Subgroups — C₁₃₉×#34204 #48028800

Order 35584.

3614 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2363×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2361×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2342×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2324×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2316×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2309×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#121×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2280×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2274×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#121×C₁₃₉	C₄	1	16	yes	complemented
18	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
22	#518×C₁₃₉	—	2	8	no	—
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	complemented
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	8	yes	complemented
26	C₂×#117×C₁₃₉	—	2	8	no	—
27	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
33	C₂×#117×C₁₃₉	C₂²	1	2	yes	complemented
34	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
36	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
38	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	complemented
40	#390×C₁₃₉	C₂²	1	4	yes	complemented
41	#390×C₁₃₉	C₂²	1	4	yes	complemented
42	#390×C₁₃₉	C₂²	1	8	yes	complemented
43	#389×C₁₃₉	C₂²	1	4	yes	complemented
44	#389×C₁₃₉	C₂²	1	4	yes	complemented
45	#388×C₁₃₉	C₂²	1	8	yes	complemented
46	#388×C₁₃₉	C₂²	1	8	yes	complemented
47	#386×C₁₃₉	C₂²	1	8	yes	complemented
48	#386×C₁₃₉	C₂²	1	8	yes	complemented
49	#385×C₁₃₉	C₂²	1	8	yes	complemented
50	#381×C₁₃₉	C₂²	1	2	yes	—
51	#380×C₁₃₉	C₂²	1	4	yes	—
52	#380×C₁₃₉	C₂²	1	2	yes	complemented
53	#380×C₁₃₉	C₂²	1	2	yes	complemented
54	#379×C₁₃₉	C₂²	1	2	yes	—
55	#379×C₁₃₉	C₂²	1	4	yes	—
56	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
57	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
58	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
59	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
60	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	complemented
62	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
63	C₂⁵×C₁₃₉	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₃₉	—	2	4	no	—
65	C₂²×D₄×C₁₃₉	—	2	4	no	—
66	C₂²×D₄×C₁₃₉	—	4	8	no	—
67	C₂²×D₄×C₁₃₉	C₂×C₄	1	8	yes	complemented
68	C₂²×D₄×C₁₃₉	C₂×C₄	1	16	yes	complemented
69	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
73	C₂³×C₄×C₁₃₉	—	2	4	no	—
74	C₂³×C₄×C₁₃₉	—	2	4	no	—
75	C₂³×C₄×C₁₃₉	C₂×C₄	1	8	yes	complemented
76	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃₉	C₂³	1	8	yes	—
83	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	#121×C₁₃₉	C₂×C₄	1	16	yes	complemented
86	#121×C₁₃₉	C₂×C₄	1	16	yes	complemented
87	#121×C₁₃₉	C₂×C₄	1	16	yes	complemented
88	#121×C₁₃₉	C₂×C₄	1	16	yes	complemented
89	C₄×D₄×C₁₃₉	—	2	16	no	—
90	C₄×D₄×C₁₃₉	—	2	16	no	—
91	C₄×D₄×C₁₃₉	—	4	16	no	—
92	#117×C₁₃₉	—	2	4	no	—
93	#117×C₁₃₉	—	2	4	no	—
94	#117×C₁₃₉	—	2	4	no	—
95	#117×C₁₃₉	—	2	8	no	—
96	#117×C₁₃₉	—	2	8	no	—
97	#117×C₁₃₉	—	2	8	no	—
98	#117×C₁₃₉	D₄	1	8	yes	complemented
99	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	1	8	yes	complemented
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	—	2	8	no	—
110	C₂×C₂²⋊C₄×C₁₃₉	—	2	16	no	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	1	16	yes	complemented
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃₉	—	2	8	no	—
125	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃₉	C₂³	1	8	yes	—
130	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
131	#95×C₁₃₉	C₂³	1	8	yes	—
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	8	yes	—
134	#95×C₁₃₉	C₂³	1	4	yes	—
135	C₂⁴×C₁₃₉	—	2	2	no	—
136	C₂⁴×C₁₃₉	—	2	2	no	—
137	C₂⁴×C₁₃₉	—	2	4	no	—
138	C₂⁴×C₁₃₉	—	2	4	no	—
139	C₂⁴×C₁₃₉	—	2	4	no	—
140	C₂⁴×C₁₃₉	—	4	2	no	—
141	C₂⁴×C₁₃₉	—	4	4	no	—
142	C₂⁴×C₁₃₉	—	4	4	no	—
143	C₂⁴×C₁₃₉	C₂²×C₄	1	4	yes	—
144	C₂⁴×C₁₃₉	C₂²×C₄	1	8	yes	—
145	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
146	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
147	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
149	C₂×D₄×C₁₃₉	—	2	16	no	—
150	C₂×D₄×C₁₃₉	—	2	32	no	—
151	C₂×D₄×C₁₃₉	—	2	4	no	—
152	C₂×D₄×C₁₃₉	—	2	4	no	—
153	C₂×D₄×C₁₃₉	—	2	4	no	—
154	C₂×D₄×C₁₃₉	—	2	4	no	—
155	C₂×D₄×C₁₃₉	—	4	8	no	—
156	C₂×D₄×C₁₃₉	—	4	32	no	—
157	C₂×D₄×C₁₃₉	C₂²×C₄	1	16	yes	—
158	C₂×D₄×C₁₃₉	C₂²×C₄	1	8	yes	—
159	C₂×D₄×C₁₃₉	C₂²×C₄	1	8	yes	—
160	C₂×D₄×C₁₃₉	C₂²×C₄	1	16	yes	—
161	C₂²×C₄×C₁₃₉	—	2	2	no	—
162	C₂²×C₄×C₁₃₉	—	2	2	no	—
163	C₂²×C₄×C₁₃₉	—	2	32	no	—
164	C₂²×C₄×C₁₃₉	—	2	2	no	—
165	C₂²×C₄×C₁₃₉	—	2	2	no	—
166	C₂²×C₄×C₁₃₉	—	2	2	no	—
167	C₂²×C₄×C₁₃₉	—	2	2	no	—
168	C₂²×C₄×C₁₃₉	—	2	2	no	—
169	C₂²×C₄×C₁₃₉	—	2	2	no	—
170	C₂²×C₄×C₁₃₉	—	2	2	no	—
171	C₂²×C₄×C₁₃₉	—	2	2	no	—
172	C₂²×C₄×C₁₃₉	—	2	8	no	—
173	C₂²×C₄×C₁₃₉	—	2	8	no	—
174	C₂²×C₄×C₁₃₉	—	2	16	no	—
175	C₂²×C₄×C₁₃₉	—	4	4	no	—
176	C₂²×C₄×C₁₃₉	—	4	4	no	—
177	C₂²×C₄×C₁₃₉	—	4	8	no	—
178	C₂²×C₄×C₁₃₉	—	4	8	no	—
179	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
180	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
181	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
183	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
185	C₂²×C₄×C₁₃₉	C₂²×C₄	1	4	yes	—
186	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
187	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
188	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
197	C₄⋊C₄×C₁₃₉	—	2	8	no	—
198	C₄⋊C₄×C₁₃₉	—	2	4	no	—
199	C₄⋊C₄×C₁₃₉	—	2	4	no	—
200	C₄⋊C₄×C₁₃₉	—	2	4	no	—
201	C₄⋊C₄×C₁₃₉	—	4	8	no	—
202	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
203	C₄⋊C₄×C₁₃₉	C₂²×C₄	1	8	yes	—
204	C₄⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	complemented
205	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
206	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
207	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
208	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
209	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
210	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
211	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
212	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
213	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
214	C₂²⋊C₄×C₁₃₉	C₂²×C₄	1	16	yes	—
215	C₂²⋊C₄×C₁₃₉	C₂²×C₄	1	16	yes	—
216	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
217	C₄²×C₁₃₉	—	2	8	no	—
218	C₄²×C₁₃₉	—	2	4	no	—
219	C₄²×C₁₃₉	—	2	4	no	—
220	C₄²×C₁₃₉	—	2	4	no	—
221	C₄²×C₁₃₉	—	4	8	no	—
222	C₄²×C₁₃₉	C₂×D₄	1	8	yes	complemented
223	C₂³×C₁₃₉	—	2	1	no	—
224	C₂³×C₁₃₉	—	2	1	no	—
225	C₂³×C₁₃₉	—	2	2	no	—
226	C₂³×C₁₃₉	—	2	2	no	—
227	C₂³×C₁₃₉	—	2	2	no	—
228	C₂³×C₁₃₉	—	2	8	no	—
229	C₂³×C₁₃₉	—	2	8	no	—
230	C₂³×C₁₃₉	—	2	1	no	—
231	C₂³×C₁₃₉	—	2	4	no	—
232	C₂³×C₁₃₉	—	2	1	no	—
233	C₂³×C₁₃₉	—	2	4	no	—
234	C₂³×C₁₃₉	—	2	8	no	—
235	C₂³×C₁₃₉	—	2	2	no	—
236	C₂³×C₁₃₉	—	2	2	no	—
237	C₂³×C₁₃₉	—	2	8	no	—
238	C₂³×C₁₃₉	—	2	16	no	—
239	C₂³×C₁₃₉	—	4	4	no	—
240	C₂³×C₁₃₉	—	4	8	no	—
241	C₂³×C₁₃₉	—	4	8	no	—
242	C₂³×C₁₃₉	—	4	8	no	—
243	C₂³×C₁₃₉	—	4	8	no	—
244	C₂³×C₁₃₉	—	8	8	no	—
245	C₂³×C₁₃₉	—	8	8	no	—
246	C₂³×C₁₃₉	C₂³×C₄	1	8	yes	—
247	C₂³×C₁₃₉	C₂³×C₄	1	2	yes	—
248	C₂³×C₁₃₉	C₂³×C₄	1	2	yes	—
249	C₂³×C₁₃₉	C₂³×C₄	1	2	yes	—
250	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
251	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
252	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
253	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
254	D₄×C₁₃₉	—	2	32	no	—
255	D₄×C₁₃₉	—	2	16	no	—
256	D₄×C₁₃₉	—	2	16	no	—
257	D₄×C₁₃₉	—	4	16	no	—
258	C₂×C₄×C₁₃₉	—	2	8	no	—
259	C₂×C₄×C₁₃₉	—	2	1	no	—
260	C₂×C₄×C₁₃₉	—	2	1	no	—
261	C₂×C₄×C₁₃₉	—	2	1	no	—
262	C₂×C₄×C₁₃₉	—	2	1	no	—
263	C₂×C₄×C₁₃₉	—	2	4	no	—
264	C₂×C₄×C₁₃₉	—	2	8	no	—
265	C₂×C₄×C₁₃₉	—	2	4	no	—
266	C₂×C₄×C₁₃₉	—	2	8	no	—
267	C₂×C₄×C₁₃₉	—	2	8	no	—
268	C₂×C₄×C₁₃₉	—	2	8	no	—
269	C₂×C₄×C₁₃₉	—	2	8	no	—
270	C₂×C₄×C₁₃₉	—	2	4	no	—
271	C₂×C₄×C₁₃₉	—	2	4	no	—
272	C₂×C₄×C₁₃₉	—	2	4	no	—
273	C₂×C₄×C₁₃₉	—	2	4	no	—
274	C₂×C₄×C₁₃₉	—	2	4	no	—
275	C₂×C₄×C₁₃₉	—	2	4	no	—
276	C₂×C₄×C₁₃₉	—	2	4	no	—
277	C₂×C₄×C₁₃₉	—	2	4	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	4	8	no	—
280	C₂×C₄×C₁₃₉	—	4	16	no	—
281	C₂×C₄×C₁₃₉	—	8	16	no	—
282	C₂×C₄×C₁₃₉	C₄×D₄	1	16	yes	complemented
283	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
284	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
285	C₂×C₄×C₁₃₉	C₂³×C₄	1	8	yes	—
286	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
287	C₂×C₄×C₁₃₉	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
289	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
292	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
293	C₂²×C₁₃₉	—	2	2	no	—
294	C₂²×C₁₃₉	—	2	2	no	—
295	C₂²×C₁₃₉	—	2	2	no	—
296	C₂²×C₁₃₉	—	2	2	no	—
297	C₂²×C₁₃₉	—	2	4	no	—
298	C₂²×C₁₃₉	—	2	4	no	—
299	C₂²×C₁₃₉	—	2	4	no	—
300	C₂²×C₁₃₉	—	2	4	no	—
301	C₂²×C₁₃₉	—	2	2	no	—
302	C₂²×C₁₃₉	—	2	8	no	—
303	C₂²×C₁₃₉	—	2	8	no	—
304	C₂²×C₁₃₉	—	2	2	no	—
305	C₂²×C₁₃₉	—	2	2	no	—
306	C₂²×C₁₃₉	—	2	8	no	—
307	C₂²×C₁₃₉	—	4	16	no	—
308	C₂²×C₁₃₉	—	4	8	no	—
309	C₂²×C₁₃₉	—	4	2	no	—
310	C₂²×C₁₃₉	—	4	2	no	—
311	C₂²×C₁₃₉	—	4	8	no	—
312	C₂²×C₁₃₉	—	8	16	no	—
313	C₂²×C₁₃₉	C₂×C₄×D₄	1	4	yes	—
314	C₂²×C₁₃₉	#518	1	4	yes	complemented
315	C₂²×C₁₃₉	C₂⁴×C₄	1	1	yes	characteristic
316	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
317	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
318	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
319	C₂²×C₁₃₉	#585	1	2	yes	—
320	C₄×C₁₃₉	—	2	2	no	—
321	C₄×C₁₃₉	—	2	2	no	—
322	C₄×C₁₃₉	—	2	8	no	—
323	C₄×C₁₃₉	—	2	8	no	—
324	C₄×C₁₃₉	—	4	4	no	—
325	C₄×C₁₃₉	—	4	4	no	—
326	C₄×C₁₃₉	—	4	4	no	—
327	C₄×C₁₃₉	C₂×C₄×D₄	1	4	yes	—
328	C₄×C₁₃₉	C₂×C₄×D₄	1	4	yes	—
329	C₂×C₁₃₉	—	2	4	no	—
330	C₂×C₁₃₉	—	2	4	no	—
331	C₂×C₁₃₉	—	4	2	no	—
332	C₂×C₁₃₉	—	4	8	no	—
333	C₂×C₁₃₉	C₂²×C₄×D₄	1	1	yes	characteristic
334	C₂×C₁₃₉	C₂×#518	1	1	yes	characteristic
335	C₂×C₁₃₉	#3428	1	1	yes	characteristic
336	C₂×C₁₃₉	#3488	1	2	yes	—
337	C₂×C₁₃₉	#3494	1	2	yes	—
338	#34204	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
339	C₁₃₉	#34204	1	1	yes	characteristic, direct product factor, Sylow
340	C₂²×#121	C₂×C₁₃₉	1	1	yes	characteristic
341	C₂×#518	C₂×C₁₃₉	1	1	yes	characteristic, complemented
342	C₂²×#117	C₂×C₁₃₉	1	1	yes	characteristic, complemented
343	#2363	C₂×C₁₃₉	1	4	yes	complemented
344	#2361	C₂×C₁₃₉	1	4	yes	complemented
345	#2342	C₂×C₁₃₉	1	4	yes	complemented
346	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	4	yes	complemented
347	#2324	C₂×C₁₃₉	1	4	yes	complemented
348	#2316	C₂×C₁₃₉	1	1	yes	characteristic, complemented
349	#2309	C₂×C₁₃₉	1	1	yes	characteristic, complemented
350	C₄×#121	C₂×C₁₃₉	1	4	yes	complemented
351	#2280	C₂×C₁₃₉	1	1	yes	characteristic, complemented
352	#2274	C₂×C₁₃₉	1	1	yes	characteristic, complemented
353	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
354	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
355	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
356	C₂×#121	C₄×C₁₃₉	1	16	yes	complemented
357	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
358	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
359	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
360	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
361	#518	—	2	8	no	—
362	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
363	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	complemented
364	C₂×C₄×D₄	C₂²×C₁₃₉	1	8	yes	complemented
365	C₂×#117	—	2	8	no	—
366	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
367	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
368	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
369	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
370	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
371	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
372	C₂×#117	C₂²×C₁₃₉	1	2	yes	complemented
373	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
374	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
375	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
376	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
377	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
378	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	complemented
379	#390	C₂²×C₁₃₉	1	4	yes	complemented
380	#390	C₂²×C₁₃₉	1	4	yes	complemented
381	#390	C₂²×C₁₃₉	1	8	yes	complemented
382	#389	C₂²×C₁₃₉	1	4	yes	complemented
383	#389	C₂²×C₁₃₉	1	4	yes	complemented
384	#388	C₂²×C₁₃₉	1	8	yes	complemented
385	#388	C₂²×C₁₃₉	1	8	yes	complemented
386	#386	C₂²×C₁₃₉	1	8	yes	complemented
387	#386	C₂²×C₁₃₉	1	8	yes	complemented
388	#385	C₂²×C₁₃₉	1	8	yes	complemented
389	#381	C₂²×C₁₃₉	1	2	yes	—
390	#380	C₂²×C₁₃₉	1	4	yes	—
391	#380	C₂²×C₁₃₉	1	2	yes	complemented
392	#380	C₂²×C₁₃₉	1	2	yes	complemented
393	#379	C₂²×C₁₃₉	1	4	yes	—
394	#379	C₂²×C₁₃₉	1	2	yes	—
395	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
396	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
397	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
398	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	complemented
399	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
400	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
401	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
402	C₂⁵	C₂³×C₁₃₉	1	2	yes	—
403	C₂²×D₄	—	2	4	no	—
404	C₂²×D₄	—	2	4	no	—
405	C₂²×D₄	—	4	8	no	—
406	C₂²×D₄	C₂×C₄×C₁₃₉	1	8	yes	complemented
407	C₂²×D₄	C₂×C₄×C₁₃₉	1	16	yes	complemented
408	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
409	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
410	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
411	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
412	C₂³×C₄	—	2	4	no	—
413	C₂³×C₄	—	2	4	no	—
414	C₂³×C₄	C₂×C₄×C₁₃₉	1	8	yes	complemented
415	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
416	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₁₃₉	1	8	yes	—
422	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
423	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
424	#121	C₂×C₄×C₁₃₉	1	16	yes	complemented
425	#121	C₂×C₄×C₁₃₉	1	16	yes	complemented
426	#121	C₂×C₄×C₁₃₉	1	16	yes	complemented
427	#121	C₂×C₄×C₁₃₉	1	16	yes	complemented
428	C₄×D₄	—	2	16	no	—
429	C₄×D₄	—	2	16	no	—
430	C₄×D₄	—	4	16	no	—
431	#117	—	2	4	no	—
432	#117	—	2	4	no	—
433	#117	—	2	4	no	—
434	#117	—	2	8	no	—
435	#117	—	2	8	no	—
436	#117	—	2	8	no	—
437	#117	D₄×C₁₃₉	1	8	yes	complemented
438	C₂×C₄⋊C₄	—	2	8	no	—
439	C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	1	8	yes	complemented
440	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
448	C₂×C₂²⋊C₄	—	2	8	no	—
449	C₂×C₂²⋊C₄	—	2	16	no	—
450	C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	1	16	yes	complemented
451	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
463	C₂×C₄²	—	2	8	no	—
464	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
465	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
466	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
467	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
468	C₂×C₄²	C₂³×C₁₃₉	1	8	yes	—
469	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
470	#95	C₂³×C₁₃₉	1	8	yes	—
471	#95	C₂³×C₁₃₉	1	4	yes	—
472	#95	C₂³×C₁₃₉	1	8	yes	—
473	#95	C₂³×C₁₃₉	1	4	yes	—
474	C₂⁴	—	2	2	no	—
475	C₂⁴	—	2	2	no	—
476	C₂⁴	—	2	4	no	—
477	C₂⁴	—	2	4	no	—
478	C₂⁴	—	2	4	no	—
479	C₂⁴	—	4	2	no	—
480	C₂⁴	—	4	4	no	—
481	C₂⁴	—	4	4	no	—
482	C₂⁴	C₂²×C₄×C₁₃₉	1	4	yes	—
483	C₂⁴	C₂²×C₄×C₁₃₉	1	8	yes	—
484	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
485	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
486	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
487	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
488	C₂×D₄	—	2	16	no	—
489	C₂×D₄	—	2	32	no	—
490	C₂×D₄	—	2	4	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	4	no	—
494	C₂×D₄	—	4	8	no	—
495	C₂×D₄	—	4	32	no	—
496	C₂×D₄	C₂²×C₄×C₁₃₉	1	16	yes	—
497	C₂×D₄	C₂²×C₄×C₁₃₉	1	8	yes	—
498	C₂×D₄	C₂²×C₄×C₁₃₉	1	8	yes	—
499	C₂×D₄	C₂²×C₄×C₁₃₉	1	16	yes	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	32	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	8	no	—
512	C₂²×C₄	—	2	8	no	—
513	C₂²×C₄	—	2	16	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	—	4	8	no	—
517	C₂²×C₄	—	4	8	no	—
518	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
519	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
520	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
521	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
522	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
523	C₂²×C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
524	C₂²×C₄	C₂²×C₄×C₁₃₉	1	4	yes	—
525	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
526	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
527	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
528	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
534	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
536	C₄⋊C₄	—	2	8	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	4	8	no	—
541	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
542	C₄⋊C₄	C₂²×C₄×C₁₃₉	1	8	yes	—
543	C₄⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	complemented
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	4	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	2	16	no	—
550	C₂²⋊C₄	—	4	8	no	—
551	C₂²⋊C₄	—	4	4	no	—
552	C₂²⋊C₄	—	4	8	no	—
553	C₂²⋊C₄	C₂²×C₄×C₁₃₉	1	16	yes	—
554	C₂²⋊C₄	C₂²×C₄×C₁₃₉	1	16	yes	—
555	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
556	C₄²	—	2	8	no	—
557	C₄²	—	2	4	no	—
558	C₄²	—	2	4	no	—
559	C₄²	—	2	4	no	—
560	C₄²	—	4	8	no	—
561	C₄²	C₂×D₄×C₁₃₉	1	8	yes	complemented
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	2	8	no	—
568	C₂³	—	2	8	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	4	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	4	no	—
573	C₂³	—	2	8	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	8	no	—
577	C₂³	—	2	16	no	—
578	C₂³	—	4	4	no	—
579	C₂³	—	4	8	no	—
580	C₂³	—	4	8	no	—
581	C₂³	—	4	8	no	—
582	C₂³	—	4	8	no	—
583	C₂³	—	8	8	no	—
584	C₂³	—	8	8	no	—
585	C₂³	C₂³×C₄×C₁₃₉	1	8	yes	—
586	C₂³	C₂³×C₄×C₁₃₉	1	2	yes	—
587	C₂³	C₂³×C₄×C₁₃₉	1	2	yes	—
588	C₂³	C₂³×C₄×C₁₃₉	1	2	yes	—
589	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
590	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
591	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
592	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
593	D₄	—	2	32	no	—
594	D₄	—	2	16	no	—
595	D₄	—	2	16	no	—
596	D₄	—	4	16	no	—
597	C₂×C₄	—	2	8	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	8	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	8	no	—
607	C₂×C₄	—	2	8	no	—
608	C₂×C₄	—	2	8	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	4	8	no	—
619	C₂×C₄	—	4	16	no	—
620	C₂×C₄	—	8	16	no	—
621	C₂×C₄	C₄×D₄×C₁₃₉	1	16	yes	complemented
622	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
624	C₂×C₄	C₂³×C₄×C₁₃₉	1	8	yes	—
625	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
626	C₂×C₄	C₂³×C₄×C₁₃₉	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
628	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
629	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
630	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
631	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	4	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	8	no	—
642	C₂²	—	2	8	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	8	no	—
646	C₂²	—	4	16	no	—
647	C₂²	—	4	8	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	8	no	—
651	C₂²	—	8	16	no	—
652	C₂²	C₂×C₄×D₄×C₁₃₉	1	4	yes	—
653	C₂²	#518×C₁₃₉	1	4	yes	complemented
654	C₂²	C₂⁴×C₄×C₁₃₉	1	1	yes	characteristic
655	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
656	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
657	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
658	C₂²	#585×C₁₃₉	1	2	yes	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	8	no	—
662	C₄	—	2	8	no	—
663	C₄	—	4	4	no	—
664	C₄	—	4	4	no	—
665	C₄	—	4	4	no	—
666	C₄	C₂×C₄×D₄×C₁₃₉	1	4	yes	—
667	C₄	C₂×C₄×D₄×C₁₃₉	1	4	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	8	no	—
672	C₂	C₂²×C₄×D₄×C₁₃₉	1	1	yes	characteristic
673	C₂	C₂×#518×C₁₃₉	1	1	yes	characteristic
674	C₂	#3428×C₁₃₉	1	1	yes	characteristic
675	C₂	#3488×C₁₃₉	1	2	yes	—
676	C₂	#3494×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃₉
Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#121×C₁₃₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#518×C₁₃₉	C₂	semidirect
3. C₂²×#117×C₁₃₉	C₂	semidirect
4. #2363×C₁₃₉	C₂	semidirect
5. #2361×C₁₃₉	C₂	semidirect
6. #2342×C₁₃₉	C₂	semidirect
7. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
8. #2324×C₁₃₉	C₂	semidirect
9. #2316×C₁₃₉	C₂	semidirect
10. #2309×C₁₃₉	C₂	semidirect
11. C₄×#121×C₁₃₉	C₂	semidirect
12. #2280×C₁₃₉	C₂	semidirect
13. #2274×C₁₃₉	C₂	semidirect
17. C₂×#121×C₁₃₉	C₄	semidirect
23. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
24. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
25. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
32. C₂×#117×C₁₃₉	C₂²	semidirect
33. C₂×#117×C₁₃₉	C₂²	semidirect
35. C₂²×C₄⋊C₄×C₁₃₉	C₂²	semidirect
39. C₂²×C₄²×C₁₃₉	C₂²	semidirect
40. #390×C₁₃₉	C₂²	semidirect
41. #390×C₁₃₉	C₂²	semidirect
42. #390×C₁₃₉	C₂²	semidirect
43. #389×C₁₃₉	C₂²	semidirect
44. #389×C₁₃₉	C₂²	semidirect
45. #388×C₁₃₉	C₂²	semidirect
46. #388×C₁₃₉	C₂²	semidirect
47. #386×C₁₃₉	C₂²	semidirect
48. #386×C₁₃₉	C₂²	semidirect
49. #385×C₁₃₉	C₂²	semidirect
52. #380×C₁₃₉	C₂²	semidirect
53. #380×C₁₃₉	C₂²	semidirect
56. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
57. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
59. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
60. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
61. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
67. C₂²×D₄×C₁₃₉	C₂×C₄	semidirect
68. C₂²×D₄×C₁₃₉	C₂×C₄	semidirect
75. C₂³×C₄×C₁₃₉	C₂×C₄	semidirect
85. #121×C₁₃₉	C₂×C₄	semidirect
86. #121×C₁₃₉	C₂×C₄	semidirect
87. #121×C₁₃₉	C₂×C₄	semidirect
88. #121×C₁₃₉	C₂×C₄	semidirect
98. #117×C₁₃₉	D₄	semidirect
100. C₂×C₄⋊C₄×C₁₃₉	C₂×C₄	semidirect
111. C₂×C₂²⋊C₄×C₁₃₉	C₂×C₄	semidirect
204. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
222. C₄²×C₁₃₉	C₂×D₄	semidirect
282. C₂×C₄×C₁₃₉	C₄×D₄	semidirect
314. C₂²×C₁₃₉	#518	semidirect
338. #34204	C₁₃₉	direct (N × H)
339. C₁₃₉	#34204	direct (N × H)
341. C₂×#518	C₂×C₁₃₉	semidirect
342. C₂²×#117	C₂×C₁₃₉	semidirect
343. #2363	C₂×C₁₃₉	semidirect
344. #2361	C₂×C₁₃₉	semidirect
345. #2342	C₂×C₁₃₉	semidirect
346. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
347. #2324	C₂×C₁₃₉	semidirect
348. #2316	C₂×C₁₃₉	semidirect
349. #2309	C₂×C₁₃₉	semidirect
350. C₄×#121	C₂×C₁₃₉	semidirect
351. #2280	C₂×C₁₃₉	semidirect
352. #2274	C₂×C₁₃₉	semidirect
356. C₂×#121	C₄×C₁₃₉	semidirect
362. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
363. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
364. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
371. C₂×#117	C₂²×C₁₃₉	semidirect
372. C₂×#117	C₂²×C₁₃₉	semidirect
374. C₂²×C₄⋊C₄	C₂²×C₁₃₉	semidirect
378. C₂²×C₄²	C₂²×C₁₃₉	semidirect
379. #390	C₂²×C₁₃₉	semidirect
380. #390	C₂²×C₁₃₉	semidirect
381. #390	C₂²×C₁₃₉	semidirect
382. #389	C₂²×C₁₃₉	semidirect
383. #389	C₂²×C₁₃₉	semidirect
384. #388	C₂²×C₁₃₉	semidirect
385. #388	C₂²×C₁₃₉	semidirect
386. #386	C₂²×C₁₃₉	semidirect
387. #386	C₂²×C₁₃₉	semidirect
388. #385	C₂²×C₁₃₉	semidirect
391. #380	C₂²×C₁₃₉	semidirect
392. #380	C₂²×C₁₃₉	semidirect
395. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
396. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
398. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
399. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
400. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
406. C₂²×D₄	C₂×C₄×C₁₃₉	semidirect
407. C₂²×D₄	C₂×C₄×C₁₃₉	semidirect
414. C₂³×C₄	C₂×C₄×C₁₃₉	semidirect
424. #121	C₂×C₄×C₁₃₉	semidirect
425. #121	C₂×C₄×C₁₃₉	semidirect
426. #121	C₂×C₄×C₁₃₉	semidirect
427. #121	C₂×C₄×C₁₃₉	semidirect
437. #117	D₄×C₁₃₉	semidirect
439. C₂×C₄⋊C₄	C₂×C₄×C₁₃₉	semidirect
450. C₂×C₂²⋊C₄	C₂×C₄×C₁₃₉	semidirect
543. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
561. C₄²	C₂×D₄×C₁₃₉	semidirect
621. C₂×C₄	C₄×D₄×C₁₃₉	semidirect
653. C₂²	#518×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#121×C₁₃₉	2
C₂×#518×C₁₃₉	2
C₂²×#117×C₁₃₉	2
#2363×C₁₃₉	2
#2361×C₁₃₉	2
#2342×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
#2324×C₁₃₉	2
#2316×C₁₃₉	2
#2309×C₁₃₉	2
C₄×#121×C₁₃₉	2
#2280×C₁₃₉	2
#2274×C₁₃₉	2
#34204	139

Subgroups — C139×#34204 #48028800

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#34204 #48028800