Subgroups — C₁₃₉×#32992 #48027588

Order 35584.

1304 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3428×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#3094×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2431×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#1888×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#1887×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1857×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1856×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1826×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	#1785×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#121×C₁₃₉	C₂²	1	1	yes	characteristic
14	#520×C₁₃₉	—	2	2	no	—
15	#520×C₁₃₉	—	2	2	no	—
16	#519×C₁₃₉	C₂²	1	2	yes	—
17	#518×C₁₃₉	—	2	2	no	—
18	#518×C₁₃₉	C₂²	1	2	yes	—
19	C₄×#41×C₁₃₉	—	2	4	no	—
20	C₂×#117×C₁₃₉	—	2	2	no	—
21	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
22	#482×C₁₃₉	—	2	4	no	—
23	#481×C₁₃₉	—	2	2	no	—
24	#480×C₁₃₉	—	2	2	no	—
25	#428×C₁₃₉	C₂²	1	4	yes	—
26	#418×C₁₃₉	C₂²	1	4	yes	—
27	C₂×#101×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#100×C₁₃₉	C₂²	1	2	yes	—
29	#407×C₁₃₉	C₂²	1	2	yes	—
30	#392×C₁₃₉	—	2	2	no	—
31	#391×C₁₃₉	C₂²	1	1	yes	characteristic
32	#390×C₁₃₉	C₂²	1	1	yes	characteristic
33	#386×C₁₃₉	—	2	2	no	—
34	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	#339×C₁₃₉	C₂²	1	4	yes	—
36	#339×C₁₃₉	C₂²	1	4	yes	—
37	C₂×#41×C₁₃₉	—	2	4	no	—
38	C₂×#41×C₁₃₉	—	2	4	no	—
39	C₂×#41×C₁₃₉	—	2	2	no	—
40	C₂×#41×C₁₃₉	—	2	2	no	—
41	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₁₃₉	—	2	2	no	—
43	C₂²×D₄×C₁₃₉	—	2	1	no	—
44	C₂²×D₄×C₁₃₉	D₄	1	2	yes	—
45	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃₉	D₄	1	2	yes	—
48	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₁₃₉	C₂³	1	4	yes	—
50	#127×C₁₃₉	—	2	4	no	—
51	#124×C₁₃₉	—	2	4	no	—
52	#121×C₁₃₉	—	2	2	no	—
53	#121×C₁₃₉	—	2	2	no	—
54	C₄×Q₈×C₁₃₉	—	2	4	no	—
55	C₄×Q₈×C₁₃₉	—	2	4	no	—
56	C₄×D₄×C₁₃₉	—	2	8	no	—
57	C₄×D₄×C₁₃₉	—	2	8	no	—
58	C₄×D₄×C₁₃₉	—	2	4	no	—
59	C₄×D₄×C₁₃₉	—	2	4	no	—
60	#117×C₁₃₉	—	2	4	no	—
61	#117×C₁₃₉	—	2	4	no	—
62	#117×C₁₃₉	—	2	2	no	—
63	#117×C₁₃₉	—	2	4	no	—
64	#117×C₁₃₉	—	2	2	no	—
65	#117×C₁₃₉	D₄	1	4	yes	complemented
66	#117×C₁₃₉	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	complemented
70	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	complemented
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
78	C₂×C₄²×C₁₃₉	—	2	4	no	—
79	C₂×C₄²×C₁₃₉	—	2	2	no	—
80	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
82	#107×C₁₃₉	—	2	4	no	—
83	#106×C₁₃₉	—	2	4	no	—
84	#102×C₁₃₉	—	2	4	no	—
85	#102×C₁₃₉	—	2	4	no	—
86	#101×C₁₃₉	—	2	4	no	—
87	#100×C₁₃₉	—	2	4	no	—
88	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
89	C₂²⋊C₈×C₁₃₉	—	2	2	no	—
90	#95×C₁₃₉	—	2	1	no	—
91	#95×C₁₃₉	—	2	2	no	—
92	C₂⁴×C₁₃₉	—	2	1	no	—
93	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
94	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
95	#41×C₁₃₉	—	2	16	no	—
96	#41×C₁₃₉	—	2	16	no	—
97	C₂×Q₈×C₁₃₉	—	2	2	no	—
98	C₂×Q₈×C₁₃₉	—	2	2	no	—
99	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
100	C₂×D₄×C₁₃₉	—	2	4	no	—
101	C₂×D₄×C₁₃₉	—	2	4	no	—
102	C₂×D₄×C₁₃₉	—	2	4	no	—
103	C₂×D₄×C₁₃₉	—	2	2	no	—
104	C₂×D₄×C₁₃₉	—	2	2	no	—
105	C₂×D₄×C₁₃₉	—	2	2	no	—
106	C₂×D₄×C₁₃₉	—	2	2	no	—
107	C₂×D₄×C₁₃₉	—	2	2	no	—
108	C₂×D₄×C₁₃₉	—	4	4	no	—
109	C₂×D₄×C₁₃₉	—	4	2	no	—
110	C₂×D₄×C₁₃₉	—	4	4	no	—
111	C₂×D₄×C₁₃₉	—	8	2	no	—
112	C₂×D₄×C₁₃₉	—	8	2	no	—
113	C₂×D₄×C₁₃₉	#41	1	4	yes	—
114	C₂²×C₄×C₁₃₉	—	2	4	no	—
115	C₂²×C₄×C₁₃₉	—	2	2	no	—
116	C₂²×C₄×C₁₃₉	—	2	2	no	—
117	C₂²×C₄×C₁₃₉	—	2	4	no	—
118	C₂²×C₄×C₁₃₉	—	2	2	no	—
119	C₂²×C₄×C₁₃₉	—	2	2	no	—
120	C₂²×C₄×C₁₃₉	—	2	1	no	—
121	C₂²×C₄×C₁₃₉	—	2	4	no	—
122	C₂²×C₄×C₁₃₉	—	2	4	no	—
123	C₂²×C₄×C₁₃₉	—	2	2	no	—
124	C₂²×C₄×C₁₃₉	—	2	2	no	—
125	C₂²×C₄×C₁₃₉	—	2	1	no	—
126	C₂²×C₄×C₁₃₉	—	2	1	no	—
127	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
132	M₁₆×C₁₃₉	—	2	4	no	—
133	M₁₆×C₁₃₉	—	2	4	no	—
134	C₂×C₈×C₁₃₉	—	2	4	no	—
135	C₄⋊C₄×C₁₃₉	—	2	4	no	—
136	C₄⋊C₄×C₁₃₉	—	2	4	no	—
137	C₄⋊C₄×C₁₃₉	—	2	2	no	—
138	C₄⋊C₄×C₁₃₉	—	2	2	no	—
139	C₄⋊C₄×C₁₃₉	—	2	2	no	—
140	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
141	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
142	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
143	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
144	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
145	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
146	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
147	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
148	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
149	C₂²⋊C₄×C₁₃₉	—	8	2	no	—
150	C₄²×C₁₃₉	—	2	8	no	—
151	C₄²×C₁₃₉	—	2	4	no	—
152	C₄²×C₁₃₉	—	2	4	no	—
153	C₄²×C₁₃₉	—	2	2	no	—
154	C₄²×C₁₃₉	—	2	2	no	—
155	C₂³×C₁₃₉	—	2	2	no	—
156	C₂³×C₁₃₉	—	2	1	no	—
157	C₂³×C₁₃₉	—	2	1	no	—
158	C₂³×C₁₃₉	—	2	2	no	—
159	C₂³×C₁₃₉	—	4	1	no	—
160	C₂³×C₁₃₉	—	4	1	no	—
161	C₂³×C₁₃₉	—	4	2	no	—
162	C₂³×C₁₃₉	—	4	2	no	—
163	C₂³×C₁₃₉	—	4	2	no	—
164	C₂³×C₁₃₉	—	4	2	no	—
165	C₂³×C₁₃₉	—	4	1	no	—
166	C₂³×C₁₃₉	—	4	1	no	—
167	C₂³×C₁₃₉	—	4	1	no	—
168	C₂³×C₁₃₉	#120	1	2	yes	—
169	C₂³×C₁₃₉	#123	1	4	yes	—
170	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₁₃₉	—	2	8	no	—
172	D₄×C₁₃₉	—	2	16	no	—
173	D₄×C₁₃₉	—	2	8	no	—
174	D₄×C₁₃₉	—	4	4	no	—
175	D₄×C₁₃₉	—	8	8	no	—
176	D₄×C₁₃₉	—	8	4	no	—
177	C₂×C₄×C₁₃₉	—	2	8	no	—
178	C₂×C₄×C₁₃₉	—	2	8	no	—
179	C₂×C₄×C₁₃₉	—	2	2	no	—
180	C₂×C₄×C₁₃₉	—	2	1	no	—
181	C₂×C₄×C₁₃₉	—	2	1	no	—
182	C₂×C₄×C₁₃₉	—	2	2	no	—
183	C₂×C₄×C₁₃₉	—	2	4	no	—
184	C₂×C₄×C₁₃₉	—	2	4	no	—
185	C₂×C₄×C₁₃₉	—	2	2	no	—
186	C₂×C₄×C₁₃₉	—	2	4	no	—
187	C₂×C₄×C₁₃₉	—	2	4	no	—
188	C₂×C₄×C₁₃₉	—	4	1	no	—
189	C₂×C₄×C₁₃₉	—	4	1	no	—
190	C₂×C₄×C₁₃₉	—	4	1	no	—
191	C₂×C₄×C₁₃₉	—	4	1	no	—
192	C₂×C₄×C₁₃₉	—	4	2	no	—
193	C₂×C₄×C₁₃₉	—	4	1	no	—
194	C₂×C₄×C₁₃₉	—	4	1	no	—
195	C₂×C₄×C₁₃₉	—	8	2	no	—
196	C₂×C₄×C₁₃₉	—	8	2	no	—
197	C₂×C₄×C₁₃₉	—	8	4	no	—
198	C₂×C₄×C₁₃₉	—	8	4	no	—
199	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
200	C₂×C₄×C₁₃₉	#120	1	1	yes	characteristic
201	C₂×C₄×C₁₃₉	#123	1	4	yes	—
202	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
204	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
205	C₈×C₁₃₉	—	4	4	no	—
206	C₂²×C₁₃₉	—	2	1	no	—
207	C₂²×C₁₃₉	—	2	1	no	—
208	C₂²×C₁₃₉	—	2	2	no	—
209	C₂²×C₁₃₉	—	2	4	no	—
210	C₂²×C₁₃₉	—	2	2	no	—
211	C₂²×C₁₃₉	—	2	2	no	—
212	C₂²×C₁₃₉	—	4	4	no	—
213	C₂²×C₁₃₉	—	4	2	no	—
214	C₂²×C₁₃₉	—	4	2	no	—
215	C₂²×C₁₃₉	—	8	1	no	—
216	C₂²×C₁₃₉	—	8	1	no	—
217	C₂²×C₁₃₉	—	8	2	no	—
218	C₂²×C₁₃₉	—	8	2	no	—
219	C₂²×C₁₃₉	—	8	2	no	—
220	C₂²×C₁₃₉	—	8	1	no	—
221	C₂²×C₁₃₉	—	8	1	no	—
222	C₂²×C₁₃₉	—	8	1	no	—
223	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
224	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
225	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
226	C₄×C₁₃₉	—	2	1	no	—
227	C₄×C₁₃₉	—	2	1	no	—
228	C₄×C₁₃₉	—	2	4	no	—
229	C₄×C₁₃₉	—	4	2	no	—
230	C₄×C₁₃₉	—	4	4	no	—
231	C₄×C₁₃₉	—	4	4	no	—
232	C₄×C₁₃₉	—	8	1	no	—
233	C₄×C₁₃₉	—	8	1	no	—
234	C₄×C₁₃₉	#525	1	4	yes	—
235	C₂×C₁₃₉	—	2	1	no	—
236	C₂×C₁₃₉	—	2	1	no	—
237	C₂×C₁₃₉	—	4	2	no	—
238	C₂×C₁₃₉	—	4	4	no	—
239	C₂×C₁₃₉	—	16	1	no	—
240	C₂×C₁₃₉	#2849	1	1	yes	characteristic
241	C₂×C₁₃₉	#3018	1	1	yes	characteristic
242	C₂×C₁₃₉	#3021	1	1	yes	characteristic
243	#32992	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₁₃₉	#32992	1	1	yes	characteristic, direct product factor, Sylow
245	#3428	C₂×C₁₃₉	1	1	yes	characteristic, complemented
246	#3094	C₂×C₁₃₉	1	2	yes	complemented
247	#2431	C₂×C₁₃₉	1	1	yes	characteristic
248	#1888	C₂×C₁₃₉	1	2	yes	complemented
249	#1887	C₂×C₁₃₉	1	2	yes	complemented
250	#1857	C₂×C₁₃₉	1	2	yes	complemented
251	#1856	C₂×C₁₃₉	1	2	yes	complemented
252	#1826	C₂×C₁₃₉	1	2	yes	complemented
253	#1785	C₂×C₁₃₉	1	1	yes	characteristic, complemented
254	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
255	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
256	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
257	C₂×#121	C₂²×C₁₃₉	1	1	yes	characteristic
258	#520	—	2	2	no	—
259	#520	—	2	2	no	—
260	#519	C₂²×C₁₃₉	1	2	yes	—
261	#518	—	2	2	no	—
262	#518	C₂²×C₁₃₉	1	2	yes	—
263	C₄×#41	—	2	4	no	—
264	C₂×#117	—	2	2	no	—
265	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
266	#482	—	2	4	no	—
267	#481	—	2	2	no	—
268	#480	—	2	2	no	—
269	#428	C₂²×C₁₃₉	1	4	yes	—
270	#418	C₂²×C₁₃₉	1	4	yes	—
271	C₂×#101	C₂²×C₁₃₉	1	2	yes	—
272	C₂×#100	C₂²×C₁₃₉	1	2	yes	—
273	#407	C₂²×C₁₃₉	1	2	yes	—
274	#392	—	2	2	no	—
275	#391	C₂²×C₁₃₉	1	1	yes	characteristic
276	#390	C₂²×C₁₃₉	1	1	yes	characteristic
277	#386	—	2	2	no	—
278	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
279	#339	C₂²×C₁₃₉	1	4	yes	—
280	#339	C₂²×C₁₃₉	1	4	yes	—
281	C₂×#41	—	2	4	no	—
282	C₂×#41	—	2	4	no	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	—	2	2	no	—
285	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	D₄×C₁₃₉	1	2	yes	—
289	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
290	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
291	C₂³×C₄	D₄×C₁₃₉	1	2	yes	—
292	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
293	C₂×M₁₆	C₂³×C₁₃₉	1	4	yes	—
294	#127	—	2	4	no	—
295	#124	—	2	4	no	—
296	#121	—	2	2	no	—
297	#121	—	2	2	no	—
298	C₄×Q₈	—	2	4	no	—
299	C₄×Q₈	—	2	4	no	—
300	C₄×D₄	—	2	8	no	—
301	C₄×D₄	—	2	8	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	4	no	—
304	#117	—	2	4	no	—
305	#117	—	2	4	no	—
306	#117	—	2	2	no	—
307	#117	—	2	4	no	—
308	#117	—	2	2	no	—
309	#117	D₄×C₁₃₉	1	4	yes	complemented
310	#117	C₂³×C₁₃₉	1	4	yes	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	complemented
314	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	complemented
315	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	4	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₄²	—	2	4	no	—
323	C₂×C₄²	—	2	2	no	—
324	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
326	#107	—	2	4	no	—
327	#106	—	2	4	no	—
328	#102	—	2	4	no	—
329	#102	—	2	4	no	—
330	#101	—	2	4	no	—
331	#100	—	2	4	no	—
332	C₂²⋊C₈	—	2	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	#95	—	2	1	no	—
335	#95	—	2	2	no	—
336	C₂⁴	—	2	1	no	—
337	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
338	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
339	#41	—	2	16	no	—
340	#41	—	2	16	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	8	2	no	—
356	C₂×D₄	—	8	2	no	—
357	C₂×D₄	#41×C₁₃₉	1	4	yes	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
374	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
376	M₁₆	—	2	4	no	—
377	M₁₆	—	2	4	no	—
378	C₂×C₈	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
385	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	8	2	no	—
394	C₄²	—	2	8	no	—
395	C₄²	—	2	4	no	—
396	C₄²	—	2	4	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	#120×C₁₃₉	1	2	yes	—
413	C₂³	#123×C₁₃₉	1	4	yes	—
414	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
415	Q₈	—	2	8	no	—
416	D₄	—	2	16	no	—
417	D₄	—	2	8	no	—
418	D₄	—	4	4	no	—
419	D₄	—	8	8	no	—
420	D₄	—	8	4	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	—	8	2	no	—
441	C₂×C₄	—	8	4	no	—
442	C₂×C₄	—	8	4	no	—
443	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
444	C₂×C₄	#120×C₁₃₉	1	1	yes	characteristic
445	C₂×C₄	#123×C₁₃₉	1	4	yes	—
446	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
447	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
448	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
449	C₈	—	4	4	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
468	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
469	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	4	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	4	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	#525×C₁₃₉	1	4	yes	—
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	4	2	no	—
482	C₂	—	4	4	no	—
483	C₂	—	16	1	no	—
484	C₂	#2849×C₁₃₉	1	1	yes	characteristic
485	C₂	#3018×C₁₃₉	1	1	yes	characteristic
486	C₂	#3021×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	#2431×C₁₃₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂³×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3428×C₁₃₉	C₂	semidirect
2. #3094×C₁₃₉	C₂	semidirect
4. #1888×C₁₃₉	C₂	semidirect
5. #1887×C₁₃₉	C₂	semidirect
6. #1857×C₁₃₉	C₂	semidirect
7. #1856×C₁₃₉	C₂	semidirect
8. #1826×C₁₃₉	C₂	semidirect
9. #1785×C₁₃₉	C₂	semidirect
65. #117×C₁₃₉	D₄	semidirect
69. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
70. C₂×C₄⋊C₄×C₁₃₉	D₄	semidirect
243. #32992	C₁₃₉	direct (N × H)
244. C₁₃₉	#32992	direct (N × H)
245. #3428	C₂×C₁₃₉	semidirect
246. #3094	C₂×C₁₃₉	semidirect
248. #1888	C₂×C₁₃₉	semidirect
249. #1887	C₂×C₁₃₉	semidirect
250. #1857	C₂×C₁₃₉	semidirect
251. #1856	C₂×C₁₃₉	semidirect
252. #1826	C₂×C₁₃₉	semidirect
253. #1785	C₂×C₁₃₉	semidirect
309. #117	D₄×C₁₃₉	semidirect
313. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect
314. C₂×C₄⋊C₄	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3428×C₁₃₉	2
#3094×C₁₃₉	2
#2431×C₁₃₉	2
#1888×C₁₃₉	2
#1887×C₁₃₉	2
#1857×C₁₃₉	2
#1856×C₁₃₉	2
#1826×C₁₃₉	2
#1785×C₁₃₉	2
#32992	139

Subgroups — C139×#32992 #48027588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#32992 #48027588