Subgroups — C₁₃₉×#37190 #48031786

Order 35584.

2378 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	#2854×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2734×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2733×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2732×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2731×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2730×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2729×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2728×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2618×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2498×C₁₃₉	C₂	1	4	yes	maximal, complemented
12	#2430×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
15	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
16	#536×C₁₃₉	—	2	16	no	—
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
18	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
22	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
24	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
30	#400×C₁₃₉	C₂²	1	4	yes	—
31	#399×C₁₃₉	C₂²	1	4	yes	—
32	#398×C₁₃₉	C₂²	1	2	yes	—
33	#398×C₁₃₉	C₂²	1	2	yes	—
34	#398×C₁₃₉	C₂²	1	4	yes	—
35	#397×C₁₃₉	C₂²	1	4	yes	—
36	#396×C₁₃₉	C₂²	1	4	yes	—
37	#396×C₁₃₉	C₂²	1	4	yes	—
38	#395×C₁₃₉	C₂²	1	4	yes	—
39	#394×C₁₃₉	C₂²	1	2	yes	—
40	#394×C₁₃₉	C₂²	1	2	yes	—
41	#394×C₁₃₉	C₂²	1	4	yes	—
42	#393×C₁₃₉	C₂²	1	4	yes	—
43	#392×C₁₃₉	C₂²	1	4	yes	—
44	#391×C₁₃₉	C₂²	1	1	yes	characteristic
45	#391×C₁₃₉	C₂²	1	4	yes	—
46	#391×C₁₃₉	C₂²	1	1	yes	characteristic
47	#391×C₁₃₉	C₂²	1	1	yes	characteristic
48	#391×C₁₃₉	C₂²	1	1	yes	characteristic
49	#390×C₁₃₉	C₂²	1	2	yes	—
50	#390×C₁₃₉	C₂²	1	2	yes	—
51	#389×C₁₃₉	C₂²	1	2	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#388×C₁₃₉	C₂²	1	4	yes	—
54	#388×C₁₃₉	C₂²	1	4	yes	—
55	#388×C₁₃₉	C₂²	1	4	yes	—
56	#388×C₁₃₉	C₂²	1	4	yes	—
57	#387×C₁₃₉	C₂²	1	4	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	#386×C₁₃₉	C₂²	1	4	yes	—
63	#385×C₁₃₉	C₂²	1	4	yes	—
64	#385×C₁₃₉	C₂²	1	4	yes	—
65	#380×C₁₃₉	C₂²	1	2	yes	—
66	#380×C₁₃₉	C₂²	1	2	yes	—
67	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
68	C₂×#41×C₁₃₉	—	2	8	no	—
69	C₂×#41×C₁₃₉	—	4	4	no	—
70	C₂×#41×C₁₃₉	—	4	4	no	—
71	C₂²×Q₈×C₁₃₉	—	4	2	no	—
72	C₂²×Q₈×C₁₃₉	—	4	2	no	—
73	C₂²×Q₈×C₁₃₉	D₄	1	8	yes	complemented
74	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
75	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
77	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
87	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
88	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
89	#124×C₁₃₉	—	2	8	no	—
90	#124×C₁₃₉	—	2	8	no	—
91	#123×C₁₃₉	—	2	16	no	—
92	#123×C₁₃₉	—	2	16	no	—
93	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
94	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
95	#121×C₁₃₉	—	4	4	no	—
96	#121×C₁₃₉	—	4	4	no	—
97	#117×C₁₃₉	—	2	8	no	—
98	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
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	4	yes	—
102	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊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	4	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	4	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₄²×C₁₃₉	—	4	2	no	—
124	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
129	#95×C₁₃₉	C₂³	1	4	yes	—
130	#95×C₁₃₉	C₂³	1	4	yes	—
131	#95×C₁₃₉	C₂³	1	4	yes	—
132	#95×C₁₃₉	C₂³	1	4	yes	—
133	#95×C₁₃₉	C₂³	1	2	yes	—
134	#95×C₁₃₉	C₂³	1	4	yes	—
135	#95×C₁₃₉	C₂³	1	4	yes	—
136	#95×C₁₃₉	C₂³	1	4	yes	—
137	#95×C₁₃₉	C₂³	1	2	yes	—
138	#95×C₁₃₉	C₂³	1	4	yes	—
139	#95×C₁₃₉	C₂³	1	4	yes	—
140	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
141	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
142	#41×C₁₃₉	—	4	32	no	—
143	C₂×Q₈×C₁₃₉	—	2	4	no	—
144	C₂×Q₈×C₁₃₉	—	4	16	no	—
145	C₂×Q₈×C₁₃₉	—	4	1	no	—
146	C₂×Q₈×C₁₃₉	—	4	2	no	—
147	C₂×Q₈×C₁₃₉	—	4	1	no	—
148	C₂×Q₈×C₁₃₉	—	4	1	no	—
149	C₂×Q₈×C₁₃₉	—	4	2	no	—
150	C₂×Q₈×C₁₃₉	—	4	1	no	—
151	C₂×Q₈×C₁₃₉	—	4	2	no	—
152	C₂×Q₈×C₁₃₉	—	4	2	no	—
153	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
154	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
155	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
156	C₂×D₄×C₁₃₉	—	2	8	no	—
157	C₂×D₄×C₁₃₉	—	2	8	no	—
158	C₂×D₄×C₁₃₉	—	2	8	no	—
159	C₂×D₄×C₁₃₉	—	2	4	no	—
160	C₂×D₄×C₁₃₉	—	2	4	no	—
161	C₂×D₄×C₁₃₉	—	4	2	no	—
162	C₂×D₄×C₁₃₉	—	4	2	no	—
163	C₂×D₄×C₁₃₉	—	4	2	no	—
164	C₂×D₄×C₁₃₉	—	4	2	no	—
165	C₂×D₄×C₁₃₉	—	4	2	no	—
166	C₂×D₄×C₁₃₉	—	4	4	no	—
167	C₂²×C₄×C₁₃₉	—	2	2	no	—
168	C₂²×C₄×C₁₃₉	—	2	2	no	—
169	C₂²×C₄×C₁₃₉	—	2	4	no	—
170	C₂²×C₄×C₁₃₉	—	2	4	no	—
171	C₂²×C₄×C₁₃₉	—	2	4	no	—
172	C₂²×C₄×C₁₃₉	—	2	4	no	—
173	C₂²×C₄×C₁₃₉	—	2	8	no	—
174	C₂²×C₄×C₁₃₉	—	2	4	no	—
175	C₂²×C₄×C₁₃₉	—	4	2	no	—
176	C₂²×C₄×C₁₃₉	—	4	4	no	—
177	C₂²×C₄×C₁₃₉	—	4	4	no	—
178	C₂²×C₄×C₁₃₉	—	4	4	no	—
179	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
180	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
186	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
192	C₄⋊C₄×C₁₃₉	—	2	8	no	—
193	C₄⋊C₄×C₁₃₉	—	2	8	no	—
194	C₄⋊C₄×C₁₃₉	—	2	8	no	—
195	C₄⋊C₄×C₁₃₉	—	2	8	no	—
196	C₄⋊C₄×C₁₃₉	—	2	8	no	—
197	C₄⋊C₄×C₁₃₉	—	2	4	no	—
198	C₄⋊C₄×C₁₃₉	—	4	1	no	—
199	C₄⋊C₄×C₁₃₉	—	4	2	no	—
200	C₄⋊C₄×C₁₃₉	—	4	1	no	—
201	C₄⋊C₄×C₁₃₉	—	4	2	no	—
202	C₄⋊C₄×C₁₃₉	—	4	4	no	—
203	C₄⋊C₄×C₁₃₉	—	4	2	no	—
204	C₄⋊C₄×C₁₃₉	—	4	2	no	—
205	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
206	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
207	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
208	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
209	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
210	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
211	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
212	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
213	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
214	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
215	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
216	C₄²×C₁₃₉	—	2	4	no	—
217	C₄²×C₁₃₉	—	2	4	no	—
218	C₄²×C₁₃₉	—	4	1	no	—
219	C₄²×C₁₃₉	—	4	2	no	—
220	C₄²×C₁₃₉	—	4	1	no	—
221	C₂³×C₁₃₉	—	2	2	no	—
222	C₂³×C₁₃₉	—	2	2	no	—
223	C₂³×C₁₃₉	—	2	4	no	—
224	C₂³×C₁₃₉	—	2	4	no	—
225	C₂³×C₁₃₉	—	2	4	no	—
226	C₂³×C₁₃₉	—	2	4	no	—
227	C₂³×C₁₃₉	—	2	4	no	—
228	C₂³×C₁₃₉	—	2	4	no	—
229	C₂³×C₁₃₉	—	2	4	no	—
230	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
231	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
232	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
233	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
234	Q₈×C₁₃₉	—	4	4	no	—
235	Q₈×C₁₃₉	—	4	8	no	—
236	Q₈×C₁₃₉	—	4	4	no	—
237	Q₈×C₁₃₉	—	4	8	no	—
238	D₄×C₁₃₉	—	4	8	no	—
239	D₄×C₁₃₉	—	4	16	no	—
240	D₄×C₁₃₉	—	8	4	no	—
241	D₄×C₁₃₉	—	8	4	no	—
242	C₂×C₄×C₁₃₉	—	2	8	no	—
243	C₂×C₄×C₁₃₉	—	2	16	no	—
244	C₂×C₄×C₁₃₉	—	2	2	no	—
245	C₂×C₄×C₁₃₉	—	2	1	no	—
246	C₂×C₄×C₁₃₉	—	2	1	no	—
247	C₂×C₄×C₁₃₉	—	2	1	no	—
248	C₂×C₄×C₁₃₉	—	2	1	no	—
249	C₂×C₄×C₁₃₉	—	2	2	no	—
250	C₂×C₄×C₁₃₉	—	2	2	no	—
251	C₂×C₄×C₁₃₉	—	2	2	no	—
252	C₂×C₄×C₁₃₉	—	2	2	no	—
253	C₂×C₄×C₁₃₉	—	2	2	no	—
254	C₂×C₄×C₁₃₉	—	2	4	no	—
255	C₂×C₄×C₁₃₉	—	2	4	no	—
256	C₂×C₄×C₁₃₉	—	2	4	no	—
257	C₂×C₄×C₁₃₉	—	2	2	no	—
258	C₂×C₄×C₁₃₉	—	2	2	no	—
259	C₂×C₄×C₁₃₉	—	2	4	no	—
260	C₂×C₄×C₁₃₉	—	2	4	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	4	no	—
263	C₂×C₄×C₁₃₉	—	2	4	no	—
264	C₂×C₄×C₁₃₉	—	2	2	no	—
265	C₂×C₄×C₁₃₉	—	2	4	no	—
266	C₂×C₄×C₁₃₉	—	2	2	no	—
267	C₂×C₄×C₁₃₉	—	2	4	no	—
268	C₂×C₄×C₁₃₉	—	2	4	no	—
269	C₂×C₄×C₁₃₉	—	2	4	no	—
270	C₂×C₄×C₁₃₉	—	4	8	no	—
271	C₂×C₄×C₁₃₉	—	4	16	no	—
272	C₂×C₄×C₁₃₉	—	8	4	no	—
273	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
274	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
277	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
278	C₂²×C₁₃₉	—	2	4	no	—
279	C₂²×C₁₃₉	—	2	4	no	—
280	C₂²×C₁₃₉	—	2	2	no	—
281	C₂²×C₁₃₉	—	2	2	no	—
282	C₂²×C₁₃₉	—	4	4	no	—
283	C₂²×C₁₃₉	—	4	4	no	—
284	C₂²×C₁₃₉	—	4	4	no	—
285	C₂²×C₁₃₉	—	4	4	no	—
286	C₂²×C₁₃₉	—	4	4	no	—
287	C₂²×C₁₃₉	—	4	4	no	—
288	C₂²×C₁₃₉	—	4	4	no	—
289	C₂²×C₁₃₉	#534	1	4	yes	—
290	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
291	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
292	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
293	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
294	C₂²×C₁₃₉	#585	1	2	yes	—
295	C₄×C₁₃₉	—	2	4	no	—
296	C₄×C₁₃₉	—	2	4	no	—
297	C₄×C₁₃₉	—	2	2	no	—
298	C₄×C₁₃₉	—	2	2	no	—
299	C₄×C₁₃₉	—	2	4	no	—
300	C₄×C₁₃₉	—	4	4	no	—
301	C₄×C₁₃₉	—	4	4	no	—
302	C₄×C₁₃₉	—	4	4	no	—
303	C₄×C₁₃₉	—	4	2	no	—
304	C₄×C₁₃₉	—	4	2	no	—
305	C₄×C₁₃₉	—	4	2	no	—
306	C₂×C₁₃₉	—	2	4	no	—
307	C₂×C₁₃₉	—	8	4	no	—
308	C₂×C₁₃₉	C₂×#534	1	1	yes	characteristic
309	C₂×C₁₃₉	#3497	1	2	yes	—
310	C₂×C₁₃₉	#3535	1	2	yes	—
311	C₂×C₁₃₉	#3544	1	1	yes	characteristic
312	C₂×C₁₃₉	#3545	1	1	yes	characteristic
313	#37190	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₁₃₉	#37190	1	1	yes	characteristic, direct product factor, Sylow
315	C₂×#536	C₂×C₁₃₉	1	2	yes	complemented
316	#2854	C₂×C₁₃₉	1	2	yes	complemented
317	#2734	C₂×C₁₃₉	1	1	yes	characteristic, complemented
318	#2733	C₂×C₁₃₉	1	1	yes	characteristic, complemented
319	#2732	C₂×C₁₃₉	1	2	yes	complemented
320	#2731	C₂×C₁₃₉	1	2	yes	complemented
321	#2730	C₂×C₁₃₉	1	4	yes	complemented
322	#2729	C₂×C₁₃₉	1	4	yes	complemented
323	#2728	C₂×C₁₃₉	1	2	yes	complemented
324	#2618	C₂×C₁₃₉	1	2	yes	complemented
325	#2498	C₂×C₁₃₉	1	4	yes	complemented
326	#2430	C₂×C₁₃₉	1	4	yes	complemented
327	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic, complemented
328	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
329	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
330	#536	—	2	16	no	—
331	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
332	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
333	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
334	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
335	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
336	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
337	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
338	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
339	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
340	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
341	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
342	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
343	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
344	#400	C₂²×C₁₃₉	1	4	yes	—
345	#399	C₂²×C₁₃₉	1	4	yes	—
346	#398	C₂²×C₁₃₉	1	2	yes	—
347	#398	C₂²×C₁₃₉	1	2	yes	—
348	#398	C₂²×C₁₃₉	1	4	yes	—
349	#397	C₂²×C₁₃₉	1	4	yes	—
350	#396	C₂²×C₁₃₉	1	4	yes	—
351	#396	C₂²×C₁₃₉	1	4	yes	—
352	#395	C₂²×C₁₃₉	1	4	yes	—
353	#394	C₂²×C₁₃₉	1	2	yes	—
354	#394	C₂²×C₁₃₉	1	2	yes	—
355	#394	C₂²×C₁₃₉	1	4	yes	—
356	#393	C₂²×C₁₃₉	1	4	yes	—
357	#392	C₂²×C₁₃₉	1	4	yes	—
358	#391	C₂²×C₁₃₉	1	1	yes	characteristic
359	#391	C₂²×C₁₃₉	1	4	yes	—
360	#391	C₂²×C₁₃₉	1	1	yes	characteristic
361	#391	C₂²×C₁₃₉	1	1	yes	characteristic
362	#391	C₂²×C₁₃₉	1	1	yes	characteristic
363	#390	C₂²×C₁₃₉	1	2	yes	—
364	#390	C₂²×C₁₃₉	1	2	yes	—
365	#389	C₂²×C₁₃₉	1	2	yes	—
366	#389	C₂²×C₁₃₉	1	2	yes	—
367	#388	C₂²×C₁₃₉	1	4	yes	—
368	#388	C₂²×C₁₃₉	1	4	yes	—
369	#388	C₂²×C₁₃₉	1	4	yes	—
370	#388	C₂²×C₁₃₉	1	4	yes	—
371	#387	C₂²×C₁₃₉	1	4	yes	—
372	#387	C₂²×C₁₃₉	1	4	yes	—
373	#386	C₂²×C₁₃₉	1	4	yes	—
374	#386	C₂²×C₁₃₉	1	4	yes	—
375	#386	C₂²×C₁₃₉	1	4	yes	—
376	#386	C₂²×C₁₃₉	1	4	yes	—
377	#385	C₂²×C₁₃₉	1	4	yes	—
378	#385	C₂²×C₁₃₉	1	4	yes	—
379	#380	C₂²×C₁₃₉	1	2	yes	—
380	#380	C₂²×C₁₃₉	1	2	yes	—
381	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
382	C₂×#41	—	2	8	no	—
383	C₂×#41	—	4	4	no	—
384	C₂×#41	—	4	4	no	—
385	C₂²×Q₈	—	4	2	no	—
386	C₂²×Q₈	—	4	2	no	—
387	C₂²×Q₈	D₄×C₁₃₉	1	8	yes	complemented
388	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
389	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
390	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
391	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
392	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
393	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
394	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
395	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
396	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
397	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
398	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
399	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
400	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
401	C₄⋊Q₈	—	2	8	no	—
402	C₄⋊Q₈	—	2	8	no	—
403	#124	—	2	8	no	—
404	#124	—	2	8	no	—
405	#123	—	2	16	no	—
406	#123	—	2	16	no	—
407	C₂²⋊Q₈	—	2	16	no	—
408	C₂²⋊Q₈	—	2	16	no	—
409	#121	—	4	4	no	—
410	#121	—	4	4	no	—
411	#117	—	2	8	no	—
412	C₂×C₄⋊C₄	—	4	2	no	—
413	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
424	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
437	C₂×C₄²	—	4	2	no	—
438	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
439	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
440	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
442	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
443	#95	C₂³×C₁₃₉	1	4	yes	—
444	#95	C₂³×C₁₃₉	1	4	yes	—
445	#95	C₂³×C₁₃₉	1	4	yes	—
446	#95	C₂³×C₁₃₉	1	4	yes	—
447	#95	C₂³×C₁₃₉	1	2	yes	—
448	#95	C₂³×C₁₃₉	1	4	yes	—
449	#95	C₂³×C₁₃₉	1	2	yes	—
450	#95	C₂³×C₁₃₉	1	4	yes	—
451	#95	C₂³×C₁₃₉	1	4	yes	—
452	#95	C₂³×C₁₃₉	1	4	yes	—
453	#95	C₂³×C₁₃₉	1	4	yes	—
454	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
455	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
456	#41	—	4	32	no	—
457	C₂×Q₈	—	2	4	no	—
458	C₂×Q₈	—	4	16	no	—
459	C₂×Q₈	—	4	1	no	—
460	C₂×Q₈	—	4	2	no	—
461	C₂×Q₈	—	4	1	no	—
462	C₂×Q₈	—	4	1	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	4	1	no	—
465	C₂×Q₈	—	4	2	no	—
466	C₂×Q₈	—	4	2	no	—
467	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
468	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
469	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
470	C₂×D₄	—	2	8	no	—
471	C₂×D₄	—	2	8	no	—
472	C₂×D₄	—	2	8	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	4	2	no	—
476	C₂×D₄	—	4	2	no	—
477	C₂×D₄	—	4	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	—	4	2	no	—
480	C₂×D₄	—	4	4	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	8	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	4	no	—
491	C₂²×C₄	—	4	4	no	—
492	C₂²×C₄	—	4	4	no	—
493	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
494	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
498	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
500	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
501	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
505	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
506	C₄⋊C₄	—	2	8	no	—
507	C₄⋊C₄	—	2	8	no	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	2	8	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	4	4	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	4	2	no	—
519	C₂²⋊C₄	—	2	8	no	—
520	C₂²⋊C₄	—	2	8	no	—
521	C₂²⋊C₄	—	2	8	no	—
522	C₂²⋊C₄	—	2	8	no	—
523	C₂²⋊C₄	—	2	8	no	—
524	C₂²⋊C₄	—	2	8	no	—
525	C₂²⋊C₄	—	4	4	no	—
526	C₂²⋊C₄	—	4	4	no	—
527	C₂²⋊C₄	—	4	4	no	—
528	C₂²⋊C₄	—	4	4	no	—
529	C₂²⋊C₄	—	4	4	no	—
530	C₄²	—	2	4	no	—
531	C₄²	—	2	4	no	—
532	C₄²	—	4	1	no	—
533	C₄²	—	4	2	no	—
534	C₄²	—	4	1	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
545	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
546	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
547	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
548	Q₈	—	4	4	no	—
549	Q₈	—	4	8	no	—
550	Q₈	—	4	4	no	—
551	Q₈	—	4	8	no	—
552	D₄	—	4	8	no	—
553	D₄	—	4	16	no	—
554	D₄	—	8	4	no	—
555	D₄	—	8	4	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	2	8	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	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	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	4	8	no	—
585	C₂×C₄	—	4	16	no	—
586	C₂×C₄	—	8	4	no	—
587	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
588	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
589	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
590	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
591	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	4	no	—
603	C₂²	#534×C₁₃₉	1	4	yes	—
604	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
605	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
606	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
607	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
608	C₂²	#585×C₁₃₉	1	2	yes	—
609	C₄	—	2	4	no	—
610	C₄	—	2	4	no	—
611	C₄	—	2	4	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	2	no	—
614	C₄	—	4	2	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	4	no	—
618	C₄	—	4	4	no	—
619	C₄	—	4	4	no	—
620	C₂	—	2	4	no	—
621	C₂	—	8	4	no	—
622	C₂	C₂×#534×C₁₃₉	1	1	yes	characteristic
623	C₂	#3497×C₁₃₉	1	2	yes	—
624	C₂	#3535×C₁₃₉	1	2	yes	—
625	C₂	#3544×C₁₃₉	1	1	yes	characteristic
626	C₂	#3545×C₁₃₉	1	1	yes	characteristic

	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. C₂×#536×C₁₃₉	C₂	semidirect
2. #2854×C₁₃₉	C₂	semidirect
3. #2734×C₁₃₉	C₂	semidirect
4. #2733×C₁₃₉	C₂	semidirect
5. #2732×C₁₃₉	C₂	semidirect
6. #2731×C₁₃₉	C₂	semidirect
7. #2730×C₁₃₉	C₂	semidirect
8. #2729×C₁₃₉	C₂	semidirect
9. #2728×C₁₃₉	C₂	semidirect
10. #2618×C₁₃₉	C₂	semidirect
11. #2498×C₁₃₉	C₂	semidirect
12. #2430×C₁₃₉	C₂	semidirect
13. C₂×#391×C₁₃₉	C₂	semidirect
73. C₂²×Q₈×C₁₃₉	D₄	semidirect
313. #37190	C₁₃₉	direct (N × H)
314. C₁₃₉	#37190	direct (N × H)
315. C₂×#536	C₂×C₁₃₉	semidirect
316. #2854	C₂×C₁₃₉	semidirect
317. #2734	C₂×C₁₃₉	semidirect
318. #2733	C₂×C₁₃₉	semidirect
319. #2732	C₂×C₁₃₉	semidirect
320. #2731	C₂×C₁₃₉	semidirect
321. #2730	C₂×C₁₃₉	semidirect
322. #2729	C₂×C₁₃₉	semidirect
323. #2728	C₂×C₁₃₉	semidirect
324. #2618	C₂×C₁₃₉	semidirect
325. #2498	C₂×C₁₃₉	semidirect
326. #2430	C₂×C₁₃₉	semidirect
327. C₂×#391	C₂×C₁₃₉	semidirect
387. C₂²×Q₈	D₄×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#536×C₁₃₉	2
#2854×C₁₃₉	2
#2734×C₁₃₉	2
#2733×C₁₃₉	2
#2732×C₁₃₉	2
#2731×C₁₃₉	2
#2730×C₁₃₉	2
#2729×C₁₃₉	2
#2728×C₁₃₉	2
#2618×C₁₃₉	2
#2498×C₁₃₉	2
#2430×C₁₃₉	2
C₂×#391×C₁₃₉	2
#37190	139

Subgroups — C139×#37190 #48031786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37190 #48031786