Subgroups — C₁₃₉×#36188 #48030784

Order 35584.

2210 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₁₃₉	C₂	1	2	yes	maximal
2	#2868×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2857×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2568×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2547×C₁₃₉	C₂	1	4	yes	maximal
6	#2499×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2496×C₁₃₉	C₂	1	8	yes	maximal, complemented
8	#2365×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2285×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
12	#556×C₁₃₉	—	2	16	no	—
13	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
14	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#126×C₁₃₉	C₂²	1	8	yes	—
17	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
18	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
19	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₁₃₉	C₂²	1	4	yes	—
24	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
25	#400×C₁₃₉	C₂²	1	8	yes	—
26	#397×C₁₃₉	C₂²	1	16	yes	—
27	#391×C₁₃₉	C₂²	1	8	yes	—
28	#391×C₁₃₉	C₂²	1	2	yes	—
29	#391×C₁₃₉	C₂²	1	4	yes	—
30	#389×C₁₃₉	C₂²	1	4	yes	—
31	#389×C₁₃₉	C₂²	1	8	yes	—
32	#387×C₁₃₉	C₂²	1	16	yes	—
33	#384×C₁₃₉	C₂²	1	1	yes	characteristic
34	#384×C₁₃₉	C₂²	1	2	yes	—
35	#384×C₁₃₉	C₂²	1	4	yes	—
36	#384×C₁₃₉	C₂²	1	2	yes	—
37	#382×C₁₃₉	C₂²	1	4	yes	—
38	#380×C₁₃₉	C₂²	1	8	yes	—
39	#380×C₁₃₉	C₂²	1	8	yes	—
40	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	8	yes	—
43	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
44	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
45	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
46	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
49	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
53	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
54	C₄⋊Q₈×C₁₃₉	—	2	16	no	—
55	#126×C₁₃₉	—	2	32	no	—
56	#124×C₁₃₉	—	2	16	no	—
57	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
58	C₄×Q₈×C₁₃₉	—	2	16	no	—
59	C₄×Q₈×C₁₃₉	—	2	8	no	—
60	C₄×D₄×C₁₃₉	—	2	8	no	—
61	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
62	#117×C₁₃₉	—	2	16	no	—
63	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
75	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
76	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
77	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃₉	—	2	8	no	—
79	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
80	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
82	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
88	#95×C₁₃₉	C₂³	1	8	yes	—
89	#95×C₁₃₉	C₂³	1	16	yes	—
90	#95×C₁₃₉	C₂³	1	16	yes	—
91	#95×C₁₃₉	C₂³	1	2	yes	—
92	#95×C₁₃₉	C₂³	1	4	yes	—
93	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
94	C₂×Q₈×C₁₃₉	—	2	4	no	—
95	C₂×Q₈×C₁₃₉	—	2	8	no	—
96	C₂×Q₈×C₁₃₉	—	2	16	no	—
97	C₂×Q₈×C₁₃₉	—	2	4	no	—
98	C₂×Q₈×C₁₃₉	—	2	4	no	—
99	C₂×D₄×C₁₃₉	—	2	4	no	—
100	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₃₉	—	2	4	no	—
102	C₂²×C₄×C₁₃₉	—	2	4	no	—
103	C₂²×C₄×C₁₃₉	—	2	8	no	—
104	C₂²×C₄×C₁₃₉	—	2	8	no	—
105	C₂²×C₄×C₁₃₉	—	2	8	no	—
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
107	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₁₃₉	C₂⁴	1	8	yes	—
111	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
113	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
117	C₄⋊C₄×C₁₃₉	—	2	4	no	—
118	C₄⋊C₄×C₁₃₉	—	2	8	no	—
119	C₄⋊C₄×C₁₃₉	—	2	16	no	—
120	C₄⋊C₄×C₁₃₉	—	2	8	no	—
121	C₄⋊C₄×C₁₃₉	—	2	8	no	—
122	C₄⋊C₄×C₁₃₉	—	2	4	no	—
123	C₄⋊C₄×C₁₃₉	—	2	16	no	—
124	C₄⋊C₄×C₁₃₉	—	2	8	no	—
125	C₄⋊C₄×C₁₃₉	—	2	16	no	—
126	C₄⋊C₄×C₁₃₉	—	2	8	no	—
127	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
128	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
129	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
130	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
131	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
132	C₄²×C₁₃₉	—	2	16	no	—
133	C₄²×C₁₃₉	—	2	8	no	—
134	C₄²×C₁₃₉	—	2	8	no	—
135	C₄²×C₁₃₉	—	2	4	no	—
136	C₄²×C₁₃₉	—	2	2	no	—
137	C₄²×C₁₃₉	—	2	4	no	—
138	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
139	C₄²×C₁₃₉	#41	1	4	yes	—
140	C₄²×C₁₃₉	#41	1	8	yes	—
141	C₂³×C₁₃₉	—	2	4	no	—
142	C₂³×C₁₃₉	—	2	2	no	—
143	C₂³×C₁₃₉	—	2	2	no	—
144	C₂³×C₁₃₉	—	2	4	no	—
145	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
146	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
147	Q₈×C₁₃₉	—	4	16	no	—
148	Q₈×C₁₃₉	—	4	8	no	—
149	D₄×C₁₃₉	—	2	8	no	—
150	C₂×C₄×C₁₃₉	—	2	2	no	—
151	C₂×C₄×C₁₃₉	—	2	2	no	—
152	C₂×C₄×C₁₃₉	—	2	2	no	—
153	C₂×C₄×C₁₃₉	—	2	2	no	—
154	C₂×C₄×C₁₃₉	—	2	2	no	—
155	C₂×C₄×C₁₃₉	—	2	16	no	—
156	C₂×C₄×C₁₃₉	—	2	4	no	—
157	C₂×C₄×C₁₃₉	—	2	8	no	—
158	C₂×C₄×C₁₃₉	—	2	4	no	—
159	C₂×C₄×C₁₃₉	—	2	4	no	—
160	C₂×C₄×C₁₃₉	—	2	4	no	—
161	C₂×C₄×C₁₃₉	—	2	16	no	—
162	C₂×C₄×C₁₃₉	—	2	4	no	—
163	C₂×C₄×C₁₃₉	—	2	8	no	—
164	C₂×C₄×C₁₃₉	—	2	4	no	—
165	C₂×C₄×C₁₃₉	—	2	4	no	—
166	C₂×C₄×C₁₃₉	—	4	16	no	—
167	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
168	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
172	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
173	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
174	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
175	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
176	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
177	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
178	C₂²×C₁₃₉	—	2	4	no	—
179	C₂²×C₁₃₉	—	2	4	no	—
180	C₂²×C₁₃₉	—	2	4	no	—
181	C₂²×C₁₃₉	—	4	4	no	—
182	C₂²×C₁₃₉	—	4	4	no	—
183	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
184	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
185	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
186	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
187	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
188	C₄×C₁₃₉	—	2	4	no	—
189	C₄×C₁₃₉	—	2	2	no	—
190	C₄×C₁₃₉	—	2	4	no	—
191	C₄×C₁₃₉	—	4	8	no	—
192	C₄×C₁₃₉	—	4	4	no	—
193	C₄×C₁₃₉	—	4	4	no	—
194	C₄×C₁₃₉	—	4	4	no	—
195	C₄×C₁₃₉	#532	1	4	yes	—
196	C₄×C₁₃₉	#547	1	4	yes	—
197	C₄×C₁₃₉	#556	1	8	yes	complemented
198	C₂×C₁₃₉	—	4	4	no	—
199	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
200	C₂×C₁₃₉	C₂×#547	1	1	yes	characteristic
201	C₂×C₁₃₉	C₂×#556	1	2	yes	—
202	C₂×C₁₃₉	#3499	1	1	yes	characteristic
203	C₂×C₁₃₉	#3509	1	2	yes	—
204	#36188	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₃₉	#36188	1	1	yes	characteristic, direct product factor, Sylow
206	C₂×#556	C₂×C₁₃₉	1	2	yes	—
207	#2868	C₂×C₁₃₉	1	1	yes	characteristic, complemented
208	#2857	C₂×C₁₃₉	1	2	yes	complemented
209	#2568	C₂×C₁₃₉	1	2	yes	complemented
210	#2547	C₂×C₁₃₉	1	4	yes	—
211	#2499	C₂×C₁₃₉	1	4	yes	complemented
212	#2496	C₂×C₁₃₉	1	8	yes	complemented
213	#2365	C₂×C₁₃₉	1	4	yes	complemented
214	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
215	#2285	C₂×C₁₃₉	1	2	yes	complemented
216	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic
217	#556	—	2	16	no	—
218	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
220	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
221	C₂×#126	C₂²×C₁₃₉	1	8	yes	—
222	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
223	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
224	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
225	C₂×C₄×Q₈	C₂²×C₁₃₉	1	4	yes	—
226	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
227	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
228	C₂×#117	C₂²×C₁₃₉	1	4	yes	—
229	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
230	#400	C₂²×C₁₃₉	1	8	yes	—
231	#397	C₂²×C₁₃₉	1	16	yes	—
232	#391	C₂²×C₁₃₉	1	2	yes	—
233	#391	C₂²×C₁₃₉	1	4	yes	—
234	#391	C₂²×C₁₃₉	1	8	yes	—
235	#389	C₂²×C₁₃₉	1	4	yes	—
236	#389	C₂²×C₁₃₉	1	8	yes	—
237	#387	C₂²×C₁₃₉	1	16	yes	—
238	#384	C₂²×C₁₃₉	1	1	yes	characteristic
239	#384	C₂²×C₁₃₉	1	2	yes	—
240	#384	C₂²×C₁₃₉	1	4	yes	—
241	#384	C₂²×C₁₃₉	1	2	yes	—
242	#382	C₂²×C₁₃₉	1	4	yes	—
243	#380	C₂²×C₁₃₉	1	8	yes	—
244	#380	C₂²×C₁₃₉	1	8	yes	—
245	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
246	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
247	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
248	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	8	yes	—
249	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
250	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
251	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
252	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
253	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
254	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
256	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
257	C₄⋊Q₈	—	2	8	no	—
258	C₄⋊Q₈	—	2	4	no	—
259	C₄⋊Q₈	—	2	16	no	—
260	#126	—	2	32	no	—
261	#124	—	2	16	no	—
262	C₂²⋊Q₈	—	2	16	no	—
263	C₄×Q₈	—	2	16	no	—
264	C₄×Q₈	—	2	8	no	—
265	C₄×D₄	—	2	8	no	—
266	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
267	#117	—	2	16	no	—
268	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
283	C₂×C₄²	—	2	8	no	—
284	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
285	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
286	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
287	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
289	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
292	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
293	#95	C₂³×C₁₃₉	1	4	yes	—
294	#95	C₂³×C₁₃₉	1	2	yes	—
295	#95	C₂³×C₁₃₉	1	16	yes	—
296	#95	C₂³×C₁₃₉	1	8	yes	—
297	#95	C₂³×C₁₃₉	1	16	yes	—
298	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	2	8	no	—
301	C₂×Q₈	—	2	16	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
312	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
313	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
314	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
315	C₂²×C₄	C₂⁴×C₁₃₉	1	8	yes	—
316	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
320	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	2	16	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	16	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	16	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
333	C₂²⋊C₄	—	2	16	no	—
334	C₂²⋊C₄	—	2	16	no	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
337	C₄²	—	2	16	no	—
338	C₄²	—	2	8	no	—
339	C₄²	—	2	8	no	—
340	C₄²	—	2	4	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	4	no	—
343	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
344	C₄²	#41×C₁₃₉	1	4	yes	—
345	C₄²	#41×C₁₃₉	1	8	yes	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	4	no	—
350	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
351	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
352	Q₈	—	4	16	no	—
353	Q₈	—	4	8	no	—
354	D₄	—	2	8	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	16	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	16	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	16	no	—
372	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
373	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
374	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
376	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
377	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
378	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
379	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
380	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
381	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
382	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
389	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
390	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
391	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
392	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	4	no	—
396	C₄	—	4	8	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	4	no	—
399	C₄	—	4	4	no	—
400	C₄	#532×C₁₃₉	1	4	yes	—
401	C₄	#547×C₁₃₉	1	4	yes	—
402	C₄	#556×C₁₃₉	1	8	yes	complemented
403	C₂	—	4	4	no	—
404	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
405	C₂	C₂×#547×C₁₃₉	1	1	yes	characteristic
406	C₂	C₂×#556×C₁₃₉	1	2	yes	—
407	C₂	#3499×C₁₃₉	1	1	yes	characteristic
408	C₂	#3509×C₁₃₉	1	2	yes	—

	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
2. #2868×C₁₃₉	C₂	semidirect
3. #2857×C₁₃₉	C₂	semidirect
4. #2568×C₁₃₉	C₂	semidirect
6. #2499×C₁₃₉	C₂	semidirect
7. #2496×C₁₃₉	C₂	semidirect
8. #2365×C₁₃₉	C₂	semidirect
9. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
10. #2285×C₁₃₉	C₂	semidirect
197. C₄×C₁₃₉	#556	semidirect
204. #36188	C₁₃₉	direct (N × H)
205. C₁₃₉	#36188	direct (N × H)
207. #2868	C₂×C₁₃₉	semidirect
208. #2857	C₂×C₁₃₉	semidirect
209. #2568	C₂×C₁₃₉	semidirect
211. #2499	C₂×C₁₃₉	semidirect
212. #2496	C₂×C₁₃₉	semidirect
213. #2365	C₂×C₁₃₉	semidirect
214. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
215. #2285	C₂×C₁₃₉	semidirect
402. C₄	#556×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#556×C₁₃₉	2
#2868×C₁₃₉	2
#2857×C₁₃₉	2
#2568×C₁₃₉	2
#2547×C₁₃₉	2
#2499×C₁₃₉	2
#2496×C₁₃₉	2
#2365×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
#2285×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36188	139

Subgroups — C139×#36188 #48030784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36188 #48030784