Subgroups — C₁₃₉×#37322 #48031918

Order 35584.

1768 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2862×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2751×C₁₃₉	C₂	1	4	yes	maximal, complemented
4	#2730×C₁₃₉	C₂	1	4	yes	maximal, complemented
5	#2712×C₁₃₉	C₂	1	4	yes	maximal, complemented
6	#2700×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2628×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2619×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	#2513×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2491×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2452×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2420×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2331×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2328×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#2298×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
18	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
25	#400×C₁₃₉	C₂²	1	2	yes	—
26	#399×C₁₃₉	C₂²	1	2	yes	—
27	#397×C₁₃₉	C₂²	1	4	yes	—
28	#397×C₁₃₉	C₂²	1	4	yes	—
29	#397×C₁₃₉	C₂²	1	4	yes	—
30	#396×C₁₃₉	C₂²	1	4	yes	—
31	#395×C₁₃₉	C₂²	1	2	yes	—
32	#394×C₁₃₉	C₂²	1	2	yes	—
33	#394×C₁₃₉	C₂²	1	2	yes	—
34	#394×C₁₃₉	C₂²	1	4	yes	—
35	#394×C₁₃₉	C₂²	1	4	yes	—
36	#393×C₁₃₉	C₂²	1	2	yes	—
37	#393×C₁₃₉	C₂²	1	4	yes	—
38	#393×C₁₃₉	C₂²	1	4	yes	—
39	#392×C₁₃₉	C₂²	1	2	yes	—
40	#392×C₁₃₉	C₂²	1	2	yes	—
41	#391×C₁₃₉	C₂²	1	4	yes	—
42	#391×C₁₃₉	C₂²	1	4	yes	—
43	#391×C₁₃₉	C₂²	1	4	yes	—
44	#390×C₁₃₉	C₂²	1	2	yes	—
45	#390×C₁₃₉	C₂²	1	2	yes	—
46	#390×C₁₃₉	C₂²	1	2	yes	—
47	#390×C₁₃₉	C₂²	1	2	yes	—
48	#390×C₁₃₉	C₂²	1	4	yes	—
49	#389×C₁₃₉	C₂²	1	2	yes	—
50	#389×C₁₃₉	C₂²	1	2	yes	—
51	#388×C₁₃₉	C₂²	1	4	yes	—
52	#388×C₁₃₉	C₂²	1	4	yes	—
53	#388×C₁₃₉	C₂²	1	2	yes	—
54	#388×C₁₃₉	C₂²	1	2	yes	—
55	#388×C₁₃₉	C₂²	1	4	yes	—
56	#387×C₁₃₉	C₂²	1	2	yes	—
57	#387×C₁₃₉	C₂²	1	2	yes	—
58	#387×C₁₃₉	C₂²	1	4	yes	—
59	#386×C₁₃₉	C₂²	1	4	yes	—
60	#386×C₁₃₉	C₂²	1	4	yes	—
61	#386×C₁₃₉	C₂²	1	4	yes	—
62	#385×C₁₃₉	C₂²	1	4	yes	—
63	#382×C₁₃₉	C₂²	1	2	yes	—
64	#382×C₁₃₉	C₂²	1	1	yes	characteristic
65	#382×C₁₃₉	C₂²	1	1	yes	characteristic
66	#381×C₁₃₉	C₂²	1	4	yes	—
67	#380×C₁₃₉	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
73	#376×C₁₃₉	C₂²	1	1	yes	characteristic
74	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
76	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
77	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
83	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
84	C₄⋊Q₈×C₁₃₉	—	4	4	no	—
85	#127×C₁₃₉	—	2	4	no	—
86	#124×C₁₃₉	—	4	8	no	—
87	#124×C₁₃₉	—	4	8	no	—
88	C₂²⋊Q₈×C₁₃₉	—	4	8	no	—
89	#121×C₁₃₉	—	4	4	no	—
90	C₄×D₄×C₁₃₉	—	4	4	no	—
91	#117×C₁₃₉	—	2	4	no	—
92	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	4	yes	—
115	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
118	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
127	#95×C₁₃₉	C₂³	1	4	yes	—
128	#95×C₁₃₉	C₂³	1	2	yes	—
129	#95×C₁₃₉	C₂³	1	4	yes	—
130	#95×C₁₃₉	C₂³	1	2	yes	—
131	#95×C₁₃₉	C₂³	1	2	yes	—
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	4	yes	—
134	#95×C₁₃₉	C₂³	1	4	yes	—
135	#95×C₁₃₉	C₂³	1	4	yes	—
136	#95×C₁₃₉	C₂³	1	2	yes	—
137	#95×C₁₃₉	C₂³	1	2	yes	—
138	#95×C₁₃₉	C₂³	1	2	yes	—
139	#95×C₁₃₉	C₂³	1	2	yes	—
140	#95×C₁₃₉	C₂³	1	2	yes	—
141	#95×C₁₃₉	C₂³	1	2	yes	—
142	#95×C₁₃₉	C₂³	1	2	yes	—
143	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
144	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
145	C₂×Q₈×C₁₃₉	—	2	4	no	—
146	C₂×Q₈×C₁₃₉	—	2	8	no	—
147	C₂×Q₈×C₁₃₉	—	4	4	no	—
148	C₂×Q₈×C₁₃₉	—	4	4	no	—
149	C₂×Q₈×C₁₃₉	—	4	4	no	—
150	C₂×D₄×C₁₃₉	—	2	4	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	4	no	—
156	C₂×D₄×C₁₃₉	—	4	4	no	—
157	C₂×D₄×C₁₃₉	—	4	4	no	—
158	C₂×D₄×C₁₃₉	—	4	4	no	—
159	C₂×D₄×C₁₃₉	—	4	4	no	—
160	C₂²×C₄×C₁₃₉	—	2	2	no	—
161	C₂²×C₄×C₁₃₉	—	2	2	no	—
162	C₂²×C₄×C₁₃₉	—	2	2	no	—
163	C₂²×C₄×C₁₃₉	—	4	4	no	—
164	C₂²×C₄×C₁₃₉	—	4	4	no	—
165	C₂²×C₄×C₁₃₉	—	4	4	no	—
166	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
179	C₄⋊C₄×C₁₃₉	—	2	2	no	—
180	C₄⋊C₄×C₁₃₉	—	2	2	no	—
181	C₄⋊C₄×C₁₃₉	—	2	4	no	—
182	C₄⋊C₄×C₁₃₉	—	2	4	no	—
183	C₄⋊C₄×C₁₃₉	—	2	4	no	—
184	C₄⋊C₄×C₁₃₉	—	2	4	no	—
185	C₄⋊C₄×C₁₃₉	—	2	4	no	—
186	C₄⋊C₄×C₁₃₉	—	4	2	no	—
187	C₄⋊C₄×C₁₃₉	—	4	4	no	—
188	C₄⋊C₄×C₁₃₉	—	4	4	no	—
189	C₄⋊C₄×C₁₃₉	—	4	4	no	—
190	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₃₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
193	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
194	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
195	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
196	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
197	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
198	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
199	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
200	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
201	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
202	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
203	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
204	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
205	C₄²×C₁₃₉	—	2	2	no	—
206	C₄²×C₁₃₉	—	2	2	no	—
207	C₄²×C₁₃₉	—	2	4	no	—
208	C₄²×C₁₃₉	—	2	2	no	—
209	C₄²×C₁₃₉	—	2	2	no	—
210	C₄²×C₁₃₉	—	2	2	no	—
211	C₄²×C₁₃₉	—	4	2	no	—
212	C₄²×C₁₃₉	—	4	4	no	—
213	C₄²×C₁₃₉	#41	1	4	yes	—
214	C₂³×C₁₃₉	—	2	1	no	—
215	C₂³×C₁₃₉	—	2	4	no	—
216	C₂³×C₁₃₉	—	2	4	no	—
217	C₂³×C₁₃₉	—	2	4	no	—
218	C₂³×C₁₃₉	—	2	2	no	—
219	C₂³×C₁₃₉	—	2	4	no	—
220	C₂³×C₁₃₉	—	2	1	no	—
221	C₂³×C₁₃₉	—	2	1	no	—
222	C₂³×C₁₃₉	—	2	4	no	—
223	C₂³×C₁₃₉	—	2	4	no	—
224	C₂³×C₁₃₉	—	2	4	no	—
225	C₂³×C₁₃₉	—	2	2	no	—
226	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
227	Q₈×C₁₃₉	—	8	4	no	—
228	Q₈×C₁₃₉	—	8	8	no	—
229	D₄×C₁₃₉	—	4	8	no	—
230	D₄×C₁₃₉	—	8	4	no	—
231	D₄×C₁₃₉	—	8	4	no	—
232	D₄×C₁₃₉	—	8	8	no	—
233	C₂×C₄×C₁₃₉	—	2	2	no	—
234	C₂×C₄×C₁₃₉	—	2	2	no	—
235	C₂×C₄×C₁₃₉	—	2	2	no	—
236	C₂×C₄×C₁₃₉	—	2	2	no	—
237	C₂×C₄×C₁₃₉	—	2	1	no	—
238	C₂×C₄×C₁₃₉	—	2	1	no	—
239	C₂×C₄×C₁₃₉	—	2	1	no	—
240	C₂×C₄×C₁₃₉	—	2	4	no	—
241	C₂×C₄×C₁₃₉	—	2	2	no	—
242	C₂×C₄×C₁₃₉	—	2	2	no	—
243	C₂×C₄×C₁₃₉	—	2	2	no	—
244	C₂×C₄×C₁₃₉	—	2	4	no	—
245	C₂×C₄×C₁₃₉	—	2	4	no	—
246	C₂×C₄×C₁₃₉	—	2	4	no	—
247	C₂×C₄×C₁₃₉	—	2	1	no	—
248	C₂×C₄×C₁₃₉	—	2	2	no	—
249	C₂×C₄×C₁₃₉	—	2	4	no	—
250	C₂×C₄×C₁₃₉	—	2	4	no	—
251	C₂×C₄×C₁₃₉	—	2	4	no	—
252	C₂×C₄×C₁₃₉	—	2	2	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	2	2	no	—
255	C₂×C₄×C₁₃₉	—	2	1	no	—
256	C₂×C₄×C₁₃₉	—	2	2	no	—
257	C₂×C₄×C₁₃₉	—	2	2	no	—
258	C₂×C₄×C₁₃₉	—	2	2	no	—
259	C₂×C₄×C₁₃₉	—	2	2	no	—
260	C₂×C₄×C₁₃₉	—	2	4	no	—
261	C₂×C₄×C₁₃₉	—	2	4	no	—
262	C₂×C₄×C₁₃₉	—	4	4	no	—
263	C₂×C₄×C₁₃₉	—	8	8	no	—
264	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
265	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
266	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
267	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	4	yes	—
268	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
269	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
270	C₂²×C₁₃₉	—	4	1	no	—
271	C₂²×C₁₃₉	—	4	4	no	—
272	C₂²×C₁₃₉	—	4	4	no	—
273	C₂²×C₁₃₉	—	4	1	no	—
274	C₂²×C₁₃₉	—	4	4	no	—
275	C₂²×C₁₃₉	—	4	1	no	—
276	C₂²×C₁₃₉	—	4	4	no	—
277	C₂²×C₁₃₉	—	4	2	no	—
278	C₂²×C₁₃₉	—	4	4	no	—
279	C₂²×C₁₃₉	—	4	4	no	—
280	C₂²×C₁₃₉	—	4	2	no	—
281	C₂²×C₁₃₉	—	4	4	no	—
282	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
283	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
284	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	2	yes	—
285	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
286	C₂²×C₁₃₉	#585	1	2	yes	—
287	C₄×C₁₃₉	—	2	2	no	—
288	C₄×C₁₃₉	—	2	2	no	—
289	C₄×C₁₃₉	—	2	4	no	—
290	C₄×C₁₃₉	—	4	1	no	—
291	C₄×C₁₃₉	—	4	1	no	—
292	C₄×C₁₃₉	—	4	4	no	—
293	C₄×C₁₃₉	—	4	1	no	—
294	C₄×C₁₃₉	—	4	2	no	—
295	C₄×C₁₃₉	—	4	2	no	—
296	C₄×C₁₃₉	—	4	2	no	—
297	C₄×C₁₃₉	—	4	4	no	—
298	C₄×C₁₃₉	—	4	4	no	—
299	C₄×C₁₃₉	#542	1	4	yes	—
300	C₂×C₁₃₉	—	8	1	no	—
301	C₂×C₁₃₉	—	8	4	no	—
302	C₂×C₁₃₉	C₂×#542	1	1	yes	characteristic
303	C₂×C₁₃₉	#3508	1	1	yes	characteristic
304	C₂×C₁₃₉	#3510	1	1	yes	characteristic
305	C₂×C₁₃₉	#3547	1	2	yes	—
306	C₂×C₁₃₉	#3558	1	2	yes	—
307	#37322	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
308	C₁₃₉	#37322	1	1	yes	characteristic, direct product factor, Sylow
309	#2862	C₂×C₁₃₉	1	1	yes	characteristic, complemented
310	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
311	#2751	C₂×C₁₃₉	1	4	yes	complemented
312	#2730	C₂×C₁₃₉	1	4	yes	complemented
313	#2712	C₂×C₁₃₉	1	4	yes	complemented
314	#2700	C₂×C₁₃₉	1	4	yes	complemented
315	#2628	C₂×C₁₃₉	1	1	yes	characteristic, complemented
316	#2619	C₂×C₁₃₉	1	1	yes	characteristic
317	#2513	C₂×C₁₃₉	1	2	yes	complemented
318	#2491	C₂×C₁₃₉	1	2	yes	complemented
319	#2452	C₂×C₁₃₉	1	2	yes	complemented
320	#2420	C₂×C₁₃₉	1	2	yes	complemented
321	#2331	C₂×C₁₃₉	1	1	yes	characteristic, complemented
322	#2328	C₂×C₁₃₉	1	1	yes	characteristic, complemented
323	#2298	C₂×C₁₃₉	1	1	yes	characteristic, complemented
324	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
325	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
326	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
327	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
328	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
329	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
330	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
331	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
332	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
333	#400	C₂²×C₁₃₉	1	2	yes	—
334	#399	C₂²×C₁₃₉	1	2	yes	—
335	#397	C₂²×C₁₃₉	1	4	yes	—
336	#397	C₂²×C₁₃₉	1	4	yes	—
337	#397	C₂²×C₁₃₉	1	4	yes	—
338	#396	C₂²×C₁₃₉	1	4	yes	—
339	#395	C₂²×C₁₃₉	1	2	yes	—
340	#394	C₂²×C₁₃₉	1	2	yes	—
341	#394	C₂²×C₁₃₉	1	2	yes	—
342	#394	C₂²×C₁₃₉	1	4	yes	—
343	#394	C₂²×C₁₃₉	1	4	yes	—
344	#393	C₂²×C₁₃₉	1	2	yes	—
345	#393	C₂²×C₁₃₉	1	4	yes	—
346	#393	C₂²×C₁₃₉	1	4	yes	—
347	#392	C₂²×C₁₃₉	1	2	yes	—
348	#392	C₂²×C₁₃₉	1	2	yes	—
349	#391	C₂²×C₁₃₉	1	4	yes	—
350	#391	C₂²×C₁₃₉	1	4	yes	—
351	#391	C₂²×C₁₃₉	1	4	yes	—
352	#390	C₂²×C₁₃₉	1	2	yes	—
353	#390	C₂²×C₁₃₉	1	2	yes	—
354	#390	C₂²×C₁₃₉	1	2	yes	—
355	#390	C₂²×C₁₃₉	1	4	yes	—
356	#390	C₂²×C₁₃₉	1	2	yes	—
357	#389	C₂²×C₁₃₉	1	2	yes	—
358	#389	C₂²×C₁₃₉	1	2	yes	—
359	#388	C₂²×C₁₃₉	1	4	yes	—
360	#388	C₂²×C₁₃₉	1	4	yes	—
361	#388	C₂²×C₁₃₉	1	2	yes	—
362	#388	C₂²×C₁₃₉	1	4	yes	—
363	#388	C₂²×C₁₃₉	1	2	yes	—
364	#387	C₂²×C₁₃₉	1	4	yes	—
365	#387	C₂²×C₁₃₉	1	2	yes	—
366	#387	C₂²×C₁₃₉	1	2	yes	—
367	#386	C₂²×C₁₃₉	1	4	yes	—
368	#386	C₂²×C₁₃₉	1	4	yes	—
369	#386	C₂²×C₁₃₉	1	4	yes	—
370	#385	C₂²×C₁₃₉	1	4	yes	—
371	#382	C₂²×C₁₃₉	1	1	yes	characteristic
372	#382	C₂²×C₁₃₉	1	1	yes	characteristic
373	#382	C₂²×C₁₃₉	1	2	yes	—
374	#381	C₂²×C₁₃₉	1	4	yes	—
375	#380	C₂²×C₁₃₉	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
377	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
378	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
379	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
380	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
381	#376	C₂²×C₁₃₉	1	1	yes	characteristic
382	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
383	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
384	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
385	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
386	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
387	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
388	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
389	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
391	C₄⋊Q₈	—	2	4	no	—
392	C₄⋊Q₈	—	4	4	no	—
393	#127	—	2	4	no	—
394	#124	—	4	8	no	—
395	#124	—	4	8	no	—
396	C₂²⋊Q₈	—	4	8	no	—
397	#121	—	4	4	no	—
398	C₄×D₄	—	4	4	no	—
399	#117	—	2	4	no	—
400	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
412	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
426	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
429	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
433	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
434	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
435	#95	C₂³×C₁₃₉	1	2	yes	—
436	#95	C₂³×C₁₃₉	1	2	yes	—
437	#95	C₂³×C₁₃₉	1	2	yes	—
438	#95	C₂³×C₁₃₉	1	2	yes	—
439	#95	C₂³×C₁₃₉	1	2	yes	—
440	#95	C₂³×C₁₃₉	1	2	yes	—
441	#95	C₂³×C₁₃₉	1	4	yes	—
442	#95	C₂³×C₁₃₉	1	4	yes	—
443	#95	C₂³×C₁₃₉	1	4	yes	—
444	#95	C₂³×C₁₃₉	1	4	yes	—
445	#95	C₂³×C₁₃₉	1	2	yes	—
446	#95	C₂³×C₁₃₉	1	2	yes	—
447	#95	C₂³×C₁₃₉	1	4	yes	—
448	#95	C₂³×C₁₃₉	1	2	yes	—
449	#95	C₂³×C₁₃₉	1	2	yes	—
450	#95	C₂³×C₁₃₉	1	4	yes	—
451	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
452	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
453	C₂×Q₈	—	2	4	no	—
454	C₂×Q₈	—	2	8	no	—
455	C₂×Q₈	—	4	4	no	—
456	C₂×Q₈	—	4	4	no	—
457	C₂×Q₈	—	4	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	4	4	no	—
464	C₂×D₄	—	4	4	no	—
465	C₂×D₄	—	4	4	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	4	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	4	no	—
472	C₂²×C₄	—	4	4	no	—
473	C₂²×C₄	—	4	4	no	—
474	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₄⋊C₄	—	4	4	no	—
496	C₄⋊C₄	—	4	4	no	—
497	C₄⋊C₄	—	4	4	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	8	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	—	4	2	no	—
504	C₂²⋊C₄	—	4	4	no	—
505	C₂²⋊C₄	—	4	4	no	—
506	C₂²⋊C₄	—	4	4	no	—
507	C₂²⋊C₄	—	4	4	no	—
508	C₂²⋊C₄	—	4	4	no	—
509	C₂²⋊C₄	—	4	4	no	—
510	C₂²⋊C₄	—	4	4	no	—
511	C₂²⋊C₄	—	4	4	no	—
512	C₂²⋊C₄	—	4	4	no	—
513	C₄²	—	2	2	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	4	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	4	2	no	—
520	C₄²	—	4	4	no	—
521	C₄²	#41×C₁₃₉	1	4	yes	—
522	C₂³	—	2	1	no	—
523	C₂³	—	2	4	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	4	no	—
534	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
535	Q₈	—	8	8	no	—
536	Q₈	—	8	4	no	—
537	D₄	—	4	8	no	—
538	D₄	—	8	4	no	—
539	D₄	—	8	4	no	—
540	D₄	—	8	8	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	8	8	no	—
572	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
573	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
574	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
575	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	4	yes	—
576	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
577	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	1	no	—
590	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
591	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	2	yes	—
592	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
593	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
594	C₂²	#585×C₁₃₉	1	2	yes	—
595	C₄	—	2	4	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	4	no	—
602	C₄	—	4	4	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	4	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	#542×C₁₃₉	1	4	yes	—
608	C₂	—	8	4	no	—
609	C₂	—	8	1	no	—
610	C₂	C₂×#542×C₁₃₉	1	1	yes	characteristic
611	C₂	#3508×C₁₃₉	1	1	yes	characteristic
612	C₂	#3510×C₁₃₉	1	1	yes	characteristic
613	C₂	#3547×C₁₃₉	1	2	yes	—
614	C₂	#3558×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	#2619×C₁₃₉	C₂
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. #2862×C₁₃₉	C₂	semidirect
2. #2858×C₁₃₉	C₂	semidirect
3. #2751×C₁₃₉	C₂	semidirect
4. #2730×C₁₃₉	C₂	semidirect
5. #2712×C₁₃₉	C₂	semidirect
6. #2700×C₁₃₉	C₂	semidirect
7. #2628×C₁₃₉	C₂	semidirect
9. #2513×C₁₃₉	C₂	semidirect
10. #2491×C₁₃₉	C₂	semidirect
11. #2452×C₁₃₉	C₂	semidirect
12. #2420×C₁₃₉	C₂	semidirect
13. #2331×C₁₃₉	C₂	semidirect
14. #2328×C₁₃₉	C₂	semidirect
15. #2298×C₁₃₉	C₂	semidirect
307. #37322	C₁₃₉	direct (N × H)
308. C₁₃₉	#37322	direct (N × H)
309. #2862	C₂×C₁₃₉	semidirect
310. #2858	C₂×C₁₃₉	semidirect
311. #2751	C₂×C₁₃₉	semidirect
312. #2730	C₂×C₁₃₉	semidirect
313. #2712	C₂×C₁₃₉	semidirect
314. #2700	C₂×C₁₃₉	semidirect
315. #2628	C₂×C₁₃₉	semidirect
317. #2513	C₂×C₁₃₉	semidirect
318. #2491	C₂×C₁₃₉	semidirect
319. #2452	C₂×C₁₃₉	semidirect
320. #2420	C₂×C₁₃₉	semidirect
321. #2331	C₂×C₁₃₉	semidirect
322. #2328	C₂×C₁₃₉	semidirect
323. #2298	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2862×C₁₃₉	2
#2858×C₁₃₉	2
#2751×C₁₃₉	2
#2730×C₁₃₉	2
#2712×C₁₃₉	2
#2700×C₁₃₉	2
#2628×C₁₃₉	2
#2619×C₁₃₉	2
#2513×C₁₃₉	2
#2491×C₁₃₉	2
#2452×C₁₃₉	2
#2420×C₁₃₉	2
#2331×C₁₃₉	2
#2328×C₁₃₉	2
#2298×C₁₃₉	2
#37322	139

Subgroups — C139×#37322 #48031918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37322 #48031918