Subgroups — C₁₃₉×#15104 #48009700

Order 35584.

1334 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#391×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#1446×C₁₃₉	C₂	1	2	yes	maximal
4	#1445×C₁₃₉	C₂	1	2	yes	maximal
5	#1444×C₁₃₉	C₂	1	2	yes	maximal
6	#1444×C₁₃₉	C₂	1	2	yes	maximal
7	#1436×C₁₃₉	C₂	1	4	yes	maximal
8	#1434×C₁₃₉	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
14	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
16	#391×C₁₃₉	—	2	4	no	—
17	C₄×C₄⋊C₄×C₁₃₉	—	2	4	no	—
18	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
19	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
20	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
21	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
25	C₂×#95×C₁₃₉	C₂²	1	4	yes	—
26	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
27	C₂²×Q₈×C₁₃₉	—	2	2	no	—
28	C₂²×Q₈×C₁₃₉	—	2	4	no	—
29	C₂²×Q₈×C₁₃₉	—	2	4	no	—
30	C₂²×Q₈×C₁₃₉	—	4	2	no	—
31	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
32	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
34	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
40	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
41	C₂×C₄⋊C₄×C₁₃₉	—	2	4	no	—
42	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₁₃₉	—	2	2	no	—
44	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
45	C₂×C₄⋊C₄×C₁₃₉	—	4	2	no	—
46	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
47	C₂×C₄⋊C₄×C₁₃₉	—	4	4	no	—
48	C₂×C₄⋊C₄×C₁₃₉	Q₈	1	4	yes	complemented
49	C₂×C₄²×C₁₃₉	—	2	4	no	—
50	C₂×C₄²×C₁₃₉	—	2	4	no	—
51	C₂×C₄²×C₁₃₉	—	4	4	no	—
52	C₂×C₄²×C₁₃₉	D₄	1	4	yes	—
53	#95×C₁₃₉	—	2	4	no	—
54	#95×C₁₃₉	—	2	4	no	—
55	#95×C₁₃₉	—	2	4	no	—
56	#95×C₁₃₉	—	2	8	no	—
57	#95×C₁₃₉	—	2	4	no	—
58	#95×C₁₃₉	—	2	4	no	—
59	#95×C₁₃₉	—	4	4	no	—
60	#95×C₁₃₉	—	4	4	no	—
61	#95×C₁₃₉	Q₈	1	8	yes	complemented
62	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
63	C₂×Q₈×C₁₃₉	—	2	8	no	—
64	C₂×Q₈×C₁₃₉	—	4	16	no	—
65	C₂×Q₈×C₁₃₉	—	4	4	no	—
66	C₂×Q₈×C₁₃₉	—	4	4	no	—
67	C₂²×C₄×C₁₃₉	—	2	2	no	—
68	C₂²×C₄×C₁₃₉	—	2	2	no	—
69	C₂²×C₄×C₁₃₉	—	2	2	no	—
70	C₂²×C₄×C₁₃₉	—	2	2	no	—
71	C₂²×C₄×C₁₃₉	—	2	2	no	—
72	C₂²×C₄×C₁₃₉	—	2	2	no	—
73	C₂²×C₄×C₁₃₉	—	2	2	no	—
74	C₂²×C₄×C₁₃₉	—	2	2	no	—
75	C₂²×C₄×C₁₃₉	—	2	2	no	—
76	C₂²×C₄×C₁₃₉	—	2	4	no	—
77	C₂²×C₄×C₁₃₉	—	2	4	no	—
78	C₂²×C₄×C₁₃₉	—	2	4	no	—
79	C₂²×C₄×C₁₃₉	—	2	4	no	—
80	C₂²×C₄×C₁₃₉	—	2	2	no	—
81	C₂²×C₄×C₁₃₉	—	2	2	no	—
82	C₂²×C₄×C₁₃₉	—	2	4	no	—
83	C₂²×C₄×C₁₃₉	—	2	2	no	—
84	C₂²×C₄×C₁₃₉	—	2	4	no	—
85	C₂²×C₄×C₁₃₉	—	2	4	no	—
86	C₂²×C₄×C₁₃₉	—	2	4	no	—
87	C₂²×C₄×C₁₃₉	—	2	4	no	—
88	C₂²×C₄×C₁₃₉	—	2	4	no	—
89	C₂²×C₄×C₁₃₉	—	2	4	no	—
90	C₂²×C₄×C₁₃₉	—	2	4	no	—
91	C₂²×C₄×C₁₃₉	—	2	2	no	—
92	C₂²×C₄×C₁₃₉	—	2	4	no	—
93	C₂²×C₄×C₁₃₉	—	2	2	no	—
94	C₂²×C₄×C₁₃₉	—	2	4	no	—
95	C₂²×C₄×C₁₃₉	—	2	2	no	—
96	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₃₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃₉	C₂×Q₈	1	8	yes	—
100	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
104	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
105	C₂²×C₄×C₁₃₉	#41	1	2	yes	—
106	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
107	C₄⋊C₄×C₁₃₉	—	2	8	no	—
108	C₄⋊C₄×C₁₃₉	—	2	8	no	—
109	C₄⋊C₄×C₁₃₉	—	4	4	no	—
110	C₄⋊C₄×C₁₃₉	—	4	16	no	—
111	C₄²×C₁₃₉	—	2	8	no	—
112	C₄²×C₁₃₉	—	4	8	no	—
113	C₂³×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
114	C₂³×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
115	C₂³×C₁₃₉	C₂²×Q₈	1	2	yes	—
116	C₂³×C₁₃₉	C₂×#41	1	1	yes	characteristic
117	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
118	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
119	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
120	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
121	C₂³×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
122	Q₈×C₁₃₉	—	4	16	no	—
123	C₂×C₄×C₁₃₉	—	2	2	no	—
124	C₂×C₄×C₁₃₉	—	2	2	no	—
125	C₂×C₄×C₁₃₉	—	2	2	no	—
126	C₂×C₄×C₁₃₉	—	2	2	no	—
127	C₂×C₄×C₁₃₉	—	2	4	no	—
128	C₂×C₄×C₁₃₉	—	2	4	no	—
129	C₂×C₄×C₁₃₉	—	2	2	no	—
130	C₂×C₄×C₁₃₉	—	2	2	no	—
131	C₂×C₄×C₁₃₉	—	2	8	no	—
132	C₂×C₄×C₁₃₉	—	2	8	no	—
133	C₂×C₄×C₁₃₉	—	2	4	no	—
134	C₂×C₄×C₁₃₉	—	2	4	no	—
135	C₂×C₄×C₁₃₉	—	2	4	no	—
136	C₂×C₄×C₁₃₉	—	2	8	no	—
137	C₂×C₄×C₁₃₉	—	2	8	no	—
138	C₂×C₄×C₁₃₉	—	2	8	no	—
139	C₂×C₄×C₁₃₉	—	2	8	no	—
140	C₂×C₄×C₁₃₉	—	2	8	no	—
141	C₂×C₄×C₁₃₉	—	2	8	no	—
142	C₂×C₄×C₁₃₉	—	4	2	no	—
143	C₂×C₄×C₁₃₉	—	4	2	no	—
144	C₂×C₄×C₁₃₉	—	4	4	no	—
145	C₂×C₄×C₁₃₉	—	4	2	no	—
146	C₂×C₄×C₁₃₉	—	4	2	no	—
147	C₂×C₄×C₁₃₉	—	4	2	no	—
148	C₂×C₄×C₁₃₉	—	4	2	no	—
149	C₂×C₄×C₁₃₉	—	4	4	no	—
150	C₂×C₄×C₁₃₉	—	4	4	no	—
151	C₂×C₄×C₁₃₉	—	4	4	no	—
152	C₂×C₄×C₁₃₉	—	4	4	no	—
153	C₂×C₄×C₁₃₉	—	4	4	no	—
154	C₂×C₄×C₁₃₉	—	4	4	no	—
155	C₂×C₄×C₁₃₉	—	4	2	no	—
156	C₂×C₄×C₁₃₉	—	4	2	no	—
157	C₂×C₄×C₁₃₉	—	4	2	no	—
158	C₂×C₄×C₁₃₉	—	4	4	no	—
159	C₂×C₄×C₁₃₉	—	4	4	no	—
160	C₂×C₄×C₁₃₉	C₂²⋊Q₈	1	4	yes	—
161	C₂×C₄×C₁₃₉	#123	1	4	yes	—
162	C₂×C₄×C₁₃₉	C₄⋊Q₈	1	4	yes	—
163	C₂²×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
164	C₂²×C₁₃₉	C₂×#123	1	1	yes	characteristic
165	C₂²×C₁₃₉	#525	1	1	yes	characteristic
166	C₂²×C₁₃₉	#525	1	1	yes	characteristic
167	C₂²×C₁₃₉	#529	1	2	yes	—
168	C₂²×C₁₃₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
169	C₂²×C₁₃₉	#533	1	2	yes	—
170	C₂²×C₁₃₉	#533	1	4	yes	—
171	C₂²×C₁₃₉	#535	1	1	yes	characteristic
172	C₂²×C₁₃₉	#535	1	1	yes	characteristic
173	C₂²×C₁₃₉	#538	1	4	yes	—
174	C₂²×C₁₃₉	#551	1	4	yes	—
175	C₂²×C₁₃₉	#554	1	2	yes	—
176	C₂²×C₁₃₉	#554	1	2	yes	—
177	C₂²×C₁₃₉	#554	1	4	yes	—
178	C₂²×C₁₃₉	Q₈²	1	2	yes	—
179	C₂²×C₁₃₉	#559	1	2	yes	—
180	C₄×C₁₃₉	—	2	4	no	—
181	C₄×C₁₃₉	—	2	4	no	—
182	C₄×C₁₃₉	—	2	4	no	—
183	C₄×C₁₃₉	—	4	4	no	—
184	C₄×C₁₃₉	—	4	8	no	—
185	C₄×C₁₃₉	—	4	4	no	—
186	C₄×C₁₃₉	—	4	4	no	—
187	C₄×C₁₃₉	—	8	2	no	—
188	C₂×C₁₃₉	#2399	1	1	yes	characteristic
189	C₂×C₁₃₉	#2482	1	1	yes	characteristic
190	C₂×C₁₃₉	#2502	1	1	yes	characteristic
191	C₂×C₁₃₉	#2567	1	1	yes	characteristic
192	C₂×C₁₃₉	#2580	1	1	yes	characteristic
193	C₂×C₁₃₉	#2586	1	4	yes	—
194	C₂×C₁₃₉	#2589	1	4	yes	—
195	C₂×C₁₃₉	#2631	1	1	yes	characteristic
196	C₂×C₁₃₉	#2855	1	1	yes	characteristic
197	#15104	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₁₃₉	#15104	1	1	yes	characteristic, direct product factor, Sylow
199	C₂×#391	C₂×C₁₃₉	1	1	yes	characteristic
200	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic
201	#1446	C₂×C₁₃₉	1	2	yes	—
202	#1445	C₂×C₁₃₉	1	2	yes	—
203	#1444	C₂×C₁₃₉	1	2	yes	—
204	#1444	C₂×C₁₃₉	1	2	yes	—
205	#1436	C₂×C₁₃₉	1	4	yes	—
206	#1434	C₂×C₁₃₉	1	1	yes	characteristic
207	C₂³×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
211	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
212	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
213	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
214	#391	—	2	4	no	—
215	C₄×C₄⋊C₄	—	2	4	no	—
216	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
217	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
218	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
219	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
220	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
221	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
222	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
223	C₂×#95	C₂²×C₁₃₉	1	4	yes	—
224	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
225	C₂²×Q₈	—	2	2	no	—
226	C₂²×Q₈	—	2	4	no	—
227	C₂²×Q₈	—	2	4	no	—
228	C₂²×Q₈	—	4	2	no	—
229	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
230	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
231	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
232	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
233	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
234	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	4	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	8	no	—
243	C₂×C₄⋊C₄	—	4	2	no	—
244	C₂×C₄⋊C₄	—	4	4	no	—
245	C₂×C₄⋊C₄	—	4	4	no	—
246	C₂×C₄⋊C₄	Q₈×C₁₃₉	1	4	yes	complemented
247	C₂×C₄²	—	2	4	no	—
248	C₂×C₄²	—	2	4	no	—
249	C₂×C₄²	—	4	4	no	—
250	C₂×C₄²	D₄×C₁₃₉	1	4	yes	—
251	#95	—	2	4	no	—
252	#95	—	2	4	no	—
253	#95	—	2	4	no	—
254	#95	—	2	8	no	—
255	#95	—	2	4	no	—
256	#95	—	2	4	no	—
257	#95	—	4	4	no	—
258	#95	—	4	4	no	—
259	#95	Q₈×C₁₃₉	1	8	yes	complemented
260	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
261	C₂×Q₈	—	2	8	no	—
262	C₂×Q₈	—	4	16	no	—
263	C₂×Q₈	—	4	4	no	—
264	C₂×Q₈	—	4	4	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₁₃₉	1	2	yes	—
297	C₂²×C₄	C₂×Q₈×C₁₃₉	1	8	yes	—
298	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
299	C₂²×C₄	C₂×Q₈×C₁₃₉	1	2	yes	—
300	C₂²×C₄	C₂×Q₈×C₁₃₉	1	4	yes	—
301	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
302	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
303	C₂²×C₄	#41×C₁₃₉	1	2	yes	—
304	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	4	4	no	—
308	C₄⋊C₄	—	4	16	no	—
309	C₄²	—	2	8	no	—
310	C₄²	—	4	8	no	—
311	C₂³	C₂²×D₄×C₁₃₉	1	1	yes	characteristic
312	C₂³	C₂²×Q₈×C₁₃₉	1	1	yes	characteristic
313	C₂³	C₂²×Q₈×C₁₃₉	1	2	yes	—
314	C₂³	C₂×#41×C₁₃₉	1	1	yes	characteristic
315	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
316	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
317	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
318	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
319	C₂³	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
320	Q₈	—	4	16	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	C₂²⋊Q₈×C₁₃₉	1	4	yes	—
359	C₂×C₄	#123×C₁₃₉	1	4	yes	—
360	C₂×C₄	C₄⋊Q₈×C₁₃₉	1	4	yes	—
361	C₂²	C₂×C₂²⋊Q₈×C₁₃₉	1	1	yes	characteristic
362	C₂²	C₂×#123×C₁₃₉	1	1	yes	characteristic
363	C₂²	#525×C₁₃₉	1	1	yes	characteristic
364	C₂²	#525×C₁₃₉	1	1	yes	characteristic
365	C₂²	#529×C₁₃₉	1	2	yes	—
366	C₂²	C₂×C₄⋊Q₈×C₁₃₉	1	1	yes	characteristic
367	C₂²	#533×C₁₃₉	1	2	yes	—
368	C₂²	#533×C₁₃₉	1	4	yes	—
369	C₂²	#535×C₁₃₉	1	1	yes	characteristic
370	C₂²	#535×C₁₃₉	1	1	yes	characteristic
371	C₂²	#538×C₁₃₉	1	4	yes	—
372	C₂²	#551×C₁₃₉	1	4	yes	—
373	C₂²	#554×C₁₃₉	1	2	yes	—
374	C₂²	#554×C₁₃₉	1	2	yes	—
375	C₂²	#554×C₁₃₉	1	4	yes	—
376	C₂²	Q₈²×C₁₃₉	1	2	yes	—
377	C₂²	#559×C₁₃₉	1	2	yes	—
378	C₄	—	2	4	no	—
379	C₄	—	2	4	no	—
380	C₄	—	2	4	no	—
381	C₄	—	4	4	no	—
382	C₄	—	4	8	no	—
383	C₄	—	4	4	no	—
384	C₄	—	4	4	no	—
385	C₄	—	8	2	no	—
386	C₂	#2399×C₁₃₉	1	1	yes	characteristic
387	C₂	#2482×C₁₃₉	1	1	yes	characteristic
388	C₂	#2502×C₁₃₉	1	1	yes	characteristic
389	C₂	#2567×C₁₃₉	1	1	yes	characteristic
390	C₂	#2580×C₁₃₉	1	1	yes	characteristic
391	C₂	#2586×C₁₃₉	1	4	yes	—
392	C₂	#2589×C₁₃₉	1	4	yes	—
393	C₂	#2631×C₁₃₉	1	1	yes	characteristic
394	C₂	#2855×C₁₃₉	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃₉
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
48. C₂×C₄⋊C₄×C₁₃₉	Q₈	semidirect
61. #95×C₁₃₉	Q₈	semidirect
197. #15104	C₁₃₉	direct (N × H)
198. C₁₃₉	#15104	direct (N × H)
246. C₂×C₄⋊C₄	Q₈×C₁₃₉	semidirect
259. #95	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×#391×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#1446×C₁₃₉	2
#1445×C₁₃₉	2
#1444×C₁₃₉	2
#1436×C₁₃₉	2
#1434×C₁₃₉	2
#15104	139

Subgroups — C139×#15104 #48009700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#15104 #48009700