Subgroups — C₁₃₉×#17606 #48012202

Order 35584.

1270 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3489×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2880×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2341×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1520×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#1513×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#1508×C₁₃₉	C₂	1	3	yes	maximal, complemented
7	#1501×C₁₃₉	C₂	1	3	yes	maximal, complemented
8	C₂×2₋¹⁺⁴×C₁₃₉	C₄	1	1	yes	characteristic, complemented
9	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂×#131×C₁₃₉	—	2	1	no	—
11	D₄×Q₈×C₁₃₉	—	2	1	no	—
12	#548×C₁₃₉	—	2	1	no	—
13	#547×C₁₃₉	—	2	3	no	—
14	#546×C₁₃₉	—	2	3	no	—
15	#537×C₁₃₉	C₄	1	3	yes	complemented
16	#536×C₁₃₉	C₄	1	3	yes	complemented
17	#525×C₁₃₉	C₂²	1	3	yes	—
18	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
19	#520×C₁₃₉	C₄	1	1	yes	characteristic, complemented
20	C₂×C₄×Q₈×C₁₃₉	—	2	1	no	—
21	#408×C₁₃₉	—	2	3	no	—
22	#407×C₁₃₉	C₂²	1	3	yes	—
23	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	3	yes	—
24	#390×C₁₃₉	—	2	3	no	—
25	#380×C₁₃₉	C₂²	1	3	yes	—
26	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	3	yes	—
27	#328×C₁₃₉	C₂²	1	3	yes	—
28	#328×C₁₃₉	C₂²	1	3	yes	—
29	#328×C₁₃₉	C₂²	1	6	yes	—
30	#327×C₁₃₉	C₂²	1	1	yes	characteristic
31	#327×C₁₃₉	C₂²	1	3	yes	—
32	2₋¹⁺⁴×C₁₃₉	—	4	4	no	—
33	C₂×#41×C₁₃₉	—	2	3	no	—
34	C₂×#41×C₁₃₉	—	4	4	no	—
35	C₂×#41×C₁₃₉	C₂×C₄	1	3	yes	—
36	C₂×#41×C₁₃₉	C₂×C₄	1	1	yes	characteristic
37	C₂×#41×C₁₃₉	C₂×C₄	1	3	yes	—
38	C₂×#41×C₁₃₉	D₄	1	1	yes	characteristic
39	C₂×#41×C₁₃₉	D₄	1	3	yes	—
40	C₂²×Q₈×C₁₃₉	—	2	1	no	—
41	C₂²×Q₈×C₁₃₉	C₂×C₄	1	3	yes	—
42	C₂²×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₁₃₉	D₄	1	3	yes	—
44	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
45	#131×C₁₃₉	—	4	4	no	—
46	C₂×M₁₆×C₁₃₉	—	2	3	no	—
47	C₂²×C₈×C₁₃₉	—	2	3	no	—
48	C₄⋊Q₈×C₁₃₉	—	2	3	no	—
49	#124×C₁₃₉	—	2	3	no	—
50	#123×C₁₃₉	—	2	6	no	—
51	#123×C₁₃₉	—	2	3	no	—
52	C₂²⋊Q₈×C₁₃₉	—	2	3	no	—
53	C₂²⋊Q₈×C₁₃₉	—	2	3	no	—
54	C₂²⋊Q₈×C₁₃₉	—	2	3	no	—
55	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	6	yes	—
56	C₂²⋊Q₈×C₁₃₉	C₂×C₄	1	3	yes	—
57	C₂²⋊Q₈×C₁₃₉	C₂³	1	3	yes	—
58	#121×C₁₃₉	—	2	6	no	—
59	#121×C₁₃₉	—	2	3	no	—
60	#121×C₁₃₉	C₂×C₄	1	3	yes	—
61	#121×C₁₃₉	C₂³	1	1	yes	characteristic
62	#120×C₁₃₉	—	2	3	no	—
63	C₄×Q₈×C₁₃₉	—	2	1	no	—
64	C₄×Q₈×C₁₃₉	—	4	4	no	—
65	C₄×D₄×C₁₃₉	—	2	3	no	—
66	C₄×D₄×C₁₃₉	—	2	3	no	—
67	C₄×D₄×C₁₃₉	—	2	3	no	—
68	#117×C₁₃₉	C₂×C₄	1	3	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	—	2	3	no	—
70	C₂×C₄⋊C₄×C₁₃₉	—	2	3	no	—
71	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	3	yes	—
72	C₂×C₂²⋊C₄×C₁₃₉	—	2	3	no	—
73	C₂×C₂²⋊C₄×C₁₃₉	—	2	3	no	—
74	C₂×C₂²⋊C₄×C₁₃₉	—	2	3	no	—
75	C₂×C₄²×C₁₃₉	—	2	3	no	—
76	C₂²⋊C₈×C₁₃₉	—	2	3	no	—
77	C₂²⋊C₈×C₁₃₉	—	2	3	no	—
78	C₂²⋊C₈×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂²⋊C₈×C₁₃₉	C₂³	1	3	yes	—
80	#95×C₁₃₉	C₂³	1	1	yes	characteristic
81	#95×C₁₃₉	C₂³	1	3	yes	—
82	C₂⁴×C₁₃₉	C₂×D₄	1	3	yes	—
83	#41×C₁₃₉	—	2	4	no	—
84	#41×C₁₃₉	—	2	4	no	—
85	#41×C₁₃₉	—	4	6	no	—
86	#41×C₁₃₉	—	4	6	no	—
87	#41×C₁₃₉	—	4	6	no	—
88	#41×C₁₃₉	—	4	12	no	—
89	C₂×Q₈×C₁₃₉	—	2	4	no	—
90	C₂×Q₈×C₁₃₉	—	2	3	no	—
91	C₂×Q₈×C₁₃₉	—	4	6	no	—
92	C₂×Q₈×C₁₃₉	—	4	4	no	—
93	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	3	yes	—
94	C₂×Q₈×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×Q₈×C₁₃₉	C₂²×C₄	1	3	yes	—
96	C₂×D₄×C₁₃₉	—	2	3	no	—
97	C₂×D₄×C₁₃₉	—	2	1	no	—
98	C₂×D₄×C₁₃₉	—	2	3	no	—
99	C₂×D₄×C₁₃₉	—	4	6	no	—
100	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	3	yes	—
101	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	3	yes	—
102	C₂×D₄×C₁₃₉	C₂²⋊C₄	1	6	yes	—
103	C₂×D₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₉	—	2	3	no	—
105	C₂²×C₄×C₁₃₉	—	2	1	no	—
106	C₂²×C₄×C₁₃₉	—	2	3	no	—
107	C₂²×C₄×C₁₃₉	—	2	3	no	—
108	C₂²×C₄×C₁₃₉	—	2	3	no	—
109	C₂²×C₄×C₁₃₉	—	4	6	no	—
110	C₂²×C₄×C₁₃₉	C₂²×C₄	1	3	yes	—
111	C₂²×C₄×C₁₃₉	C₂²×C₄	1	3	yes	—
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	3	yes	—
113	C₂²×C₄×C₁₃₉	C₂×D₄	1	3	yes	—
114	C₂²×C₄×C₁₃₉	C₂×D₄	1	3	yes	—
115	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
116	M₁₆×C₁₃₉	—	4	6	no	—
117	C₂×C₈×C₁₃₉	—	2	1	no	—
118	C₂×C₈×C₁₃₉	—	2	3	no	—
119	C₂×C₈×C₁₃₉	—	4	6	no	—
120	C₄⋊C₄×C₁₃₉	—	2	6	no	—
121	C₄⋊C₄×C₁₃₉	—	2	3	no	—
122	C₄⋊C₄×C₁₃₉	—	2	3	no	—
123	C₄⋊C₄×C₁₃₉	—	2	3	no	—
124	C₄⋊C₄×C₁₃₉	—	4	6	no	—
125	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	3	yes	—
126	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
128	C₂²⋊C₄×C₁₃₉	—	2	3	no	—
129	C₂²⋊C₄×C₁₃₉	—	2	3	no	—
130	C₂²⋊C₄×C₁₃₉	—	2	3	no	—
131	C₂²⋊C₄×C₁₃₉	—	2	3	no	—
132	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
133	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
134	C₂²⋊C₄×C₁₃₉	—	8	3	no	—
135	C₄²×C₁₃₉	—	2	3	no	—
136	C₄²×C₁₃₉	—	4	6	no	—
137	C₂³×C₁₃₉	—	2	3	no	—
138	C₂³×C₁₃₉	—	2	3	no	—
139	C₂³×C₁₃₉	—	2	1	no	—
140	C₂³×C₁₃₉	—	4	3	no	—
141	C₂³×C₁₃₉	—	4	3	no	—
142	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	3	yes	—
143	C₂³×C₁₃₉	C₂×C₂²⋊C₄	1	3	yes	—
144	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
145	Q₈×C₁₃₉	—	2	6	no	—
146	Q₈×C₁₃₉	—	4	3	no	—
147	Q₈×C₁₃₉	—	4	6	no	—
148	Q₈×C₁₃₉	#99	1	4	yes	—
149	D₄×C₁₃₉	—	2	6	no	—
150	D₄×C₁₃₉	—	2	6	no	—
151	D₄×C₁₃₉	—	4	6	no	—
152	D₄×C₁₃₉	—	4	1	no	—
153	D₄×C₁₃₉	—	4	6	no	—
154	D₄×C₁₃₉	—	4	1	no	—
155	D₄×C₁₃₉	—	4	1	no	—
156	D₄×C₁₃₉	—	8	3	no	—
157	C₂×C₄×C₁₃₉	—	2	6	no	—
158	C₂×C₄×C₁₃₉	—	2	6	no	—
159	C₂×C₄×C₁₃₉	—	2	6	no	—
160	C₂×C₄×C₁₃₉	—	2	2	no	—
161	C₂×C₄×C₁₃₉	—	2	1	no	—
162	C₂×C₄×C₁₃₉	—	2	3	no	—
163	C₂×C₄×C₁₃₉	—	2	3	no	—
164	C₂×C₄×C₁₃₉	—	4	1	no	—
165	C₂×C₄×C₁₃₉	—	4	3	no	—
166	C₂×C₄×C₁₃₉	—	4	3	no	—
167	C₂×C₄×C₁₃₉	—	4	1	no	—
168	C₂×C₄×C₁₃₉	—	4	6	no	—
169	C₂×C₄×C₁₃₉	—	4	1	no	—
170	C₂×C₄×C₁₃₉	—	4	6	no	—
171	C₂×C₄×C₁₃₉	—	4	3	no	—
172	C₂×C₄×C₁₃₉	—	4	3	no	—
173	C₂×C₄×C₁₃₉	—	4	3	no	—
174	C₂×C₄×C₁₃₉	—	8	3	no	—
175	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	3	yes	—
176	C₂×C₄×C₁₃₉	C₂×C₂²⋊C₄	1	3	yes	—
177	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
179	C₈×C₁₃₉	—	4	1	no	—
180	C₈×C₁₃₉	—	4	3	no	—
181	C₂²×C₁₃₉	—	2	1	no	—
182	C₂²×C₁₃₉	—	2	1	no	—
183	C₂²×C₁₃₉	—	2	3	no	—
184	C₂²×C₁₃₉	—	2	3	no	—
185	C₂²×C₁₃₉	—	2	3	no	—
186	C₂²×C₁₃₉	—	2	3	no	—
187	C₂²×C₁₃₉	—	2	3	no	—
188	C₂²×C₁₃₉	—	2	3	no	—
189	C₂²×C₁₃₉	—	4	1	no	—
190	C₂²×C₁₃₉	—	4	1	no	—
191	C₂²×C₁₃₉	—	4	1	no	—
192	C₂²×C₁₃₉	—	8	3	no	—
193	C₂²×C₁₃₉	—	8	3	no	—
194	C₂²×C₁₃₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₁₃₉	#577	1	1	yes	characteristic
196	C₂²×C₁₃₉	#578	1	1	yes	characteristic
197	C₄×C₁₃₉	—	2	1	no	—
198	C₄×C₁₃₉	—	2	1	no	—
199	C₄×C₁₃₉	—	2	3	no	—
200	C₄×C₁₃₉	—	4	2	no	—
201	C₄×C₁₃₉	—	4	3	no	—
202	C₄×C₁₃₉	—	4	1	no	—
203	C₄×C₁₃₉	—	4	3	no	—
204	C₄×C₁₃₉	—	8	3	no	—
205	C₄×C₁₃₉	C₂×#99	1	6	yes	—
206	C₂×C₁₃₉	—	2	1	no	—
207	C₂×C₁₃₉	—	2	1	no	—
208	C₂×C₁₃₉	—	4	3	no	—
209	C₂×C₁₃₉	—	4	3	no	—
210	C₂×C₁₃₉	—	8	1	no	—
211	C₂×C₁₃₉	C₂²×#99	1	1	yes	characteristic
212	C₂×C₁₃₉	#2898	1	1	yes	characteristic
213	C₂×C₁₃₉	#2901	1	1	yes	characteristic
214	#17606	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₁₃₉	#17606	1	1	yes	characteristic, direct product factor, Sylow
216	#3489	C₂×C₁₃₉	1	1	yes	characteristic
217	#2880	C₂×C₁₃₉	1	1	yes	characteristic, complemented
218	#2341	C₂×C₁₃₉	1	1	yes	characteristic, complemented
219	#1520	C₂×C₁₃₉	1	3	yes	complemented
220	#1513	C₂×C₁₃₉	1	3	yes	complemented
221	#1508	C₂×C₁₃₉	1	3	yes	complemented
222	#1501	C₂×C₁₃₉	1	3	yes	complemented
223	C₂×2₋¹⁺⁴	C₄×C₁₃₉	1	1	yes	characteristic, complemented
224	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
225	C₂×#131	—	2	1	no	—
226	D₄×Q₈	—	2	1	no	—
227	#548	—	2	1	no	—
228	#547	—	2	3	no	—
229	#546	—	2	3	no	—
230	#537	C₄×C₁₃₉	1	3	yes	complemented
231	#536	C₄×C₁₃₉	1	3	yes	complemented
232	#525	C₂²×C₁₃₉	1	3	yes	—
233	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
234	#520	C₄×C₁₃₉	1	1	yes	characteristic, complemented
235	C₂×C₄×Q₈	—	2	1	no	—
236	#408	—	2	3	no	—
237	#407	C₂²×C₁₃₉	1	3	yes	—
238	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	3	yes	—
239	#390	—	2	3	no	—
240	#380	C₂²×C₁₃₉	1	3	yes	—
241	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	3	yes	—
242	#328	C₂²×C₁₃₉	1	3	yes	—
243	#328	C₂²×C₁₃₉	1	3	yes	—
244	#328	C₂²×C₁₃₉	1	6	yes	—
245	#327	C₂²×C₁₃₉	1	1	yes	characteristic
246	#327	C₂²×C₁₃₉	1	3	yes	—
247	2₋¹⁺⁴	—	4	4	no	—
248	C₂×#41	—	2	3	no	—
249	C₂×#41	—	4	4	no	—
250	C₂×#41	C₂×C₄×C₁₃₉	1	3	yes	—
251	C₂×#41	C₂×C₄×C₁₃₉	1	1	yes	characteristic
252	C₂×#41	C₂×C₄×C₁₃₉	1	3	yes	—
253	C₂×#41	D₄×C₁₃₉	1	1	yes	characteristic
254	C₂×#41	D₄×C₁₃₉	1	3	yes	—
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×Q₈	C₂×C₄×C₁₃₉	1	3	yes	—
257	C₂²×Q₈	D₄×C₁₃₉	1	1	yes	characteristic
258	C₂²×D₄	D₄×C₁₃₉	1	3	yes	—
259	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
260	#131	—	4	4	no	—
261	C₂×M₁₆	—	2	3	no	—
262	C₂²×C₈	—	2	3	no	—
263	C₄⋊Q₈	—	2	3	no	—
264	#124	—	2	3	no	—
265	#123	—	2	6	no	—
266	#123	—	2	3	no	—
267	C₂²⋊Q₈	—	2	3	no	—
268	C₂²⋊Q₈	—	2	3	no	—
269	C₂²⋊Q₈	—	2	3	no	—
270	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	6	yes	—
271	C₂²⋊Q₈	C₂×C₄×C₁₃₉	1	3	yes	—
272	C₂²⋊Q₈	C₂³×C₁₃₉	1	3	yes	—
273	#121	—	2	6	no	—
274	#121	—	2	3	no	—
275	#121	C₂×C₄×C₁₃₉	1	3	yes	—
276	#121	C₂³×C₁₃₉	1	1	yes	characteristic
277	#120	—	2	3	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×Q₈	—	4	4	no	—
280	C₄×D₄	—	2	3	no	—
281	C₄×D₄	—	2	3	no	—
282	C₄×D₄	—	2	3	no	—
283	#117	C₂×C₄×C₁₃₉	1	3	yes	—
284	C₂×C₄⋊C₄	—	2	3	no	—
285	C₂×C₄⋊C₄	—	2	3	no	—
286	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	3	yes	—
287	C₂×C₂²⋊C₄	—	2	3	no	—
288	C₂×C₂²⋊C₄	—	2	3	no	—
289	C₂×C₂²⋊C₄	—	2	3	no	—
290	C₂×C₄²	—	2	3	no	—
291	C₂²⋊C₈	—	2	3	no	—
292	C₂²⋊C₈	—	2	3	no	—
293	C₂²⋊C₈	C₂³×C₁₃₉	1	1	yes	characteristic
294	C₂²⋊C₈	C₂³×C₁₃₉	1	3	yes	—
295	#95	C₂³×C₁₃₉	1	1	yes	characteristic
296	#95	C₂³×C₁₃₉	1	3	yes	—
297	C₂⁴	C₂×D₄×C₁₃₉	1	3	yes	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	4	6	no	—
301	#41	—	4	6	no	—
302	#41	—	4	6	no	—
303	#41	—	4	12	no	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	—	2	3	no	—
306	C₂×Q₈	—	4	6	no	—
307	C₂×Q₈	—	4	4	no	—
308	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	3	yes	—
309	C₂×Q₈	C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
310	C₂×Q₈	C₂²×C₄×C₁₃₉	1	3	yes	—
311	C₂×D₄	—	2	3	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	3	no	—
314	C₂×D₄	—	4	6	no	—
315	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	3	yes	—
316	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	3	yes	—
317	C₂×D₄	C₂²⋊C₄×C₁₃₉	1	6	yes	—
318	C₂×D₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
319	C₂²×C₄	—	2	3	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	3	no	—
322	C₂²×C₄	—	2	3	no	—
323	C₂²×C₄	—	2	3	no	—
324	C₂²×C₄	—	4	6	no	—
325	C₂²×C₄	C₂²×C₄×C₁₃₉	1	3	yes	—
326	C₂²×C₄	C₂²×C₄×C₁₃₉	1	3	yes	—
327	C₂²×C₄	C₂×D₄×C₁₃₉	1	3	yes	—
328	C₂²×C₄	C₂×D₄×C₁₃₉	1	3	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃₉	1	3	yes	—
330	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
331	M₁₆	—	4	6	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	3	no	—
334	C₂×C₈	—	4	6	no	—
335	C₄⋊C₄	—	2	6	no	—
336	C₄⋊C₄	—	2	3	no	—
337	C₄⋊C₄	—	2	3	no	—
338	C₄⋊C₄	—	2	3	no	—
339	C₄⋊C₄	—	4	6	no	—
340	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	3	yes	—
341	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
342	C₂²⋊C₄	—	2	6	no	—
343	C₂²⋊C₄	—	2	3	no	—
344	C₂²⋊C₄	—	2	3	no	—
345	C₂²⋊C₄	—	2	3	no	—
346	C₂²⋊C₄	—	2	3	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	4	6	no	—
349	C₂²⋊C₄	—	8	3	no	—
350	C₄²	—	2	3	no	—
351	C₄²	—	4	6	no	—
352	C₂³	—	2	3	no	—
353	C₂³	—	2	3	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	4	3	no	—
356	C₂³	—	4	3	no	—
357	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	3	yes	—
358	C₂³	C₂×C₂²⋊C₄×C₁₃₉	1	3	yes	—
359	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
360	Q₈	—	2	6	no	—
361	Q₈	—	4	3	no	—
362	Q₈	—	4	6	no	—
363	Q₈	#99×C₁₃₉	1	4	yes	—
364	D₄	—	2	6	no	—
365	D₄	—	2	6	no	—
366	D₄	—	4	6	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	6	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	1	no	—
371	D₄	—	8	3	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	3	no	—
378	C₂×C₄	—	2	3	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	3	no	—
381	C₂×C₄	—	4	3	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	6	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	6	no	—
386	C₂×C₄	—	4	3	no	—
387	C₂×C₄	—	4	3	no	—
388	C₂×C₄	—	4	3	no	—
389	C₂×C₄	—	8	3	no	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	3	yes	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₉	1	3	yes	—
392	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
394	C₈	—	4	1	no	—
395	C₈	—	4	3	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	3	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	2	3	no	—
401	C₂²	—	2	3	no	—
402	C₂²	—	2	3	no	—
403	C₂²	—	2	3	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	8	3	no	—
408	C₂²	—	8	3	no	—
409	C₂²	C₂²×C₂²⋊C₄×C₁₃₉	1	1	yes	characteristic
410	C₂²	#577×C₁₃₉	1	1	yes	characteristic
411	C₂²	#578×C₁₃₉	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	3	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	3	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	3	no	—
419	C₄	—	8	3	no	—
420	C₄	C₂×#99×C₁₃₉	1	6	yes	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	4	3	no	—
424	C₂	—	4	3	no	—
425	C₂	—	8	1	no	—
426	C₂	C₂²×#99×C₁₃₉	1	1	yes	characteristic
427	C₂	#2898×C₁₃₉	1	1	yes	characteristic
428	C₂	#2901×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	#3489×C₁₃₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₉ ◁ C₂²×#41×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2880×C₁₃₉	C₂	semidirect
3. #2341×C₁₃₉	C₂	semidirect
4. #1520×C₁₃₉	C₂	semidirect
5. #1513×C₁₃₉	C₂	semidirect
6. #1508×C₁₃₉	C₂	semidirect
7. #1501×C₁₃₉	C₂	semidirect
8. C₂×2₋¹⁺⁴×C₁₃₉	C₄	semidirect
15. #537×C₁₃₉	C₄	semidirect
16. #536×C₁₃₉	C₄	semidirect
19. #520×C₁₃₉	C₄	semidirect
214. #17606	C₁₃₉	direct (N × H)
215. C₁₃₉	#17606	direct (N × H)
217. #2880	C₂×C₁₃₉	semidirect
218. #2341	C₂×C₁₃₉	semidirect
219. #1520	C₂×C₁₃₉	semidirect
220. #1513	C₂×C₁₃₉	semidirect
221. #1508	C₂×C₁₃₉	semidirect
222. #1501	C₂×C₁₃₉	semidirect
223. C₂×2₋¹⁺⁴	C₄×C₁₃₉	semidirect
230. #537	C₄×C₁₃₉	semidirect
231. #536	C₄×C₁₃₉	semidirect
234. #520	C₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#3489×C₁₃₉	2
#2880×C₁₃₉	2
#2341×C₁₃₉	2
#1520×C₁₃₉	2
#1513×C₁₃₉	2
#1508×C₁₃₉	2
#1501×C₁₃₉	2
#17606	139

Subgroups — C139×#17606 #48012202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#17606 #48012202