Subgroups — C₁₃₉×#25578 #48020174

Order 35584.

1226 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#489×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#463×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2540×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2000×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#1999×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#1988×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#1955×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#1875×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#1873×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#1762×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₁₃₉	C₂²	1	1	yes	characteristic
14	#555×C₁₃₉	—	2	4	no	—
15	#555×C₁₃₉	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×#124×C₁₃₉	—	2	2	no	—
18	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#121×C₁₃₉	—	2	1	no	—
21	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₁₃₉	—	2	1	no	—
26	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
27	#489×C₁₃₉	—	2	4	no	—
28	#463×C₁₃₉	—	2	4	no	—
29	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₁₃₉	C₂²	1	2	yes	—
31	C₂×#103×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#102×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#102×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₁₃₉	C₂²	1	2	yes	—
37	C₂×#97×C₁₃₉	C₂²	1	1	yes	characteristic
38	#399×C₁₃₉	—	2	1	no	—
39	#392×C₁₃₉	—	2	1	no	—
40	#390×C₁₃₉	—	2	2	no	—
41	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
42	#340×C₁₃₉	C₂²	1	2	yes	—
43	#340×C₁₃₉	C₂²	1	2	yes	—
44	#340×C₁₃₉	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃₉	—	2	1	no	—
46	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₃₉	—	2	2	no	—
48	C₂²×D₄×C₁₃₉	—	2	2	no	—
49	C₂²×D₄×C₁₃₉	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃₉	—	2	1	no	—
53	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
54	C₂×SD₁₆×C₁₃₉	—	2	2	no	—
55	C₂×SD₁₆×C₁₃₉	—	4	2	no	—
56	C₂×D₈×C₁₃₉	—	2	2	no	—
57	C₂×D₈×C₁₃₉	—	4	2	no	—
58	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₁₃₉	—	2	2	no	—
62	C₄⋊Q₈×C₁₃₉	D₄	1	4	yes	complemented
63	#124×C₁₃₉	—	2	16	no	—
64	#124×C₁₃₉	—	2	2	no	—
65	#124×C₁₃₉	—	2	2	no	—
66	C₂²⋊Q₈×C₁₃₉	—	2	4	no	—
67	C₂²⋊Q₈×C₁₃₉	—	4	2	no	—
68	#121×C₁₃₉	—	2	8	no	—
69	#121×C₁₃₉	—	2	4	no	—
70	#121×C₁₃₉	—	2	4	no	—
71	#121×C₁₃₉	—	2	4	no	—
72	#121×C₁₃₉	—	4	2	no	—
73	C₄×D₄×C₁₃₉	—	2	2	no	—
74	C₄×D₄×C₁₃₉	—	2	2	no	—
75	C₄×D₄×C₁₃₉	—	2	2	no	—
76	C₄×D₄×C₁₃₉	D₄	1	4	yes	complemented
77	#117×C₁₃₉	—	2	8	no	—
78	#117×C₁₃₉	—	2	4	no	—
79	#117×C₁₃₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
82	C₂×C₄⋊C₄×C₁₃₉	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₃₉	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	2	yes	—
94	C₂×C₄²×C₁₃₉	—	2	2	no	—
95	C₂×C₄²×C₁₃₉	—	2	1	no	—
96	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₁₃₉	—	2	2	no	—
98	#103×C₁₃₉	—	2	2	no	—
99	#103×C₁₃₉	—	2	4	no	—
100	#102×C₁₃₉	—	2	2	no	—
101	#102×C₁₃₉	—	2	4	no	—
102	#102×C₁₃₉	—	2	4	no	—
103	C₂²⋊C₈×C₁₃₉	—	4	2	no	—
104	C₂²⋊C₈×C₁₃₉	—	4	2	no	—
105	#97×C₁₃₉	—	2	2	no	—
106	#95×C₁₃₉	—	2	1	no	—
107	C₂⁴×C₁₃₉	—	2	1	no	—
108	C₂⁴×C₁₃₉	—	2	1	no	—
109	C₂⁴×C₁₃₉	C₂×D₄	1	2	yes	—
110	C₂×Q₈×C₁₃₉	—	2	4	no	—
111	C₂×Q₈×C₁₃₉	—	2	1	no	—
112	C₂×Q₈×C₁₃₉	—	2	1	no	—
113	C₂×Q₈×C₁₃₉	—	2	2	no	—
114	C₂×Q₈×C₁₃₉	—	2	2	no	—
115	C₂×Q₈×C₁₃₉	—	8	1	no	—
116	C₂×Q₈×C₁₃₉	—	8	1	no	—
117	C₂×D₄×C₁₃₉	—	2	8	no	—
118	C₂×D₄×C₁₃₉	—	2	2	no	—
119	C₂×D₄×C₁₃₉	—	2	1	no	—
120	C₂×D₄×C₁₃₉	—	2	1	no	—
121	C₂×D₄×C₁₃₉	—	2	1	no	—
122	C₂×D₄×C₁₃₉	—	2	2	no	—
123	C₂×D₄×C₁₃₉	—	2	2	no	—
124	C₂×D₄×C₁₃₉	—	2	2	no	—
125	C₂×D₄×C₁₃₉	—	2	2	no	—
126	C₂×D₄×C₁₃₉	—	4	2	no	—
127	C₂×D₄×C₁₃₉	—	4	4	no	—
128	C₂×D₄×C₁₃₉	—	4	4	no	—
129	C₂×D₄×C₁₃₉	—	8	2	no	—
130	C₂×D₄×C₁₃₉	—	8	2	no	—
131	C₂×D₄×C₁₃₉	—	8	2	no	—
132	C₂×D₄×C₁₃₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃₉	—	2	2	no	—
134	C₂²×C₄×C₁₃₉	—	2	1	no	—
135	C₂²×C₄×C₁₃₉	—	2	2	no	—
136	C₂²×C₄×C₁₃₉	—	2	4	no	—
137	C₂²×C₄×C₁₃₉	—	2	2	no	—
138	C₂²×C₄×C₁₃₉	—	2	2	no	—
139	C₂²×C₄×C₁₃₉	—	2	2	no	—
140	C₂²×C₄×C₁₃₉	—	2	2	no	—
141	C₂²×C₄×C₁₃₉	—	2	2	no	—
142	C₂²×C₄×C₁₃₉	—	2	2	no	—
143	C₂²×C₄×C₁₃₉	—	2	1	no	—
144	C₂²×C₄×C₁₃₉	—	4	4	no	—
145	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
149	SD₁₆×C₁₃₉	—	4	4	no	—
150	D₈×C₁₃₉	—	4	4	no	—
151	C₂×C₈×C₁₃₉	—	2	2	no	—
152	C₂×C₈×C₁₃₉	—	2	1	no	—
153	C₂×C₈×C₁₃₉	—	2	1	no	—
154	C₂×C₈×C₁₃₉	—	2	2	no	—
155	C₂×C₈×C₁₃₉	—	2	2	no	—
156	C₂×C₈×C₁₃₉	—	2	2	no	—
157	C₂×C₈×C₁₃₉	—	2	2	no	—
158	C₄⋊C₄×C₁₃₉	—	2	4	no	—
159	C₄⋊C₄×C₁₃₉	—	2	2	no	—
160	C₄⋊C₄×C₁₃₉	—	2	1	no	—
161	C₄⋊C₄×C₁₃₉	—	2	2	no	—
162	C₄⋊C₄×C₁₃₉	—	2	2	no	—
163	C₄⋊C₄×C₁₃₉	—	4	4	no	—
164	C₄⋊C₄×C₁₃₉	C₂×D₄	1	2	yes	—
165	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
166	C₄⋊C₄×C₁₃₉	#41	1	4	yes	—
167	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
168	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
169	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
170	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
172	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
173	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
174	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
175	C₄²×C₁₃₉	—	2	8	no	—
176	C₄²×C₁₃₉	—	8	1	no	—
177	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
178	C₄²×C₁₃₉	C₂×D₄	1	2	yes	—
179	C₂³×C₁₃₉	—	2	2	no	—
180	C₂³×C₁₃₉	—	2	2	no	—
181	C₂³×C₁₃₉	—	2	2	no	—
182	C₂³×C₁₃₉	—	2	2	no	—
183	C₂³×C₁₃₉	—	2	2	no	—
184	C₂³×C₁₃₉	—	2	2	no	—
185	C₂³×C₁₃₉	—	2	2	no	—
186	C₂³×C₁₃₉	—	2	2	no	—
187	C₂³×C₁₃₉	—	4	2	no	—
188	C₂³×C₁₃₉	—	4	2	no	—
189	C₂³×C₁₃₉	—	4	1	no	—
190	C₂³×C₁₃₉	—	4	1	no	—
191	C₂³×C₁₃₉	—	4	1	no	—
192	C₂³×C₁₃₉	—	4	2	no	—
193	C₂³×C₁₃₉	—	4	2	no	—
194	C₂³×C₁₃₉	—	4	1	no	—
195	C₂³×C₁₃₉	—	4	1	no	—
196	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₁₃₉	—	4	1	no	—
198	Q₈×C₁₃₉	—	4	1	no	—
199	Q₈×C₁₃₉	—	4	2	no	—
200	Q₈×C₁₃₉	—	8	4	no	—
201	D₄×C₁₃₉	—	2	2	no	—
202	D₄×C₁₃₉	—	2	2	no	—
203	D₄×C₁₃₉	—	4	4	no	—
204	D₄×C₁₃₉	—	4	1	no	—
205	D₄×C₁₃₉	—	4	1	no	—
206	D₄×C₁₃₉	—	4	2	no	—
207	D₄×C₁₃₉	—	4	2	no	—
208	D₄×C₁₃₉	—	8	8	no	—
209	D₄×C₁₃₉	—	8	8	no	—
210	C₂×C₄×C₁₃₉	—	2	2	no	—
211	C₂×C₄×C₁₃₉	—	2	1	no	—
212	C₂×C₄×C₁₃₉	—	2	1	no	—
213	C₂×C₄×C₁₃₉	—	2	2	no	—
214	C₂×C₄×C₁₃₉	—	2	2	no	—
215	C₂×C₄×C₁₃₉	—	2	4	no	—
216	C₂×C₄×C₁₃₉	—	2	4	no	—
217	C₂×C₄×C₁₃₉	—	2	2	no	—
218	C₂×C₄×C₁₃₉	—	2	2	no	—
219	C₂×C₄×C₁₃₉	—	4	8	no	—
220	C₂×C₄×C₁₃₉	—	4	2	no	—
221	C₂×C₄×C₁₃₉	—	4	2	no	—
222	C₂×C₄×C₁₃₉	—	4	2	no	—
223	C₂×C₄×C₁₃₉	—	4	2	no	—
224	C₂×C₄×C₁₃₉	—	4	2	no	—
225	C₂×C₄×C₁₃₉	—	4	2	no	—
226	C₂×C₄×C₁₃₉	—	4	2	no	—
227	C₂×C₄×C₁₃₉	—	4	2	no	—
228	C₂×C₄×C₁₃₉	—	4	2	no	—
229	C₂×C₄×C₁₃₉	—	4	1	no	—
230	C₂×C₄×C₁₃₉	—	4	2	no	—
231	C₂×C₄×C₁₃₉	#120	1	2	yes	—
232	C₂×C₄×C₁₃₉	#120	1	2	yes	—
233	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
236	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
237	C₈×C₁₃₉	—	4	1	no	—
238	C₈×C₁₃₉	—	4	1	no	—
239	C₈×C₁₃₉	—	4	2	no	—
240	C₂²×C₁₃₉	—	4	2	no	—
241	C₂²×C₁₃₉	—	4	2	no	—
242	C₂²×C₁₃₉	—	4	2	no	—
243	C₂²×C₁₃₉	—	4	2	no	—
244	C₂²×C₁₃₉	—	4	2	no	—
245	C₂²×C₁₃₉	—	4	2	no	—
246	C₂²×C₁₃₉	—	4	2	no	—
247	C₂²×C₁₃₉	—	4	2	no	—
248	C₂²×C₁₃₉	—	4	2	no	—
249	C₂²×C₁₃₉	—	4	2	no	—
250	C₂²×C₁₃₉	—	8	2	no	—
251	C₂²×C₁₃₉	—	8	2	no	—
252	C₂²×C₁₃₉	—	8	1	no	—
253	C₂²×C₁₃₉	—	8	1	no	—
254	C₂²×C₁₃₉	—	8	1	no	—
255	C₂²×C₁₃₉	—	8	2	no	—
256	C₂²×C₁₃₉	—	8	2	no	—
257	C₂²×C₁₃₉	C₂×#120	1	1	yes	characteristic
258	C₂²×C₁₃₉	#546	1	2	yes	—
259	C₂²×C₁₃₉	#575	1	2	yes	—
260	C₂²×C₁₃₉	#576	1	1	yes	characteristic
261	C₂²×C₁₃₉	#577	1	1	yes	characteristic
262	C₄×C₁₃₉	—	2	2	no	—
263	C₄×C₁₃₉	—	2	2	no	—
264	C₄×C₁₃₉	—	4	2	no	—
265	C₄×C₁₃₉	—	4	2	no	—
266	C₄×C₁₃₉	—	4	4	no	—
267	C₄×C₁₃₉	—	4	4	no	—
268	C₄×C₁₃₉	—	8	1	no	—
269	C₄×C₁₃₉	#532	1	1	yes	characteristic
270	C₄×C₁₃₉	#535	1	1	yes	characteristic
271	C₄×C₁₃₉	#550	1	2	yes	—
272	C₂×C₁₃₉	—	8	2	no	—
273	C₂×C₁₃₉	—	8	2	no	—
274	C₂×C₁₃₉	—	16	1	no	—
275	C₂×C₁₃₉	#2431	1	1	yes	characteristic
276	C₂×C₁₃₉	#3005	1	1	yes	characteristic
277	C₂×C₁₃₉	#3012	1	1	yes	characteristic
278	C₂×C₁₃₉	#3319	1	2	yes	—
279	C₂×C₁₃₉	#3321	1	2	yes	—
280	#25578	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₁₃₉	#25578	1	1	yes	characteristic, direct product factor, Sylow
282	C₂×#555	C₂×C₁₃₉	1	1	yes	characteristic, complemented
283	C₂×#489	C₂×C₁₃₉	1	1	yes	characteristic, complemented
284	C₂×#463	C₂×C₁₃₉	1	1	yes	characteristic, complemented
285	#2540	C₂×C₁₃₉	1	1	yes	characteristic, complemented
286	#2000	C₂×C₁₃₉	1	2	yes	complemented
287	#1999	C₂×C₁₃₉	1	2	yes	complemented
288	#1988	C₂×C₁₃₉	1	1	yes	characteristic, complemented
289	#1955	C₂×C₁₃₉	1	1	yes	characteristic, complemented
290	#1875	C₂×C₁₃₉	1	2	yes	complemented
291	#1873	C₂×C₁₃₉	1	2	yes	complemented
292	#1762	C₂×C₁₃₉	1	1	yes	characteristic, complemented
293	C₂²×SD₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
294	C₂²×D₈	C₂²×C₁₃₉	1	1	yes	characteristic
295	#555	—	2	4	no	—
296	#555	—	2	4	no	—
297	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
298	C₂×#124	—	2	2	no	—
299	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
300	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
301	C₂×#121	—	2	1	no	—
302	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
303	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
304	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
305	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
306	C₂×#117	—	2	1	no	—
307	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
308	#489	—	2	4	no	—
309	#463	—	2	4	no	—
310	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	1	yes	characteristic
311	C₂×#103	C₂²×C₁₃₉	1	2	yes	—
312	C₂×#103	C₂²×C₁₃₉	1	1	yes	characteristic
313	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
314	C₂×#102	C₂²×C₁₃₉	1	1	yes	characteristic
315	C₂×#102	C₂²×C₁₃₉	1	2	yes	—
316	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
317	C₂×C₂²⋊C₈	C₂²×C₁₃₉	1	2	yes	—
318	C₂×#97	C₂²×C₁₃₉	1	1	yes	characteristic
319	#399	—	2	1	no	—
320	#392	—	2	1	no	—
321	#390	—	2	2	no	—
322	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
323	#340	C₂²×C₁₃₉	1	2	yes	—
324	#340	C₂²×C₁₃₉	1	2	yes	—
325	#340	C₂²×C₁₃₉	1	2	yes	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	D₄×C₁₃₉	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
332	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
335	C₂×SD₁₆	—	2	2	no	—
336	C₂×SD₁₆	—	4	2	no	—
337	C₂×D₈	—	2	2	no	—
338	C₂×D₈	—	4	2	no	—
339	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₁₃₉	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	D₄×C₁₃₉	1	4	yes	complemented
344	#124	—	2	16	no	—
345	#124	—	2	2	no	—
346	#124	—	2	2	no	—
347	C₂²⋊Q₈	—	2	4	no	—
348	C₂²⋊Q₈	—	4	2	no	—
349	#121	—	2	8	no	—
350	#121	—	2	4	no	—
351	#121	—	2	4	no	—
352	#121	—	2	4	no	—
353	#121	—	4	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	D₄×C₁₃₉	1	4	yes	complemented
358	#117	—	2	8	no	—
359	#117	—	2	4	no	—
360	#117	—	2	4	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	D₄×C₁₃₉	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	2	yes	—
375	C₂×C₄²	—	2	2	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
378	C₄⋊C₈	—	2	2	no	—
379	#103	—	2	2	no	—
380	#103	—	2	4	no	—
381	#102	—	2	2	no	—
382	#102	—	2	4	no	—
383	#102	—	2	4	no	—
384	C₂²⋊C₈	—	4	2	no	—
385	C₂²⋊C₈	—	4	2	no	—
386	#97	—	2	2	no	—
387	#95	—	2	1	no	—
388	C₂⁴	—	2	1	no	—
389	C₂⁴	—	2	1	no	—
390	C₂⁴	C₂×D₄×C₁₃₉	1	2	yes	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	8	1	no	—
397	C₂×Q₈	—	8	1	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	8	2	no	—
411	C₂×D₄	—	8	2	no	—
412	C₂×D₄	—	8	2	no	—
413	C₂×D₄	C₂×D₄×C₁₃₉	1	2	yes	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
430	SD₁₆	—	4	4	no	—
431	D₈	—	4	4	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	4	4	no	—
445	C₄⋊C₄	C₂×D₄×C₁₃₉	1	2	yes	—
446	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
447	C₄⋊C₄	#41×C₁₃₉	1	4	yes	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	4	4	no	—
453	C₂²⋊C₄	—	4	4	no	—
454	C₂²⋊C₄	—	4	2	no	—
455	C₂²⋊C₄	—	4	2	no	—
456	C₄²	—	2	8	no	—
457	C₄²	—	8	1	no	—
458	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
459	C₄²	C₂×D₄×C₁₃₉	1	2	yes	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
478	Q₈	—	4	1	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	8	4	no	—
482	D₄	—	2	2	no	—
483	D₄	—	2	2	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	1	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	8	8	no	—
490	D₄	—	8	8	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	#120×C₁₃₉	1	2	yes	—
513	C₂×C₄	#120×C₁₃₉	1	2	yes	—
514	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
517	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	8	2	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	C₂×#120×C₁₃₉	1	1	yes	characteristic
539	C₂²	#546×C₁₃₉	1	2	yes	—
540	C₂²	#575×C₁₃₉	1	2	yes	—
541	C₂²	#576×C₁₃₉	1	1	yes	characteristic
542	C₂²	#577×C₁₃₉	1	1	yes	characteristic
543	C₄	—	2	2	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	4	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	4	no	—
549	C₄	—	8	1	no	—
550	C₄	#532×C₁₃₉	1	1	yes	characteristic
551	C₄	#535×C₁₃₉	1	1	yes	characteristic
552	C₄	#550×C₁₃₉	1	2	yes	—
553	C₂	—	8	2	no	—
554	C₂	—	8	2	no	—
555	C₂	—	16	1	no	—
556	C₂	#2431×C₁₃₉	1	1	yes	characteristic
557	C₂	#3005×C₁₃₉	1	1	yes	characteristic
558	C₂	#3012×C₁₃₉	1	1	yes	characteristic
559	C₂	#3319×C₁₃₉	1	2	yes	—
560	C₂	#3321×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×C₄×D₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#555×C₁₃₉	C₂	semidirect
2. C₂×#489×C₁₃₉	C₂	semidirect
3. C₂×#463×C₁₃₉	C₂	semidirect
4. #2540×C₁₃₉	C₂	semidirect
5. #2000×C₁₃₉	C₂	semidirect
6. #1999×C₁₃₉	C₂	semidirect
7. #1988×C₁₃₉	C₂	semidirect
8. #1955×C₁₃₉	C₂	semidirect
9. #1875×C₁₃₉	C₂	semidirect
10. #1873×C₁₃₉	C₂	semidirect
11. #1762×C₁₃₉	C₂	semidirect
62. C₄⋊Q₈×C₁₃₉	D₄	semidirect
76. C₄×D₄×C₁₃₉	D₄	semidirect
280. #25578	C₁₃₉	direct (N × H)
281. C₁₃₉	#25578	direct (N × H)
282. C₂×#555	C₂×C₁₃₉	semidirect
283. C₂×#489	C₂×C₁₃₉	semidirect
284. C₂×#463	C₂×C₁₃₉	semidirect
285. #2540	C₂×C₁₃₉	semidirect
286. #2000	C₂×C₁₃₉	semidirect
287. #1999	C₂×C₁₃₉	semidirect
288. #1988	C₂×C₁₃₉	semidirect
289. #1955	C₂×C₁₃₉	semidirect
290. #1875	C₂×C₁₃₉	semidirect
291. #1873	C₂×C₁₃₉	semidirect
292. #1762	C₂×C₁₃₉	semidirect
343. C₄⋊Q₈	D₄×C₁₃₉	semidirect
357. C₄×D₄	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×#555×C₁₃₉	2
C₂×#489×C₁₃₉	2
C₂×#463×C₁₃₉	2
#2540×C₁₃₉	2
#2000×C₁₃₉	2
#1999×C₁₃₉	2
#1988×C₁₃₉	2
#1955×C₁₃₉	2
#1875×C₁₃₉	2
#1873×C₁₃₉	2
#1762×C₁₃₉	2
#25578	139

Subgroups — C139×#25578 #48020174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#25578 #48020174