Subgroups — C₁₃₉×#21945 #48016541

Order 35584.

1010 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#408×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2311×C₁₃₉	C₂	1	2	yes	maximal
3	#1854×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#1854×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1853×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1852×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1809×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1808×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1807×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
16	C₂×#107×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#106×C₁₃₉	C₂²	1	2	yes	—
19	#408×C₁₃₉	C₄	1	8	yes	complemented
20	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
22	#391×C₁₃₉	—	2	2	no	—
23	#390×C₁₃₉	—	2	2	no	—
24	#386×C₁₃₉	—	2	2	no	—
25	#386×C₁₃₉	—	2	2	no	—
26	#380×C₁₃₉	C₂²	1	2	yes	—
27	#380×C₁₃₉	C₂²	1	2	yes	—
28	#380×C₁₃₉	C₂²	1	2	yes	—
29	#380×C₁₃₉	C₂²	1	2	yes	—
30	#340×C₁₃₉	C₂²	1	1	yes	characteristic
31	#340×C₁₃₉	C₂²	1	1	yes	characteristic
32	#340×C₁₃₉	C₂²	1	1	yes	characteristic
33	#340×C₁₃₉	C₂²	1	1	yes	characteristic
34	#340×C₁₃₉	C₂²	1	2	yes	—
35	#340×C₁₃₉	C₂²	1	2	yes	—
36	C₂×#41×C₁₃₉	—	4	2	no	—
37	C₂×#41×C₁₃₉	—	4	2	no	—
38	C₂×#41×C₁₃₉	C₂×C₄	1	4	yes	—
39	C₂×#41×C₁₃₉	Q₈	1	4	yes	—
40	C₂²×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₃₉	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₃₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₃₉	—	2	2	no	—
44	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₃₉	—	4	2	no	—
47	C₂×M₁₆×C₁₃₉	C₂×C₄	1	4	yes	complemented
48	C₂²×C₈×C₁₃₉	—	4	2	no	—
49	C₂²×C₈×C₁₃₉	C₂×C₄	1	4	yes	complemented
50	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
53	#117×C₁₃₉	—	4	2	no	—
54	#117×C₁₃₉	—	4	2	no	—
55	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
67	C₂×C₄²×C₁₃₉	—	2	2	no	—
68	#107×C₁₃₉	—	4	2	no	—
69	#107×C₁₃₉	—	4	2	no	—
70	#106×C₁₃₉	—	4	2	no	—
71	#106×C₁₃₉	—	4	2	no	—
72	C₂²⋊C₈×C₁₃₉	C₂×C₄	1	8	yes	complemented
73	C₂²⋊C₈×C₁₃₉	C₂×C₄	1	8	yes	complemented
74	#95×C₁₃₉	—	2	2	no	—
75	#95×C₁₃₉	—	2	2	no	—
76	#95×C₁₃₉	—	2	2	no	—
77	#95×C₁₃₉	—	2	2	no	—
78	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
79	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
80	#41×C₁₃₉	—	4	4	no	—
81	#41×C₁₃₉	—	4	4	no	—
82	#41×C₁₃₉	—	4	8	no	—
83	C₂×Q₈×C₁₃₉	—	4	2	no	—
84	C₂×Q₈×C₁₃₉	C₄⋊C₄	1	4	yes	—
85	C₂×D₄×C₁₃₉	—	4	2	no	—
86	C₂×D₄×C₁₃₉	—	4	2	no	—
87	C₂×D₄×C₁₃₉	—	4	2	no	—
88	C₂×D₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
89	C₂×D₄×C₁₃₉	C₄⋊C₄	1	8	yes	—
90	C₂²×C₄×C₁₃₉	—	2	2	no	—
91	C₂²×C₄×C₁₃₉	—	2	2	no	—
92	C₂²×C₄×C₁₃₉	—	2	2	no	—
93	C₂²×C₄×C₁₃₉	—	2	2	no	—
94	C₂²×C₄×C₁₃₉	—	2	2	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	—	2	2	no	—
97	C₂²×C₄×C₁₃₉	—	2	2	no	—
98	C₂²×C₄×C₁₃₉	—	2	2	no	—
99	C₂²×C₄×C₁₃₉	—	2	2	no	—
100	C₂²×C₄×C₁₃₉	—	4	4	no	—
101	C₂²×C₄×C₁₃₉	—	8	2	no	—
102	C₂²×C₄×C₁₃₉	—	8	2	no	—
103	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
108	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₁₃₉	—	4	4	no	—
111	C₂×C₈×C₁₃₉	—	2	2	no	—
112	C₂×C₈×C₁₃₉	—	2	2	no	—
113	C₂×C₈×C₁₃₉	—	2	2	no	—
114	C₂×C₈×C₁₃₉	—	2	2	no	—
115	C₂×C₈×C₁₃₉	—	4	4	no	—
116	C₂×C₈×C₁₃₉	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₃₉	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃₉	C₂²×C₄	1	4	yes	—
119	C₄⋊C₄×C₁₃₉	—	2	2	no	—
120	C₄⋊C₄×C₁₃₉	—	2	2	no	—
121	C₄⋊C₄×C₁₃₉	—	2	2	no	—
122	C₄⋊C₄×C₁₃₉	—	2	2	no	—
123	C₄⋊C₄×C₁₃₉	—	2	2	no	—
124	C₄⋊C₄×C₁₃₉	—	2	2	no	—
125	C₄⋊C₄×C₁₃₉	—	2	2	no	—
126	C₄⋊C₄×C₁₃₉	—	2	2	no	—
127	C₄⋊C₄×C₁₃₉	—	4	4	no	—
128	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
129	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
130	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
131	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
132	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
133	C₄²×C₁₃₉	—	4	4	no	—
134	C₂³×C₁₃₉	—	2	2	no	—
135	C₂³×C₁₃₉	—	2	2	no	—
136	C₂³×C₁₃₉	—	2	2	no	—
137	C₂³×C₁₃₉	—	2	1	no	—
138	C₂³×C₁₃₉	—	2	2	no	—
139	C₂³×C₁₃₉	—	2	2	no	—
140	C₂³×C₁₃₉	—	2	2	no	—
141	C₂³×C₁₃₉	—	2	2	no	—
142	C₂³×C₁₃₉	—	2	1	no	—
143	C₂³×C₁₃₉	—	2	2	no	—
144	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
145	C₂³×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
146	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₁₃₉	—	4	4	no	—
148	D₄×C₁₃₉	—	4	8	no	—
149	D₄×C₁₃₉	—	4	4	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	4	no	—
156	C₂×C₄×C₁₃₉	—	2	4	no	—
157	C₂×C₄×C₁₃₉	—	2	4	no	—
158	C₂×C₄×C₁₃₉	—	2	4	no	—
159	C₂×C₄×C₁₃₉	—	2	4	no	—
160	C₂×C₄×C₁₃₉	—	4	2	no	—
161	C₂×C₄×C₁₃₉	—	4	2	no	—
162	C₂×C₄×C₁₃₉	—	4	2	no	—
163	C₂×C₄×C₁₃₉	—	4	2	no	—
164	C₂×C₄×C₁₃₉	—	4	2	no	—
165	C₂×C₄×C₁₃₉	—	4	2	no	—
166	C₂×C₄×C₁₃₉	—	4	2	no	—
167	C₂×C₄×C₁₃₉	—	4	2	no	—
168	C₂×C₄×C₁₃₉	—	4	2	no	—
169	C₂×C₄×C₁₃₉	—	4	2	no	—
170	C₂×C₄×C₁₃₉	—	4	2	no	—
171	C₂×C₄×C₁₃₉	—	4	2	no	—
172	C₂×C₄×C₁₃₉	—	8	8	no	—
173	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	4	yes	—
174	C₂×C₄×C₁₃₉	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
178	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
179	C₈×C₁₃₉	—	2	2	no	—
180	C₈×C₁₃₉	—	2	2	no	—
181	C₈×C₁₃₉	—	2	4	no	—
182	C₂²×C₁₃₉	—	2	2	no	—
183	C₂²×C₁₃₉	—	2	4	no	—
184	C₂²×C₁₃₉	—	2	2	no	—
185	C₂²×C₁₃₉	—	2	4	no	—
186	C₂²×C₁₃₉	—	2	2	no	—
187	C₂²×C₁₃₉	—	2	4	no	—
188	C₂²×C₁₃₉	—	4	2	no	—
189	C₂²×C₁₃₉	—	4	2	no	—
190	C₂²×C₁₃₉	—	4	2	no	—
191	C₂²×C₁₃₉	—	4	2	no	—
192	C₂²×C₁₃₉	—	4	2	no	—
193	C₂²×C₁₃₉	—	4	2	no	—
194	C₂²×C₁₃₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
195	C₂²×C₁₃₉	#534	1	2	yes	—
196	C₂²×C₁₃₉	#576	1	1	yes	characteristic
197	C₂²×C₁₃₉	#577	1	2	yes	—
198	C₂²×C₁₃₉	#578	1	1	yes	characteristic
199	C₄×C₁₃₉	—	2	4	no	—
200	C₄×C₁₃₉	—	2	2	no	—
201	C₄×C₁₃₉	—	8	2	no	—
202	C₄×C₁₃₉	—	8	2	no	—
203	C₄×C₁₃₉	—	8	2	no	—
204	C₄×C₁₃₉	—	8	2	no	—
205	C₄×C₁₃₉	#518	1	1	yes	characteristic
206	C₄×C₁₃₉	#518	1	1	yes	characteristic
207	C₄×C₁₃₉	#543	1	2	yes	—
208	C₂×C₁₃₉	—	4	4	no	—
209	C₂×C₁₃₉	—	4	2	no	—
210	C₂×C₁₃₉	#2315	1	1	yes	characteristic
211	C₂×C₁₃₉	#2912	1	1	yes	characteristic
212	C₂×C₁₃₉	#2913	1	1	yes	characteristic
213	C₂×C₁₃₉	#3198	1	2	yes	—
214	C₂×C₁₃₉	#3201	1	2	yes	—
215	#21945	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₁₃₉	#21945	1	1	yes	characteristic, direct product factor, Sylow
217	C₂×#408	C₂×C₁₃₉	1	1	yes	characteristic
218	#2311	C₂×C₁₃₉	1	2	yes	—
219	#1854	C₂×C₁₃₉	1	2	yes	complemented
220	#1854	C₂×C₁₃₉	1	2	yes	complemented
221	#1853	C₂×C₁₃₉	1	2	yes	complemented
222	#1852	C₂×C₁₃₉	1	2	yes	complemented
223	#1809	C₂×C₁₃₉	1	2	yes	complemented
224	#1808	C₂×C₁₃₉	1	1	yes	characteristic, complemented
225	#1807	C₂×C₁₃₉	1	1	yes	characteristic, complemented
226	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
228	C₂³×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
229	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
230	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
231	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
232	C₂×#107	C₂²×C₁₃₉	1	2	yes	—
233	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
234	C₂×#106	C₂²×C₁₃₉	1	2	yes	—
235	#408	C₄×C₁₃₉	1	8	yes	complemented
236	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
237	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
238	#391	—	2	2	no	—
239	#390	—	2	2	no	—
240	#386	—	2	2	no	—
241	#386	—	2	2	no	—
242	#380	C₂²×C₁₃₉	1	2	yes	—
243	#380	C₂²×C₁₃₉	1	2	yes	—
244	#380	C₂²×C₁₃₉	1	2	yes	—
245	#380	C₂²×C₁₃₉	1	2	yes	—
246	#340	C₂²×C₁₃₉	1	1	yes	characteristic
247	#340	C₂²×C₁₃₉	1	1	yes	characteristic
248	#340	C₂²×C₁₃₉	1	1	yes	characteristic
249	#340	C₂²×C₁₃₉	1	1	yes	characteristic
250	#340	C₂²×C₁₃₉	1	2	yes	—
251	#340	C₂²×C₁₃₉	1	2	yes	—
252	C₂×#41	—	4	2	no	—
253	C₂×#41	—	4	2	no	—
254	C₂×#41	C₂×C₄×C₁₃₉	1	4	yes	—
255	C₂×#41	Q₈×C₁₃₉	1	4	yes	—
256	C₂²×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
257	C₂²×D₄	D₄×C₁₃₉	1	1	yes	characteristic
258	C₂²×D₄	D₄×C₁₃₉	1	2	yes	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
261	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
262	C₂×M₁₆	—	4	2	no	—
263	C₂×M₁₆	C₂×C₄×C₁₃₉	1	4	yes	complemented
264	C₂²×C₈	—	4	2	no	—
265	C₂²×C₈	C₂×C₄×C₁₃₉	1	4	yes	complemented
266	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
269	#117	—	4	2	no	—
270	#117	—	4	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	4	2	no	—
273	C₂×C₄⋊C₄	—	4	2	no	—
274	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	#107	—	4	2	no	—
285	#107	—	4	2	no	—
286	#106	—	4	2	no	—
287	#106	—	4	2	no	—
288	C₂²⋊C₈	C₂×C₄×C₁₃₉	1	8	yes	complemented
289	C₂²⋊C₈	C₂×C₄×C₁₃₉	1	8	yes	complemented
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
295	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
296	#41	—	4	4	no	—
297	#41	—	4	4	no	—
298	#41	—	4	8	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	C₄⋊C₄×C₁₃₉	1	4	yes	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	C₄⋊C₄×C₁₃₉	1	4	yes	—
305	C₂×D₄	C₄⋊C₄×C₁₃₉	1	8	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	8	2	no	—
318	C₂²×C₄	—	8	2	no	—
319	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
320	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
323	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
324	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
326	M₁₆	—	4	4	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	4	4	no	—
332	C₂×C₈	C₂²×C₄×C₁₃₉	1	2	yes	—
333	C₂×C₈	C₂²×C₄×C₁₃₉	1	2	yes	—
334	C₂×C₈	C₂²×C₄×C₁₃₉	1	4	yes	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	8	2	no	—
346	C₂²⋊C₄	—	8	2	no	—
347	C₂²⋊C₄	—	8	2	no	—
348	C₂²⋊C₄	—	8	2	no	—
349	C₄²	—	4	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	2	no	—
360	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
361	C₂³	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
362	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
363	Q₈	—	4	4	no	—
364	D₄	—	4	8	no	—
365	D₄	—	4	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	8	no	—
389	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	4	yes	—
390	C₂×C₄	C₂×C₄⋊C₄×C₁₃₉	1	2	yes	—
391	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
392	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
393	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
394	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	4	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	C₂²×C₄⋊C₄×C₁₃₉	1	1	yes	characteristic
411	C₂²	#534×C₁₃₉	1	2	yes	—
412	C₂²	#576×C₁₃₉	1	1	yes	characteristic
413	C₂²	#577×C₁₃₉	1	2	yes	—
414	C₂²	#578×C₁₃₉	1	1	yes	characteristic
415	C₄	—	2	4	no	—
416	C₄	—	2	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	2	no	—
421	C₄	#518×C₁₃₉	1	1	yes	characteristic
422	C₄	#518×C₁₃₉	1	1	yes	characteristic
423	C₄	#543×C₁₃₉	1	2	yes	—
424	C₂	—	4	4	no	—
425	C₂	—	4	2	no	—
426	C₂	#2315×C₁₃₉	1	1	yes	characteristic
427	C₂	#2912×C₁₃₉	1	1	yes	characteristic
428	C₂	#2913×C₁₃₉	1	1	yes	characteristic
429	C₂	#3198×C₁₃₉	1	2	yes	—
430	C₂	#3201×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂²×#41×C₁₃₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #1854×C₁₃₉	C₂	semidirect
4. #1854×C₁₃₉	C₂	semidirect
5. #1853×C₁₃₉	C₂	semidirect
6. #1852×C₁₃₉	C₂	semidirect
7. #1809×C₁₃₉	C₂	semidirect
8. #1808×C₁₃₉	C₂	semidirect
9. #1807×C₁₃₉	C₂	semidirect
19. #408×C₁₃₉	C₄	semidirect
47. C₂×M₁₆×C₁₃₉	C₂×C₄	semidirect
49. C₂²×C₈×C₁₃₉	C₂×C₄	semidirect
72. C₂²⋊C₈×C₁₃₉	C₂×C₄	semidirect
73. C₂²⋊C₈×C₁₃₉	C₂×C₄	semidirect
215. #21945	C₁₃₉	direct (N × H)
216. C₁₃₉	#21945	direct (N × H)
219. #1854	C₂×C₁₃₉	semidirect
220. #1854	C₂×C₁₃₉	semidirect
221. #1853	C₂×C₁₃₉	semidirect
222. #1852	C₂×C₁₃₉	semidirect
223. #1809	C₂×C₁₃₉	semidirect
224. #1808	C₂×C₁₃₉	semidirect
225. #1807	C₂×C₁₃₉	semidirect
235. #408	C₄×C₁₃₉	semidirect
263. C₂×M₁₆	C₂×C₄×C₁₃₉	semidirect
265. C₂²×C₈	C₂×C₄×C₁₃₉	semidirect
288. C₂²⋊C₈	C₂×C₄×C₁₃₉	semidirect
289. C₂²⋊C₈	C₂×C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#408×C₁₃₉	2
#2311×C₁₃₉	2
#1854×C₁₃₉	2
#1853×C₁₃₉	2
#1852×C₁₃₉	2
#1809×C₁₃₉	2
#1808×C₁₃₉	2
#1807×C₁₃₉	2
#21945	139

Subgroups — C139×#21945 #48016541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#21945 #48016541