Subgroups — C₁₃₉×#32914 #48027510

Order 35584.

1546 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×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#461×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	C₂×#450×C₁₃₉	C₂	1	2	yes	maximal
4	#2621×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#1877×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#1873×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1804×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#1798×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₁₃₉	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
13	#518×C₁₃₉	—	2	8	no	—
14	C₂×C₄×D₄×C₁₃₉	—	2	2	no	—
15	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
17	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
20	#461×C₁₃₉	—	2	8	no	—
21	#450×C₁₃₉	—	2	8	no	—
22	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	2	yes	complemented
23	C₂×#103×C₁₃₉	C₂²	1	4	yes	complemented
24	C₂×#102×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
26	#398×C₁₃₉	—	2	2	no	—
27	#397×C₁₃₉	—	2	2	no	—
28	#391×C₁₃₉	C₂²	1	2	yes	complemented
29	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
30	#340×C₁₃₉	C₂²	1	4	yes	complemented
31	#336×C₁₃₉	C₂²	1	2	yes	complemented
32	C₂⁵×C₁₃₉	—	2	1	no	—
33	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
34	C₂²×D₄×C₁₃₉	—	2	4	no	—
35	C₂²×D₄×C₁₃₉	—	2	4	no	—
36	C₂²×D₄×C₁₃₉	—	2	1	no	—
37	C₂²×D₄×C₁₃₉	—	2	2	no	—
38	C₂²×D₄×C₁₃₉	D₄	1	4	yes	—
39	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃₉	—	2	2	no	—
41	C₂³×C₄×C₁₃₉	—	2	2	no	—
42	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂×SD₁₆×C₁₃₉	—	2	8	no	—
44	C₂×SD₁₆×C₁₃₉	—	2	8	no	—
45	C₂×SD₁₆×C₁₃₉	—	2	8	no	—
46	C₂²×C₈×C₁₃₉	C₂³	1	4	yes	—
47	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
48	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
49	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
50	C₄×D₄×C₁₃₉	—	2	16	no	—
51	C₄×D₄×C₁₃₉	—	2	4	no	—
52	C₄×D₄×C₁₃₉	—	2	4	no	—
53	C₄×D₄×C₁₃₉	—	2	4	no	—
54	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
55	#117×C₁₃₉	—	2	4	no	—
56	#117×C₁₃₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₃₉	D₄	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	16	no	—
63	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	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×C₂²⋊C₄×C₁₃₉	D₄	1	2	yes	—
68	C₂×C₄²×C₁₃₉	—	2	1	no	—
69	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₁₃₉	—	2	4	no	—
72	#103×C₁₃₉	—	2	8	no	—
73	#102×C₁₃₉	—	2	8	no	—
74	C₂²⋊C₈×C₁₃₉	—	2	4	no	—
75	#95×C₁₃₉	—	2	2	no	—
76	#95×C₁₃₉	—	2	4	no	—
77	C₂⁴×C₁₃₉	—	2	4	no	—
78	C₂⁴×C₁₃₉	—	2	4	no	—
79	C₂⁴×C₁₃₉	—	2	2	no	—
80	C₂⁴×C₁₃₉	—	2	4	no	—
81	C₂⁴×C₁₃₉	—	8	4	no	—
82	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
83	C₂×Q₈×C₁₃₉	—	2	4	no	—
84	C₂×Q₈×C₁₃₉	—	2	2	no	—
85	C₂×Q₈×C₁₃₉	—	2	2	no	—
86	C₂×Q₈×C₁₃₉	—	2	4	no	—
87	C₂×D₄×C₁₃₉	—	2	4	no	—
88	C₂×D₄×C₁₃₉	—	2	4	no	—
89	C₂×D₄×C₁₃₉	—	2	16	no	—
90	C₂×D₄×C₁₃₉	—	2	16	no	—
91	C₂×D₄×C₁₃₉	—	2	4	no	—
92	C₂×D₄×C₁₃₉	—	2	2	no	—
93	C₂×D₄×C₁₃₉	—	2	2	no	—
94	C₂×D₄×C₁₃₉	—	2	2	no	—
95	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
96	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
97	C₂×D₄×C₁₃₉	#41	1	4	yes	—
98	C₂²×C₄×C₁₃₉	—	2	2	no	—
99	C₂²×C₄×C₁₃₉	—	2	2	no	—
100	C₂²×C₄×C₁₃₉	—	2	2	no	—
101	C₂²×C₄×C₁₃₉	—	2	8	no	—
102	C₂²×C₄×C₁₃₉	—	2	8	no	—
103	C₂²×C₄×C₁₃₉	—	2	2	no	—
104	C₂²×C₄×C₁₃₉	—	2	2	no	—
105	C₂²×C₄×C₁₃₉	—	8	4	no	—
106	C₂²×C₄×C₁₃₉	—	8	4	no	—
107	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
113	SD₁₆×C₁₃₉	—	4	16	no	—
114	C₂×C₈×C₁₃₉	—	2	4	no	—
115	C₂×C₈×C₁₃₉	—	2	4	no	—
116	C₂×C₈×C₁₃₉	—	2	4	no	—
117	C₄⋊C₄×C₁₃₉	—	2	4	no	—
118	C₄⋊C₄×C₁₃₉	—	2	2	no	—
119	C₄⋊C₄×C₁₃₉	—	2	2	no	—
120	C₄⋊C₄×C₁₃₉	—	2	2	no	—
121	C₄⋊C₄×C₁₃₉	—	4	4	no	—
122	C₄⋊C₄×C₁₃₉	—	4	4	no	—
123	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
124	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
125	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
126	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
127	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
128	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
129	C₄²×C₁₃₉	—	2	4	no	—
130	C₄²×C₁₃₉	—	2	2	no	—
131	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
132	C₂³×C₁₃₉	—	2	16	no	—
133	C₂³×C₁₃₉	—	2	1	no	—
134	C₂³×C₁₃₉	—	2	4	no	—
135	C₂³×C₁₃₉	—	2	4	no	—
136	C₂³×C₁₃₉	—	2	1	no	—
137	C₂³×C₁₃₉	—	2	4	no	—
138	C₂³×C₁₃₉	—	2	4	no	—
139	C₂³×C₁₃₉	—	4	4	no	—
140	C₂³×C₁₃₉	—	4	4	no	—
141	C₂³×C₁₃₉	—	8	8	no	—
142	C₂³×C₁₃₉	—	8	8	no	—
143	C₂³×C₁₃₉	—	8	8	no	—
144	C₂³×C₁₃₉	#121	1	2	yes	—
145	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₁₃₉	—	4	4	no	—
147	Q₈×C₁₃₉	—	4	4	no	—
148	D₄×C₁₃₉	—	2	16	no	—
149	D₄×C₁₃₉	—	2	4	no	—
150	D₄×C₁₃₉	—	2	4	no	—
151	D₄×C₁₃₉	—	2	4	no	—
152	D₄×C₁₃₉	#121	1	8	yes	—
153	C₂×C₄×C₁₃₉	—	2	1	no	—
154	C₂×C₄×C₁₃₉	—	2	1	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	2	no	—
159	C₂×C₄×C₁₃₉	—	2	4	no	—
160	C₂×C₄×C₁₃₉	—	2	4	no	—
161	C₂×C₄×C₁₃₉	—	4	4	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	4	no	—
167	C₂×C₄×C₁₃₉	—	8	8	no	—
168	C₂×C₄×C₁₃₉	—	8	8	no	—
169	C₂×C₄×C₁₃₉	#120	1	4	yes	—
170	C₂×C₄×C₁₃₉	#121	1	2	yes	—
171	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
174	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
175	C₈×C₁₃₉	—	4	4	no	—
176	C₂²×C₁₃₉	—	2	2	no	—
177	C₂²×C₁₃₉	—	2	8	no	—
178	C₂²×C₁₃₉	—	2	4	no	—
179	C₂²×C₁₃₉	—	4	2	no	—
180	C₂²×C₁₃₉	—	4	8	no	—
181	C₂²×C₁₃₉	—	4	4	no	—
182	C₂²×C₁₃₉	—	4	4	no	—
183	C₂²×C₁₃₉	—	4	2	no	—
184	C₂²×C₁₃₉	—	4	8	no	—
185	C₂²×C₁₃₉	—	8	16	no	—
186	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
187	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
188	C₂²×C₁₃₉	#525	1	1	yes	characteristic
189	C₂²×C₁₃₉	#577	1	4	yes	—
190	C₄×C₁₃₉	—	2	2	no	—
191	C₄×C₁₃₉	—	2	4	no	—
192	C₄×C₁₃₉	—	4	2	no	—
193	C₄×C₁₃₉	—	4	4	no	—
194	C₄×C₁₃₉	—	8	2	no	—
195	C₄×C₁₃₉	—	8	2	no	—
196	C₄×C₁₃₉	C₂×#121	1	2	yes	—
197	C₄×C₁₃₉	#525	1	2	yes	—
198	C₂×C₁₃₉	—	4	2	no	—
199	C₂×C₁₃₉	—	4	8	no	—
200	C₂×C₁₃₉	#2847	1	1	yes	characteristic
201	C₂×C₁₃₉	#3009	1	2	yes	—
202	C₂×C₁₃₉	#3042	1	2	yes	—
203	C₂×C₁₃₉	#3123	1	2	yes	—
204	#32914	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₁₃₉	#32914	1	1	yes	characteristic, direct product factor, Sylow
206	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic
207	C₂×#461	C₂×C₁₃₉	1	2	yes	complemented
208	C₂×#450	C₂×C₁₃₉	1	2	yes	—
209	#2621	C₂×C₁₃₉	1	1	yes	characteristic, complemented
210	#1877	C₂×C₁₃₉	1	4	yes	complemented
211	#1873	C₂×C₁₃₉	1	2	yes	complemented
212	#1804	C₂×C₁₃₉	1	2	yes	complemented
213	#1798	C₂×C₁₃₉	1	1	yes	characteristic, complemented
214	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
215	C₂²×SD₁₆	C₂²×C₁₃₉	1	4	yes	—
216	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
217	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
218	#518	—	2	8	no	—
219	C₂×C₄×D₄	—	2	2	no	—
220	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
221	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
222	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
223	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
224	C₂²×C₂²⋊C₄	—	2	2	no	—
225	#461	—	2	8	no	—
226	#450	—	2	8	no	—
227	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	2	yes	complemented
228	C₂×#103	C₂²×C₁₃₉	1	4	yes	complemented
229	C₂×#102	C₂²×C₁₃₉	1	4	yes	—
230	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
231	#398	—	2	2	no	—
232	#397	—	2	2	no	—
233	#391	C₂²×C₁₃₉	1	2	yes	complemented
234	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
235	#340	C₂²×C₁₃₉	1	4	yes	complemented
236	#336	C₂²×C₁₃₉	1	2	yes	complemented
237	C₂⁵	—	2	1	no	—
238	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	D₄×C₁₃₉	1	4	yes	—
244	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	—	2	2	no	—
247	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
248	C₂×SD₁₆	—	2	8	no	—
249	C₂×SD₁₆	—	2	8	no	—
250	C₂×SD₁₆	—	2	8	no	—
251	C₂²×C₈	C₂³×C₁₃₉	1	4	yes	—
252	C₄⋊Q₈	—	2	4	no	—
253	C₂²⋊Q₈	—	2	4	no	—
254	C₂²⋊Q₈	—	2	4	no	—
255	C₄×D₄	—	2	16	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	—	2	4	no	—
259	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
260	#117	—	2	4	no	—
261	#117	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	16	no	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	2	yes	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
276	C₄⋊C₈	—	2	4	no	—
277	#103	—	2	8	no	—
278	#102	—	2	8	no	—
279	C₂²⋊C₈	—	2	4	no	—
280	#95	—	2	2	no	—
281	#95	—	2	4	no	—
282	C₂⁴	—	2	4	no	—
283	C₂⁴	—	2	4	no	—
284	C₂⁴	—	2	2	no	—
285	C₂⁴	—	2	4	no	—
286	C₂⁴	—	8	4	no	—
287	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	16	no	—
295	C₂×D₄	—	2	16	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
301	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
302	C₂×D₄	#41×C₁₃₉	1	4	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	8	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	8	4	no	—
311	C₂²×C₄	—	8	4	no	—
312	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
316	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
318	SD₁₆	—	4	16	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	2	no	—
336	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
337	C₂³	—	2	16	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	4	4	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	8	8	no	—
347	C₂³	—	8	8	no	—
348	C₂³	—	8	8	no	—
349	C₂³	#121×C₁₃₉	1	2	yes	—
350	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
351	Q₈	—	4	4	no	—
352	Q₈	—	4	4	no	—
353	D₄	—	2	16	no	—
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	4	no	—
357	D₄	#121×C₁₃₉	1	8	yes	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	8	8	no	—
373	C₂×C₄	—	8	8	no	—
374	C₂×C₄	#120×C₁₃₉	1	4	yes	—
375	C₂×C₄	#121×C₁₃₉	1	2	yes	—
376	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
378	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
379	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
380	C₈	—	4	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	8	no	—
384	C₂²	—	4	8	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	8	16	no	—
391	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
392	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
393	C₂²	#525×C₁₃₉	1	1	yes	characteristic
394	C₂²	#577×C₁₃₉	1	4	yes	—
395	C₄	—	2	2	no	—
396	C₄	—	2	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	2	no	—
401	C₄	C₂×#121×C₁₃₉	1	2	yes	—
402	C₄	#525×C₁₃₉	1	2	yes	—
403	C₂	—	4	2	no	—
404	C₂	—	4	8	no	—
405	C₂	#2847×C₁₃₉	1	1	yes	characteristic
406	C₂	#3009×C₁₃₉	1	2	yes	—
407	C₂	#3042×C₁₃₉	1	2	yes	—
408	C₂	#3123×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×#117×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#461×C₁₃₉	C₂	semidirect
4. #2621×C₁₃₉	C₂	semidirect
5. #1877×C₁₃₉	C₂	semidirect
6. #1873×C₁₃₉	C₂	semidirect
7. #1804×C₁₃₉	C₂	semidirect
8. #1798×C₁₃₉	C₂	semidirect
11. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
22. C₂×C₄⋊C₈×C₁₃₉	C₂²	semidirect
23. C₂×#103×C₁₃₉	C₂²	semidirect
28. #391×C₁₃₉	C₂²	semidirect
29. #382×C₁₃₉	C₂²	semidirect
30. #340×C₁₃₉	C₂²	semidirect
31. #336×C₁₃₉	C₂²	semidirect
204. #32914	C₁₃₉	direct (N × H)
205. C₁₃₉	#32914	direct (N × H)
207. C₂×#461	C₂×C₁₃₉	semidirect
209. #2621	C₂×C₁₃₉	semidirect
210. #1877	C₂×C₁₃₉	semidirect
211. #1873	C₂×C₁₃₉	semidirect
212. #1804	C₂×C₁₃₉	semidirect
213. #1798	C₂×C₁₃₉	semidirect
216. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
227. C₂×C₄⋊C₈	C₂²×C₁₃₉	semidirect
228. C₂×#103	C₂²×C₁₃₉	semidirect
233. #391	C₂²×C₁₃₉	semidirect
234. #382	C₂²×C₁₃₉	semidirect
235. #340	C₂²×C₁₃₉	semidirect
236. #336	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#518×C₁₃₉	2
C₂×#461×C₁₃₉	2
C₂×#450×C₁₃₉	2
#2621×C₁₃₉	2
#1877×C₁₃₉	2
#1873×C₁₃₉	2
#1804×C₁₃₉	2
#1798×C₁₃₉	2
#32914	139

Subgroups — C139×#32914 #48027510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#32914 #48027510