Subgroups — C₁₃₉×#33506 #48028102

Order 35584.

494 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2966×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	#2183×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2168×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2168×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	D₄×C₁₆×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2164×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2163×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2151×C₁₃₉	C₂	1	2	yes	maximal, complemented
9	C₂×C₄⋊C₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#529×C₁₃₉	C₄	1	1	yes	characteristic
11	C₂×M₃₂×C₁₃₉	C₂²	1	2	yes	—
12	C₂²×C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂²×C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²×C₁₆×C₁₃₉	C₂²	1	2	yes	—
15	#446×C₁₃₉	C₄	1	1	yes	characteristic
16	C₈×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	#436×C₁₃₉	C₄	1	1	yes	characteristic
18	#435×C₁₃₉	C₄	1	2	yes	—
19	C₈×D₄×C₁₃₉	C₂²	1	2	yes	—
20	C₈×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
21	#433×C₁₃₉	C₄	1	2	yes	—
22	#432×C₁₃₉	C₄	1	1	yes	characteristic
23	#405×C₁₃₉	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₄⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
26	C₄⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
27	C₄⋊C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₄⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
29	C₄⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
30	C₄⋊C₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂²⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
32	C₂²⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
33	C₂²⋊C₁₆×C₁₃₉	C₂²	1	2	yes	—
34	#346×C₁₃₉	C₂²	1	2	yes	—
35	#346×C₁₃₉	C₂²	1	2	yes	—
36	C₄×C₁₆×C₁₃₉	C₂²	1	2	yes	—
37	C₂×M₁₆×C₁₃₉	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
41	#126×C₁₃₉	C₈	1	2	yes	—
42	#125×C₁₃₉	C₈	1	1	yes	characteristic
43	#124×C₁₃₉	C₈	1	1	yes	characteristic
44	#123×C₁₃₉	C₈	1	2	yes	—
45	C₂²⋊Q₈×C₁₃₉	C₈	1	1	yes	characteristic
46	#121×C₁₃₉	C₈	1	1	yes	characteristic
47	C₄×Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₁₃₉	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
50	#117×C₁₃₉	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
52	M₃₂×C₁₃₉	—	4	2	no	—
53	C₂×C₁₆×C₁₃₉	—	4	1	no	—
54	C₂×C₁₆×C₁₃₉	—	4	2	no	—
55	C₂×C₁₆×C₁₃₉	—	4	1	no	—
56	C₂×C₁₆×C₁₃₉	C₂³	1	2	yes	—
57	C₂×C₁₆×C₁₃₉	C₂³	1	2	yes	—
58	C₂×C₁₆×C₁₃₉	C₂³	1	2	yes	—
59	C₂×C₁₆×C₁₃₉	C₂³	1	2	yes	—
60	C₄⋊C₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
61	C₄⋊C₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
62	C₄⋊C₈×C₁₃₉	C₂×C₄	1	2	yes	—
63	C₄⋊C₈×C₁₃₉	C₂×C₄	1	2	yes	—
64	C₂²⋊C₈×C₁₃₉	C₂×C₄	1	2	yes	—
65	C₂²⋊C₈×C₁₃₉	C₂×C₄	1	2	yes	—
66	C₂²⋊C₈×C₁₃₉	C₂×C₄	1	2	yes	—
67	#97×C₁₃₉	C₂×C₄	1	2	yes	—
68	#97×C₁₃₉	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
72	C₄×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₁₃₉	C₂³	1	2	yes	—
74	C₂×Q₈×C₁₃₉	C₂×C₈	1	1	yes	characteristic
75	C₂×D₄×C₁₃₉	C₂×C₈	1	2	yes	—
76	C₂×D₄×C₁₃₉	C₂×C₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₃₉	C₂×C₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₃₉	C₂×C₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
81	M₁₆×C₁₃₉	—	4	2	no	—
82	C₂×C₈×C₁₃₉	—	2	1	no	—
83	C₂×C₈×C₁₃₉	—	2	2	no	—
84	C₂×C₈×C₁₃₉	—	2	1	no	—
85	C₂×C₈×C₁₃₉	—	2	2	no	—
86	C₂×C₈×C₁₃₉	—	4	1	no	—
87	C₂×C₈×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₈×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₈×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₈×C₁₃₉	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₁₃₉	C₂²×C₄	1	2	yes	—
92	C₂×C₈×C₁₃₉	C₂⁴	1	1	yes	characteristic
93	C₄⋊C₄×C₁₃₉	C₂×C₈	1	2	yes	—
94	C₄⋊C₄×C₁₃₉	C₂×C₈	1	2	yes	—
95	C₄⋊C₄×C₁₃₉	C₂×C₈	1	1	yes	characteristic
96	C₄⋊C₄×C₁₃₉	C₂×C₈	1	2	yes	—
97	C₄⋊C₄×C₁₃₉	C₂×C₈	1	1	yes	characteristic
98	C₄⋊C₄×C₁₃₉	C₂×C₈	1	2	yes	—
99	C₂²⋊C₄×C₁₃₉	C₂×C₈	1	2	yes	—
100	C₂²⋊C₄×C₁₃₉	C₂×C₈	1	2	yes	—
101	C₂²⋊C₄×C₁₃₉	C₂×C₈	1	2	yes	—
102	C₂²⋊C₄×C₁₃₉	C₂×C₈	1	2	yes	—
103	C₂²⋊C₄×C₁₃₉	C₂×C₈	1	2	yes	—
104	C₄²×C₁₃₉	C₂×C₈	1	1	yes	characteristic
105	C₄²×C₁₃₉	C₂×C₈	1	1	yes	characteristic
106	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₃₉	C₂²×C₄	1	2	yes	—
109	C₁₆×C₁₃₉	—	2	2	no	—
110	C₁₆×C₁₃₉	—	2	2	no	—
111	C₁₆×C₁₃₉	—	2	2	no	—
112	C₁₆×C₁₃₉	—	2	2	no	—
113	C₂³×C₁₃₉	C₂²×C₈	1	2	yes	—
114	C₂³×C₁₃₉	C₂²×C₈	1	1	yes	characteristic
115	Q₈×C₁₃₉	—	4	1	no	—
116	D₄×C₁₃₉	—	2	4	no	—
117	D₄×C₁₃₉	—	4	1	no	—
118	C₂×C₄×C₁₃₉	—	2	2	no	—
119	C₂×C₄×C₁₃₉	—	2	1	no	—
120	C₂×C₄×C₁₃₉	—	2	2	no	—
121	C₂×C₄×C₁₃₉	—	2	1	no	—
122	C₂×C₄×C₁₃₉	—	2	2	no	—
123	C₂×C₄×C₁₃₉	—	4	1	no	—
124	C₂×C₄×C₁₃₉	C₂²×C₈	1	1	yes	characteristic
125	C₂×C₄×C₁₃₉	C₂²×C₈	1	1	yes	characteristic
126	C₂×C₄×C₁₃₉	C₂²×C₈	1	1	yes	characteristic
127	C₂×C₄×C₁₃₉	C₂²×C₈	1	1	yes	characteristic
128	C₂×C₄×C₁₃₉	C₂²×C₈	1	1	yes	characteristic
129	C₂×C₄×C₁₃₉	C₂²×C₈	1	2	yes	—
130	C₂×C₄×C₁₃₉	C₂²×C₈	1	2	yes	—
131	C₂×C₄×C₁₃₉	C₂²×C₈	1	2	yes	—
132	C₂×C₄×C₁₃₉	C₂³×C₄	1	1	yes	characteristic
133	C₈×C₁₃₉	—	2	1	no	—
134	C₈×C₁₃₉	—	2	2	no	—
135	C₈×C₁₃₉	—	2	1	no	—
136	C₈×C₁₃₉	—	2	1	no	—
137	C₈×C₁₃₉	—	2	2	no	—
138	C₈×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
139	C₈×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
140	C₂²×C₁₃₉	—	2	1	no	—
141	C₂²×C₁₃₉	—	2	1	no	—
142	C₂²×C₁₃₉	—	2	2	no	—
143	C₂²×C₁₃₉	—	2	2	no	—
144	C₂²×C₁₃₉	—	2	2	no	—
145	C₂²×C₁₃₉	#504	1	2	yes	—
146	C₂²×C₁₃₉	C₂³×C₈	1	1	yes	characteristic
147	C₄×C₁₃₉	—	2	1	no	—
148	C₄×C₁₃₉	—	2	1	no	—
149	C₄×C₁₃₉	—	2	2	no	—
150	C₄×C₁₃₉	—	2	1	no	—
151	C₄×C₁₃₉	—	2	1	no	—
152	C₄×C₁₃₉	—	2	2	no	—
153	C₄×C₁₃₉	—	2	1	no	—
154	C₄×C₁₃₉	—	2	2	no	—
155	C₄×C₁₃₉	#520	1	1	yes	characteristic
156	C₄×C₁₃₉	#568	1	1	yes	characteristic
157	C₂×C₁₃₉	—	2	2	no	—
158	C₂×C₁₃₉	—	4	2	no	—
159	C₂×C₁₃₉	#2988	1	1	yes	characteristic
160	C₂×C₁₃₉	C₂×#504	1	1	yes	characteristic
161	C₂×C₁₃₉	#3407	1	1	yes	characteristic
162	#33506	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₁₃₉	#33506	1	1	yes	characteristic, direct product factor, Sylow
164	#2966	C₂×C₁₃₉	1	1	yes	characteristic
165	#2183	C₂×C₁₃₉	1	2	yes	complemented
166	#2168	C₂×C₁₃₉	1	2	yes	complemented
167	#2168	C₂×C₁₃₉	1	2	yes	complemented
168	D₄×C₁₆	C₂×C₁₃₉	1	2	yes	complemented
169	#2164	C₂×C₁₃₉	1	2	yes	complemented
170	#2163	C₂×C₁₃₉	1	1	yes	characteristic, complemented
171	#2151	C₂×C₁₃₉	1	2	yes	complemented
172	C₂×C₄⋊C₁₆	C₂×C₁₃₉	1	1	yes	characteristic, complemented
173	#529	C₄×C₁₃₉	1	1	yes	characteristic
174	C₂×M₃₂	C₂²×C₁₃₉	1	2	yes	—
175	C₂²×C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
176	C₂²×C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
177	C₂²×C₁₆	C₂²×C₁₃₉	1	2	yes	—
178	#446	C₄×C₁₃₉	1	1	yes	characteristic
179	C₈×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
180	#436	C₄×C₁₃₉	1	1	yes	characteristic
181	#435	C₄×C₁₃₉	1	2	yes	—
182	C₈×D₄	C₂²×C₁₃₉	1	2	yes	—
183	C₈×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
184	#433	C₄×C₁₃₉	1	2	yes	—
185	#432	C₄×C₁₃₉	1	1	yes	characteristic
186	#405	C₂²×C₁₃₉	1	2	yes	—
187	C₂×C₄×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
188	C₄⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
189	C₄⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
190	C₄⋊C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
191	C₄⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
192	C₄⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
193	C₄⋊C₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
194	C₂²⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
195	C₂²⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
196	C₂²⋊C₁₆	C₂²×C₁₃₉	1	2	yes	—
197	#346	C₂²×C₁₃₉	1	2	yes	—
198	#346	C₂²×C₁₃₉	1	2	yes	—
199	C₄×C₁₆	C₂²×C₁₃₉	1	2	yes	—
200	C₂×M₁₆	C₂×C₄×C₁₃₉	1	2	yes	—
201	C₂²×C₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
202	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
203	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
204	#126	C₈×C₁₃₉	1	2	yes	—
205	#125	C₈×C₁₃₉	1	1	yes	characteristic
206	#124	C₈×C₁₃₉	1	1	yes	characteristic
207	#123	C₈×C₁₃₉	1	2	yes	—
208	C₂²⋊Q₈	C₈×C₁₃₉	1	1	yes	characteristic
209	#121	C₈×C₁₃₉	1	1	yes	characteristic
210	C₄×Q₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
211	C₄×D₄	C₂×C₄×C₁₃₉	1	2	yes	—
212	C₄×D₄	C₂×C₄×C₁₃₉	1	1	yes	characteristic
213	#117	C₂×C₄×C₁₃₉	1	2	yes	—
214	C₂×C₄²	C₂×C₄×C₁₃₉	1	1	yes	characteristic
215	M₃₂	—	4	2	no	—
216	C₂×C₁₆	—	4	1	no	—
217	C₂×C₁₆	—	4	2	no	—
218	C₂×C₁₆	—	4	1	no	—
219	C₂×C₁₆	C₂³×C₁₃₉	1	2	yes	—
220	C₂×C₁₆	C₂³×C₁₃₉	1	2	yes	—
221	C₂×C₁₆	C₂³×C₁₃₉	1	2	yes	—
222	C₂×C₁₆	C₂³×C₁₃₉	1	2	yes	—
223	C₄⋊C₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
224	C₄⋊C₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
225	C₄⋊C₈	C₂×C₄×C₁₃₉	1	2	yes	—
226	C₄⋊C₈	C₂×C₄×C₁₃₉	1	2	yes	—
227	C₂²⋊C₈	C₂×C₄×C₁₃₉	1	2	yes	—
228	C₂²⋊C₈	C₂×C₄×C₁₃₉	1	2	yes	—
229	C₂²⋊C₈	C₂×C₄×C₁₃₉	1	2	yes	—
230	#97	C₂×C₄×C₁₃₉	1	2	yes	—
231	#97	C₂×C₄×C₁₃₉	1	2	yes	—
232	C₄×C₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
233	C₄×C₈	C₂×C₄×C₁₃₉	1	1	yes	characteristic
234	C₄×C₈	C₂³×C₁₃₉	1	2	yes	—
235	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
236	C₄×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
237	C₂×Q₈	C₂×C₈×C₁₃₉	1	1	yes	characteristic
238	C₂×D₄	C₂×C₈×C₁₃₉	1	2	yes	—
239	C₂×D₄	C₂×C₈×C₁₃₉	1	1	yes	characteristic
240	C₂²×C₄	C₂×C₈×C₁₃₉	1	1	yes	characteristic
241	C₂²×C₄	C₂×C₈×C₁₃₉	1	1	yes	characteristic
242	C₂²×C₄	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
243	C₂²×C₄	C₂²×C₄×C₁₃₉	1	2	yes	—
244	M₁₆	—	4	2	no	—
245	C₂×C₈	—	2	1	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	1	no	—
248	C₂×C₈	—	2	2	no	—
249	C₂×C₈	—	4	1	no	—
250	C₂×C₈	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
251	C₂×C₈	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
252	C₂×C₈	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
253	C₂×C₈	C₂²×C₄×C₁₃₉	1	2	yes	—
254	C₂×C₈	C₂²×C₄×C₁₃₉	1	2	yes	—
255	C₂×C₈	C₂⁴×C₁₃₉	1	1	yes	characteristic
256	C₄⋊C₄	C₂×C₈×C₁₃₉	1	2	yes	—
257	C₄⋊C₄	C₂×C₈×C₁₃₉	1	2	yes	—
258	C₄⋊C₄	C₂×C₈×C₁₃₉	1	1	yes	characteristic
259	C₄⋊C₄	C₂×C₈×C₁₃₉	1	2	yes	—
260	C₄⋊C₄	C₂×C₈×C₁₃₉	1	1	yes	characteristic
261	C₄⋊C₄	C₂×C₈×C₁₃₉	1	2	yes	—
262	C₂²⋊C₄	C₂×C₈×C₁₃₉	1	2	yes	—
263	C₂²⋊C₄	C₂×C₈×C₁₃₉	1	2	yes	—
264	C₂²⋊C₄	C₂×C₈×C₁₃₉	1	2	yes	—
265	C₂²⋊C₄	C₂×C₈×C₁₃₉	1	2	yes	—
266	C₂²⋊C₄	C₂×C₈×C₁₃₉	1	2	yes	—
267	C₄²	C₂×C₈×C₁₃₉	1	1	yes	characteristic
268	C₄²	C₂×C₈×C₁₃₉	1	1	yes	characteristic
269	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
270	C₄²	C₂²×C₄×C₁₃₉	1	1	yes	characteristic
271	C₄²	C₂²×C₄×C₁₃₉	1	2	yes	—
272	C₁₆	—	2	2	no	—
273	C₁₆	—	2	2	no	—
274	C₁₆	—	2	2	no	—
275	C₁₆	—	2	2	no	—
276	C₂³	C₂²×C₈×C₁₃₉	1	2	yes	—
277	C₂³	C₂²×C₈×C₁₃₉	1	1	yes	characteristic
278	Q₈	—	4	1	no	—
279	D₄	—	2	4	no	—
280	D₄	—	4	1	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	1	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	4	1	no	—
287	C₂×C₄	C₂²×C₈×C₁₃₉	1	1	yes	characteristic
288	C₂×C₄	C₂²×C₈×C₁₃₉	1	1	yes	characteristic
289	C₂×C₄	C₂²×C₈×C₁₃₉	1	1	yes	characteristic
290	C₂×C₄	C₂²×C₈×C₁₃₉	1	1	yes	characteristic
291	C₂×C₄	C₂²×C₈×C₁₃₉	1	1	yes	characteristic
292	C₂×C₄	C₂²×C₈×C₁₃₉	1	2	yes	—
293	C₂×C₄	C₂²×C₈×C₁₃₉	1	2	yes	—
294	C₂×C₄	C₂²×C₈×C₁₃₉	1	2	yes	—
295	C₂×C₄	C₂³×C₄×C₁₃₉	1	1	yes	characteristic
296	C₈	—	2	1	no	—
297	C₈	—	2	2	no	—
298	C₈	—	2	1	no	—
299	C₈	—	2	1	no	—
300	C₈	—	2	2	no	—
301	C₈	H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
302	C₈	2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
303	C₂²	—	2	1	no	—
304	C₂²	—	2	1	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	2	no	—
308	C₂²	#504×C₁₃₉	1	2	yes	—
309	C₂²	C₂³×C₈×C₁₃₉	1	1	yes	characteristic
310	C₄	—	2	1	no	—
311	C₄	—	2	1	no	—
312	C₄	—	2	2	no	—
313	C₄	—	2	1	no	—
314	C₄	—	2	1	no	—
315	C₄	—	2	2	no	—
316	C₄	—	2	1	no	—
317	C₄	—	2	2	no	—
318	C₄	#520×C₁₃₉	1	1	yes	characteristic
319	C₄	#568×C₁₃₉	1	1	yes	characteristic
320	C₂	—	2	2	no	—
321	C₂	—	4	2	no	—
322	C₂	#2988×C₁₃₉	1	1	yes	characteristic
323	C₂	C₂×#504×C₁₃₉	1	1	yes	characteristic
324	C₂	#3407×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃₉	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃₉
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃₉
socle	C₂²×C₁₃₉	C₂³×C₈
prime radical	#121×C₁₃₉	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2183×C₁₃₉	C₂	semidirect
3. #2168×C₁₃₉	C₂	semidirect
4. #2168×C₁₃₉	C₂	semidirect
5. D₄×C₁₆×C₁₃₉	C₂	semidirect
6. #2164×C₁₃₉	C₂	semidirect
7. #2163×C₁₃₉	C₂	semidirect
8. #2151×C₁₃₉	C₂	semidirect
9. C₂×C₄⋊C₁₆×C₁₃₉	C₂	semidirect
162. #33506	C₁₃₉	direct (N × H)
163. C₁₃₉	#33506	direct (N × H)
165. #2183	C₂×C₁₃₉	semidirect
166. #2168	C₂×C₁₃₉	semidirect
167. #2168	C₂×C₁₃₉	semidirect
168. D₄×C₁₆	C₂×C₁₃₉	semidirect
169. #2164	C₂×C₁₃₉	semidirect
170. #2163	C₂×C₁₃₉	semidirect
171. #2151	C₂×C₁₃₉	semidirect
172. C₂×C₄⋊C₁₆	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2966×C₁₃₉	2
#2183×C₁₃₉	2
#2168×C₁₃₉	2
D₄×C₁₆×C₁₃₉	2
#2164×C₁₃₉	2
#2163×C₁₃₉	2
#2151×C₁₃₉	2
C₂×C₄⋊C₁₆×C₁₃₉	2
#33506	139

Subgroups — C139×#33506 #48028102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#33506 #48028102