Subgroups — C₁₃₉×#36040 #48030636

Order 35584.

2266 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#2628×C₁₃₉	C₂	1	3	yes	maximal, complemented
4	#2580×C₁₃₉	C₂	1	3	yes	maximal, complemented
5	#2563×C₁₃₉	C₂	1	3	yes	maximal, complemented
6	#2454×C₁₃₉	C₂	1	6	yes	maximal, complemented
7	#2442×C₁₃₉	C₂	1	6	yes	maximal, complemented
8	#2396×C₁₃₉	C₂	1	3	yes	maximal, complemented
9	#2351×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#2351×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2341×C₁₃₉	C₂	1	2	yes	maximal
12	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
13	#557×C₁₃₉	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	3	yes	—
15	C₂×#125×C₁₃₉	C₂²	1	6	yes	—
16	#520×C₁₃₉	—	2	8	no	—
17	C₂×C₄×Q₈×C₁₃₉	C₂²	1	3	yes	—
18	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
23	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
24	C₂×#117×C₁₃₉	C₂²	1	3	yes	—
25	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
26	#400×C₁₃₉	C₂²	1	6	yes	—
27	#400×C₁₃₉	C₂²	1	1	yes	characteristic
28	#399×C₁₃₉	C₂²	1	3	yes	—
29	#399×C₁₃₉	C₂²	1	6	yes	—
30	#398×C₁₃₉	C₂²	1	6	yes	—
31	#396×C₁₃₉	C₂²	1	6	yes	—
32	#395×C₁₃₉	C₂²	1	3	yes	—
33	#393×C₁₃₉	C₂²	1	3	yes	—
34	#393×C₁₃₉	C₂²	1	6	yes	—
35	#390×C₁₃₉	C₂²	1	6	yes	—
36	#390×C₁₃₉	C₂²	1	6	yes	—
37	#389×C₁₃₉	C₂²	1	6	yes	—
38	#389×C₁₃₉	C₂²	1	6	yes	—
39	#389×C₁₃₉	C₂²	1	6	yes	—
40	#385×C₁₃₉	C₂²	1	12	yes	—
41	#382×C₁₃₉	C₂²	1	6	yes	—
42	#382×C₁₃₉	C₂²	1	3	yes	—
43	#380×C₁₃₉	C₂²	1	12	yes	—
44	#380×C₁₃₉	C₂²	1	6	yes	—
45	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	—
46	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	6	yes	—
47	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	—
48	C₂×#41×C₁₃₉	—	2	4	no	—
49	C₂×#41×C₁₃₉	—	2	4	no	—
50	C₂×#41×C₁₃₉	Q₈	1	8	yes	complemented
51	C₂²×Q₈×C₁₃₉	C₂³	1	3	yes	—
52	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃₉	C₂³	1	3	yes	—
54	C₂³×C₄×C₁₃₉	C₂³	1	3	yes	—
55	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
56	C₄⋊Q₈×C₁₃₉	—	2	12	no	—
57	#125×C₁₃₉	—	2	24	no	—
58	C₄×Q₈×C₁₃₉	—	2	4	no	—
59	C₄×Q₈×C₁₃₉	—	2	8	no	—
60	C₄×Q₈×C₁₃₉	—	2	8	no	—
61	C₄×Q₈×C₁₃₉	—	2	12	no	—
62	C₄×Q₈×C₁₃₉	D₄	1	8	yes	—
63	C₄×D₄×C₁₃₉	—	2	12	no	—
64	C₄×D₄×C₁₃₉	—	2	12	no	—
65	#117×C₁₃₉	—	2	12	no	—
66	C₂×C₄⋊C₄×C₁₃₉	—	2	12	no	—
67	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
69	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
70	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
72	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
73	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
74	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
75	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
76	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
77	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
78	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
79	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
80	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	3	yes	—
81	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
83	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
84	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
85	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
86	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
87	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
88	#95×C₁₃₉	C₂³	1	6	yes	—
89	#95×C₁₃₉	C₂³	1	3	yes	—
90	#95×C₁₃₉	C₂³	1	2	yes	—
91	#95×C₁₃₉	C₂³	1	2	yes	—
92	#95×C₁₃₉	C₂³	1	6	yes	—
93	#95×C₁₃₉	C₂³	1	6	yes	—
94	#95×C₁₃₉	C₂³	1	1	yes	characteristic
95	#95×C₁₃₉	C₂³	1	12	yes	—
96	C₂⁴×C₁₃₉	C₂⁴	1	3	yes	—
97	#41×C₁₃₉	—	2	32	no	—
98	C₂×Q₈×C₁₃₉	—	2	6	no	—
99	C₂×Q₈×C₁₃₉	—	4	6	no	—
100	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
101	C₂×Q₈×C₁₃₉	C₂×Q₈	1	4	yes	—
102	C₂×Q₈×C₁₃₉	#41	1	4	yes	—
103	C₂×D₄×C₁₃₉	—	2	6	no	—
104	C₂×D₄×C₁₃₉	—	2	6	no	—
105	C₂×D₄×C₁₃₉	C₂×Q₈	1	12	yes	—
106	C₂²×C₄×C₁₃₉	—	2	6	no	—
107	C₂²×C₄×C₁₃₉	—	2	6	no	—
108	C₂²×C₄×C₁₃₉	—	2	12	no	—
109	C₂²×C₄×C₁₃₉	—	4	12	no	—
110	C₂²×C₄×C₁₃₉	C₂×Q₈	1	12	yes	—
111	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
113	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
114	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
115	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
119	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
121	C₄⋊C₄×C₁₃₉	—	2	6	no	—
122	C₄⋊C₄×C₁₃₉	—	2	6	no	—
123	C₄⋊C₄×C₁₃₉	—	2	2	no	—
124	C₄⋊C₄×C₁₃₉	—	2	2	no	—
125	C₄⋊C₄×C₁₃₉	—	2	12	no	—
126	C₄⋊C₄×C₁₃₉	—	2	12	no	—
127	C₄⋊C₄×C₁₃₉	—	2	12	no	—
128	C₄⋊C₄×C₁₃₉	—	2	12	no	—
129	C₄⋊C₄×C₁₃₉	—	4	6	no	—
130	C₄⋊C₄×C₁₃₉	—	4	6	no	—
131	C₄⋊C₄×C₁₃₉	—	4	6	no	—
132	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	—
133	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
134	C₂²⋊C₄×C₁₃₉	—	2	6	no	—
135	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
136	C₂²⋊C₄×C₁₃₉	—	4	6	no	—
137	C₂²⋊C₄×C₁₃₉	—	4	12	no	—
138	C₄²×C₁₃₉	—	2	6	no	—
139	C₄²×C₁₃₉	—	2	12	no	—
140	C₄²×C₁₃₉	—	2	12	no	—
141	C₄²×C₁₃₉	C₂×D₄	1	12	yes	—
142	C₂³×C₁₃₉	—	2	3	no	—
143	C₂³×C₁₃₉	—	2	3	no	—
144	C₂³×C₁₃₉	—	2	6	no	—
145	C₂³×C₁₃₉	—	2	6	no	—
146	C₂³×C₁₃₉	C₂²×Q₈	1	6	yes	—
147	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
148	Q₈×C₁₃₉	—	4	12	no	—
149	Q₈×C₁₃₉	C₂²⋊Q₈	1	16	yes	—
150	D₄×C₁₃₉	—	2	24	no	—
151	C₂×C₄×C₁₃₉	—	2	1	no	—
152	C₂×C₄×C₁₃₉	—	2	1	no	—
153	C₂×C₄×C₁₃₉	—	2	6	no	—
154	C₂×C₄×C₁₃₉	—	2	2	no	—
155	C₂×C₄×C₁₃₉	—	2	24	no	—
156	C₂×C₄×C₁₃₉	—	2	1	no	—
157	C₂×C₄×C₁₃₉	—	2	2	no	—
158	C₂×C₄×C₁₃₉	—	2	3	no	—
159	C₂×C₄×C₁₃₉	—	2	6	no	—
160	C₂×C₄×C₁₃₉	—	2	2	no	—
161	C₂×C₄×C₁₃₉	—	2	6	no	—
162	C₂×C₄×C₁₃₉	—	2	2	no	—
163	C₂×C₄×C₁₃₉	—	2	2	no	—
164	C₂×C₄×C₁₃₉	—	2	6	no	—
165	C₂×C₄×C₁₃₉	—	2	6	no	—
166	C₂×C₄×C₁₃₉	—	2	6	no	—
167	C₂×C₄×C₁₃₉	—	2	6	no	—
168	C₂×C₄×C₁₃₉	—	2	2	no	—
169	C₂×C₄×C₁₃₉	—	2	2	no	—
170	C₂×C₄×C₁₃₉	—	2	2	no	—
171	C₂×C₄×C₁₃₉	—	2	6	no	—
172	C₂×C₄×C₁₃₉	—	8	12	no	—
173	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
174	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
175	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
176	C₂×C₄×C₁₃₉	C₂²×Q₈	1	2	yes	—
177	C₂×C₄×C₁₃₉	C₂²×Q₈	1	6	yes	—
178	C₂×C₄×C₁₃₉	C₂×#41	1	6	yes	—
179	C₂²×C₁₃₉	—	2	6	no	—
180	C₂²×C₁₃₉	—	2	12	no	—
181	C₂²×C₁₃₉	—	4	3	no	—
182	C₂²×C₁₃₉	—	4	3	no	—
183	C₂²×C₁₃₉	—	4	6	no	—
184	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
185	C₂²×C₁₃₉	C₂³×Q₈	1	1	yes	characteristic
186	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
187	C₂²×C₁₃₉	#585	1	2	yes	—
188	C₂²×C₁₃₉	#585	1	2	yes	—
189	C₄×C₁₃₉	—	2	2	no	—
190	C₄×C₁₃₉	—	2	2	no	—
191	C₄×C₁₃₉	—	2	6	no	—
192	C₄×C₁₃₉	—	4	1	no	—
193	C₄×C₁₃₉	—	4	6	no	—
194	C₄×C₁₃₉	—	4	2	no	—
195	C₄×C₁₃₉	—	4	3	no	—
196	C₄×C₁₃₉	—	4	2	no	—
197	C₄×C₁₃₉	—	4	6	no	—
198	C₄×C₁₃₉	C₂×C₂²⋊Q₈	1	12	yes	—
199	C₂×C₁₃₉	—	4	6	no	—
200	C₂×C₁₃₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
201	C₂×C₁₃₉	#3487	1	1	yes	characteristic
202	C₂×C₁₃₉	#3500	1	1	yes	characteristic
203	C₂×C₁₃₉	#3504	1	2	yes	—
204	C₂×C₁₃₉	#3524	1	2	yes	—
205	#36040	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₁₃₉	#36040	1	1	yes	characteristic, direct product factor, Sylow
207	C₂×#557	C₂×C₁₃₉	1	1	yes	characteristic, complemented
208	C₂×#520	C₂×C₁₃₉	1	1	yes	characteristic
209	#2628	C₂×C₁₃₉	1	3	yes	complemented
210	#2580	C₂×C₁₃₉	1	3	yes	complemented
211	#2563	C₂×C₁₃₉	1	3	yes	complemented
212	#2454	C₂×C₁₃₉	1	6	yes	complemented
213	#2442	C₂×C₁₃₉	1	6	yes	complemented
214	#2396	C₂×C₁₃₉	1	3	yes	complemented
215	#2351	C₂×C₁₃₉	1	1	yes	characteristic, complemented
216	#2351	C₂×C₁₃₉	1	2	yes	complemented
217	#2341	C₂×C₁₃₉	1	2	yes	—
218	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
219	#557	—	2	8	no	—
220	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	3	yes	—
221	C₂×#125	C₂²×C₁₃₉	1	6	yes	—
222	#520	—	2	8	no	—
223	C₂×C₄×Q₈	C₂²×C₁₃₉	1	3	yes	—
224	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
225	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
226	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
228	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
229	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
230	C₂×#117	C₂²×C₁₃₉	1	3	yes	—
231	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
232	#400	C₂²×C₁₃₉	1	6	yes	—
233	#400	C₂²×C₁₃₉	1	1	yes	characteristic
234	#399	C₂²×C₁₃₉	1	3	yes	—
235	#399	C₂²×C₁₃₉	1	6	yes	—
236	#398	C₂²×C₁₃₉	1	6	yes	—
237	#396	C₂²×C₁₃₉	1	6	yes	—
238	#395	C₂²×C₁₃₉	1	3	yes	—
239	#393	C₂²×C₁₃₉	1	3	yes	—
240	#393	C₂²×C₁₃₉	1	6	yes	—
241	#390	C₂²×C₁₃₉	1	6	yes	—
242	#390	C₂²×C₁₃₉	1	6	yes	—
243	#389	C₂²×C₁₃₉	1	6	yes	—
244	#389	C₂²×C₁₃₉	1	6	yes	—
245	#389	C₂²×C₁₃₉	1	6	yes	—
246	#385	C₂²×C₁₃₉	1	12	yes	—
247	#382	C₂²×C₁₃₉	1	6	yes	—
248	#382	C₂²×C₁₃₉	1	3	yes	—
249	#380	C₂²×C₁₃₉	1	12	yes	—
250	#380	C₂²×C₁₃₉	1	6	yes	—
251	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	—
252	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	6	yes	—
253	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	—
254	C₂×#41	—	2	4	no	—
255	C₂×#41	—	2	4	no	—
256	C₂×#41	Q₈×C₁₃₉	1	8	yes	complemented
257	C₂²×Q₈	C₂³×C₁₃₉	1	3	yes	—
258	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₁₃₉	1	3	yes	—
260	C₂³×C₄	C₂³×C₁₃₉	1	3	yes	—
261	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
262	C₄⋊Q₈	—	2	12	no	—
263	#125	—	2	24	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	8	no	—
266	C₄×Q₈	—	2	8	no	—
267	C₄×Q₈	—	2	12	no	—
268	C₄×Q₈	D₄×C₁₃₉	1	8	yes	—
269	C₄×D₄	—	2	12	no	—
270	C₄×D₄	—	2	12	no	—
271	#117	—	2	12	no	—
272	C₂×C₄⋊C₄	—	2	12	no	—
273	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	3	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
290	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
291	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
292	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
293	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
294	#95	C₂³×C₁₃₉	1	2	yes	—
295	#95	C₂³×C₁₃₉	1	6	yes	—
296	#95	C₂³×C₁₃₉	1	1	yes	characteristic
297	#95	C₂³×C₁₃₉	1	2	yes	—
298	#95	C₂³×C₁₃₉	1	6	yes	—
299	#95	C₂³×C₁₃₉	1	3	yes	—
300	#95	C₂³×C₁₃₉	1	12	yes	—
301	#95	C₂³×C₁₃₉	1	6	yes	—
302	C₂⁴	C₂⁴×C₁₃₉	1	3	yes	—
303	#41	—	2	32	no	—
304	C₂×Q₈	—	2	6	no	—
305	C₂×Q₈	—	4	6	no	—
306	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
307	C₂×Q₈	C₂×Q₈×C₁₃₉	1	4	yes	—
308	C₂×Q₈	#41×C₁₃₉	1	4	yes	—
309	C₂×D₄	—	2	6	no	—
310	C₂×D₄	—	2	6	no	—
311	C₂×D₄	C₂×Q₈×C₁₃₉	1	12	yes	—
312	C₂²×C₄	—	2	6	no	—
313	C₂²×C₄	—	2	6	no	—
314	C₂²×C₄	—	2	12	no	—
315	C₂²×C₄	—	4	12	no	—
316	C₂²×C₄	C₂×Q₈×C₁₃₉	1	12	yes	—
317	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
319	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
320	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
321	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
325	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
327	C₄⋊C₄	—	2	6	no	—
328	C₄⋊C₄	—	2	6	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	12	no	—
332	C₄⋊C₄	—	2	12	no	—
333	C₄⋊C₄	—	2	12	no	—
334	C₄⋊C₄	—	2	12	no	—
335	C₄⋊C₄	—	4	6	no	—
336	C₄⋊C₄	—	4	6	no	—
337	C₄⋊C₄	—	4	6	no	—
338	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	—
339	C₂²⋊C₄	—	2	6	no	—
340	C₂²⋊C₄	—	2	6	no	—
341	C₂²⋊C₄	—	4	6	no	—
342	C₂²⋊C₄	—	4	6	no	—
343	C₂²⋊C₄	—	4	12	no	—
344	C₄²	—	2	6	no	—
345	C₄²	—	2	12	no	—
346	C₄²	—	2	12	no	—
347	C₄²	C₂×D₄×C₁₃₉	1	12	yes	—
348	C₂³	—	2	3	no	—
349	C₂³	—	2	3	no	—
350	C₂³	—	2	6	no	—
351	C₂³	—	2	6	no	—
352	C₂³	C₂²×Q₈×C₁₃₉	1	6	yes	—
353	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
354	Q₈	—	4	12	no	—
355	Q₈	C₂²⋊Q₈×C₁₃₉	1	16	yes	—
356	D₄	—	2	24	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	6	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	24	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	3	no	—
365	C₂×C₄	—	2	6	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	6	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	6	no	—
378	C₂×C₄	—	8	12	no	—
379	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
381	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
382	C₂×C₄	C₂²×Q₈×C₁₃₉	1	2	yes	—
383	C₂×C₄	C₂²×Q₈×C₁₃₉	1	6	yes	—
384	C₂×C₄	C₂×#41×C₁₃₉	1	6	yes	—
385	C₂²	—	2	6	no	—
386	C₂²	—	2	12	no	—
387	C₂²	—	4	3	no	—
388	C₂²	—	4	3	no	—
389	C₂²	—	4	6	no	—
390	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
391	C₂²	C₂³×Q₈×C₁₃₉	1	1	yes	characteristic
392	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
393	C₂²	#585×C₁₃₉	1	2	yes	—
394	C₂²	#585×C₁₃₉	1	2	yes	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	6	no	—
398	C₄	—	4	6	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	3	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	6	no	—
404	C₄	C₂×C₂²⋊Q₈×C₁₃₉	1	12	yes	—
405	C₂	—	4	6	no	—
406	C₂	C₂²×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
407	C₂	#3487×C₁₃₉	1	1	yes	characteristic
408	C₂	#3500×C₁₃₉	1	1	yes	characteristic
409	C₂	#3504×C₁₃₉	1	2	yes	—
410	C₂	#3524×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂²×#41×C₁₃₉	C₂²
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×#557×C₁₃₉	C₂	semidirect
3. #2628×C₁₃₉	C₂	semidirect
4. #2580×C₁₃₉	C₂	semidirect
5. #2563×C₁₃₉	C₂	semidirect
6. #2454×C₁₃₉	C₂	semidirect
7. #2442×C₁₃₉	C₂	semidirect
8. #2396×C₁₃₉	C₂	semidirect
9. #2351×C₁₃₉	C₂	semidirect
10. #2351×C₁₃₉	C₂	semidirect
50. C₂×#41×C₁₃₉	Q₈	semidirect
205. #36040	C₁₃₉	direct (N × H)
206. C₁₃₉	#36040	direct (N × H)
207. C₂×#557	C₂×C₁₃₉	semidirect
209. #2628	C₂×C₁₃₉	semidirect
210. #2580	C₂×C₁₃₉	semidirect
211. #2563	C₂×C₁₃₉	semidirect
212. #2454	C₂×C₁₃₉	semidirect
213. #2442	C₂×C₁₃₉	semidirect
214. #2396	C₂×C₁₃₉	semidirect
215. #2351	C₂×C₁₃₉	semidirect
216. #2351	C₂×C₁₃₉	semidirect
256. C₂×#41	Q₈×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#557×C₁₃₉	2
C₂×#520×C₁₃₉	2
#2628×C₁₃₉	2
#2580×C₁₃₉	2
#2563×C₁₃₉	2
#2454×C₁₃₉	2
#2442×C₁₃₉	2
#2396×C₁₃₉	2
#2351×C₁₃₉	2
#2341×C₁₃₉	2
#36040	139

Subgroups — C139×#36040 #48030636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36040 #48030636