Subgroups — D₄×#127×C₁₃₉ #48030715

Order 35584.

5730 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₁₃₉	C₂	1	6	yes	maximal, complemented
2	C₂²×#127×C₁₃₉	C₂	1	2	yes	maximal, complemented
3	#2867×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2856×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2541×C₁₃₉	C₂	1	6	yes	maximal, complemented
6	#2433×C₁₃₉	C₂	1	12	yes	maximal, complemented
7	C₄×#127×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₁₃₉	C₂²	1	4	yes	—
10	C₂³×D₄×C₁₃₉	C₂²	1	12	yes	complemented
11	D₄²×C₁₃₉	—	2	48	no	—
12	C₂×#127×C₁₃₉	—	2	16	no	—
13	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×#127×C₁₃₉	C₂²	1	6	yes	complemented
15	C₂×#127×C₁₃₉	C₂²	1	12	yes	complemented
16	C₂×#127×C₁₃₉	C₂²	1	2	yes	complemented
17	C₂×#127×C₁₃₉	C₂²	1	6	yes	complemented
18	C₂×#121×C₁₃₉	C₂²	1	12	yes	complemented
19	C₂×#121×C₁₃₉	C₂²	1	12	yes	complemented
20	C₂×#120×C₁₃₉	C₂²	1	24	yes	complemented
21	C₂×C₄×D₄×C₁₃₉	C₂²	1	3	yes	—
22	C₂×C₄×D₄×C₁₃₉	C₂²	1	6	yes	complemented
23	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	complemented
24	#392×C₁₃₉	C₂²	1	24	yes	complemented
25	#390×C₁₃₉	C₂²	1	12	yes	complemented
26	#390×C₁₃₉	C₂²	1	6	yes	complemented
27	#384×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	3	yes	complemented
29	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	6	yes	complemented
30	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
31	C₂⁵×C₁₃₉	C₂³	1	8	yes	—
32	C₂²×D₄×C₁₃₉	—	2	48	no	—
33	C₂²×D₄×C₁₃₉	—	2	48	no	—
34	C₂²×D₄×C₁₃₉	—	2	48	no	—
35	C₂²×D₄×C₁₃₉	—	4	24	no	—
36	C₂²×D₄×C₁₃₉	C₂³	1	8	yes	—
37	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
38	C₂²×D₄×C₁₃₉	C₂³	1	12	yes	—
39	C₂²×D₄×C₁₃₉	C₂³	1	24	yes	—
40	C₂²×D₄×C₁₃₉	C₂³	1	6	yes	—
41	C₂²×D₄×C₁₃₉	C₂³	1	12	yes	—
42	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₃₉	C₂³	1	6	yes	—
45	#127×C₁₃₉	—	2	48	no	—
46	#127×C₁₃₉	—	2	8	no	—
47	#127×C₁₃₉	—	2	24	no	—
48	#127×C₁₃₉	—	4	12	no	—
49	#127×C₁₃₉	D₄	1	8	yes	direct product factor
50	#121×C₁₃₉	—	2	48	no	—
51	#121×C₁₃₉	—	2	48	no	—
52	#120×C₁₃₉	—	2	96	no	—
53	C₄×D₄×C₁₃₉	—	2	24	no	—
54	C₄×D₄×C₁₃₉	D₄	1	24	yes	complemented
55	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	6	yes	—
56	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	3	yes	—
57	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	12	yes	—
58	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	24	yes	—
59	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	6	yes	—
60	C₂×C₄²×C₁₃₉	—	2	8	no	—
61	C₂×C₄²×C₁₃₉	C₂³	1	6	yes	—
62	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
63	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃₉	C₂³	1	3	yes	—
65	#95×C₁₃₉	C₂³	1	6	yes	—
66	C₂⁴×C₁₃₉	—	2	16	no	—
67	C₂⁴×C₁₃₉	—	2	48	no	—
68	C₂⁴×C₁₃₉	—	4	24	no	—
69	C₂⁴×C₁₃₉	C₂⁴	1	8	yes	—
70	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
71	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
72	C₂×D₄×C₁₃₉	—	2	48	no	—
73	C₂×D₄×C₁₃₉	—	2	48	no	—
74	C₂×D₄×C₁₃₉	—	2	12	no	—
75	C₂×D₄×C₁₃₉	—	2	48	no	—
76	C₂×D₄×C₁₃₉	—	2	24	no	—
77	C₂×D₄×C₁₃₉	—	2	24	no	—
78	C₂×D₄×C₁₃₉	—	2	24	no	—
79	C₂×D₄×C₁₃₉	—	2	24	no	—
80	C₂×D₄×C₁₃₉	—	2	12	no	—
81	C₂×D₄×C₁₃₉	—	2	24	no	—
82	C₂×D₄×C₁₃₉	—	4	192	no	—
83	C₂×D₄×C₁₃₉	—	4	24	no	—
84	C₂×D₄×C₁₃₉	—	4	24	no	—
85	C₂×D₄×C₁₃₉	—	4	64	no	—
86	C₂×D₄×C₁₃₉	C₂×D₄	1	12	yes	—
87	C₂×D₄×C₁₃₉	C₂×D₄	1	24	yes	complemented
88	C₂²×C₄×C₁₃₉	—	2	12	no	—
89	C₂²×C₄×C₁₃₉	—	2	12	no	—
90	C₂²×C₄×C₁₃₉	—	2	24	no	—
91	C₂²×C₄×C₁₃₉	C₂×D₄	1	24	yes	complemented
92	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
93	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
94	C₂²×C₄×C₁₃₉	C₂⁴	1	6	yes	—
95	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
96	C₂²×C₄×C₁₃₉	C₂⁴	1	3	yes	—
97	C₄⋊C₄×C₁₃₉	—	2	12	no	—
98	C₄⋊C₄×C₁₃₉	C₂×D₄	1	12	yes	complemented
99	C₂²⋊C₄×C₁₃₉	—	2	24	no	—
100	C₂²⋊C₄×C₁₃₉	—	2	48	no	—
101	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	24	yes	complemented
102	C₄²×C₁₃₉	—	2	12	no	—
103	C₄²×C₁₃₉	—	2	6	no	—
104	C₄²×C₁₃₉	C₂×D₄	1	4	yes	complemented
105	C₄²×C₁₃₉	C₂×D₄	1	12	yes	complemented
106	C₂³×C₁₃₉	—	2	2	no	—
107	C₂³×C₁₃₉	—	2	6	no	—
108	C₂³×C₁₃₉	—	2	12	no	—
109	C₂³×C₁₃₉	—	2	12	no	—
110	C₂³×C₁₃₉	—	2	24	no	—
111	C₂³×C₁₃₉	—	2	8	no	—
112	C₂³×C₁₃₉	—	2	24	no	—
113	C₂³×C₁₃₉	—	4	96	no	—
114	C₂³×C₁₃₉	—	4	32	no	—
115	C₂³×C₁₃₉	—	8	48	no	—
116	C₂³×C₁₃₉	C₂²×D₄	1	8	yes	—
117	C₂³×C₁₃₉	C₂²×D₄	1	12	yes	—
118	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
119	D₄×C₁₃₉	—	2	48	no	—
120	D₄×C₁₃₉	—	4	96	no	—
121	D₄×C₁₃₉	—	4	32	no	—
122	D₄×C₁₃₉	—	4	16	no	—
123	D₄×C₁₃₉	—	4	48	no	—
124	D₄×C₁₃₉	—	8	24	no	—
125	D₄×C₁₃₉	#127	1	16	yes	direct product factor
126	C₂×C₄×C₁₃₉	—	2	6	no	—
127	C₂×C₄×C₁₃₉	—	2	6	no	—
128	C₂×C₄×C₁₃₉	—	2	6	no	—
129	C₂×C₄×C₁₃₉	—	2	48	no	—
130	C₂×C₄×C₁₃₉	—	2	12	no	—
131	C₂×C₄×C₁₃₉	—	4	16	no	—
132	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
133	C₂×C₄×C₁₃₉	C₂²×D₄	1	12	yes	—
134	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
135	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
136	C₂×C₄×C₁₃₉	C₂²×D₄	1	6	yes	—
137	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	6	yes	—
138	C₂²×C₁₃₉	—	2	12	no	—
139	C₂²×C₁₃₉	—	2	12	no	—
140	C₂²×C₁₃₉	—	2	24	no	—
141	C₂²×C₁₃₉	—	4	4	no	—
142	C₂²×C₁₃₉	—	4	12	no	—
143	C₂²×C₁₃₉	—	4	8	no	—
144	C₂²×C₁₃₉	—	4	24	no	—
145	C₂²×C₁₃₉	—	4	24	no	—
146	C₂²×C₁₃₉	—	8	64	no	—
147	C₂²×C₁₃₉	C₂×#127	1	8	yes	complemented
148	C₂²×C₁₃₉	C₂³×D₄	1	3	yes	—
149	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
150	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	3	yes	—
151	C₄×C₁₃₉	—	2	12	no	—
152	C₄×C₁₃₉	—	2	6	no	—
153	C₄×C₁₃₉	—	4	4	no	—
154	C₄×C₁₃₉	C₂×#127	1	4	yes	complemented
155	C₄×C₁₃₉	D₄²	1	12	yes	complemented
156	C₂×C₁₃₉	—	2	8	no	—
157	C₂×C₁₃₉	—	4	8	no	—
158	C₂×C₁₃₉	—	8	8	no	—
159	C₂×C₁₃₉	C₂²×#127	1	1	yes	characteristic
160	C₂×C₁₃₉	C₂×D₄²	1	3	yes	—
161	C₂×C₁₃₉	#3498	1	3	yes	—
162	D₄×#127	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₁₃₉	D₄×#127	1	1	yes	characteristic, direct product factor, Sylow
164	C₂×D₄²	C₂×C₁₃₉	1	6	yes	complemented
165	C₂²×#127	C₂×C₁₃₉	1	2	yes	complemented
166	#2867	C₂×C₁₃₉	1	1	yes	characteristic, complemented
167	#2856	C₂×C₁₃₉	1	2	yes	complemented
168	#2541	C₂×C₁₃₉	1	6	yes	complemented
169	#2433	C₂×C₁₃₉	1	12	yes	complemented
170	C₄×#127	C₂×C₁₃₉	1	1	yes	characteristic, complemented
171	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
172	C₂³×D₄	C₂²×C₁₃₉	1	4	yes	—
173	C₂³×D₄	C₂²×C₁₃₉	1	12	yes	complemented
174	D₄²	—	2	48	no	—
175	C₂×#127	—	2	16	no	—
176	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
177	C₂×#127	C₂²×C₁₃₉	1	2	yes	complemented
178	C₂×#127	C₂²×C₁₃₉	1	6	yes	complemented
179	C₂×#127	C₂²×C₁₃₉	1	12	yes	complemented
180	C₂×#127	C₂²×C₁₃₉	1	6	yes	complemented
181	C₂×#121	C₂²×C₁₃₉	1	12	yes	complemented
182	C₂×#121	C₂²×C₁₃₉	1	12	yes	complemented
183	C₂×#120	C₂²×C₁₃₉	1	24	yes	complemented
184	C₂×C₄×D₄	C₂²×C₁₃₉	1	3	yes	—
185	C₂×C₄×D₄	C₂²×C₁₃₉	1	6	yes	complemented
186	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	complemented
187	#392	C₂²×C₁₃₉	1	24	yes	complemented
188	#390	C₂²×C₁₃₉	1	6	yes	complemented
189	#390	C₂²×C₁₃₉	1	12	yes	complemented
190	#384	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
191	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	3	yes	complemented
192	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	6	yes	complemented
193	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
194	C₂⁵	C₂³×C₁₃₉	1	8	yes	—
195	C₂²×D₄	—	2	48	no	—
196	C₂²×D₄	—	2	48	no	—
197	C₂²×D₄	—	2	48	no	—
198	C₂²×D₄	—	4	24	no	—
199	C₂²×D₄	C₂³×C₁₃₉	1	8	yes	—
200	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
201	C₂²×D₄	C₂³×C₁₃₉	1	12	yes	—
202	C₂²×D₄	C₂³×C₁₃₉	1	24	yes	—
203	C₂²×D₄	C₂³×C₁₃₉	1	6	yes	—
204	C₂²×D₄	C₂³×C₁₃₉	1	12	yes	—
205	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
206	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
207	C₂³×C₄	C₂³×C₁₃₉	1	6	yes	—
208	#127	—	2	48	no	—
209	#127	—	2	8	no	—
210	#127	—	2	24	no	—
211	#127	—	4	12	no	—
212	#127	D₄×C₁₃₉	1	8	yes	direct product factor
213	#121	—	2	48	no	—
214	#121	—	2	48	no	—
215	#120	—	2	96	no	—
216	C₄×D₄	—	2	24	no	—
217	C₄×D₄	D₄×C₁₃₉	1	24	yes	complemented
218	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	6	yes	—
219	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	3	yes	—
220	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	12	yes	—
221	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	24	yes	—
222	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	6	yes	—
223	C₂×C₄²	—	2	8	no	—
224	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
225	C₂×C₄²	C₂³×C₁₃₉	1	6	yes	—
226	C₂×C₄²	C₂³×C₁₃₉	1	3	yes	—
227	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
228	#95	C₂³×C₁₃₉	1	6	yes	—
229	C₂⁴	—	2	16	no	—
230	C₂⁴	—	2	48	no	—
231	C₂⁴	—	4	24	no	—
232	C₂⁴	C₂⁴×C₁₃₉	1	8	yes	—
233	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
234	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
235	C₂×D₄	—	2	48	no	—
236	C₂×D₄	—	2	48	no	—
237	C₂×D₄	—	2	12	no	—
238	C₂×D₄	—	2	48	no	—
239	C₂×D₄	—	2	24	no	—
240	C₂×D₄	—	2	24	no	—
241	C₂×D₄	—	2	24	no	—
242	C₂×D₄	—	2	24	no	—
243	C₂×D₄	—	2	12	no	—
244	C₂×D₄	—	2	24	no	—
245	C₂×D₄	—	4	192	no	—
246	C₂×D₄	—	4	24	no	—
247	C₂×D₄	—	4	24	no	—
248	C₂×D₄	—	4	64	no	—
249	C₂×D₄	C₂×D₄×C₁₃₉	1	12	yes	—
250	C₂×D₄	C₂×D₄×C₁₃₉	1	24	yes	complemented
251	C₂²×C₄	—	2	12	no	—
252	C₂²×C₄	—	2	12	no	—
253	C₂²×C₄	—	2	24	no	—
254	C₂²×C₄	C₂×D₄×C₁₃₉	1	24	yes	complemented
255	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
256	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
257	C₂²×C₄	C₂⁴×C₁₃₉	1	6	yes	—
258	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
259	C₂²×C₄	C₂⁴×C₁₃₉	1	3	yes	—
260	C₄⋊C₄	—	2	12	no	—
261	C₄⋊C₄	C₂×D₄×C₁₃₉	1	12	yes	complemented
262	C₂²⋊C₄	—	2	24	no	—
263	C₂²⋊C₄	—	2	48	no	—
264	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	24	yes	complemented
265	C₄²	—	2	12	no	—
266	C₄²	—	2	6	no	—
267	C₄²	C₂×D₄×C₁₃₉	1	4	yes	complemented
268	C₄²	C₂×D₄×C₁₃₉	1	12	yes	complemented
269	C₂³	—	2	2	no	—
270	C₂³	—	2	6	no	—
271	C₂³	—	2	12	no	—
272	C₂³	—	2	12	no	—
273	C₂³	—	2	24	no	—
274	C₂³	—	2	8	no	—
275	C₂³	—	2	24	no	—
276	C₂³	—	4	96	no	—
277	C₂³	—	4	32	no	—
278	C₂³	—	8	48	no	—
279	C₂³	C₂²×D₄×C₁₃₉	1	8	yes	—
280	C₂³	C₂²×D₄×C₁₃₉	1	12	yes	—
281	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
282	D₄	—	2	48	no	—
283	D₄	—	4	96	no	—
284	D₄	—	4	32	no	—
285	D₄	—	4	16	no	—
286	D₄	—	4	48	no	—
287	D₄	—	8	24	no	—
288	D₄	#127×C₁₃₉	1	16	yes	direct product factor
289	C₂×C₄	—	2	6	no	—
290	C₂×C₄	—	2	6	no	—
291	C₂×C₄	—	2	6	no	—
292	C₂×C₄	—	2	48	no	—
293	C₂×C₄	—	2	12	no	—
294	C₂×C₄	—	4	16	no	—
295	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
296	C₂×C₄	C₂²×D₄×C₁₃₉	1	12	yes	—
297	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
298	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
299	C₂×C₄	C₂²×D₄×C₁₃₉	1	6	yes	—
300	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	6	yes	—
301	C₂²	—	2	12	no	—
302	C₂²	—	2	12	no	—
303	C₂²	—	2	24	no	—
304	C₂²	—	4	4	no	—
305	C₂²	—	4	12	no	—
306	C₂²	—	4	8	no	—
307	C₂²	—	4	24	no	—
308	C₂²	—	4	24	no	—
309	C₂²	—	8	64	no	—
310	C₂²	C₂×#127×C₁₃₉	1	8	yes	complemented
311	C₂²	C₂³×D₄×C₁₃₉	1	3	yes	—
312	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
313	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	3	yes	—
314	C₄	—	2	12	no	—
315	C₄	—	2	6	no	—
316	C₄	—	4	4	no	—
317	C₄	C₂×#127×C₁₃₉	1	4	yes	complemented
318	C₄	D₄²×C₁₃₉	1	12	yes	complemented
319	C₂	—	2	8	no	—
320	C₂	—	4	8	no	—
321	C₂	—	8	8	no	—
322	C₂	C₂²×#127×C₁₃₉	1	1	yes	characteristic
323	C₂	C₂×D₄²×C₁₃₉	1	3	yes	—
324	C₂	#3498×C₁₃₉	1	3	yes	—

	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×D₄²×C₁₃₉	C₂	semidirect
2. C₂²×#127×C₁₃₉	C₂	semidirect
3. #2867×C₁₃₉	C₂	semidirect
4. #2856×C₁₃₉	C₂	semidirect
5. #2541×C₁₃₉	C₂	semidirect
6. #2433×C₁₃₉	C₂	semidirect
7. C₄×#127×C₁₃₉	C₂	semidirect
8. C₄²×D₄×C₁₃₉	C₂	semidirect
10. C₂³×D₄×C₁₃₉	C₂²	semidirect
14. C₂×#127×C₁₃₉	C₂²	semidirect
15. C₂×#127×C₁₃₉	C₂²	semidirect
16. C₂×#127×C₁₃₉	C₂²	semidirect
17. C₂×#127×C₁₃₉	C₂²	semidirect
18. C₂×#121×C₁₃₉	C₂²	semidirect
19. C₂×#121×C₁₃₉	C₂²	semidirect
20. C₂×#120×C₁₃₉	C₂²	semidirect
22. C₂×C₄×D₄×C₁₃₉	C₂²	semidirect
23. C₂²×C₄²×C₁₃₉	C₂²	semidirect
24. #392×C₁₃₉	C₂²	semidirect
25. #390×C₁₃₉	C₂²	semidirect
26. #390×C₁₃₉	C₂²	semidirect
27. #384×C₁₃₉	C₂²	semidirect
28. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
29. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
30. C₄³×C₁₃₉	C₂²	semidirect
49. #127×C₁₃₉	D₄	direct (N × H)
54. C₄×D₄×C₁₃₉	D₄	semidirect
87. C₂×D₄×C₁₃₉	C₂×D₄	semidirect
91. C₂²×C₄×C₁₃₉	C₂×D₄	semidirect
98. C₄⋊C₄×C₁₃₉	C₂×D₄	semidirect
101. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
104. C₄²×C₁₃₉	C₂×D₄	semidirect
105. C₄²×C₁₃₉	C₂×D₄	semidirect
125. D₄×C₁₃₉	#127	direct (N × H)
147. C₂²×C₁₃₉	C₂×#127	semidirect
154. C₄×C₁₃₉	C₂×#127	semidirect
155. C₄×C₁₃₉	D₄²	semidirect
162. D₄×#127	C₁₃₉	direct (N × H)
163. C₁₃₉	D₄×#127	direct (N × H)
164. C₂×D₄²	C₂×C₁₃₉	semidirect
165. C₂²×#127	C₂×C₁₃₉	semidirect
166. #2867	C₂×C₁₃₉	semidirect
167. #2856	C₂×C₁₃₉	semidirect
168. #2541	C₂×C₁₃₉	semidirect
169. #2433	C₂×C₁₃₉	semidirect
170. C₄×#127	C₂×C₁₃₉	semidirect
171. C₄²×D₄	C₂×C₁₃₉	semidirect
173. C₂³×D₄	C₂²×C₁₃₉	semidirect
177. C₂×#127	C₂²×C₁₃₉	semidirect
178. C₂×#127	C₂²×C₁₃₉	semidirect
179. C₂×#127	C₂²×C₁₃₉	semidirect
180. C₂×#127	C₂²×C₁₃₉	semidirect
181. C₂×#121	C₂²×C₁₃₉	semidirect
182. C₂×#121	C₂²×C₁₃₉	semidirect
183. C₂×#120	C₂²×C₁₃₉	semidirect
185. C₂×C₄×D₄	C₂²×C₁₃₉	semidirect
186. C₂²×C₄²	C₂²×C₁₃₉	semidirect
187. #392	C₂²×C₁₃₉	semidirect
188. #390	C₂²×C₁₃₉	semidirect
189. #390	C₂²×C₁₃₉	semidirect
190. #384	C₂²×C₁₃₉	semidirect
191. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
192. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
193. C₄³	C₂²×C₁₃₉	semidirect
212. #127	D₄×C₁₃₉	direct (N × H)
217. C₄×D₄	D₄×C₁₃₉	semidirect
250. C₂×D₄	C₂×D₄×C₁₃₉	semidirect
254. C₂²×C₄	C₂×D₄×C₁₃₉	semidirect
261. C₄⋊C₄	C₂×D₄×C₁₃₉	semidirect
264. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
267. C₄²	C₂×D₄×C₁₃₉	semidirect
268. C₄²	C₂×D₄×C₁₃₉	semidirect
288. D₄	#127×C₁₃₉	direct (N × H)
310. C₂²	C₂×#127×C₁₃₉	semidirect
317. C₄	C₂×#127×C₁₃₉	semidirect
318. C₄	D₄²×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₁₃₉	2
C₂²×#127×C₁₃₉	2
#2867×C₁₃₉	2
#2856×C₁₃₉	2
#2541×C₁₃₉	2
#2433×C₁₃₉	2
C₄×#127×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
D₄×#127	139

Subgroups — D4×#127×C139 #48030715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#127×C₁₃₉ #48030715