented
278	#2799	C₂×C₁₃₉	1	4	yes	complemented
279	#2799	C₂×C₁₃₉	1	2	yes	complemented
280	#2627	C₂×C₁₃₉	1	2	yes	—
281	#2438	C₂×C₁₃₉	1	4	yes	—
282	#2438	C₂×C₁₃₉	1	4	yes	—
283	#2310	C₂×C₁₃₉	1	2	yes	—
284	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic
285	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
286	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
287	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
288	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
289	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
290	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
291	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
292	#400	C₂²×C₁₃₉	1	2	yes	—
293	#400	C₂²×C₁₃₉	1	2	yes	—
294	#400	C₂²×C₁₃₉	1	4	yes	—
295	#400	C₂²×C₁₃₉	1	4	yes	—
296	#398	C₂²×C₁₃₉	1	4	yes	—
297	#398	C₂²×C₁₃₉	1	4	yes	—
298	#398	C₂²×C₁₃₉	1	4	yes	—
299	#398	C₂²×C₁₃₉	1	4	yes	—
300	#398	C₂²×C₁₃₉	1	4	yes	—
301	#398	C₂²×C₁₃₉	1	4	yes	—
302	#395	C₂²×C₁₃₉	1	2	yes	—
303	#395	C₂²×C₁₃₉	1	2	yes	—
304	#395	C₂²×C₁₃₉	1	4	yes	—
305	#395	C₂²×C₁₃₉	1	4	yes	—
306	#391	C₂²×C₁₃₉	1	2	yes	—
307	#391	C₂²×C₁₃₉	1	4	yes	—
308	#391	C₂²×C₁₃₉	1	4	yes	—
309	#391	C₂²×C₁₃₉	1	2	yes	—
310	#391	C₂²×C₁₃₉	1	2	yes	—
311	#391	C₂²×C₁₃₉	1	2	yes	—
312	#391	C₂²×C₁₃₉	1	2	yes	—
313	#391	C₂²×C₁₃₉	1	2	yes	—
314	#391	C₂²×C₁₃₉	1	4	yes	—
315	#391	C₂²×C₁₃₉	1	4	yes	—
316	#391	C₂²×C₁₃₉	1	1	yes	characteristic
317	#391	C₂²×C₁₃₉	1	4	yes	—
318	#391	C₂²×C₁₃₉	1	1	yes	characteristic
319	#391	C₂²×C₁₃₉	1	1	yes	characteristic
320	#391	C₂²×C₁₃₉	1	1	yes	characteristic
321	#389	C₂²×C₁₃₉	1	2	yes	—
322	#389	C₂²×C₁₃₉	1	2	yes	—
323	#389	C₂²×C₁₃₉	1	4	yes	—
324	#389	C₂²×C₁₃₉	1	4	yes	—
325	#387	C₂²×C₁₃₉	1	4	yes	—
326	#387	C₂²×C₁₃₉	1	4	yes	—
327	#387	C₂²×C₁₃₉	1	4	yes	—
328	#387	C₂²×C₁₃₉	1	4	yes	—
329	#387	C₂²×C₁₃₉	1	4	yes	—
330	#387	C₂²×C₁₃₉	1	4	yes	—
331	#385	C₂²×C₁₃₉	1	4	yes	—
332	#385	C₂²×C₁₃₉	1	4	yes	—
333	#381	C₂²×C₁₃₉	1	4	yes	—
334	#381	C₂²×C₁₃₉	1	4	yes	—
335	#380	C₂²×C₁₃₉	1	2	yes	—
336	#380	C₂²×C₁₃₉	1	2	yes	—
337	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
338	C₂²×Q₈	—	4	2	no	—
339	C₂²×Q₈	—	4	2	no	—
340	C₂²×Q₈	Q₈×C₁₃₉	1	8	yes	complemented
341	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
342	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
343	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
344	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
345	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
347	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
348	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
349	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
350	C₂²⋊Q₈	—	4	4	no	—
351	C₂²⋊Q₈	—	4	4	no	—
352	#117	—	4	4	no	—
353	#117	—	4	4	no	—
354	C₂×C₄⋊C₄	—	4	2	no	—
355	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
356	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
374	C₂×C₄²	—	4	2	no	—
375	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
376	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
377	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
378	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
380	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
381	#95	C₂³×C₁₃₉	1	4	yes	—
382	#95	C₂³×C₁₃₉	1	4	yes	—
383	#95	C₂³×C₁₃₉	1	4	yes	—
384	#95	C₂³×C₁₃₉	1	4	yes	—
385	#95	C₂³×C₁₃₉	1	4	yes	—
386	#95	C₂³×C₁₃₉	1	2	yes	—
387	#95	C₂³×C₁₃₉	1	2	yes	—
388	#95	C₂³×C₁₃₉	1	4	yes	—
389	#95	C₂³×C₁₃₉	1	4	yes	—
390	#95	C₂³×C₁₃₉	1	4	yes	—
391	#95	C₂³×C₁₃₉	1	4	yes	—
392	#95	C₂³×C₁₃₉	1	4	yes	—
393	#95	C₂³×C₁₃₉	1	4	yes	—
394	#95	C₂³×C₁₃₉	1	4	yes	—
395	#95	C₂³×C₁₃₉	1	4	yes	—
396	#95	C₂³×C₁₃₉	1	4	yes	—
397	#95	C₂³×C₁₃₉	1	4	yes	—
398	#95	C₂³×C₁₃₉	1	4	yes	—
399	#95	C₂³×C₁₃₉	1	4	yes	—
400	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	4	16	no	—
403	C₂×Q₈	—	4	1	no	—
404	C₂×Q₈	—	4	2	no	—
405	C₂×Q₈	—	4	1	no	—
406	C₂×Q₈	—	4	1	no	—
407	C₂×Q₈	—	4	2	no	—
408	C₂×Q₈	—	4	1	no	—
409	C₂×Q₈	—	4	2	no	—
410	C₂×Q₈	—	4	2	no	—
411	C₂×Q₈	—	4	2	no	—
412	C₂×Q₈	—	4	4	no	—
413	C₂×Q₈	C₂×Q₈×C₁₃₉	1	8	yes	—
414	C₂×Q₈	C₂×Q₈×C₁₃₉	1	4	yes	—
415	C₂×Q₈	C₂×Q₈×C₁₃₉	1	4	yes	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	4	no	—
425	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
426	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
427	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
430	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	4	1	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	—	4	1	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	4	4	no	—
446	C₄⋊C₄	—	4	4	no	—
447	C₄⋊C₄	—	4	4	no	—
448	C₄⋊C₄	—	4	4	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₄⋊C₄	—	4	4	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	—	4	4	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₄²	—	4	1	no	—
459	C₄²	—	4	2	no	—
460	C₄²	—	4	1	no	—
461	C₄²	—	4	2	no	—
462	C₄²	—	4	4	no	—
463	C₄²	—	4	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
467	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
468	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
469	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
470	Q₈	—	4	4	no	—
471	Q₈	—	4	8	no	—
472	Q₈	—	4	4	no	—
473	Q₈	—	8	4	no	—
474	Q₈	—	8	4	no	—
475	C₂×C₄	—	2	8	no	—
476	C₂×C₄	—	2	16	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	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	—	4	8	no	—
507	C₂×C₄	—	8	4	no	—
508	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
509	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
510	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
511	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
512	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	4	no	—
517	C₂²	#543×C₁₃₉	1	4	yes	—
518	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
519	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
520	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
521	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
522	C₂²	#585×C₁₃₉	1	2	yes	—
523	C₄	—	2	4	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	4	no	—
527	C₄	—	2	4	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	4	no	—
530	C₄	—	4	4	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	4	no	—
535	C₂	—	2	4	no	—
536	C₂	C₂×#543×C₁₃₉	1	1	yes	characteristic
537	C₂	#3502×C₁₃₉	1	2	yes	—
538	C₂	#3535×C₁₃₉	1	2	yes	—
539	C₂	#3544×C₁₃₉	1	1	yes	characteristic
540	C₂	#3545×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂⁴×C₁₃₉	C₂⁴
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. #2811×C₁₃₉	C₂	semidirect
3. #2809×C₁₃₉	C₂	semidirect
4. #2809×C₁₃₉	C₂	semidirect
5. #2806×C₁₃₉	C₂	semidirect
6. #2806×C₁₃₉	C₂	semidirect
7. #2799×C₁₃₉	C₂	semidirect
8. #2799×C₁₃₉	C₂	semidirect
69. C₂²×Q₈×C₁₃₉	Q₈	semidirect
270. #37194	C₁₃₉	direct (N × H)
271. C₁₃₉	#37194	direct (N × H)
273. #2811	C₂×C₁₃₉	semidirect
274. #2809	C₂×C₁₃₉	semidirect
275. #2809	C₂×C₁₃₉	semidirect
276. #2806	C₂×C₁₃₉	semidirect
277. #2806	C₂×C₁₃₉	semidirect
278. #2799	C₂×C₁₃₉	semidirect
279. #2799	C₂×C₁₃₉	semidirect
340. C₂²×Q₈	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2855×C₁₃₉	2
#2811×C₁₃₉	2
#2809×C₁₃₉	2
#2806×C₁₃₉	2
#2799×C₁₃₉	2
#2627×C₁₃₉	2
#2438×C₁₃₉	2
#2310×C₁₃₉	2
C₂×#391×C₁₃₉	2
#37194	139

Subgroups — C139×#37194 #48031790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37194 #48031790