Subgroups — C₁₃₉×#37284 #48031880

Order 35584.

2102 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2847×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2778×C₁₃₉	C₂	1	4	yes	maximal, complemented
3	#2760×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2752×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2686×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2670×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2668×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2628×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#2619×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2494×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2491×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2428×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2420×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2324×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2280×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	complemented
26	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
28	#401×C₁₃₉	C₂²	1	4	yes	complemented
29	#400×C₁₃₉	C₂²	1	2	yes	complemented
30	#399×C₁₃₉	C₂²	1	2	yes	—
31	#397×C₁₃₉	C₂²	1	4	yes	—
32	#397×C₁₃₉	C₂²	1	4	yes	complemented
33	#395×C₁₃₉	C₂²	1	2	yes	complemented
34	#394×C₁₃₉	C₂²	1	4	yes	—
35	#394×C₁₃₉	C₂²	1	4	yes	—
36	#394×C₁₃₉	C₂²	1	2	yes	complemented
37	#394×C₁₃₉	C₂²	1	2	yes	complemented
38	#394×C₁₃₉	C₂²	1	4	yes	complemented
39	#393×C₁₃₉	C₂²	1	2	yes	—
40	#393×C₁₃₉	C₂²	1	4	yes	complemented
41	#392×C₁₃₉	C₂²	1	4	yes	—
42	#392×C₁₃₉	C₂²	1	2	yes	—
43	#392×C₁₃₉	C₂²	1	2	yes	—
44	#390×C₁₃₉	C₂²	1	4	yes	—
45	#390×C₁₃₉	C₂²	1	2	yes	complemented
46	#390×C₁₃₉	C₂²	1	2	yes	complemented
47	#389×C₁₃₉	C₂²	1	2	yes	complemented
48	#389×C₁₃₉	C₂²	1	2	yes	complemented
49	#388×C₁₃₉	C₂²	1	4	yes	—
50	#388×C₁₃₉	C₂²	1	4	yes	complemented
51	#388×C₁₃₉	C₂²	1	4	yes	complemented
52	#387×C₁₃₉	C₂²	1	4	yes	complemented
53	#386×C₁₃₉	C₂²	1	4	yes	—
54	#386×C₁₃₉	C₂²	1	4	yes	—
55	#386×C₁₃₉	C₂²	1	4	yes	—
56	#386×C₁₃₉	C₂²	1	4	yes	—
57	#386×C₁₃₉	C₂²	1	4	yes	—
58	#386×C₁₃₉	C₂²	1	4	yes	complemented
59	#385×C₁₃₉	C₂²	1	4	yes	complemented
60	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	#381×C₁₃₉	C₂²	1	1	yes	characteristic
63	#381×C₁₃₉	C₂²	1	1	yes	characteristic
64	#381×C₁₃₉	C₂²	1	4	yes	complemented
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	#380×C₁₃₉	C₂²	1	2	yes	—
67	#380×C₁₃₉	C₂²	1	2	yes	—
68	#380×C₁₃₉	C₂²	1	2	yes	—
69	#380×C₁₃₉	C₂²	1	2	yes	—
70	#379×C₁₃₉	C₂²	1	1	yes	characteristic
71	#379×C₁₃₉	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
75	C₂⁵×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
80	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃₉	—	2	4	no	—
84	C₂³×C₄×C₁₃₉	—	4	2	no	—
85	C₂³×C₄×C₁₃₉	—	4	2	no	—
86	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
91	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
92	#127×C₁₃₉	—	4	2	no	—
93	#124×C₁₃₉	—	4	8	no	—
94	#121×C₁₃₉	—	2	8	no	—
95	#121×C₁₃₉	—	4	8	no	—
96	#121×C₁₃₉	—	4	4	no	—
97	#121×C₁₃₉	—	4	4	no	—
98	#120×C₁₃₉	—	4	8	no	—
99	C₄×D₄×C₁₃₉	—	4	4	no	—
100	#117×C₁₃₉	—	4	2	no	—
101	#117×C₁₃₉	—	4	2	no	—
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	1	yes	characteristic
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
134	#95×C₁₃₉	C₂³	1	4	yes	—
135	#95×C₁₃₉	C₂³	1	2	yes	—
136	#95×C₁₃₉	C₂³	1	2	yes	—
137	#95×C₁₃₉	C₂³	1	4	yes	—
138	#95×C₁₃₉	C₂³	1	4	yes	—
139	#95×C₁₃₉	C₂³	1	2	yes	—
140	#95×C₁₃₉	C₂³	1	2	yes	—
141	#95×C₁₃₉	C₂³	1	4	yes	—
142	#95×C₁₃₉	C₂³	1	4	yes	—
143	#95×C₁₃₉	C₂³	1	2	yes	—
144	#95×C₁₃₉	C₂³	1	2	yes	—
145	#95×C₁₃₉	C₂³	1	4	yes	—
146	#95×C₁₃₉	C₂³	1	2	yes	—
147	#95×C₁₃₉	C₂³	1	2	yes	—
148	C₂⁴×C₁₃₉	—	2	2	no	—
149	C₂⁴×C₁₃₉	—	2	4	no	—
150	C₂⁴×C₁₃₉	—	4	1	no	—
151	C₂⁴×C₁₃₉	—	4	1	no	—
152	C₂⁴×C₁₃₉	—	4	2	no	—
153	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
154	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
155	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
156	C₂×Q₈×C₁₃₉	—	4	4	no	—
157	C₂×Q₈×C₁₃₉	—	4	2	no	—
158	C₂×D₄×C₁₃₉	—	2	8	no	—
159	C₂×D₄×C₁₃₉	—	2	8	no	—
160	C₂×D₄×C₁₃₉	—	2	8	no	—
161	C₂×D₄×C₁₃₉	—	2	4	no	—
162	C₂×D₄×C₁₃₉	—	2	4	no	—
163	C₂×D₄×C₁₃₉	—	2	4	no	—
164	C₂×D₄×C₁₃₉	—	4	4	no	—
165	C₂×D₄×C₁₃₉	—	4	4	no	—
166	C₂×D₄×C₁₃₉	—	4	4	no	—
167	C₂×D₄×C₁₃₉	—	4	4	no	—
168	C₂×D₄×C₁₃₉	—	4	4	no	—
169	C₂×D₄×C₁₃₉	—	4	2	no	—
170	C₂×D₄×C₁₃₉	—	4	2	no	—
171	C₂×D₄×C₁₃₉	—	4	4	no	—
172	C₂×D₄×C₁₃₉	—	4	4	no	—
173	C₂×D₄×C₁₃₉	—	4	4	no	—
174	C₂²×C₄×C₁₃₉	—	2	2	no	—
175	C₂²×C₄×C₁₃₉	—	2	2	no	—
176	C₂²×C₄×C₁₃₉	—	2	2	no	—
177	C₂²×C₄×C₁₃₉	—	2	4	no	—
178	C₂²×C₄×C₁₃₉	—	2	4	no	—
179	C₂²×C₄×C₁₃₉	—	2	4	no	—
180	C₂²×C₄×C₁₃₉	—	2	4	no	—
181	C₂²×C₄×C₁₃₉	—	4	2	no	—
182	C₂²×C₄×C₁₃₉	—	4	2	no	—
183	C₂²×C₄×C₁₃₉	—	4	1	no	—
184	C₂²×C₄×C₁₃₉	—	4	1	no	—
185	C₂²×C₄×C₁₃₉	—	4	4	no	—
186	C₂²×C₄×C₁₃₉	—	4	4	no	—
187	C₂²×C₄×C₁₃₉	—	4	4	no	—
188	C₂²×C₄×C₁₃₉	—	4	16	no	—
189	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
190	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
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	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
202	C₄⋊C₄×C₁₃₉	—	2	4	no	—
203	C₄⋊C₄×C₁₃₉	—	2	4	no	—
204	C₄⋊C₄×C₁₃₉	—	2	4	no	—
205	C₄⋊C₄×C₁₃₉	—	4	4	no	—
206	C₄⋊C₄×C₁₃₉	—	4	2	no	—
207	C₄⋊C₄×C₁₃₉	—	4	1	no	—
208	C₄⋊C₄×C₁₃₉	—	4	1	no	—
209	C₄⋊C₄×C₁₃₉	—	4	4	no	—
210	C₄⋊C₄×C₁₃₉	—	4	2	no	—
211	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
212	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
213	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
214	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
215	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
216	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
217	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
218	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
219	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
220	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
221	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
222	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
223	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
224	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
225	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
226	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
227	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
228	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
229	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
230	C₄²×C₁₃₉	—	2	4	no	—
231	C₄²×C₁₃₉	—	2	2	no	—
232	C₄²×C₁₃₉	—	2	2	no	—
233	C₄²×C₁₃₉	—	4	4	no	—
234	C₂³×C₁₃₉	—	2	2	no	—
235	C₂³×C₁₃₉	—	2	1	no	—
236	C₂³×C₁₃₉	—	2	1	no	—
237	C₂³×C₁₃₉	—	2	2	no	—
238	C₂³×C₁₃₉	—	2	2	no	—
239	C₂³×C₁₃₉	—	2	2	no	—
240	C₂³×C₁₃₉	—	2	2	no	—
241	C₂³×C₁₃₉	—	2	2	no	—
242	C₂³×C₁₃₉	—	2	2	no	—
243	C₂³×C₁₃₉	—	2	2	no	—
244	C₂³×C₁₃₉	—	2	4	no	—
245	C₂³×C₁₃₉	—	2	4	no	—
246	C₂³×C₁₃₉	—	2	4	no	—
247	C₂³×C₁₃₉	—	2	4	no	—
248	C₂³×C₁₃₉	—	2	4	no	—
249	C₂³×C₁₃₉	—	2	4	no	—
250	C₂³×C₁₃₉	—	2	4	no	—
251	C₂³×C₁₃₉	—	4	8	no	—
252	C₂³×C₁₃₉	—	4	4	no	—
253	C₂³×C₁₃₉	—	4	4	no	—
254	C₂³×C₁₃₉	—	4	8	no	—
255	C₂³×C₁₃₉	—	4	4	no	—
256	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
257	C₂³×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
258	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
259	Q₈×C₁₃₉	—	8	4	no	—
260	D₄×C₁₃₉	—	4	8	no	—
261	D₄×C₁₃₉	—	8	8	no	—
262	D₄×C₁₃₉	—	8	8	no	—
263	D₄×C₁₃₉	—	8	8	no	—
264	D₄×C₁₃₉	—	8	4	no	—
265	D₄×C₁₃₉	—	8	4	no	—
266	C₂×C₄×C₁₃₉	—	2	1	no	—
267	C₂×C₄×C₁₃₉	—	2	1	no	—
268	C₂×C₄×C₁₃₉	—	2	8	no	—
269	C₂×C₄×C₁₃₉	—	2	4	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	2	no	—
272	C₂×C₄×C₁₃₉	—	2	1	no	—
273	C₂×C₄×C₁₃₉	—	2	2	no	—
274	C₂×C₄×C₁₃₉	—	2	1	no	—
275	C₂×C₄×C₁₃₉	—	2	1	no	—
276	C₂×C₄×C₁₃₉	—	2	1	no	—
277	C₂×C₄×C₁₃₉	—	2	2	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	2	4	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	4	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	4	no	—
285	C₂×C₄×C₁₃₉	—	2	4	no	—
286	C₂×C₄×C₁₃₉	—	2	2	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	4	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	4	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	4	no	—
295	C₂×C₄×C₁₃₉	—	4	8	no	—
296	C₂×C₄×C₁₃₉	—	4	4	no	—
297	C₂×C₄×C₁₃₉	—	4	8	no	—
298	C₂×C₄×C₁₃₉	—	8	8	no	—
299	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
300	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
301	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
302	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
303	C₂²×C₁₃₉	—	2	2	no	—
304	C₂²×C₁₃₉	—	2	4	no	—
305	C₂²×C₁₃₉	—	2	4	no	—
306	C₂²×C₁₃₉	—	2	4	no	—
307	C₂²×C₁₃₉	—	2	4	no	—
308	C₂²×C₁₃₉	—	4	16	no	—
309	C₂²×C₁₃₉	—	4	2	no	—
310	C₂²×C₁₃₉	—	4	2	no	—
311	C₂²×C₁₃₉	—	4	1	no	—
312	C₂²×C₁₃₉	—	4	1	no	—
313	C₂²×C₁₃₉	—	4	2	no	—
314	C₂²×C₁₃₉	—	4	2	no	—
315	C₂²×C₁₃₉	—	4	2	no	—
316	C₂²×C₁₃₉	—	4	4	no	—
317	C₂²×C₁₃₉	—	4	4	no	—
318	C₂²×C₁₃₉	—	4	4	no	—
319	C₂²×C₁₃₉	—	4	4	no	—
320	C₂²×C₁₃₉	—	4	4	no	—
321	C₂²×C₁₃₉	—	4	4	no	—
322	C₂²×C₁₃₉	—	4	4	no	—
323	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
324	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
327	C₂²×C₁₃₉	#585	1	2	yes	—
328	C₄×C₁₃₉	—	2	2	no	—
329	C₄×C₁₃₉	—	4	2	no	—
330	C₄×C₁₃₉	—	4	4	no	—
331	C₄×C₁₃₉	—	4	1	no	—
332	C₄×C₁₃₉	—	4	4	no	—
333	C₄×C₁₃₉	—	4	1	no	—
334	C₄×C₁₃₉	—	4	1	no	—
335	C₄×C₁₃₉	—	4	1	no	—
336	C₄×C₁₃₉	—	4	2	no	—
337	C₄×C₁₃₉	—	4	2	no	—
338	C₄×C₁₃₉	—	4	4	no	—
339	C₄×C₁₃₉	#538	1	4	yes	—
340	C₂×C₁₃₉	—	4	2	no	—
341	C₂×C₁₃₉	—	4	4	no	—
342	C₂×C₁₃₉	—	8	4	no	—
343	C₂×C₁₃₉	C₂×#538	1	1	yes	characteristic
344	C₂×C₁₃₉	#3494	1	2	yes	—
345	C₂×C₁₃₉	#3537	1	1	yes	characteristic
346	C₂×C₁₃₉	#3540	1	1	yes	characteristic
347	C₂×C₁₃₉	#3542	1	2	yes	—
348	#37284	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
349	C₁₃₉	#37284	1	1	yes	characteristic, direct product factor, Sylow
350	#2847	C₂×C₁₃₉	1	2	yes	complemented
351	#2778	C₂×C₁₃₉	1	4	yes	complemented
352	#2760	C₂×C₁₃₉	1	2	yes	complemented
353	#2752	C₂×C₁₃₉	1	2	yes	complemented
354	#2686	C₂×C₁₃₉	1	4	yes	complemented
355	#2670	C₂×C₁₃₉	1	2	yes	complemented
356	#2668	C₂×C₁₃₉	1	2	yes	complemented
357	#2628	C₂×C₁₃₉	1	1	yes	characteristic, complemented
358	#2619	C₂×C₁₃₉	1	1	yes	characteristic, complemented
359	#2494	C₂×C₁₃₉	1	2	yes	complemented
360	#2491	C₂×C₁₃₉	1	2	yes	complemented
361	#2428	C₂×C₁₃₉	1	2	yes	complemented
362	#2420	C₂×C₁₃₉	1	2	yes	complemented
363	#2324	C₂×C₁₃₉	1	2	yes	complemented
364	#2280	C₂×C₁₃₉	1	1	yes	characteristic, complemented
365	C₂⁴×C₄	C₂²×C₁₃₉	1	1	yes	characteristic
366	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
367	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
368	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
369	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
370	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
371	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
372	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
373	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
374	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	complemented
375	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
376	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
377	#401	C₂²×C₁₃₉	1	4	yes	complemented
378	#400	C₂²×C₁₃₉	1	2	yes	complemented
379	#399	C₂²×C₁₃₉	1	2	yes	—
380	#397	C₂²×C₁₃₉	1	4	yes	—
381	#397	C₂²×C₁₃₉	1	4	yes	complemented
382	#395	C₂²×C₁₃₉	1	2	yes	complemented
383	#394	C₂²×C₁₃₉	1	4	yes	—
384	#394	C₂²×C₁₃₉	1	4	yes	—
385	#394	C₂²×C₁₃₉	1	2	yes	complemented
386	#394	C₂²×C₁₃₉	1	2	yes	complemented
387	#394	C₂²×C₁₃₉	1	4	yes	complemented
388	#393	C₂²×C₁₃₉	1	2	yes	—
389	#393	C₂²×C₁₃₉	1	4	yes	complemented
390	#392	C₂²×C₁₃₉	1	2	yes	—
391	#392	C₂²×C₁₃₉	1	2	yes	—
392	#392	C₂²×C₁₃₉	1	4	yes	—
393	#390	C₂²×C₁₃₉	1	4	yes	—
394	#390	C₂²×C₁₃₉	1	2	yes	complemented
395	#390	C₂²×C₁₃₉	1	2	yes	complemented
396	#389	C₂²×C₁₃₉	1	2	yes	complemented
397	#389	C₂²×C₁₃₉	1	2	yes	complemented
398	#388	C₂²×C₁₃₉	1	4	yes	—
399	#388	C₂²×C₁₃₉	1	4	yes	complemented
400	#388	C₂²×C₁₃₉	1	4	yes	complemented
401	#387	C₂²×C₁₃₉	1	4	yes	complemented
402	#386	C₂²×C₁₃₉	1	4	yes	—
403	#386	C₂²×C₁₃₉	1	4	yes	—
404	#386	C₂²×C₁₃₉	1	4	yes	—
405	#386	C₂²×C₁₃₉	1	4	yes	—
406	#386	C₂²×C₁₃₉	1	4	yes	—
407	#386	C₂²×C₁₃₉	1	4	yes	complemented
408	#385	C₂²×C₁₃₉	1	4	yes	complemented
409	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
410	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
411	#381	C₂²×C₁₃₉	1	1	yes	characteristic
412	#381	C₂²×C₁₃₉	1	1	yes	characteristic
413	#381	C₂²×C₁₃₉	1	4	yes	complemented
414	#380	C₂²×C₁₃₉	1	2	yes	—
415	#380	C₂²×C₁₃₉	1	2	yes	—
416	#380	C₂²×C₁₃₉	1	2	yes	—
417	#380	C₂²×C₁₃₉	1	2	yes	—
418	#380	C₂²×C₁₃₉	1	2	yes	—
419	#379	C₂²×C₁₃₉	1	1	yes	characteristic
420	#379	C₂²×C₁₃₉	1	1	yes	characteristic
421	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
422	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
424	C₂⁵	C₂³×C₁₃₉	1	1	yes	characteristic
425	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
426	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
427	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
428	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
429	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
430	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
431	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
432	C₂³×C₄	—	2	4	no	—
433	C₂³×C₄	—	4	2	no	—
434	C₂³×C₄	—	4	2	no	—
435	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
436	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
438	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
440	C₄⋊Q₈	—	4	2	no	—
441	#127	—	4	2	no	—
442	#124	—	4	8	no	—
443	#121	—	2	8	no	—
444	#121	—	4	8	no	—
445	#121	—	4	4	no	—
446	#121	—	4	4	no	—
447	#120	—	4	8	no	—
448	C₄×D₄	—	4	4	no	—
449	#117	—	4	2	no	—
450	#117	—	4	2	no	—
451	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
467	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
479	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
480	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
482	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
483	#95	C₂³×C₁₃₉	1	2	yes	—
484	#95	C₂³×C₁₃₉	1	2	yes	—
485	#95	C₂³×C₁₃₉	1	2	yes	—
486	#95	C₂³×C₁₃₉	1	2	yes	—
487	#95	C₂³×C₁₃₉	1	4	yes	—
488	#95	C₂³×C₁₃₉	1	4	yes	—
489	#95	C₂³×C₁₃₉	1	4	yes	—
490	#95	C₂³×C₁₃₉	1	4	yes	—
491	#95	C₂³×C₁₃₉	1	2	yes	—
492	#95	C₂³×C₁₃₉	1	4	yes	—
493	#95	C₂³×C₁₃₉	1	2	yes	—
494	#95	C₂³×C₁₃₉	1	2	yes	—
495	#95	C₂³×C₁₃₉	1	2	yes	—
496	#95	C₂³×C₁₃₉	1	4	yes	—
497	C₂⁴	—	2	2	no	—
498	C₂⁴	—	2	4	no	—
499	C₂⁴	—	4	1	no	—
500	C₂⁴	—	4	1	no	—
501	C₂⁴	—	4	2	no	—
502	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
503	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
504	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
505	C₂×Q₈	—	4	4	no	—
506	C₂×Q₈	—	4	2	no	—
507	C₂×D₄	—	2	8	no	—
508	C₂×D₄	—	2	8	no	—
509	C₂×D₄	—	2	8	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	4	4	no	—
514	C₂×D₄	—	4	4	no	—
515	C₂×D₄	—	4	4	no	—
516	C₂×D₄	—	4	4	no	—
517	C₂×D₄	—	4	4	no	—
518	C₂×D₄	—	4	2	no	—
519	C₂×D₄	—	4	2	no	—
520	C₂×D₄	—	4	4	no	—
521	C₂×D₄	—	4	4	no	—
522	C₂×D₄	—	4	4	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	4	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	4	2	no	—
531	C₂²×C₄	—	4	2	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	—	4	4	no	—
535	C₂²×C₄	—	4	4	no	—
536	C₂²×C₄	—	4	4	no	—
537	C₂²×C₄	—	4	16	no	—
538	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
542	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
545	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
547	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	4	4	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	1	no	—
557	C₄⋊C₄	—	4	1	no	—
558	C₄⋊C₄	—	4	4	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	2	8	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	8	no	—
564	C₂²⋊C₄	—	4	4	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₂²⋊C₄	—	4	2	no	—
567	C₂²⋊C₄	—	4	1	no	—
568	C₂²⋊C₄	—	4	1	no	—
569	C₂²⋊C₄	—	4	1	no	—
570	C₂²⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	—	4	4	no	—
572	C₂²⋊C₄	—	4	4	no	—
573	C₂²⋊C₄	—	4	4	no	—
574	C₂²⋊C₄	—	4	4	no	—
575	C₂²⋊C₄	—	4	4	no	—
576	C₂²⋊C₄	—	4	4	no	—
577	C₂²⋊C₄	—	4	4	no	—
578	C₂²⋊C₄	—	4	4	no	—
579	C₄²	—	2	4	no	—
580	C₄²	—	2	2	no	—
581	C₄²	—	2	2	no	—
582	C₄²	—	4	4	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	4	no	—
594	C₂³	—	2	4	no	—
595	C₂³	—	2	4	no	—
596	C₂³	—	2	4	no	—
597	C₂³	—	2	4	no	—
598	C₂³	—	2	4	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	4	4	no	—
601	C₂³	—	4	8	no	—
602	C₂³	—	4	4	no	—
603	C₂³	—	4	8	no	—
604	C₂³	—	4	4	no	—
605	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
606	C₂³	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
607	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
608	Q₈	—	8	4	no	—
609	D₄	—	4	8	no	—
610	D₄	—	8	8	no	—
611	D₄	—	8	8	no	—
612	D₄	—	8	8	no	—
613	D₄	—	8	4	no	—
614	D₄	—	8	4	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	8	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	4	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	4	8	no	—
647	C₂×C₄	—	8	8	no	—
648	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
649	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
650	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
651	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
652	C₂²	—	2	4	no	—
653	C₂²	—	2	4	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	4	no	—
656	C₂²	—	2	4	no	—
657	C₂²	—	4	16	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	4	4	no	—
669	C₂²	—	4	4	no	—
670	C₂²	—	4	4	no	—
671	C₂²	—	4	4	no	—
672	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
673	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
674	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
675	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
676	C₂²	#585×C₁₃₉	1	2	yes	—
677	C₄	—	2	2	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	4	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	4	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	4	no	—
688	C₄	#538×C₁₃₉	1	4	yes	—
689	C₂	—	4	4	no	—
690	C₂	—	4	2	no	—
691	C₂	—	8	4	no	—
692	C₂	C₂×#538×C₁₃₉	1	1	yes	characteristic
693	C₂	#3494×C₁₃₉	1	2	yes	—
694	C₂	#3537×C₁₃₉	1	1	yes	characteristic
695	C₂	#3540×C₁₃₉	1	1	yes	characteristic
696	C₂	#3542×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. #2847×C₁₃₉	C₂	semidirect
2. #2778×C₁₃₉	C₂	semidirect
3. #2760×C₁₃₉	C₂	semidirect
4. #2752×C₁₃₉	C₂	semidirect
5. #2686×C₁₃₉	C₂	semidirect
6. #2670×C₁₃₉	C₂	semidirect
7. #2668×C₁₃₉	C₂	semidirect
8. #2628×C₁₃₉	C₂	semidirect
9. #2619×C₁₃₉	C₂	semidirect
10. #2494×C₁₃₉	C₂	semidirect
11. #2491×C₁₃₉	C₂	semidirect
12. #2428×C₁₃₉	C₂	semidirect
13. #2420×C₁₃₉	C₂	semidirect
14. #2324×C₁₃₉	C₂	semidirect
15. #2280×C₁₃₉	C₂	semidirect
17. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
18. C₂×#127×C₁₃₉	C₂²	semidirect
25. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
28. #401×C₁₃₉	C₂²	semidirect
29. #400×C₁₃₉	C₂²	semidirect
32. #397×C₁₃₉	C₂²	semidirect
33. #395×C₁₃₉	C₂²	semidirect
36. #394×C₁₃₉	C₂²	semidirect
37. #394×C₁₃₉	C₂²	semidirect
38. #394×C₁₃₉	C₂²	semidirect
40. #393×C₁₃₉	C₂²	semidirect
45. #390×C₁₃₉	C₂²	semidirect
46. #390×C₁₃₉	C₂²	semidirect
47. #389×C₁₃₉	C₂²	semidirect
48. #389×C₁₃₉	C₂²	semidirect
50. #388×C₁₃₉	C₂²	semidirect
51. #388×C₁₃₉	C₂²	semidirect
52. #387×C₁₃₉	C₂²	semidirect
58. #386×C₁₃₉	C₂²	semidirect
59. #385×C₁₃₉	C₂²	semidirect
60. #382×C₁₃₉	C₂²	semidirect
61. #382×C₁₃₉	C₂²	semidirect
64. #381×C₁₃₉	C₂²	semidirect
72. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
348. #37284	C₁₃₉	direct (N × H)
349. C₁₃₉	#37284	direct (N × H)
350. #2847	C₂×C₁₃₉	semidirect
351. #2778	C₂×C₁₃₉	semidirect
352. #2760	C₂×C₁₃₉	semidirect
353. #2752	C₂×C₁₃₉	semidirect
354. #2686	C₂×C₁₃₉	semidirect
355. #2670	C₂×C₁₃₉	semidirect
356. #2668	C₂×C₁₃₉	semidirect
357. #2628	C₂×C₁₃₉	semidirect
358. #2619	C₂×C₁₃₉	semidirect
359. #2494	C₂×C₁₃₉	semidirect
360. #2491	C₂×C₁₃₉	semidirect
361. #2428	C₂×C₁₃₉	semidirect
362. #2420	C₂×C₁₃₉	semidirect
363. #2324	C₂×C₁₃₉	semidirect
364. #2280	C₂×C₁₃₉	semidirect
366. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
367. C₂×#127	C₂²×C₁₃₉	semidirect
374. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
377. #401	C₂²×C₁₃₉	semidirect
378. #400	C₂²×C₁₃₉	semidirect
381. #397	C₂²×C₁₃₉	semidirect
382. #395	C₂²×C₁₃₉	semidirect
385. #394	C₂²×C₁₃₉	semidirect
386. #394	C₂²×C₁₃₉	semidirect
387. #394	C₂²×C₁₃₉	semidirect
389. #393	C₂²×C₁₃₉	semidirect
394. #390	C₂²×C₁₃₉	semidirect
395. #390	C₂²×C₁₃₉	semidirect
396. #389	C₂²×C₁₃₉	semidirect
397. #389	C₂²×C₁₃₉	semidirect
399. #388	C₂²×C₁₃₉	semidirect
400. #388	C₂²×C₁₃₉	semidirect
401. #387	C₂²×C₁₃₉	semidirect
407. #386	C₂²×C₁₃₉	semidirect
408. #385	C₂²×C₁₃₉	semidirect
409. #382	C₂²×C₁₃₉	semidirect
410. #382	C₂²×C₁₃₉	semidirect
413. #381	C₂²×C₁₃₉	semidirect
421. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2847×C₁₃₉	2
#2778×C₁₃₉	2
#2760×C₁₃₉	2
#2752×C₁₃₉	2
#2686×C₁₃₉	2
#2670×C₁₃₉	2
#2668×C₁₃₉	2
#2628×C₁₃₉	2
#2619×C₁₃₉	2
#2494×C₁₃₉	2
#2491×C₁₃₉	2
#2428×C₁₃₉	2
#2420×C₁₃₉	2
#2324×C₁₃₉	2
#2280×C₁₃₉	2
#37284	139

Subgroups — C139×#37284 #48031880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37284 #48031880