Subgroups — D₄×#124×C₁₃₉ #48030700

Order 35584.

3574 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#124×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2850×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2548×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2547×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#2491×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2472×C₁₃₉	C₂	1	8	yes	maximal, complemented
10	#2436×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2435×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊C₄×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	C₄×#124×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	complemented
16	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
17	C₂³×D₄×C₁₃₉	C₂²	1	2	yes	—
18	D₄×Q₈×C₁₃₉	—	2	8	no	—
19	D₄²×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
22	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#124×C₁₃₉	—	2	16	no	—
24	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
27	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
28	C₂×#124×C₁₃₉	C₂²	1	8	yes	complemented
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	complemented
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	complemented
32	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#120×C₁₃₉	C₂²	1	4	yes	—
35	C₂×C₄×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₁₃₉	C₂²	1	8	yes	complemented
41	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	complemented
42	#397×C₁₃₉	C₂²	1	4	yes	complemented
43	#394×C₁₃₉	C₂²	1	4	yes	complemented
44	#394×C₁₃₉	C₂²	1	8	yes	complemented
45	#393×C₁₃₉	C₂²	1	8	yes	complemented
46	#391×C₁₃₉	C₂²	1	2	yes	complemented
47	#391×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
48	#390×C₁₃₉	C₂²	1	1	yes	characteristic
49	#390×C₁₃₉	C₂²	1	4	yes	complemented
50	#390×C₁₃₉	C₂²	1	2	yes	complemented
51	#390×C₁₃₉	C₂²	1	4	yes	complemented
52	#390×C₁₃₉	C₂²	1	4	yes	complemented
53	#388×C₁₃₉	C₂²	1	4	yes	complemented
54	#388×C₁₃₉	C₂²	1	8	yes	complemented
55	#386×C₁₃₉	C₂²	1	8	yes	complemented
56	#386×C₁₃₉	C₂²	1	8	yes	complemented
57	#382×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
58	#380×C₁₃₉	C₂²	1	4	yes	complemented
59	#379×C₁₃₉	C₂²	1	8	yes	complemented
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
62	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	complemented
65	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
66	C₂⁵×C₁₃₉	C₂³	1	4	yes	—
67	C₂²×Q₈×C₁₃₉	—	2	8	no	—
68	C₂²×Q₈×C₁₃₉	—	2	8	no	—
69	C₂²×Q₈×C₁₃₉	—	4	4	no	—
70	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
71	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
72	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃₉	—	2	8	no	—
74	C₂²×D₄×C₁₃₉	—	2	8	no	—
75	C₂²×D₄×C₁₃₉	—	2	16	no	—
76	C₂²×D₄×C₁₃₉	—	2	8	no	—
77	C₂²×D₄×C₁₃₉	—	4	4	no	—
78	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
82	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
90	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
91	#127×C₁₃₉	—	2	4	no	—
92	#124×C₁₃₉	—	2	8	no	—
93	#124×C₁₃₉	—	2	8	no	—
94	#124×C₁₃₉	—	2	32	no	—
95	#124×C₁₃₉	—	2	8	no	—
96	#124×C₁₃₉	—	4	4	no	—
97	#124×C₁₃₉	D₄	1	8	yes	direct product factor
98	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
99	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
100	#121×C₁₃₉	—	2	8	no	—
101	#121×C₁₃₉	—	2	8	no	—
102	#120×C₁₃₉	—	2	16	no	—
103	C₄×Q₈×C₁₃₉	—	2	4	no	—
104	C₄×D₄×C₁₃₉	—	2	8	no	—
105	C₄×D₄×C₁₃₉	—	2	8	no	—
106	C₄×D₄×C₁₃₉	—	2	4	no	—
107	C₄×D₄×C₁₃₉	D₄	1	8	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₁₃₉	—	2	32	no	—
117	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	8	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₃₉	—	2	8	no	—
130	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
138	#95×C₁₃₉	C₂³	1	2	yes	—
139	#95×C₁₃₉	C₂³	1	8	yes	—
140	#95×C₁₃₉	C₂³	1	4	yes	—
141	#95×C₁₃₉	C₂³	1	4	yes	—
142	#95×C₁₃₉	C₂³	1	4	yes	—
143	C₂⁴×C₁₃₉	—	2	8	no	—
144	C₂⁴×C₁₃₉	—	2	8	no	—
145	C₂⁴×C₁₃₉	—	2	16	no	—
146	C₂⁴×C₁₃₉	—	4	4	no	—
147	C₂⁴×C₁₃₉	—	4	8	no	—
148	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
149	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
150	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
151	C₂×Q₈×C₁₃₉	—	2	2	no	—
152	C₂×Q₈×C₁₃₉	—	2	8	no	—
153	C₂×Q₈×C₁₃₉	—	2	4	no	—
154	C₂×Q₈×C₁₃₉	—	2	8	no	—
155	C₂×Q₈×C₁₃₉	—	2	4	no	—
156	C₂×Q₈×C₁₃₉	—	2	2	no	—
157	C₂×Q₈×C₁₃₉	—	2	4	no	—
158	C₂×Q₈×C₁₃₉	—	4	4	no	—
159	C₂×Q₈×C₁₃₉	—	4	32	no	—
160	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	complemented
161	C₂×D₄×C₁₃₉	—	2	8	no	—
162	C₂×D₄×C₁₃₉	—	2	8	no	—
163	C₂×D₄×C₁₃₉	—	2	16	no	—
164	C₂×D₄×C₁₃₉	—	2	2	no	—
165	C₂×D₄×C₁₃₉	—	2	8	no	—
166	C₂×D₄×C₁₃₉	—	2	4	no	—
167	C₂×D₄×C₁₃₉	—	2	4	no	—
168	C₂×D₄×C₁₃₉	—	2	4	no	—
169	C₂×D₄×C₁₃₉	—	2	4	no	—
170	C₂×D₄×C₁₃₉	—	2	8	no	—
171	C₂×D₄×C₁₃₉	—	2	2	no	—
172	C₂×D₄×C₁₃₉	—	2	4	no	—
173	C₂×D₄×C₁₃₉	—	4	32	no	—
174	C₂×D₄×C₁₃₉	—	4	4	no	—
175	C₂×D₄×C₁₃₉	—	4	4	no	—
176	C₂×D₄×C₁₃₉	—	4	32	no	—
177	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
178	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
179	C₂×D₄×C₁₃₉	#41	1	8	yes	—
180	C₂²×C₄×C₁₃₉	—	2	4	no	—
181	C₂²×C₄×C₁₃₉	—	2	4	no	—
182	C₂²×C₄×C₁₃₉	—	2	8	no	—
183	C₂²×C₄×C₁₃₉	—	2	8	no	—
184	C₂²×C₄×C₁₃₉	—	2	8	no	—
185	C₂²×C₄×C₁₃₉	—	2	8	no	—
186	C₂²×C₄×C₁₃₉	—	2	4	no	—
187	C₂²×C₄×C₁₃₉	—	2	8	no	—
188	C₂²×C₄×C₁₃₉	—	4	4	no	—
189	C₂²×C₄×C₁₃₉	—	4	4	no	—
190	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
191	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
196	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
202	C₄⋊C₄×C₁₃₉	—	2	2	no	—
203	C₄⋊C₄×C₁₃₉	—	2	4	no	—
204	C₄⋊C₄×C₁₃₉	—	2	4	no	—
205	C₄⋊C₄×C₁₃₉	—	2	2	no	—
206	C₄⋊C₄×C₁₃₉	—	2	8	no	—
207	C₄⋊C₄×C₁₃₉	—	2	4	no	—
208	C₄⋊C₄×C₁₃₉	—	2	4	no	—
209	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
210	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
211	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
212	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
213	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
214	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
215	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
216	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
217	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
218	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
219	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
220	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	8	yes	—
221	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	complemented
222	C₄²×C₁₃₉	—	2	8	no	—
223	C₄²×C₁₃₉	—	2	4	no	—
224	C₄²×C₁₃₉	—	2	4	no	—
225	C₄²×C₁₃₉	—	2	4	no	—
226	C₄²×C₁₃₉	—	2	2	no	—
227	C₄²×C₁₃₉	—	4	2	no	—
228	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
229	C₄²×C₁₃₉	C₂×D₄	1	4	yes	complemented
230	C₂³×C₁₃₉	—	2	2	no	—
231	C₂³×C₁₃₉	—	2	2	no	—
232	C₂³×C₁₃₉	—	2	4	no	—
233	C₂³×C₁₃₉	—	2	2	no	—
234	C₂³×C₁₃₉	—	2	4	no	—
235	C₂³×C₁₃₉	—	2	2	no	—
236	C₂³×C₁₃₉	—	2	4	no	—
237	C₂³×C₁₃₉	—	2	4	no	—
238	C₂³×C₁₃₉	—	2	4	no	—
239	C₂³×C₁₃₉	—	2	8	no	—
240	C₂³×C₁₃₉	—	2	4	no	—
241	C₂³×C₁₃₉	—	2	8	no	—
242	C₂³×C₁₃₉	—	4	16	no	—
243	C₂³×C₁₃₉	—	4	32	no	—
244	C₂³×C₁₃₉	—	4	16	no	—
245	C₂³×C₁₃₉	—	8	8	no	—
246	C₂³×C₁₃₉	—	8	16	no	—
247	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
248	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
249	C₂³×C₁₃₉	C₂×#41	1	8	yes	—
250	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
251	Q₈×C₁₃₉	—	2	8	no	—
252	Q₈×C₁₃₉	—	4	16	no	—
253	Q₈×C₁₃₉	—	4	8	no	—
254	D₄×C₁₃₉	—	2	8	no	—
255	D₄×C₁₃₉	—	4	16	no	—
256	D₄×C₁₃₉	—	4	16	no	—
257	D₄×C₁₃₉	—	4	8	no	—
258	D₄×C₁₃₉	—	4	8	no	—
259	D₄×C₁₃₉	—	8	4	no	—
260	D₄×C₁₃₉	#124	1	16	yes	direct product factor
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	2	no	—
263	C₂×C₄×C₁₃₉	—	2	2	no	—
264	C₂×C₄×C₁₃₉	—	2	2	no	—
265	C₂×C₄×C₁₃₉	—	2	2	no	—
266	C₂×C₄×C₁₃₉	—	2	2	no	—
267	C₂×C₄×C₁₃₉	—	2	2	no	—
268	C₂×C₄×C₁₃₉	—	2	16	no	—
269	C₂×C₄×C₁₃₉	—	2	4	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	4	no	—
272	C₂×C₄×C₁₃₉	—	2	2	no	—
273	C₂×C₄×C₁₃₉	—	2	4	no	—
274	C₂×C₄×C₁₃₉	—	2	2	no	—
275	C₂×C₄×C₁₃₉	—	2	4	no	—
276	C₂×C₄×C₁₃₉	—	2	4	no	—
277	C₂×C₄×C₁₃₉	—	2	2	no	—
278	C₂×C₄×C₁₃₉	—	2	4	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	4	no	—
281	C₂×C₄×C₁₃₉	—	2	4	no	—
282	C₂×C₄×C₁₃₉	—	4	16	no	—
283	C₂×C₄×C₁₃₉	—	4	16	no	—
284	C₂×C₄×C₁₃₉	—	4	8	no	—
285	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
288	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
289	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
293	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
294	C₂²×C₁₃₉	—	2	4	no	—
295	C₂²×C₁₃₉	—	2	8	no	—
296	C₂²×C₁₃₉	—	2	4	no	—
297	C₂²×C₁₃₉	—	2	8	no	—
298	C₂²×C₁₃₉	—	2	4	no	—
299	C₂²×C₁₃₉	—	2	8	no	—
300	C₂²×C₁₃₉	—	4	2	no	—
301	C₂²×C₁₃₉	—	4	2	no	—
302	C₂²×C₁₃₉	—	4	4	no	—
303	C₂²×C₁₃₉	—	4	4	no	—
304	C₂²×C₁₃₉	—	4	4	no	—
305	C₂²×C₁₃₉	—	4	8	no	—
306	C₂²×C₁₃₉	—	4	4	no	—
307	C₂²×C₁₃₉	—	4	8	no	—
308	C₂²×C₁₃₉	—	8	32	no	—
309	C₂²×C₁₃₉	C₂×#124	1	8	yes	complemented
310	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
311	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
312	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
313	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂²×C₁₃₉	#585	1	2	yes	—
315	C₄×C₁₃₉	—	2	4	no	—
316	C₄×C₁₃₉	—	2	4	no	—
317	C₄×C₁₃₉	—	2	4	no	—
318	C₄×C₁₃₉	—	2	2	no	—
319	C₄×C₁₃₉	—	4	2	no	—
320	C₄×C₁₃₉	—	4	4	no	—
321	C₄×C₁₃₉	—	4	4	no	—
322	C₄×C₁₃₉	—	4	2	no	—
323	C₄×C₁₃₉	—	4	2	no	—
324	C₄×C₁₃₉	C₂×#124	1	4	yes	complemented
325	C₄×C₁₃₉	D₄²	1	4	yes	—
326	C₂×C₁₃₉	—	2	8	no	—
327	C₂×C₁₃₉	—	4	4	no	—
328	C₂×C₁₃₉	—	8	4	no	—
329	C₂×C₁₃₉	C₂²×#124	1	1	yes	characteristic
330	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
331	C₂×C₁₃₉	D₄×#41	1	2	yes	—
332	C₂×C₁₃₉	#3500	1	1	yes	characteristic
333	C₂×C₁₃₉	#3514	1	2	yes	—
334	D₄×#124	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₁₃₉	D₄×#124	1	1	yes	characteristic, direct product factor, Sylow
336	C₂×D₄×Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
337	C₂×D₄²	C₂×C₁₃₉	1	1	yes	characteristic
338	C₂²×#124	C₂×C₁₃₉	1	2	yes	complemented
339	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
340	#2850	C₂×C₁₃₉	1	2	yes	complemented
341	#2548	C₂×C₁₃₉	1	1	yes	characteristic, complemented
342	#2547	C₂×C₁₃₉	1	1	yes	characteristic, complemented
343	#2491	C₂×C₁₃₉	1	4	yes	complemented
344	#2472	C₂×C₁₃₉	1	8	yes	complemented
345	#2436	C₂×C₁₃₉	1	2	yes	complemented
346	#2435	C₂×C₁₃₉	1	2	yes	complemented
347	D₄×C₂²⋊C₄	C₂×C₁₃₉	1	4	yes	complemented
348	C₄×#124	C₂×C₁₃₉	1	1	yes	characteristic, complemented
349	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
350	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	complemented
351	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
352	C₂³×D₄	C₂²×C₁₃₉	1	2	yes	—
353	D₄×Q₈	—	2	8	no	—
354	D₄²	—	2	8	no	—
355	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
356	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
357	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
358	C₂×#124	—	2	16	no	—
359	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
360	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
361	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
362	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
363	C₂×#124	C₂²×C₁₃₉	1	8	yes	complemented
364	C₂×#124	C₂²×C₁₃₉	1	2	yes	complemented
365	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	complemented
366	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	complemented
367	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
368	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
369	C₂×#120	C₂²×C₁₃₉	1	4	yes	—
370	C₂×C₄×Q₈	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
371	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
372	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
373	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
375	C₂²×C₂²⋊C₄	C₂²×C₁₃₉	1	8	yes	complemented
376	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	complemented
377	#397	C₂²×C₁₃₉	1	4	yes	complemented
378	#394	C₂²×C₁₃₉	1	8	yes	complemented
379	#394	C₂²×C₁₃₉	1	4	yes	complemented
380	#393	C₂²×C₁₃₉	1	8	yes	complemented
381	#391	C₂²×C₁₃₉	1	2	yes	complemented
382	#391	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
383	#390	C₂²×C₁₃₉	1	1	yes	characteristic
384	#390	C₂²×C₁₃₉	1	4	yes	complemented
385	#390	C₂²×C₁₃₉	1	4	yes	complemented
386	#390	C₂²×C₁₃₉	1	2	yes	complemented
387	#390	C₂²×C₁₃₉	1	4	yes	complemented
388	#388	C₂²×C₁₃₉	1	8	yes	complemented
389	#388	C₂²×C₁₃₉	1	4	yes	complemented
390	#386	C₂²×C₁₃₉	1	8	yes	complemented
391	#386	C₂²×C₁₃₉	1	8	yes	complemented
392	#382	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
393	#380	C₂²×C₁₃₉	1	4	yes	complemented
394	#379	C₂²×C₁₃₉	1	8	yes	complemented
395	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
396	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
397	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
398	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	complemented
399	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	complemented
400	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic, complemented
401	C₂⁵	C₂³×C₁₃₉	1	4	yes	—
402	C₂²×Q₈	—	2	8	no	—
403	C₂²×Q₈	—	2	8	no	—
404	C₂²×Q₈	—	4	4	no	—
405	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
406	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
407	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
408	C₂²×D₄	—	2	8	no	—
409	C₂²×D₄	—	2	8	no	—
410	C₂²×D₄	—	2	16	no	—
411	C₂²×D₄	—	2	8	no	—
412	C₂²×D₄	—	4	4	no	—
413	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
414	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
415	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
416	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
417	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
418	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
419	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
421	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
422	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
423	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
424	C₄⋊Q₈	—	2	8	no	—
425	C₄⋊Q₈	—	2	4	no	—
426	#127	—	2	4	no	—
427	#124	—	2	8	no	—
428	#124	—	2	8	no	—
429	#124	—	2	32	no	—
430	#124	—	2	8	no	—
431	#124	—	4	4	no	—
432	#124	D₄×C₁₃₉	1	8	yes	direct product factor
433	C₂²⋊Q₈	—	2	8	no	—
434	C₂²⋊Q₈	—	2	16	no	—
435	#121	—	2	8	no	—
436	#121	—	2	8	no	—
437	#120	—	2	16	no	—
438	C₄×Q₈	—	2	4	no	—
439	C₄×D₄	—	2	8	no	—
440	C₄×D₄	—	2	8	no	—
441	C₄×D₄	—	2	4	no	—
442	C₄×D₄	D₄×C₁₃₉	1	8	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	—	2	32	no	—
452	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
464	C₂×C₄²	—	2	8	no	—
465	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
466	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
467	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
468	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
470	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
471	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
473	#95	C₂³×C₁₃₉	1	4	yes	—
474	#95	C₂³×C₁₃₉	1	2	yes	—
475	#95	C₂³×C₁₃₉	1	4	yes	—
476	#95	C₂³×C₁₃₉	1	4	yes	—
477	#95	C₂³×C₁₃₉	1	8	yes	—
478	C₂⁴	—	2	8	no	—
479	C₂⁴	—	2	8	no	—
480	C₂⁴	—	2	16	no	—
481	C₂⁴	—	4	4	no	—
482	C₂⁴	—	4	8	no	—
483	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
484	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
485	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
486	C₂×Q₈	—	2	2	no	—
487	C₂×Q₈	—	2	8	no	—
488	C₂×Q₈	—	2	4	no	—
489	C₂×Q₈	—	2	8	no	—
490	C₂×Q₈	—	2	4	no	—
491	C₂×Q₈	—	2	2	no	—
492	C₂×Q₈	—	2	4	no	—
493	C₂×Q₈	—	4	4	no	—
494	C₂×Q₈	—	4	32	no	—
495	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	complemented
496	C₂×D₄	—	2	8	no	—
497	C₂×D₄	—	2	8	no	—
498	C₂×D₄	—	2	16	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	8	no	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	2	4	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	8	no	—
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	4	32	no	—
509	C₂×D₄	—	4	4	no	—
510	C₂×D₄	—	4	4	no	—
511	C₂×D₄	—	4	32	no	—
512	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
513	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
514	C₂×D₄	#41×C₁₃₉	1	8	yes	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	8	no	—
518	C₂²×C₄	—	2	8	no	—
519	C₂²×C₄	—	2	8	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	2	8	no	—
523	C₂²×C₄	—	4	4	no	—
524	C₂²×C₄	—	4	4	no	—
525	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
526	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	8	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
545	C₂²⋊C₄	—	2	16	no	—
546	C₂²⋊C₄	—	2	8	no	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	16	no	—
549	C₂²⋊C₄	—	2	16	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	8	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	8	no	—
554	C₂²⋊C₄	—	4	8	no	—
555	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	8	yes	—
556	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	complemented
557	C₄²	—	2	8	no	—
558	C₄²	—	2	4	no	—
559	C₄²	—	2	4	no	—
560	C₄²	—	2	4	no	—
561	C₄²	—	2	2	no	—
562	C₄²	—	4	2	no	—
563	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
564	C₄²	C₂×D₄×C₁₃₉	1	4	yes	complemented
565	C₂³	—	2	2	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	2	4	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	2	4	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	2	4	no	—
573	C₂³	—	2	4	no	—
574	C₂³	—	2	8	no	—
575	C₂³	—	2	4	no	—
576	C₂³	—	2	8	no	—
577	C₂³	—	4	16	no	—
578	C₂³	—	4	32	no	—
579	C₂³	—	4	16	no	—
580	C₂³	—	8	8	no	—
581	C₂³	—	8	16	no	—
582	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
583	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
584	C₂³	C₂×#41×C₁₃₉	1	8	yes	—
585	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
586	Q₈	—	2	8	no	—
587	Q₈	—	4	16	no	—
588	Q₈	—	4	8	no	—
589	D₄	—	2	8	no	—
590	D₄	—	4	16	no	—
591	D₄	—	4	16	no	—
592	D₄	—	4	8	no	—
593	D₄	—	4	8	no	—
594	D₄	—	8	4	no	—
595	D₄	#124×C₁₃₉	1	16	yes	direct product factor
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	16	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	4	16	no	—
618	C₂×C₄	—	4	16	no	—
619	C₂×C₄	—	4	8	no	—
620	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
621	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
622	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
623	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
624	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
625	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
626	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
627	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
628	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
629	C₂²	—	2	4	no	—
630	C₂²	—	2	8	no	—
631	C₂²	—	2	4	no	—
632	C₂²	—	2	8	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	8	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	4	no	—
638	C₂²	—	4	4	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	4	8	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	8	no	—
643	C₂²	—	8	32	no	—
644	C₂²	C₂×#124×C₁₃₉	1	8	yes	complemented
645	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
646	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
647	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
648	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
649	C₂²	#585×C₁₃₉	1	2	yes	—
650	C₄	—	2	4	no	—
651	C₄	—	2	4	no	—
652	C₄	—	2	4	no	—
653	C₄	—	2	2	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	4	no	—
656	C₄	—	4	4	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	C₂×#124×C₁₃₉	1	4	yes	complemented
660	C₄	D₄²×C₁₃₉	1	4	yes	—
661	C₂	—	2	8	no	—
662	C₂	—	4	4	no	—
663	C₂	—	8	4	no	—
664	C₂	C₂²×#124×C₁₃₉	1	1	yes	characteristic
665	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
666	C₂	D₄×#41×C₁₃₉	1	2	yes	—
667	C₂	#3500×C₁₃₉	1	1	yes	characteristic
668	C₂	#3514×C₁₃₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
prime radical	C₂×D₄²×C₁₃₉	C₂
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×D₄×Q₈×C₁₃₉	C₂	semidirect
3. C₂²×#124×C₁₃₉	C₂	semidirect
4. #2858×C₁₃₉	C₂	semidirect
5. #2850×C₁₃₉	C₂	semidirect
6. #2548×C₁₃₉	C₂	semidirect
7. #2547×C₁₃₉	C₂	semidirect
8. #2491×C₁₃₉	C₂	semidirect
9. #2472×C₁₃₉	C₂	semidirect
10. #2436×C₁₃₉	C₂	semidirect
11. #2435×C₁₃₉	C₂	semidirect
12. D₄×C₂²⋊C₄×C₁₃₉	C₂	semidirect
13. C₄×#124×C₁₃₉	C₂	semidirect
14. C₄²×D₄×C₁₃₉	C₂	semidirect
15. C₂³×Q₈×C₁₃₉	C₂²	semidirect
20. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
21. C₂×C₄⋊Q₈×C₁₃₉	C₂²	semidirect
26. C₂×#124×C₁₃₉	C₂²	semidirect
27. C₂×#124×C₁₃₉	C₂²	semidirect
28. C₂×#124×C₁₃₉	C₂²	semidirect
29. C₂×#124×C₁₃₉	C₂²	semidirect
30. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₁₃₉	C₂²	semidirect
35. C₂×C₄×Q₈×C₁₃₉	C₂²	semidirect
40. C₂²×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
41. C₂²×C₄²×C₁₃₉	C₂²	semidirect
42. #397×C₁₃₉	C₂²	semidirect
43. #394×C₁₃₉	C₂²	semidirect
44. #394×C₁₃₉	C₂²	semidirect
45. #393×C₁₃₉	C₂²	semidirect
46. #391×C₁₃₉	C₂²	semidirect
47. #391×C₁₃₉	C₂²	semidirect
49. #390×C₁₃₉	C₂²	semidirect
50. #390×C₁₃₉	C₂²	semidirect
51. #390×C₁₃₉	C₂²	semidirect
52. #390×C₁₃₉	C₂²	semidirect
53. #388×C₁₃₉	C₂²	semidirect
54. #388×C₁₃₉	C₂²	semidirect
55. #386×C₁₃₉	C₂²	semidirect
56. #386×C₁₃₉	C₂²	semidirect
57. #382×C₁₃₉	C₂²	semidirect
58. #380×C₁₃₉	C₂²	semidirect
59. #379×C₁₃₉	C₂²	semidirect
60. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
61. C₄×C₄⋊C₄×C₁₃₉	C₂²	semidirect
62. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
63. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
64. C₄×C₂²⋊C₄×C₁₃₉	C₂²	semidirect
65. C₄³×C₁₃₉	C₂²	semidirect
97. #124×C₁₃₉	D₄	direct (N × H)
160. C₂×Q₈×C₁₃₉	C₂×D₄	semidirect
221. C₂²⋊C₄×C₁₃₉	C₂×D₄	semidirect
229. C₄²×C₁₃₉	C₂×D₄	semidirect
260. D₄×C₁₃₉	#124	direct (N × H)
309. C₂²×C₁₃₉	C₂×#124	semidirect
324. C₄×C₁₃₉	C₂×#124	semidirect
334. D₄×#124	C₁₃₉	direct (N × H)
335. C₁₃₉	D₄×#124	direct (N × H)
336. C₂×D₄×Q₈	C₂×C₁₃₉	semidirect
338. C₂²×#124	C₂×C₁₃₉	semidirect
339. #2858	C₂×C₁₃₉	semidirect
340. #2850	C₂×C₁₃₉	semidirect
341. #2548	C₂×C₁₃₉	semidirect
342. #2547	C₂×C₁₃₉	semidirect
343. #2491	C₂×C₁₃₉	semidirect
344. #2472	C₂×C₁₃₉	semidirect
345. #2436	C₂×C₁₃₉	semidirect
346. #2435	C₂×C₁₃₉	semidirect
347. D₄×C₂²⋊C₄	C₂×C₁₃₉	semidirect
348. C₄×#124	C₂×C₁₃₉	semidirect
349. C₄²×D₄	C₂×C₁₃₉	semidirect
350. C₂³×Q₈	C₂²×C₁₃₉	semidirect
355. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
356. C₂×C₄⋊Q₈	C₂²×C₁₃₉	semidirect
361. C₂×#124	C₂²×C₁₃₉	semidirect
362. C₂×#124	C₂²×C₁₃₉	semidirect
363. C₂×#124	C₂²×C₁₃₉	semidirect
364. C₂×#124	C₂²×C₁₃₉	semidirect
365. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
366. C₂×C₂²⋊Q₈	C₂²×C₁₃₉	semidirect
370. C₂×C₄×Q₈	C₂²×C₁₃₉	semidirect
375. C₂²×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
376. C₂²×C₄²	C₂²×C₁₃₉	semidirect
377. #397	C₂²×C₁₃₉	semidirect
378. #394	C₂²×C₁₃₉	semidirect
379. #394	C₂²×C₁₃₉	semidirect
380. #393	C₂²×C₁₃₉	semidirect
381. #391	C₂²×C₁₃₉	semidirect
382. #391	C₂²×C₁₃₉	semidirect
384. #390	C₂²×C₁₃₉	semidirect
385. #390	C₂²×C₁₃₉	semidirect
386. #390	C₂²×C₁₃₉	semidirect
387. #390	C₂²×C₁₃₉	semidirect
388. #388	C₂²×C₁₃₉	semidirect
389. #388	C₂²×C₁₃₉	semidirect
390. #386	C₂²×C₁₃₉	semidirect
391. #386	C₂²×C₁₃₉	semidirect
392. #382	C₂²×C₁₃₉	semidirect
393. #380	C₂²×C₁₃₉	semidirect
394. #379	C₂²×C₁₃₉	semidirect
395. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
396. C₄×C₄⋊C₄	C₂²×C₁₃₉	semidirect
397. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
398. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
399. C₄×C₂²⋊C₄	C₂²×C₁₃₉	semidirect
400. C₄³	C₂²×C₁₃₉	semidirect
432. #124	D₄×C₁₃₉	direct (N × H)
495. C₂×Q₈	C₂×D₄×C₁₃₉	semidirect
556. C₂²⋊C₄	C₂×D₄×C₁₃₉	semidirect
564. C₄²	C₂×D₄×C₁₃₉	semidirect
595. D₄	#124×C₁₃₉	direct (N × H)
644. C₂²	C₂×#124×C₁₃₉	semidirect
659. C₄	C₂×#124×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₃₉	2
C₂×D₄²×C₁₃₉	2
C₂²×#124×C₁₃₉	2
#2858×C₁₃₉	2
#2850×C₁₃₉	2
#2548×C₁₃₉	2
#2547×C₁₃₉	2
#2491×C₁₃₉	2
#2472×C₁₃₉	2
#2436×C₁₃₉	2
#2435×C₁₃₉	2
D₄×C₂²⋊C₄×C₁₃₉	2
C₄×#124×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
D₄×#124	139

Subgroups — D4×#124×C139 #48030700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#124×C₁₃₉ #48030700