Subgroups — C₁₃₉×#37320 #48031916

Order 35584.

1508 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2868×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2864×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2794×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2721×C₁₃₉	C₂	1	4	yes	maximal
5	#2716×C₁₃₉	C₂	1	4	yes	maximal
6	#2713×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2628×C₁₃₉	C₂	1	1	yes	maximal, characteristic
8	#2628×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#2507×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2506×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2497×C₁₃₉	C₂	1	2	yes	maximal
12	#2496×C₁₃₉	C₂	1	2	yes	maximal
13	#2331×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2331×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
19	C₂×#126×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#125×C₁₃₉	C₂²	1	4	yes	—
21	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
22	#400×C₁₃₉	C₂²	1	2	yes	—
23	#400×C₁₃₉	C₂²	1	2	yes	—
24	#400×C₁₃₉	C₂²	1	4	yes	—
25	#400×C₁₃₉	C₂²	1	4	yes	—
26	#400×C₁₃₉	C₂²	1	4	yes	—
27	#399×C₁₃₉	C₂²	1	2	yes	—
28	#399×C₁₃₉	C₂²	1	2	yes	—
29	#398×C₁₃₉	C₂²	1	4	yes	—
30	#398×C₁₃₉	C₂²	1	4	yes	—
31	#398×C₁₃₉	C₂²	1	4	yes	—
32	#397×C₁₃₉	C₂²	1	4	yes	—
33	#396×C₁₃₉	C₂²	1	4	yes	—
34	#395×C₁₃₉	C₂²	1	2	yes	—
35	#395×C₁₃₉	C₂²	1	2	yes	—
36	#393×C₁₃₉	C₂²	1	2	yes	—
37	#393×C₁₃₉	C₂²	1	2	yes	—
38	#391×C₁₃₉	C₂²	1	4	yes	—
39	#391×C₁₃₉	C₂²	1	4	yes	—
40	#389×C₁₃₉	C₂²	1	2	yes	—
41	#389×C₁₃₉	C₂²	1	2	yes	—
42	#389×C₁₃₉	C₂²	1	2	yes	—
43	#389×C₁₃₉	C₂²	1	2	yes	—
44	#389×C₁₃₉	C₂²	1	2	yes	—
45	#389×C₁₃₉	C₂²	1	2	yes	—
46	#389×C₁₃₉	C₂²	1	4	yes	—
47	#388×C₁₃₉	C₂²	1	2	yes	—
48	#388×C₁₃₉	C₂²	1	2	yes	—
49	#388×C₁₃₉	C₂²	1	4	yes	—
50	#387×C₁₃₉	C₂²	1	2	yes	—
51	#387×C₁₃₉	C₂²	1	4	yes	—
52	#387×C₁₃₉	C₂²	1	4	yes	—
53	#387×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	2	yes	—
59	#387×C₁₃₉	C₂²	1	4	yes	—
60	#384×C₁₃₉	C₂²	1	4	yes	—
61	#384×C₁₃₉	C₂²	1	2	yes	—
62	#384×C₁₃₉	C₂²	1	2	yes	—
63	#382×C₁₃₉	C₂²	1	1	yes	characteristic
64	#382×C₁₃₉	C₂²	1	1	yes	characteristic
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	#380×C₁₃₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
68	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
73	#376×C₁₃₉	C₂²	1	1	yes	characteristic
74	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
76	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
79	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
80	C₄⋊Q₈×C₁₃₉	—	4	8	no	—
81	#126×C₁₃₉	—	4	8	no	—
82	#125×C₁₃₉	—	4	8	no	—
83	#117×C₁₃₉	—	2	4	no	—
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	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	4	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
120	#95×C₁₃₉	C₂³	1	4	yes	—
121	#95×C₁₃₉	C₂³	1	4	yes	—
122	#95×C₁₃₉	C₂³	1	2	yes	—
123	#95×C₁₃₉	C₂³	1	2	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	2	yes	—
129	#95×C₁₃₉	C₂³	1	4	yes	—
130	#95×C₁₃₉	C₂³	1	4	yes	—
131	#95×C₁₃₉	C₂³	1	4	yes	—
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	2	yes	—
134	#95×C₁₃₉	C₂³	1	2	yes	—
135	#95×C₁₃₉	C₂³	1	2	yes	—
136	#95×C₁₃₉	C₂³	1	2	yes	—
137	#95×C₁₃₉	C₂³	1	2	yes	—
138	#95×C₁₃₉	C₂³	1	2	yes	—
139	#95×C₁₃₉	C₂³	1	2	yes	—
140	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
141	C₂×Q₈×C₁₃₉	—	2	4	no	—
142	C₂×Q₈×C₁₃₉	—	2	4	no	—
143	C₂×Q₈×C₁₃₉	—	4	4	no	—
144	C₂×Q₈×C₁₃₉	—	4	4	no	—
145	C₂²×C₄×C₁₃₉	—	2	2	no	—
146	C₂²×C₄×C₁₃₉	—	2	2	no	—
147	C₂²×C₄×C₁₃₉	—	2	2	no	—
148	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
157	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
162	C₄⋊C₄×C₁₃₉	—	2	2	no	—
163	C₄⋊C₄×C₁₃₉	—	2	2	no	—
164	C₄⋊C₄×C₁₃₉	—	2	4	no	—
165	C₄⋊C₄×C₁₃₉	—	2	4	no	—
166	C₄⋊C₄×C₁₃₉	—	2	4	no	—
167	C₄⋊C₄×C₁₃₉	—	2	4	no	—
168	C₄⋊C₄×C₁₃₉	—	2	4	no	—
169	C₄⋊C₄×C₁₃₉	—	2	8	no	—
170	C₄⋊C₄×C₁₃₉	—	2	8	no	—
171	C₄⋊C₄×C₁₃₉	—	2	8	no	—
172	C₄⋊C₄×C₁₃₉	—	2	8	no	—
173	C₄⋊C₄×C₁₃₉	—	2	4	no	—
174	C₄⋊C₄×C₁₃₉	—	2	4	no	—
175	C₄⋊C₄×C₁₃₉	—	2	4	no	—
176	C₄⋊C₄×C₁₃₉	—	4	4	no	—
177	C₄⋊C₄×C₁₃₉	—	4	4	no	—
178	C₄⋊C₄×C₁₃₉	—	4	4	no	—
179	C₄⋊C₄×C₁₃₉	—	4	4	no	—
180	C₄⋊C₄×C₁₃₉	—	4	4	no	—
181	C₄⋊C₄×C₁₃₉	—	4	4	no	—
182	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
183	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
184	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
185	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
186	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
187	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
188	C₄²×C₁₃₉	—	2	2	no	—
189	C₄²×C₁₃₉	—	2	4	no	—
190	C₄²×C₁₃₉	—	2	4	no	—
191	C₄²×C₁₃₉	—	2	2	no	—
192	C₄²×C₁₃₉	—	2	2	no	—
193	C₄²×C₁₃₉	—	2	2	no	—
194	C₄²×C₁₃₉	—	2	2	no	—
195	C₄²×C₁₃₉	—	4	4	no	—
196	C₄²×C₁₃₉	—	4	4	no	—
197	C₄²×C₁₃₉	#41	1	4	yes	—
198	C₂³×C₁₃₉	—	2	1	no	—
199	C₂³×C₁₃₉	—	2	2	no	—
200	C₂³×C₁₃₉	—	2	2	no	—
201	C₂³×C₁₃₉	—	2	1	no	—
202	C₂³×C₁₃₉	—	2	1	no	—
203	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
204	Q₈×C₁₃₉	—	8	4	no	—
205	Q₈×C₁₃₉	—	8	4	no	—
206	C₂×C₄×C₁₃₉	—	2	2	no	—
207	C₂×C₄×C₁₃₉	—	2	2	no	—
208	C₂×C₄×C₁₃₉	—	2	2	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	1	no	—
215	C₂×C₄×C₁₃₉	—	2	4	no	—
216	C₂×C₄×C₁₃₉	—	2	4	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	4	no	—
221	C₂×C₄×C₁₃₉	—	2	4	no	—
222	C₂×C₄×C₁₃₉	—	2	4	no	—
223	C₂×C₄×C₁₃₉	—	2	4	no	—
224	C₂×C₄×C₁₃₉	—	2	2	no	—
225	C₂×C₄×C₁₃₉	—	2	4	no	—
226	C₂×C₄×C₁₃₉	—	2	2	no	—
227	C₂×C₄×C₁₃₉	—	2	2	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	—	2	2	no	—
234	C₂×C₄×C₁₃₉	—	2	4	no	—
235	C₂×C₄×C₁₃₉	—	2	1	no	—
236	C₂×C₄×C₁₃₉	—	2	1	no	—
237	C₂×C₄×C₁₃₉	—	4	4	no	—
238	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
239	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
240	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
241	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
242	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
243	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
244	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
245	C₂²×C₁₃₉	—	4	1	no	—
246	C₂²×C₁₃₉	—	4	1	no	—
247	C₂²×C₁₃₉	—	4	1	no	—
248	C₂²×C₁₃₉	—	4	2	no	—
249	C₂²×C₁₃₉	—	4	2	no	—
250	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
251	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
252	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
253	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
254	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
255	C₄×C₁₃₉	—	2	2	no	—
256	C₄×C₁₃₉	—	2	2	no	—
257	C₄×C₁₃₉	—	2	4	no	—
258	C₄×C₁₃₉	—	2	4	no	—
259	C₄×C₁₃₉	—	4	1	no	—
260	C₄×C₁₃₉	—	4	1	no	—
261	C₄×C₁₃₉	—	4	4	no	—
262	C₄×C₁₃₉	—	4	4	no	—
263	C₄×C₁₃₉	—	4	1	no	—
264	C₄×C₁₃₉	—	4	2	no	—
265	C₄×C₁₃₉	—	4	4	no	—
266	C₄×C₁₃₉	—	4	2	no	—
267	C₄×C₁₃₉	—	4	4	no	—
268	C₄×C₁₃₉	#541	1	4	yes	—
269	C₂×C₁₃₉	—	8	1	no	—
270	C₂×C₁₃₉	C₂×#541	1	1	yes	characteristic
271	C₂×C₁₃₉	#3508	1	1	yes	characteristic
272	C₂×C₁₃₉	#3509	1	1	yes	characteristic
273	C₂×C₁₃₉	#3544	1	2	yes	—
274	C₂×C₁₃₉	#3552	1	2	yes	—
275	#37320	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₁₃₉	#37320	1	1	yes	characteristic, direct product factor, Sylow
277	#2868	C₂×C₁₃₉	1	1	yes	characteristic, complemented
278	#2864	C₂×C₁₃₉	1	1	yes	characteristic, complemented
279	#2794	C₂×C₁₃₉	1	4	yes	complemented
280	#2721	C₂×C₁₃₉	1	4	yes	—
281	#2716	C₂×C₁₃₉	1	4	yes	—
282	#2713	C₂×C₁₃₉	1	4	yes	complemented
283	#2628	C₂×C₁₃₉	1	1	yes	characteristic
284	#2628	C₂×C₁₃₉	1	1	yes	characteristic
285	#2507	C₂×C₁₃₉	1	2	yes	complemented
286	#2506	C₂×C₁₃₉	1	2	yes	complemented
287	#2497	C₂×C₁₃₉	1	2	yes	—
288	#2496	C₂×C₁₃₉	1	2	yes	—
289	#2331	C₂×C₁₃₉	1	1	yes	characteristic, complemented
290	#2331	C₂×C₁₃₉	1	1	yes	characteristic, complemented
291	#2298	C₂×C₁₃₉	1	1	yes	characteristic
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	4	yes	—
295	C₂×#126	C₂²×C₁₃₉	1	4	yes	—
296	C₂×#125	C₂²×C₁₃₉	1	4	yes	—
297	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
298	#400	C₂²×C₁₃₉	1	2	yes	—
299	#400	C₂²×C₁₃₉	1	2	yes	—
300	#400	C₂²×C₁₃₉	1	4	yes	—
301	#400	C₂²×C₁₃₉	1	4	yes	—
302	#400	C₂²×C₁₃₉	1	4	yes	—
303	#399	C₂²×C₁₃₉	1	2	yes	—
304	#399	C₂²×C₁₃₉	1	2	yes	—
305	#398	C₂²×C₁₃₉	1	4	yes	—
306	#398	C₂²×C₁₃₉	1	4	yes	—
307	#398	C₂²×C₁₃₉	1	4	yes	—
308	#397	C₂²×C₁₃₉	1	4	yes	—
309	#396	C₂²×C₁₃₉	1	4	yes	—
310	#395	C₂²×C₁₃₉	1	2	yes	—
311	#395	C₂²×C₁₃₉	1	2	yes	—
312	#393	C₂²×C₁₃₉	1	2	yes	—
313	#393	C₂²×C₁₃₉	1	2	yes	—
314	#391	C₂²×C₁₃₉	1	4	yes	—
315	#391	C₂²×C₁₃₉	1	4	yes	—
316	#389	C₂²×C₁₃₉	1	2	yes	—
317	#389	C₂²×C₁₃₉	1	2	yes	—
318	#389	C₂²×C₁₃₉	1	2	yes	—
319	#389	C₂²×C₁₃₉	1	2	yes	—
320	#389	C₂²×C₁₃₉	1	2	yes	—
321	#389	C₂²×C₁₃₉	1	2	yes	—
322	#389	C₂²×C₁₃₉	1	4	yes	—
323	#388	C₂²×C₁₃₉	1	2	yes	—
324	#388	C₂²×C₁₃₉	1	4	yes	—
325	#388	C₂²×C₁₃₉	1	2	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	2	yes	—
331	#387	C₂²×C₁₃₉	1	4	yes	—
332	#387	C₂²×C₁₃₉	1	4	yes	—
333	#387	C₂²×C₁₃₉	1	4	yes	—
334	#387	C₂²×C₁₃₉	1	4	yes	—
335	#387	C₂²×C₁₃₉	1	2	yes	—
336	#384	C₂²×C₁₃₉	1	4	yes	—
337	#384	C₂²×C₁₃₉	1	2	yes	—
338	#384	C₂²×C₁₃₉	1	2	yes	—
339	#382	C₂²×C₁₃₉	1	1	yes	characteristic
340	#382	C₂²×C₁₃₉	1	1	yes	characteristic
341	#380	C₂²×C₁₃₉	1	2	yes	—
342	#380	C₂²×C₁₃₉	1	2	yes	—
343	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
344	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
345	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
347	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
348	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
349	#376	C₂²×C₁₃₉	1	1	yes	characteristic
350	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
351	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
352	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
353	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
354	C₄⋊Q₈	—	2	4	no	—
355	C₄⋊Q₈	—	2	4	no	—
356	C₄⋊Q₈	—	4	8	no	—
357	#126	—	4	8	no	—
358	#125	—	4	8	no	—
359	#117	—	2	4	no	—
360	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
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	4	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	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	4	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	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
383	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
386	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
388	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
391	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
394	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
395	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
396	#95	C₂³×C₁₃₉	1	2	yes	—
397	#95	C₂³×C₁₃₉	1	2	yes	—
398	#95	C₂³×C₁₃₉	1	2	yes	—
399	#95	C₂³×C₁₃₉	1	2	yes	—
400	#95	C₂³×C₁₃₉	1	2	yes	—
401	#95	C₂³×C₁₃₉	1	2	yes	—
402	#95	C₂³×C₁₃₉	1	4	yes	—
403	#95	C₂³×C₁₃₉	1	4	yes	—
404	#95	C₂³×C₁₃₉	1	4	yes	—
405	#95	C₂³×C₁₃₉	1	4	yes	—
406	#95	C₂³×C₁₃₉	1	2	yes	—
407	#95	C₂³×C₁₃₉	1	2	yes	—
408	#95	C₂³×C₁₃₉	1	2	yes	—
409	#95	C₂³×C₁₃₉	1	2	yes	—
410	#95	C₂³×C₁₃₉	1	4	yes	—
411	#95	C₂³×C₁₃₉	1	4	yes	—
412	#95	C₂³×C₁₃₉	1	4	yes	—
413	#95	C₂³×C₁₃₉	1	4	yes	—
414	#95	C₂³×C₁₃₉	1	4	yes	—
415	#95	C₂³×C₁₃₉	1	4	yes	—
416	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	—	4	4	no	—
420	C₂×Q₈	—	4	4	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₁₃₉	1	2	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	4	yes	—
431	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	8	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	4	no	—
452	C₄⋊C₄	—	4	4	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₄⋊C₄	—	4	4	no	—
456	C₄⋊C₄	—	4	4	no	—
457	C₄⋊C₄	—	4	4	no	—
458	C₂²⋊C₄	—	2	2	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	4	no	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	4	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	4	4	no	—
472	C₄²	—	4	4	no	—
473	C₄²	#41×C₁₃₉	1	4	yes	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
480	Q₈	—	8	4	no	—
481	Q₈	—	8	4	no	—
482	C₂×C₄	—	2	2	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	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	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	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	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	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
515	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
516	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
517	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
518	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
519	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
520	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
527	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
528	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
529	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
530	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
531	C₄	—	2	4	no	—
532	C₄	—	2	4	no	—
533	C₄	—	2	2	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	4	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	4	no	—
541	C₄	—	4	4	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	#541×C₁₃₉	1	4	yes	—
545	C₂	—	8	1	no	—
546	C₂	C₂×#541×C₁₃₉	1	1	yes	characteristic
547	C₂	#3508×C₁₃₉	1	1	yes	characteristic
548	C₂	#3509×C₁₃₉	1	1	yes	characteristic
549	C₂	#3544×C₁₃₉	1	2	yes	—
550	C₂	#3552×C₁₃₉	1	2	yes	—

	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
1. #2868×C₁₃₉	C₂	semidirect
2. #2864×C₁₃₉	C₂	semidirect
3. #2794×C₁₃₉	C₂	semidirect
6. #2713×C₁₃₉	C₂	semidirect
9. #2507×C₁₃₉	C₂	semidirect
10. #2506×C₁₃₉	C₂	semidirect
13. #2331×C₁₃₉	C₂	semidirect
14. #2331×C₁₃₉	C₂	semidirect
275. #37320	C₁₃₉	direct (N × H)
276. C₁₃₉	#37320	direct (N × H)
277. #2868	C₂×C₁₃₉	semidirect
278. #2864	C₂×C₁₃₉	semidirect
279. #2794	C₂×C₁₃₉	semidirect
282. #2713	C₂×C₁₃₉	semidirect
285. #2507	C₂×C₁₃₉	semidirect
286. #2506	C₂×C₁₃₉	semidirect
289. #2331	C₂×C₁₃₉	semidirect
290. #2331	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2868×C₁₃₉	2
#2864×C₁₃₉	2
#2794×C₁₃₉	2
#2721×C₁₃₉	2
#2716×C₁₃₉	2
#2713×C₁₃₉	2
#2628×C₁₃₉	2
#2507×C₁₃₉	2
#2506×C₁₃₉	2
#2497×C₁₃₉	2
#2496×C₁₃₉	2
#2331×C₁₃₉	2
#2298×C₁₃₉	2
#37320	139

Subgroups — C139×#37320 #48031916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37320 #48031916