Subgroups — C₁₃₉×#23614 #48018210

Order 35584.

1214 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#424×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#418×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#102×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#2316×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2309×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	#2067×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2065×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#1735×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	#428×C₁₃₉	—	2	4	no	—
18	C₂×#107×C₁₃₉	C₂²	1	2	yes	complemented
19	C₂×#106×C₁₃₉	C₂²	1	2	yes	complemented
20	#424×C₁₃₉	—	2	4	no	—
21	C₂×C₄⋊C₈×C₁₃₉	C₂²	1	4	yes	complemented
22	#418×C₁₃₉	—	2	4	no	—
23	C₂×#102×C₁₃₉	—	2	4	no	—
24	C₂×#102×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#102×C₁₃₉	C₂²	1	4	yes	—
26	#390×C₁₃₉	—	2	2	no	—
27	#390×C₁₃₉	C₂²	1	2	yes	—
28	#390×C₁₃₉	C₂²	1	2	yes	—
29	#389×C₁₃₉	—	2	2	no	—
30	#389×C₁₃₉	C₂²	1	4	yes	complemented
31	#380×C₁₃₉	—	2	2	no	—
32	#379×C₁₃₉	—	2	2	no	—
33	#340×C₁₃₉	C₂²	1	2	yes	complemented
34	#340×C₁₃₉	C₂²	1	2	yes	complemented
35	C₂⁵×C₁₃₉	—	2	1	no	—
36	C₂²×D₄×C₁₃₉	—	2	2	no	—
37	C₂²×D₄×C₁₃₉	—	2	2	no	—
38	C₂²×D₄×C₁₃₉	—	2	1	no	—
39	C₂²×D₄×C₁₃₉	—	2	2	no	—
40	C₂²×D₄×C₁₃₉	—	2	2	no	—
41	C₂²×D₄×C₁₃₉	—	2	2	no	—
42	C₂²×D₄×C₁₃₉	Q₈	1	4	yes	—
43	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃₉	—	2	1	no	—
45	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₃₉	—	2	2	no	—
47	C₂×M₁₆×C₁₃₉	—	2	2	no	—
48	C₂×M₁₆×C₁₃₉	D₄	1	4	yes	—
49	C₂²×C₈×C₁₃₉	—	2	2	no	—
50	C₂²×C₈×C₁₃₉	—	2	2	no	—
51	C₂²×C₈×C₁₃₉	—	2	2	no	—
52	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃₉	C₂³	1	2	yes	—
54	#117×C₁₃₉	—	2	2	no	—
55	#117×C₁₃₉	—	2	2	no	—
56	#117×C₁₃₉	—	2	2	no	—
57	#117×C₁₃₉	—	2	2	no	—
58	#117×C₁₃₉	—	2	2	no	—
59	#117×C₁₃₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₃₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₃₉	D₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₃₉	D₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₃₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₁₃₉	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₁₃₉	D₄	1	2	yes	—
74	C₂×C₄²×C₁₃₉	—	2	1	no	—
75	C₂×C₄²×C₁₃₉	—	2	1	no	—
76	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
77	#107×C₁₃₉	—	2	4	no	—
78	#106×C₁₃₉	—	2	4	no	—
79	C₄⋊C₈×C₁₃₉	—	2	8	no	—
80	#102×C₁₃₉	—	2	8	no	—
81	#102×C₁₃₉	—	2	8	no	—
82	#95×C₁₃₉	—	2	4	no	—
83	C₂⁴×C₁₃₉	—	2	2	no	—
84	C₂⁴×C₁₃₉	—	2	4	no	—
85	C₂⁴×C₁₃₉	—	4	2	no	—
86	C₂⁴×C₁₃₉	—	4	2	no	—
87	C₂⁴×C₁₃₉	—	8	2	no	—
88	C₂⁴×C₁₃₉	—	8	2	no	—
89	C₂⁴×C₁₃₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₁₃₉	—	2	8	no	—
91	C₂×D₄×C₁₃₉	—	2	8	no	—
92	C₂×D₄×C₁₃₉	—	2	4	no	—
93	C₂×D₄×C₁₃₉	—	2	2	no	—
94	C₂×D₄×C₁₃₉	—	2	2	no	—
95	C₂×D₄×C₁₃₉	—	2	2	no	—
96	C₂×D₄×C₁₃₉	—	2	2	no	—
97	C₂×D₄×C₁₃₉	—	2	2	no	—
98	C₂×D₄×C₁₃₉	—	4	4	no	—
99	C₂×D₄×C₁₃₉	—	4	2	no	—
100	C₂×D₄×C₁₃₉	—	4	2	no	—
101	C₂×D₄×C₁₃₉	—	4	4	no	—
102	C₂×D₄×C₁₃₉	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₁₃₉	—	2	2	no	—
104	C₂²×C₄×C₁₃₉	—	2	4	no	—
105	C₂²×C₄×C₁₃₉	—	2	2	no	—
106	C₂²×C₄×C₁₃₉	—	2	1	no	—
107	C₂²×C₄×C₁₃₉	—	2	1	no	—
108	C₂²×C₄×C₁₃₉	—	8	2	no	—
109	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
114	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
115	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
116	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
117	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
118	M₁₆×C₁₃₉	—	2	8	no	—
119	C₂×C₈×C₁₃₉	—	2	2	no	—
120	C₂×C₈×C₁₃₉	—	2	2	no	—
121	C₂×C₈×C₁₃₉	—	2	2	no	—
122	C₂×C₈×C₁₃₉	—	2	2	no	—
123	C₂×C₈×C₁₃₉	—	2	2	no	—
124	C₂×C₈×C₁₃₉	—	4	4	no	—
125	C₂×C₈×C₁₃₉	C₂×D₄	1	4	yes	—
126	C₄⋊C₄×C₁₃₉	—	2	4	no	—
127	C₄⋊C₄×C₁₃₉	—	2	4	no	—
128	C₄⋊C₄×C₁₃₉	—	2	2	no	—
129	C₄⋊C₄×C₁₃₉	—	2	2	no	—
130	C₄⋊C₄×C₁₃₉	—	2	1	no	—
131	C₄⋊C₄×C₁₃₉	—	2	1	no	—
132	C₄⋊C₄×C₁₃₉	—	2	2	no	—
133	C₄⋊C₄×C₁₃₉	—	2	1	no	—
134	C₄⋊C₄×C₁₃₉	—	2	1	no	—
135	C₄⋊C₄×C₁₃₉	—	8	4	no	—
136	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
137	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
138	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
139	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
140	C₂²⋊C₄×C₁₃₉	—	8	4	no	—
141	C₂²⋊C₄×C₁₃₉	—	8	4	no	—
142	C₄²×C₁₃₉	—	2	2	no	—
143	C₄²×C₁₃₉	—	2	2	no	—
144	C₄²×C₁₃₉	—	4	2	no	—
145	C₄²×C₁₃₉	—	4	2	no	—
146	C₂³×C₁₃₉	—	2	2	no	—
147	C₂³×C₁₃₉	—	2	2	no	—
148	C₂³×C₁₃₉	—	2	4	no	—
149	C₂³×C₁₃₉	—	4	2	no	—
150	C₂³×C₁₃₉	—	4	2	no	—
151	C₂³×C₁₃₉	—	4	4	no	—
152	C₂³×C₁₃₉	—	4	4	no	—
153	C₂³×C₁₃₉	—	4	8	no	—
154	C₂³×C₁₃₉	—	8	8	no	—
155	C₂³×C₁₃₉	—	8	4	no	—
156	C₂³×C₁₃₉	—	8	4	no	—
157	C₂³×C₁₃₉	—	8	8	no	—
158	C₂³×C₁₃₉	#121	1	2	yes	—
159	C₂³×C₁₃₉	#121	1	2	yes	—
160	C₂³×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
161	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
162	D₄×C₁₃₉	—	2	4	no	—
163	D₄×C₁₃₉	—	2	4	no	—
164	D₄×C₁₃₉	—	4	2	no	—
165	D₄×C₁₃₉	—	4	2	no	—
166	D₄×C₁₃₉	—	4	8	no	—
167	C₂×C₄×C₁₃₉	—	2	4	no	—
168	C₂×C₄×C₁₃₉	—	2	4	no	—
169	C₂×C₄×C₁₃₉	—	2	4	no	—
170	C₂×C₄×C₁₃₉	—	2	4	no	—
171	C₂×C₄×C₁₃₉	—	4	4	no	—
172	C₂×C₄×C₁₃₉	—	4	1	no	—
173	C₂×C₄×C₁₃₉	—	4	1	no	—
174	C₂×C₄×C₁₃₉	—	4	2	no	—
175	C₂×C₄×C₁₃₉	—	4	2	no	—
176	C₂×C₄×C₁₃₉	—	4	2	no	—
177	C₂×C₄×C₁₃₉	—	4	2	no	—
178	C₂×C₄×C₁₃₉	—	4	2	no	—
179	C₂×C₄×C₁₃₉	—	8	4	no	—
180	C₂×C₄×C₁₃₉	#121	1	4	yes	—
181	C₂×C₄×C₁₃₉	#121	1	2	yes	—
182	C₂×C₄×C₁₃₉	#121	1	2	yes	—
183	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
184	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
185	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	2	yes	—
186	C₂×C₄×C₁₃₉	#126	1	4	yes	—
187	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
193	C₈×C₁₃₉	—	2	4	no	—
194	C₈×C₁₃₉	—	4	2	no	—
195	C₂²×C₁₃₉	—	2	4	no	—
196	C₂²×C₁₃₉	—	2	2	no	—
197	C₂²×C₁₃₉	—	2	2	no	—
198	C₂²×C₁₃₉	—	2	4	no	—
199	C₂²×C₁₃₉	—	4	8	no	—
200	C₂²×C₁₃₉	—	4	4	no	—
201	C₂²×C₁₃₉	—	8	16	no	—
202	C₂²×C₁₃₉	—	8	2	no	—
203	C₂²×C₁₃₉	—	8	2	no	—
204	C₂²×C₁₃₉	—	8	4	no	—
205	C₂²×C₁₃₉	#396	1	4	yes	—
206	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
207	C₂²×C₁₃₉	C₂×#121	1	1	yes	characteristic
208	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
209	C₂²×C₁₃₉	#576	1	2	yes	—
210	C₂²×C₁₃₉	#577	1	2	yes	—
211	C₄×C₁₃₉	—	4	4	no	—
212	C₄×C₁₃₉	—	4	4	no	—
213	C₄×C₁₃₉	—	8	1	no	—
214	C₄×C₁₃₉	—	8	1	no	—
215	C₄×C₁₃₉	—	8	2	no	—
216	C₄×C₁₃₉	#396	1	4	yes	—
217	C₄×C₁₃₉	C₂×#121	1	1	yes	characteristic
218	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
219	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
220	C₄×C₁₃₉	C₂×#126	1	1	yes	characteristic
221	C₂×C₁₃₉	—	2	4	no	—
222	C₂×C₁₃₉	—	8	4	no	—
223	C₂×C₁₃₉	C₂×#396	1	1	yes	characteristic
224	C₂×C₁₃₉	#3041	1	1	yes	characteristic
225	C₂×C₁₃₉	#3043	1	1	yes	characteristic
226	C₂×C₁₃₉	#3062	1	2	yes	—
227	C₂×C₁₃₉	#3081	1	2	yes	—
228	#23614	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₁₃₉	#23614	1	1	yes	characteristic, direct product factor, Sylow
230	C₂×#428	C₂×C₁₃₉	1	1	yes	characteristic, complemented
231	C₂×#424	C₂×C₁₃₉	1	1	yes	characteristic, complemented
232	C₂×#418	C₂×C₁₃₉	1	1	yes	characteristic
233	C₂²×#102	C₂×C₁₃₉	1	1	yes	characteristic
234	#2316	C₂×C₁₃₉	1	1	yes	characteristic, complemented
235	#2309	C₂×C₁₃₉	1	1	yes	characteristic
236	#2067	C₂×C₁₃₉	1	4	yes	complemented
237	#2065	C₂×C₁₃₉	1	4	yes	complemented
238	#1735	C₂×C₁₃₉	1	1	yes	characteristic, complemented
239	C₂³×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
240	C₂²×M₁₆	C₂²×C₁₃₉	1	1	yes	characteristic
241	C₂³×C₈	C₂²×C₁₃₉	1	1	yes	characteristic
242	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
243	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
244	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
246	#428	—	2	4	no	—
247	C₂×#107	C₂²×C₁₃₉	1	2	yes	complemented
248	C₂×#106	C₂²×C₁₃₉	1	2	yes	complemented
249	#424	—	2	4	no	—
250	C₂×C₄⋊C₈	C₂²×C₁₃₉	1	4	yes	complemented
251	#418	—	2	4	no	—
252	C₂×#102	—	2	4	no	—
253	C₂×#102	C₂²×C₁₃₉	1	4	yes	—
254	C₂×#102	C₂²×C₁₃₉	1	4	yes	—
255	#390	—	2	2	no	—
256	#390	C₂²×C₁₃₉	1	2	yes	—
257	#390	C₂²×C₁₃₉	1	2	yes	—
258	#389	—	2	2	no	—
259	#389	C₂²×C₁₃₉	1	4	yes	complemented
260	#380	—	2	2	no	—
261	#379	—	2	2	no	—
262	#340	C₂²×C₁₃₉	1	2	yes	complemented
263	#340	C₂²×C₁₃₉	1	2	yes	complemented
264	C₂⁵	—	2	1	no	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	Q₈×C₁₃₉	1	4	yes	—
272	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	D₄×C₁₃₉	1	4	yes	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₃₉	1	2	yes	—
283	#117	—	2	2	no	—
284	#117	—	2	2	no	—
285	#117	—	2	2	no	—
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	#117	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	D₄×C₁₃₉	1	2	yes	—
293	C₂×C₄⋊C₄	D₄×C₁₃₉	1	4	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	4	no	—
301	C₂×C₂²⋊C₄	—	2	4	no	—
302	C₂×C₂²⋊C₄	D₄×C₁₃₉	1	2	yes	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
306	#107	—	2	4	no	—
307	#106	—	2	4	no	—
308	C₄⋊C₈	—	2	8	no	—
309	#102	—	2	8	no	—
310	#102	—	2	8	no	—
311	#95	—	2	4	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	2	4	no	—
314	C₂⁴	—	4	2	no	—
315	C₂⁴	—	4	2	no	—
316	C₂⁴	—	8	2	no	—
317	C₂⁴	—	8	2	no	—
318	C₂⁴	C₂×D₄×C₁₃₉	1	1	yes	characteristic
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	C₂×Q₈×C₁₃₉	1	4	yes	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
342	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
343	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
344	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
345	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
347	M₁₆	—	2	8	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	4	no	—
354	C₂×C₈	C₂×D₄×C₁₃₉	1	4	yes	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	8	4	no	—
365	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	8	4	no	—
370	C₂²⋊C₄	—	8	4	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	4	2	no	—
374	C₄²	—	4	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	4	8	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	8	8	no	—
384	C₂³	—	8	4	no	—
385	C₂³	—	8	4	no	—
386	C₂³	—	8	8	no	—
387	C₂³	#121×C₁₃₉	1	2	yes	—
388	C₂³	#121×C₁₃₉	1	2	yes	—
389	C₂³	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
390	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
391	D₄	—	2	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	4	8	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	4	no	—
409	C₂×C₄	#121×C₁₃₉	1	2	yes	—
410	C₂×C₄	#121×C₁₃₉	1	2	yes	—
411	C₂×C₄	#121×C₁₃₉	1	4	yes	—
412	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	2	yes	—
413	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
414	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
415	C₂×C₄	#126×C₁₃₉	1	4	yes	—
416	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
418	C₂×C₄	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₁₃₉	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	4	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	8	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	8	16	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	4	no	—
434	C₂²	#396×C₁₃₉	1	4	yes	—
435	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
436	C₂²	C₂×#121×C₁₃₉	1	1	yes	characteristic
437	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
438	C₂²	#576×C₁₃₉	1	2	yes	—
439	C₂²	#577×C₁₃₉	1	2	yes	—
440	C₄	—	4	4	no	—
441	C₄	—	4	4	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	8	2	no	—
445	C₄	#396×C₁₃₉	1	4	yes	—
446	C₄	C₂×#121×C₁₃₉	1	1	yes	characteristic
447	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
448	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
449	C₄	C₂×#126×C₁₃₉	1	1	yes	characteristic
450	C₂	—	2	4	no	—
451	C₂	—	8	4	no	—
452	C₂	C₂×#396×C₁₃₉	1	1	yes	characteristic
453	C₂	#3041×C₁₃₉	1	1	yes	characteristic
454	C₂	#3043×C₁₃₉	1	1	yes	characteristic
455	C₂	#3062×C₁₃₉	1	2	yes	—
456	C₂	#3081×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₉
prime radical	C₂³×D₄×C₁₃₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₉ ◁ C₂×#117×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#428×C₁₃₉	C₂	semidirect
2. C₂×#424×C₁₃₉	C₂	semidirect
5. #2316×C₁₃₉	C₂	semidirect
7. #2067×C₁₃₉	C₂	semidirect
8. #2065×C₁₃₉	C₂	semidirect
9. #1735×C₁₃₉	C₂	semidirect
18. C₂×#107×C₁₃₉	C₂²	semidirect
19. C₂×#106×C₁₃₉	C₂²	semidirect
21. C₂×C₄⋊C₈×C₁₃₉	C₂²	semidirect
30. #389×C₁₃₉	C₂²	semidirect
33. #340×C₁₃₉	C₂²	semidirect
34. #340×C₁₃₉	C₂²	semidirect
228. #23614	C₁₃₉	direct (N × H)
229. C₁₃₉	#23614	direct (N × H)
230. C₂×#428	C₂×C₁₃₉	semidirect
231. C₂×#424	C₂×C₁₃₉	semidirect
234. #2316	C₂×C₁₃₉	semidirect
236. #2067	C₂×C₁₃₉	semidirect
237. #2065	C₂×C₁₃₉	semidirect
238. #1735	C₂×C₁₃₉	semidirect
247. C₂×#107	C₂²×C₁₃₉	semidirect
248. C₂×#106	C₂²×C₁₃₉	semidirect
250. C₂×C₄⋊C₈	C₂²×C₁₃₉	semidirect
259. #389	C₂²×C₁₃₉	semidirect
262. #340	C₂²×C₁₃₉	semidirect
263. #340	C₂²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#428×C₁₃₉	2
C₂×#424×C₁₃₉	2
C₂×#418×C₁₃₉	2
C₂²×#102×C₁₃₉	2
#2316×C₁₃₉	2
#2309×C₁₃₉	2
#2067×C₁₃₉	2
#2065×C₁₃₉	2
#1735×C₁₃₉	2
#23614	139

Subgroups — C139×#23614 #48018210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#23614 #48018210