Subgroups — C₁₃₉×#36194 #48030790

Order 35584.

1890 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	#2857×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2571×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2563×C₁₃₉	C₂	1	2	yes	maximal
5	#2538×C₁₃₉	C₂	1	2	yes	maximal
6	#2497×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2492×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2439×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2369×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2355×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2354×C₁₃₉	C₂	1	2	yes	maximal
12	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2285×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
25	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
26	#400×C₁₃₉	C₂²	1	8	yes	—
27	#396×C₁₃₉	C₂²	1	8	yes	—
28	#393×C₁₃₉	C₂²	1	8	yes	—
29	#391×C₁₃₉	C₂²	1	2	yes	—
30	#391×C₁₃₉	C₂²	1	4	yes	—
31	#391×C₁₃₉	C₂²	1	8	yes	—
32	#390×C₁₃₉	C₂²	1	4	yes	—
33	#389×C₁₃₉	C₂²	1	4	yes	—
34	#389×C₁₃₉	C₂²	1	2	yes	—
35	#389×C₁₃₉	C₂²	1	2	yes	—
36	#389×C₁₃₉	C₂²	1	4	yes	—
37	#389×C₁₃₉	C₂²	1	4	yes	—
38	#388×C₁₃₉	C₂²	1	8	yes	—
39	#387×C₁₃₉	C₂²	1	8	yes	—
40	#384×C₁₃₉	C₂²	1	2	yes	—
41	#384×C₁₃₉	C₂²	1	1	yes	characteristic
42	#384×C₁₃₉	C₂²	1	2	yes	—
43	#384×C₁₃₉	C₂²	1	2	yes	—
44	#384×C₁₃₉	C₂²	1	2	yes	—
45	#382×C₁₃₉	C₂²	1	4	yes	—
46	#382×C₁₃₉	C₂²	1	4	yes	—
47	#380×C₁₃₉	C₂²	1	4	yes	—
48	#380×C₁₃₉	C₂²	1	4	yes	—
49	#380×C₁₃₉	C₂²	1	4	yes	—
50	#380×C₁₃₉	C₂²	1	4	yes	—
51	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
55	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
56	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
57	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
58	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
59	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
60	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
62	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
64	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
65	C₂²×D₄×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	2	yes	—
69	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
70	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
71	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
72	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
73	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
74	C₄×Q₈×C₁₃₉	—	2	8	no	—
75	C₄×D₄×C₁₃₉	—	2	4	no	—
76	C₄×D₄×C₁₃₉	—	2	4	no	—
77	C₄×D₄×C₁₃₉	Q₈	1	8	yes	complemented
78	#117×C₁₃₉	—	4	8	no	—
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	4	yes	—
82	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
99	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
100	C₂×C₄²×C₁₃₉	—	2	8	no	—
101	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
103	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
105	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
109	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
113	#95×C₁₃₉	C₂³	1	8	yes	—
114	#95×C₁₃₉	C₂³	1	2	yes	—
115	#95×C₁₃₉	C₂³	1	4	yes	—
116	#95×C₁₃₉	C₂³	1	8	yes	—
117	#95×C₁₃₉	C₂³	1	8	yes	—
118	#95×C₁₃₉	C₂³	1	2	yes	—
119	#95×C₁₃₉	C₂³	1	2	yes	—
120	#95×C₁₃₉	C₂³	1	8	yes	—
121	#95×C₁₃₉	C₂³	1	4	yes	—
122	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
123	C₂×Q₈×C₁₃₉	—	2	4	no	—
124	C₂×Q₈×C₁₃₉	—	2	4	no	—
125	C₂×Q₈×C₁₃₉	—	2	8	no	—
126	C₂×Q₈×C₁₃₉	—	2	4	no	—
127	C₂×Q₈×C₁₃₉	—	4	4	no	—
128	C₂×Q₈×C₁₃₉	—	4	4	no	—
129	C₂×D₄×C₁₃₉	—	2	2	no	—
130	C₂×D₄×C₁₃₉	—	2	2	no	—
131	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
132	C₂²×C₄×C₁₃₉	—	2	4	no	—
133	C₂²×C₄×C₁₃₉	—	2	4	no	—
134	C₂²×C₄×C₁₃₉	—	2	4	no	—
135	C₂²×C₄×C₁₃₉	—	2	4	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	—	2	4	no	—
140	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
141	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
146	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
153	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
154	C₄⋊C₄×C₁₃₉	—	2	2	no	—
155	C₄⋊C₄×C₁₃₉	—	2	2	no	—
156	C₄⋊C₄×C₁₃₉	—	2	4	no	—
157	C₄⋊C₄×C₁₃₉	—	2	8	no	—
158	C₄⋊C₄×C₁₃₉	—	2	8	no	—
159	C₄⋊C₄×C₁₃₉	—	2	4	no	—
160	C₄⋊C₄×C₁₃₉	—	2	4	no	—
161	C₄⋊C₄×C₁₃₉	—	2	8	no	—
162	C₄⋊C₄×C₁₃₉	—	2	4	no	—
163	C₄⋊C₄×C₁₃₉	—	2	8	no	—
164	C₄⋊C₄×C₁₃₉	—	2	8	no	—
165	C₄⋊C₄×C₁₃₉	—	2	4	no	—
166	C₄⋊C₄×C₁₃₉	—	4	8	no	—
167	C₄⋊C₄×C₁₃₉	—	4	4	no	—
168	C₄⋊C₄×C₁₃₉	—	4	4	no	—
169	C₄⋊C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
170	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
173	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
174	C₂²⋊C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
175	C₄²×C₁₃₉	—	2	4	no	—
176	C₄²×C₁₃₉	—	2	4	no	—
177	C₄²×C₁₃₉	—	2	4	no	—
178	C₄²×C₁₃₉	—	2	8	no	—
179	C₄²×C₁₃₉	—	2	2	no	—
180	C₄²×C₁₃₉	—	2	2	no	—
181	C₄²×C₁₃₉	—	2	2	no	—
182	C₄²×C₁₃₉	—	4	8	no	—
183	C₄²×C₁₃₉	C₂×Q₈	1	4	yes	—
184	C₄²×C₁₃₉	#41	1	4	yes	—
185	C₄²×C₁₃₉	#41	1	4	yes	—
186	C₄²×C₁₃₉	#41	1	4	yes	—
187	C₂³×C₁₃₉	—	2	2	no	—
188	C₂³×C₁₃₉	—	2	2	no	—
189	C₂³×C₁₃₉	—	2	2	no	—
190	C₂³×C₁₃₉	—	2	2	no	—
191	C₂³×C₁₃₉	—	2	2	no	—
192	C₂³×C₁₃₉	—	2	2	no	—
193	C₂³×C₁₃₉	C₂²×Q₈	1	4	yes	—
194	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
195	Q₈×C₁₃₉	—	4	8	no	—
196	Q₈×C₁₃₉	—	8	8	no	—
197	D₄×C₁₃₉	—	2	8	no	—
198	C₂×C₄×C₁₃₉	—	2	2	no	—
199	C₂×C₄×C₁₃₉	—	2	1	no	—
200	C₂×C₄×C₁₃₉	—	2	1	no	—
201	C₂×C₄×C₁₃₉	—	2	1	no	—
202	C₂×C₄×C₁₃₉	—	2	1	no	—
203	C₂×C₄×C₁₃₉	—	2	2	no	—
204	C₂×C₄×C₁₃₉	—	2	1	no	—
205	C₂×C₄×C₁₃₉	—	2	1	no	—
206	C₂×C₄×C₁₃₉	—	2	16	no	—
207	C₂×C₄×C₁₃₉	—	2	2	no	—
208	C₂×C₄×C₁₃₉	—	2	2	no	—
209	C₂×C₄×C₁₃₉	—	2	4	no	—
210	C₂×C₄×C₁₃₉	—	2	4	no	—
211	C₂×C₄×C₁₃₉	—	2	2	no	—
212	C₂×C₄×C₁₃₉	—	2	2	no	—
213	C₂×C₄×C₁₃₉	—	2	4	no	—
214	C₂×C₄×C₁₃₉	—	2	8	no	—
215	C₂×C₄×C₁₃₉	—	2	4	no	—
216	C₂×C₄×C₁₃₉	—	2	8	no	—
217	C₂×C₄×C₁₃₉	—	2	4	no	—
218	C₂×C₄×C₁₃₉	—	2	8	no	—
219	C₂×C₄×C₁₃₉	—	2	2	no	—
220	C₂×C₄×C₁₃₉	—	2	4	no	—
221	C₂×C₄×C₁₃₉	—	2	2	no	—
222	C₂×C₄×C₁₃₉	—	4	8	no	—
223	C₂×C₄×C₁₃₉	—	4	8	no	—
224	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
225	C₂×C₄×C₁₃₉	C₂²×Q₈	1	4	yes	—
226	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
227	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
228	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
229	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
230	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
231	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
232	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
233	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
234	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
236	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
237	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
238	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
239	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
240	C₂²×C₁₃₉	—	2	4	no	—
241	C₂²×C₁₃₉	—	2	4	no	—
242	C₂²×C₁₃₉	—	2	4	no	—
243	C₂²×C₁₃₉	—	4	2	no	—
244	C₂²×C₁₃₉	—	4	2	no	—
245	C₂²×C₁₃₉	—	4	2	no	—
246	C₂²×C₁₃₉	—	4	2	no	—
247	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
248	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
249	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
250	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
251	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
252	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
253	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
254	C₄×C₁₃₉	—	2	4	no	—
255	C₄×C₁₃₉	—	2	2	no	—
256	C₄×C₁₃₉	—	2	2	no	—
257	C₄×C₁₃₉	—	2	2	no	—
258	C₄×C₁₃₉	—	4	2	no	—
259	C₄×C₁₃₉	—	4	4	no	—
260	C₄×C₁₃₉	—	4	2	no	—
261	C₄×C₁₃₉	—	4	8	no	—
262	C₄×C₁₃₉	—	4	4	no	—
263	C₄×C₁₃₉	#533	1	4	yes	—
264	C₄×C₁₃₉	#554	1	4	yes	—
265	C₄×C₁₃₉	#555	1	4	yes	—
266	C₄×C₁₃₉	#556	1	4	yes	—
267	C₂×C₁₃₉	—	4	4	no	—
268	C₂×C₁₃₉	C₂×#533	1	1	yes	characteristic
269	C₂×C₁₃₉	C₂×#554	1	1	yes	characteristic
270	C₂×C₁₃₉	C₂×#555	1	1	yes	characteristic
271	C₂×C₁₃₉	C₂×#556	1	1	yes	characteristic
272	C₂×C₁₃₉	#3503	1	1	yes	characteristic
273	C₂×C₁₃₉	#3508	1	1	yes	characteristic
274	C₂×C₁₃₉	#3511	1	1	yes	characteristic
275	#36194	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₁₃₉	#36194	1	1	yes	characteristic, direct product factor, Sylow
277	#2868	C₂×C₁₃₉	1	1	yes	characteristic, complemented
278	#2857	C₂×C₁₃₉	1	2	yes	complemented
279	#2571	C₂×C₁₃₉	1	2	yes	complemented
280	#2563	C₂×C₁₃₉	1	2	yes	—
281	#2538	C₂×C₁₃₉	1	2	yes	—
282	#2497	C₂×C₁₃₉	1	4	yes	complemented
283	#2492	C₂×C₁₃₉	1	4	yes	complemented
284	#2439	C₂×C₁₃₉	1	4	yes	complemented
285	#2369	C₂×C₁₃₉	1	2	yes	complemented
286	#2355	C₂×C₁₃₉	1	2	yes	complemented
287	#2354	C₂×C₁₃₉	1	2	yes	—
288	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
289	#2285	C₂×C₁₃₉	1	2	yes	complemented
290	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
291	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
292	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
293	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
294	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
296	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
297	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
298	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
299	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
300	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
301	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
302	#400	C₂²×C₁₃₉	1	8	yes	—
303	#396	C₂²×C₁₃₉	1	8	yes	—
304	#393	C₂²×C₁₃₉	1	8	yes	—
305	#391	C₂²×C₁₃₉	1	2	yes	—
306	#391	C₂²×C₁₃₉	1	4	yes	—
307	#391	C₂²×C₁₃₉	1	8	yes	—
308	#390	C₂²×C₁₃₉	1	4	yes	—
309	#389	C₂²×C₁₃₉	1	2	yes	—
310	#389	C₂²×C₁₃₉	1	2	yes	—
311	#389	C₂²×C₁₃₉	1	4	yes	—
312	#389	C₂²×C₁₃₉	1	4	yes	—
313	#389	C₂²×C₁₃₉	1	4	yes	—
314	#388	C₂²×C₁₃₉	1	8	yes	—
315	#387	C₂²×C₁₃₉	1	8	yes	—
316	#384	C₂²×C₁₃₉	1	1	yes	characteristic
317	#384	C₂²×C₁₃₉	1	2	yes	—
318	#384	C₂²×C₁₃₉	1	2	yes	—
319	#384	C₂²×C₁₃₉	1	2	yes	—
320	#384	C₂²×C₁₃₉	1	2	yes	—
321	#382	C₂²×C₁₃₉	1	4	yes	—
322	#382	C₂²×C₁₃₉	1	4	yes	—
323	#380	C₂²×C₁₃₉	1	4	yes	—
324	#380	C₂²×C₁₃₉	1	4	yes	—
325	#380	C₂²×C₁₃₉	1	4	yes	—
326	#380	C₂²×C₁₃₉	1	4	yes	—
327	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
328	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
329	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
330	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
331	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
332	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
333	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
334	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
335	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
336	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
337	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
338	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
339	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
340	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
341	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
343	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
344	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
345	C₄⋊Q₈	—	2	4	no	—
346	C₄⋊Q₈	—	2	8	no	—
347	C₄⋊Q₈	—	4	4	no	—
348	C₄⋊Q₈	—	4	4	no	—
349	C₂²⋊Q₈	—	4	8	no	—
350	C₄×Q₈	—	2	8	no	—
351	C₄×D₄	—	2	4	no	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	Q₈×C₁₃₉	1	8	yes	complemented
354	#117	—	4	8	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	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	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	8	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
371	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
376	C₂×C₄²	—	2	8	no	—
377	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
378	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
382	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
383	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
384	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
385	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
389	#95	C₂³×C₁₃₉	1	2	yes	—
390	#95	C₂³×C₁₃₉	1	2	yes	—
391	#95	C₂³×C₁₃₉	1	2	yes	—
392	#95	C₂³×C₁₃₉	1	8	yes	—
393	#95	C₂³×C₁₃₉	1	8	yes	—
394	#95	C₂³×C₁₃₉	1	8	yes	—
395	#95	C₂³×C₁₃₉	1	4	yes	—
396	#95	C₂³×C₁₃₉	1	4	yes	—
397	#95	C₂³×C₁₃₉	1	8	yes	—
398	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	8	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	4	4	no	—
404	C₂×Q₈	—	4	4	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
417	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
419	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
422	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
423	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	4	8	no	—
443	C₄⋊C₄	—	4	4	no	—
444	C₄⋊C₄	—	4	4	no	—
445	C₄⋊C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	4	8	no	—
449	C₂²⋊C₄	—	4	8	no	—
450	C₂²⋊C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
451	C₄²	—	2	4	no	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	4	no	—
454	C₄²	—	2	8	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	4	8	no	—
459	C₄²	C₂×Q₈×C₁₃₉	1	4	yes	—
460	C₄²	#41×C₁₃₉	1	4	yes	—
461	C₄²	#41×C₁₃₉	1	4	yes	—
462	C₄²	#41×C₁₃₉	1	4	yes	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	C₂²×Q₈×C₁₃₉	1	4	yes	—
470	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
471	Q₈	—	4	8	no	—
472	Q₈	—	8	8	no	—
473	D₄	—	2	8	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	16	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	8	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	8	no	—
499	C₂×C₄	—	4	8	no	—
500	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
501	C₂×C₄	C₂²×Q₈×C₁₃₉	1	4	yes	—
502	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
503	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
504	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
505	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
506	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
507	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
508	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
509	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
510	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
511	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
512	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
513	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
514	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
515	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
524	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
525	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
526	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
527	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
528	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
529	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	8	no	—
538	C₄	—	4	4	no	—
539	C₄	#533×C₁₃₉	1	4	yes	—
540	C₄	#554×C₁₃₉	1	4	yes	—
541	C₄	#555×C₁₃₉	1	4	yes	—
542	C₄	#556×C₁₃₉	1	4	yes	—
543	C₂	—	4	4	no	—
544	C₂	C₂×#533×C₁₃₉	1	1	yes	characteristic
545	C₂	C₂×#554×C₁₃₉	1	1	yes	characteristic
546	C₂	C₂×#555×C₁₃₉	1	1	yes	characteristic
547	C₂	C₂×#556×C₁₃₉	1	1	yes	characteristic
548	C₂	#3503×C₁₃₉	1	1	yes	characteristic
549	C₂	#3508×C₁₃₉	1	1	yes	characteristic
550	C₂	#3511×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×D₄×C₁₃₉	C₂³
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. #2857×C₁₃₉	C₂	semidirect
3. #2571×C₁₃₉	C₂	semidirect
6. #2497×C₁₃₉	C₂	semidirect
7. #2492×C₁₃₉	C₂	semidirect
8. #2439×C₁₃₉	C₂	semidirect
9. #2369×C₁₃₉	C₂	semidirect
10. #2355×C₁₃₉	C₂	semidirect
12. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
13. #2285×C₁₃₉	C₂	semidirect
77. C₄×D₄×C₁₃₉	Q₈	semidirect
275. #36194	C₁₃₉	direct (N × H)
276. C₁₃₉	#36194	direct (N × H)
277. #2868	C₂×C₁₃₉	semidirect
278. #2857	C₂×C₁₃₉	semidirect
279. #2571	C₂×C₁₃₉	semidirect
282. #2497	C₂×C₁₃₉	semidirect
283. #2492	C₂×C₁₃₉	semidirect
284. #2439	C₂×C₁₃₉	semidirect
285. #2369	C₂×C₁₃₉	semidirect
286. #2355	C₂×C₁₃₉	semidirect
288. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
289. #2285	C₂×C₁₃₉	semidirect
353. C₄×D₄	Q₈×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
#2857×C₁₃₉	2
#2571×C₁₃₉	2
#2563×C₁₃₉	2
#2538×C₁₃₉	2
#2497×C₁₃₉	2
#2492×C₁₃₉	2
#2439×C₁₃₉	2
#2369×C₁₃₉	2
#2355×C₁₃₉	2
#2354×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
#2285×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36194	139

Subgroups — C139×#36194 #48030790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36194 #48030790