Subgroups — C₁₃₉×#36456 #48031052

Order 35584.

2468 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2857×C₁₃₉	C₂	1	3	yes	maximal, complemented
4	#2563×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2538×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2452×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2439×C₁₃₉	C₂	1	6	yes	maximal, complemented
8	#2351×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	Q₈×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2341×C₁₃₉	C₂	1	2	yes	maximal
11	C₄×C₂²⋊Q₈×C₁₃₉	C₂	1	3	yes	maximal, complemented
12	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
13	Q₈²×C₁₃₉	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
16	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
17	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	6	yes	—
18	C₄×#41×C₁₃₉	—	2	8	no	—
19	C₂×C₄×Q₈×C₁₃₉	C₂²	1	3	yes	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
26	C₂×#117×C₁₃₉	C₂²	1	3	yes	—
27	C₂²×C₄²×C₁₃₉	C₂²	1	3	yes	—
28	#396×C₁₃₉	C₂²	1	12	yes	—
29	#393×C₁₃₉	C₂²	1	12	yes	—
30	#391×C₁₃₉	C₂²	1	1	yes	characteristic
31	#391×C₁₃₉	C₂²	1	6	yes	—
32	#390×C₁₃₉	C₂²	1	6	yes	—
33	#390×C₁₃₉	C₂²	1	6	yes	—
34	#389×C₁₃₉	C₂²	1	6	yes	—
35	#389×C₁₃₉	C₂²	1	3	yes	—
36	#389×C₁₃₉	C₂²	1	6	yes	—
37	#389×C₁₃₉	C₂²	1	6	yes	—
38	#387×C₁₃₉	C₂²	1	6	yes	—
39	#385×C₁₃₉	C₂²	1	6	yes	—
40	#384×C₁₃₉	C₂²	1	3	yes	—
41	#382×C₁₃₉	C₂²	1	6	yes	—
42	#380×C₁₃₉	C₂²	1	6	yes	—
43	#380×C₁₃₉	C₂²	1	3	yes	—
44	#380×C₁₃₉	C₂²	1	6	yes	—
45	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
46	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	6	yes	—
47	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
48	C₂×#41×C₁₃₉	—	2	4	no	—
49	C₂×#41×C₁₃₉	—	2	4	no	—
50	C₂×#41×C₁₃₉	Q₈	1	8	yes	complemented
51	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃₉	C₂³	1	6	yes	—
53	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
55	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
56	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
57	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
58	C₄⋊Q₈×C₁₃₉	—	2	24	no	—
59	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
60	C₂²⋊Q₈×C₁₃₉	—	2	12	no	—
61	C₂²⋊Q₈×C₁₃₉	—	4	12	no	—
62	C₄×Q₈×C₁₃₉	—	2	4	no	—
63	C₄×Q₈×C₁₃₉	—	2	8	no	—
64	C₄×Q₈×C₁₃₉	—	2	8	no	—
65	C₄×Q₈×C₁₃₉	—	2	12	no	—
66	C₄×Q₈×C₁₃₉	D₄	1	8	yes	—
67	C₄×D₄×C₁₃₉	—	2	12	no	—
68	C₄×D₄×C₁₃₉	—	2	12	no	—
69	#117×C₁₃₉	—	2	12	no	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
74	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
75	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
80	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
81	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
83	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
84	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
85	C₂×C₄²×C₁₃₉	—	2	12	no	—
86	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
88	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
89	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
90	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
91	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
92	#95×C₁₃₉	C₂³	1	12	yes	—
93	#95×C₁₃₉	C₂³	1	2	yes	—
94	#95×C₁₃₉	C₂³	1	6	yes	—
95	#95×C₁₃₉	C₂³	1	2	yes	—
96	#95×C₁₃₉	C₂³	1	6	yes	—
97	#95×C₁₃₉	C₂³	1	6	yes	—
98	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
99	#41×C₁₃₉	—	2	32	no	—
100	C₂×Q₈×C₁₃₉	—	2	2	no	—
101	C₂×Q₈×C₁₃₉	—	2	12	no	—
102	C₂×Q₈×C₁₃₉	—	2	2	no	—
103	C₂×Q₈×C₁₃₉	—	4	6	no	—
104	C₂×Q₈×C₁₃₉	—	4	6	no	—
105	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
106	C₂×Q₈×C₁₃₉	C₂×Q₈	1	4	yes	—
107	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
108	C₂×Q₈×C₁₃₉	#41	1	4	yes	complemented
109	C₂×D₄×C₁₃₉	—	2	6	no	—
110	C₂×D₄×C₁₃₉	—	2	6	no	—
111	C₂×D₄×C₁₃₉	C₂×Q₈	1	12	yes	—
112	C₂²×C₄×C₁₃₉	—	2	6	no	—
113	C₂²×C₄×C₁₃₉	—	2	6	no	—
114	C₂²×C₄×C₁₃₉	—	2	6	no	—
115	C₂²×C₄×C₁₃₉	—	2	6	no	—
116	C₂²×C₄×C₁₃₉	—	2	6	no	—
117	C₂²×C₄×C₁₃₉	—	2	6	no	—
118	C₂²×C₄×C₁₃₉	—	2	6	no	—
119	C₂²×C₄×C₁₃₉	—	4	3	no	—
120	C₂²×C₄×C₁₃₉	C₂×Q₈	1	12	yes	—
121	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
123	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
124	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
125	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
126	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
130	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₁₃₉	—	2	6	no	—
132	C₄⋊C₄×C₁₃₉	—	2	12	no	—
133	C₄⋊C₄×C₁₃₉	—	2	12	no	—
134	C₄⋊C₄×C₁₃₉	—	2	6	no	—
135	C₄⋊C₄×C₁₃₉	—	2	12	no	—
136	C₄⋊C₄×C₁₃₉	—	2	6	no	—
137	C₄⋊C₄×C₁₃₉	—	2	12	no	—
138	C₄⋊C₄×C₁₃₉	—	2	12	no	—
139	C₄⋊C₄×C₁₃₉	—	2	2	no	—
140	C₄⋊C₄×C₁₃₉	—	4	6	no	—
141	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
142	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
143	C₂²⋊C₄×C₁₃₉	—	2	12	no	—
144	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
145	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
146	C₄²×C₁₃₉	—	2	2	no	—
147	C₄²×C₁₃₉	—	2	6	no	—
148	C₄²×C₁₃₉	—	2	6	no	—
149	C₄²×C₁₃₉	—	2	12	no	—
150	C₄²×C₁₃₉	—	2	12	no	—
151	C₄²×C₁₃₉	C₂×D₄	1	12	yes	—
152	C₂³×C₁₃₉	—	2	3	no	—
153	C₂³×C₁₃₉	—	2	3	no	—
154	C₂³×C₁₃₉	—	2	3	no	—
155	C₂³×C₁₃₉	—	2	3	no	—
156	C₂³×C₁₃₉	—	2	3	no	—
157	C₂³×C₁₃₉	—	2	3	no	—
158	C₂³×C₁₃₉	C₂²×Q₈	1	6	yes	—
159	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
160	Q₈×C₁₃₉	—	2	8	no	—
161	Q₈×C₁₃₉	—	8	12	no	—
162	Q₈×C₁₃₉	C₂²⋊Q₈	1	16	yes	complemented
163	D₄×C₁₃₉	—	2	24	no	—
164	C₂×C₄×C₁₃₉	—	2	1	no	—
165	C₂×C₄×C₁₃₉	—	2	1	no	—
166	C₂×C₄×C₁₃₉	—	2	2	no	—
167	C₂×C₄×C₁₃₉	—	2	1	no	—
168	C₂×C₄×C₁₃₉	—	2	3	no	—
169	C₂×C₄×C₁₃₉	—	2	2	no	—
170	C₂×C₄×C₁₃₉	—	2	1	no	—
171	C₂×C₄×C₁₃₉	—	2	3	no	—
172	C₂×C₄×C₁₃₉	—	2	24	no	—
173	C₂×C₄×C₁₃₉	—	2	3	no	—
174	C₂×C₄×C₁₃₉	—	2	6	no	—
175	C₂×C₄×C₁₃₉	—	2	2	no	—
176	C₂×C₄×C₁₃₉	—	2	6	no	—
177	C₂×C₄×C₁₃₉	—	2	6	no	—
178	C₂×C₄×C₁₃₉	—	2	3	no	—
179	C₂×C₄×C₁₃₉	—	2	6	no	—
180	C₂×C₄×C₁₃₉	—	2	6	no	—
181	C₂×C₄×C₁₃₉	—	2	2	no	—
182	C₂×C₄×C₁₃₉	—	2	3	no	—
183	C₂×C₄×C₁₃₉	—	2	2	no	—
184	C₂×C₄×C₁₃₉	—	2	6	no	—
185	C₂×C₄×C₁₃₉	—	4	12	no	—
186	C₂×C₄×C₁₃₉	—	4	12	no	—
187	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
188	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
189	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
191	C₂×C₄×C₁₃₉	C₂²×Q₈	1	6	yes	—
192	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
193	C₂×C₄×C₁₃₉	C₂×#41	1	6	yes	—
194	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
195	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
197	C₂²×C₁₃₉	—	2	6	no	—
198	C₂²×C₁₃₉	—	2	6	no	—
199	C₂²×C₁₃₉	—	2	6	no	—
200	C₂²×C₁₃₉	—	4	3	no	—
201	C₂²×C₁₃₉	—	4	3	no	—
202	C₂²×C₁₃₉	—	4	3	no	—
203	C₂²×C₁₃₉	—	4	3	no	—
204	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
205	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
206	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
207	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
208	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
209	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
210	C₂²×C₁₃₉	#585	1	1	yes	characteristic
211	C₄×C₁₃₉	—	2	2	no	—
212	C₄×C₁₃₉	—	2	4	no	—
213	C₄×C₁₃₉	—	2	2	no	—
214	C₄×C₁₃₉	—	2	6	no	—
215	C₄×C₁₃₉	—	4	3	no	—
216	C₄×C₁₃₉	—	4	6	no	—
217	C₄×C₁₃₉	—	4	6	no	—
218	C₄×C₁₃₉	—	4	2	no	—
219	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	12	yes	—
220	C₄×C₁₃₉	#548	1	4	yes	—
221	C₂×C₁₃₉	—	4	6	no	—
222	C₂×C₁₃₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
223	C₂×C₁₃₉	C₂×#548	1	1	yes	characteristic
224	C₂×C₁₃₉	Q₈×#41	1	1	yes	characteristic
225	C₂×C₁₃₉	#3483	1	1	yes	characteristic
226	C₂×C₁₃₉	#3488	1	1	yes	characteristic
227	C₂×C₁₃₉	#3503	1	1	yes	characteristic
228	C₂×C₁₃₉	#3518	1	1	yes	characteristic
229	#36456	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₁₃₉	#36456	1	1	yes	characteristic, direct product factor, Sylow
231	C₂×Q₈²	C₂×C₁₃₉	1	1	yes	characteristic, complemented
232	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic
233	#2857	C₂×C₁₃₉	1	3	yes	complemented
234	#2563	C₂×C₁₃₉	1	3	yes	complemented
235	#2538	C₂×C₁₃₉	1	3	yes	complemented
236	#2452	C₂×C₁₃₉	1	6	yes	complemented
237	#2439	C₂×C₁₃₉	1	6	yes	complemented
238	#2351	C₂×C₁₃₉	1	2	yes	complemented
239	Q₈×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
240	#2341	C₂×C₁₃₉	1	2	yes	—
241	C₄×C₂²⋊Q₈	C₂×C₁₃₉	1	3	yes	complemented
242	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
243	Q₈²	—	2	8	no	—
244	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
245	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
246	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
247	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	6	yes	—
248	C₄×#41	—	2	8	no	—
249	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×C₁₃₉	1	3	yes	—
253	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
255	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
256	C₂×#117	C₂²×C₁₃₉	1	3	yes	—
257	C₂²×C₄²	C₂²×C₁₃₉	1	3	yes	—
258	#396	C₂²×C₁₃₉	1	12	yes	—
259	#393	C₂²×C₁₃₉	1	12	yes	—
260	#391	C₂²×C₁₃₉	1	6	yes	—
261	#391	C₂²×C₁₃₉	1	1	yes	characteristic
262	#390	C₂²×C₁₃₉	1	6	yes	—
263	#390	C₂²×C₁₃₉	1	6	yes	—
264	#389	C₂²×C₁₃₉	1	3	yes	—
265	#389	C₂²×C₁₃₉	1	6	yes	—
266	#389	C₂²×C₁₃₉	1	6	yes	—
267	#389	C₂²×C₁₃₉	1	6	yes	—
268	#387	C₂²×C₁₃₉	1	6	yes	—
269	#385	C₂²×C₁₃₉	1	6	yes	—
270	#384	C₂²×C₁₃₉	1	3	yes	—
271	#382	C₂²×C₁₃₉	1	6	yes	—
272	#380	C₂²×C₁₃₉	1	3	yes	—
273	#380	C₂²×C₁₃₉	1	6	yes	—
274	#380	C₂²×C₁₃₉	1	6	yes	—
275	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
276	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	6	yes	—
277	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
278	C₂×#41	—	2	4	no	—
279	C₂×#41	—	2	4	no	—
280	C₂×#41	Q₈×C₁₃₉	1	8	yes	complemented
281	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
282	C₂²×Q₈	C₂³×C₁₃₉	1	6	yes	—
283	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
284	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
285	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
286	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
287	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
288	C₄⋊Q₈	—	2	24	no	—
289	C₄⋊Q₈	—	2	12	no	—
290	C₂²⋊Q₈	—	2	12	no	—
291	C₂²⋊Q₈	—	4	12	no	—
292	C₄×Q₈	—	2	4	no	—
293	C₄×Q₈	—	2	8	no	—
294	C₄×Q₈	—	2	8	no	—
295	C₄×Q₈	—	2	12	no	—
296	C₄×Q₈	D₄×C₁₃₉	1	8	yes	—
297	C₄×D₄	—	2	12	no	—
298	C₄×D₄	—	2	12	no	—
299	#117	—	2	12	no	—
300	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
302	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
311	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
315	C₂×C₄²	—	2	12	no	—
316	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
317	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
318	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
319	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
320	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
322	#95	C₂³×C₁₃₉	1	2	yes	—
323	#95	C₂³×C₁₃₉	1	6	yes	—
324	#95	C₂³×C₁₃₉	1	2	yes	—
325	#95	C₂³×C₁₃₉	1	6	yes	—
326	#95	C₂³×C₁₃₉	1	6	yes	—
327	#95	C₂³×C₁₃₉	1	12	yes	—
328	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
329	#41	—	2	32	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	12	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	4	6	no	—
334	C₂×Q₈	—	4	6	no	—
335	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
336	C₂×Q₈	C₂×Q₈×C₁₃₉	1	4	yes	—
337	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
338	C₂×Q₈	#41×C₁₃₉	1	4	yes	complemented
339	C₂×D₄	—	2	6	no	—
340	C₂×D₄	—	2	6	no	—
341	C₂×D₄	C₂×Q₈×C₁₃₉	1	12	yes	—
342	C₂²×C₄	—	2	6	no	—
343	C₂²×C₄	—	2	6	no	—
344	C₂²×C₄	—	2	6	no	—
345	C₂²×C₄	—	2	6	no	—
346	C₂²×C₄	—	2	6	no	—
347	C₂²×C₄	—	2	6	no	—
348	C₂²×C₄	—	2	6	no	—
349	C₂²×C₄	—	4	3	no	—
350	C₂²×C₄	C₂×Q₈×C₁₃₉	1	12	yes	—
351	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
353	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
354	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
355	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
356	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
360	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
361	C₄⋊C₄	—	2	6	no	—
362	C₄⋊C₄	—	2	12	no	—
363	C₄⋊C₄	—	2	12	no	—
364	C₄⋊C₄	—	2	6	no	—
365	C₄⋊C₄	—	2	12	no	—
366	C₄⋊C₄	—	2	6	no	—
367	C₄⋊C₄	—	2	12	no	—
368	C₄⋊C₄	—	2	12	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	6	no	—
371	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
372	C₂²⋊C₄	—	2	12	no	—
373	C₂²⋊C₄	—	2	12	no	—
374	C₂²⋊C₄	—	4	6	no	—
375	C₂²⋊C₄	—	4	12	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	6	no	—
378	C₄²	—	2	6	no	—
379	C₄²	—	2	12	no	—
380	C₄²	—	2	12	no	—
381	C₄²	C₂×D₄×C₁₃₉	1	12	yes	—
382	C₂³	—	2	3	no	—
383	C₂³	—	2	3	no	—
384	C₂³	—	2	3	no	—
385	C₂³	—	2	3	no	—
386	C₂³	—	2	3	no	—
387	C₂³	—	2	3	no	—
388	C₂³	C₂²×Q₈×C₁₃₉	1	6	yes	—
389	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
390	Q₈	—	2	8	no	—
391	Q₈	—	8	12	no	—
392	Q₈	C₂²⋊Q₈×C₁₃₉	1	16	yes	complemented
393	D₄	—	2	24	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	3	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	3	no	—
402	C₂×C₄	—	2	24	no	—
403	C₂×C₄	—	2	3	no	—
404	C₂×C₄	—	2	6	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	6	no	—
407	C₂×C₄	—	2	6	no	—
408	C₂×C₄	—	2	3	no	—
409	C₂×C₄	—	2	6	no	—
410	C₂×C₄	—	2	6	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	3	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	6	no	—
415	C₂×C₄	—	4	12	no	—
416	C₂×C₄	—	4	12	no	—
417	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
418	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
419	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
420	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
421	C₂×C₄	C₂²×Q₈×C₁₃₉	1	6	yes	—
422	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
423	C₂×C₄	C₂×#41×C₁₃₉	1	6	yes	—
424	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
425	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
426	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
427	C₂²	—	2	6	no	—
428	C₂²	—	2	6	no	—
429	C₂²	—	2	6	no	—
430	C₂²	—	4	3	no	—
431	C₂²	—	4	3	no	—
432	C₂²	—	4	3	no	—
433	C₂²	—	4	3	no	—
434	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
435	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
436	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
437	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
438	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
439	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
440	C₂²	#585×C₁₃₉	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	6	no	—
445	C₄	—	4	3	no	—
446	C₄	—	4	6	no	—
447	C₄	—	4	6	no	—
448	C₄	—	4	2	no	—
449	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	12	yes	—
450	C₄	#548×C₁₃₉	1	4	yes	—
451	C₂	—	4	6	no	—
452	C₂	C₂²×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
453	C₂	C₂×#548×C₁₃₉	1	1	yes	characteristic
454	C₂	Q₈×#41×C₁₃₉	1	1	yes	characteristic
455	C₂	#3483×C₁₃₉	1	1	yes	characteristic
456	C₂	#3488×C₁₃₉	1	1	yes	characteristic
457	C₂	#3503×C₁₃₉	1	1	yes	characteristic
458	C₂	#3518×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×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×Q₈²×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2563×C₁₃₉	C₂	semidirect
5. #2538×C₁₃₉	C₂	semidirect
6. #2452×C₁₃₉	C₂	semidirect
7. #2439×C₁₃₉	C₂	semidirect
8. #2351×C₁₃₉	C₂	semidirect
9. Q₈×C₄⋊C₄×C₁₃₉	C₂	semidirect
11. C₄×C₂²⋊Q₈×C₁₃₉	C₂	semidirect
50. C₂×#41×C₁₃₉	Q₈	semidirect
108. C₂×Q₈×C₁₃₉	#41	semidirect
162. Q₈×C₁₃₉	C₂²⋊Q₈	semidirect
229. #36456	C₁₃₉	direct (N × H)
230. C₁₃₉	#36456	direct (N × H)
231. C₂×Q₈²	C₂×C₁₃₉	semidirect
233. #2857	C₂×C₁₃₉	semidirect
234. #2563	C₂×C₁₃₉	semidirect
235. #2538	C₂×C₁₃₉	semidirect
236. #2452	C₂×C₁₃₉	semidirect
237. #2439	C₂×C₁₃₉	semidirect
238. #2351	C₂×C₁₃₉	semidirect
239. Q₈×C₄⋊C₄	C₂×C₁₃₉	semidirect
241. C₄×C₂²⋊Q₈	C₂×C₁₃₉	semidirect
280. C₂×#41	Q₈×C₁₃₉	semidirect
338. C₂×Q₈	#41×C₁₃₉	semidirect
392. Q₈	C₂²⋊Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈²×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2857×C₁₃₉	2
#2563×C₁₃₉	2
#2538×C₁₃₉	2
#2452×C₁₃₉	2
#2439×C₁₃₉	2
#2351×C₁₃₉	2
Q₈×C₄⋊C₄×C₁₃₉	2
#2341×C₁₃₉	2
C₄×C₂²⋊Q₈×C₁₃₉	2
#36456	139

Subgroups — C139×#36456 #48031052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36456 #48031052