Subgroups — C₁₃₉×#36122 #48030718

Order 35584.

3214 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#548×C₁₃₉	C₂	1	2	yes	maximal, complemented
2	C₂×#532×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#2858×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#2545×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2491×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2452×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	#2436×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2432×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2416×C₁₃₉	C₂	1	4	yes	maximal, complemented
13	#2361×C₁₃₉	C₂	1	4	yes	maximal, complemented
14	C₄×C₄⋊Q₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄²×D₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₃₉	C₂²	1	2	yes	—
17	C₂³×Q₈×C₁₃₉	C₂²	1	2	yes	—
18	#548×C₁₃₉	—	2	16	no	—
19	#532×C₁₃₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₁₃₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
24	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
25	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
26	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
28	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
29	C₂×#124×C₁₃₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	4	yes	—
32	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
33	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
34	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
35	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
36	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
39	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
40	C₂×C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
42	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
44	#396×C₁₃₉	C₂²	1	8	yes	—
45	#394×C₁₃₉	C₂²	1	8	yes	—
46	#393×C₁₃₉	C₂²	1	8	yes	—
47	#391×C₁₃₉	C₂²	1	2	yes	—
48	#391×C₁₃₉	C₂²	1	2	yes	—
49	#390×C₁₃₉	C₂²	1	2	yes	—
50	#390×C₁₃₉	C₂²	1	4	yes	—
51	#390×C₁₃₉	C₂²	1	4	yes	—
52	#390×C₁₃₉	C₂²	1	4	yes	—
53	#389×C₁₃₉	C₂²	1	4	yes	—
54	#389×C₁₃₉	C₂²	1	4	yes	—
55	#388×C₁₃₉	C₂²	1	8	yes	—
56	#386×C₁₃₉	C₂²	1	8	yes	—
57	#385×C₁₃₉	C₂²	1	8	yes	—
58	#384×C₁₃₉	C₂²	1	1	yes	characteristic
59	#380×C₁₃₉	C₂²	1	4	yes	—
60	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
61	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
63	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
67	C₄³×C₁₃₉	C₂²	1	1	yes	characteristic
68	C₂×#41×C₁₃₉	—	2	8	no	—
69	C₂×#41×C₁₃₉	—	2	8	no	—
70	C₂×#41×C₁₃₉	—	4	4	no	—
71	C₂²×Q₈×C₁₃₉	—	2	8	no	—
72	C₂²×Q₈×C₁₃₉	—	2	8	no	—
73	C₂²×Q₈×C₁₃₉	—	4	4	no	—
74	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
75	C₂²×Q₈×C₁₃₉	C₂³	1	4	yes	—
76	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
78	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
79	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
81	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
88	C₄⋊Q₈×C₁₃₉	—	2	8	no	—
89	C₄⋊Q₈×C₁₃₉	—	2	16	no	—
90	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
91	C₄⋊Q₈×C₁₃₉	D₄	1	8	yes	complemented
92	#127×C₁₃₉	—	2	4	no	—
93	#124×C₁₃₉	—	2	8	no	—
94	#124×C₁₃₉	—	2	16	no	—
95	#124×C₁₃₉	—	2	8	no	—
96	#124×C₁₃₉	—	4	4	no	—
97	C₂²⋊Q₈×C₁₃₉	—	2	8	no	—
98	C₂²⋊Q₈×C₁₃₉	—	2	16	no	—
99	#121×C₁₃₉	—	2	16	no	—
100	#121×C₁₃₉	—	2	8	no	—
101	#121×C₁₃₉	—	2	16	no	—
102	#121×C₁₃₉	—	2	16	no	—
103	C₄×Q₈×C₁₃₉	—	2	8	no	—
104	C₄×D₄×C₁₃₉	—	2	8	no	—
105	C₄×D₄×C₁₃₉	—	2	16	no	—
106	C₄×D₄×C₁₃₉	—	2	16	no	—
107	C₄×D₄×C₁₃₉	D₄	1	8	yes	complemented
108	C₂×C₄⋊C₄×C₁₃₉	—	2	16	no	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	8	yes	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	2	yes	—
123	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃₉	—	2	4	no	—
130	C₂×C₄²×C₁₃₉	—	2	4	no	—
131	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
136	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
141	#95×C₁₃₉	C₂³	1	8	yes	—
142	#95×C₁₃₉	C₂³	1	2	yes	—
143	#95×C₁₃₉	C₂³	1	2	yes	—
144	#95×C₁₃₉	C₂³	1	2	yes	—
145	#95×C₁₃₉	C₂³	1	8	yes	—
146	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
147	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
149	#41×C₁₃₉	—	4	32	no	—
150	C₂×Q₈×C₁₃₉	—	2	4	no	—
151	C₂×Q₈×C₁₃₉	—	2	8	no	—
152	C₂×Q₈×C₁₃₉	—	2	4	no	—
153	C₂×Q₈×C₁₃₉	—	2	8	no	—
154	C₂×Q₈×C₁₃₉	—	2	4	no	—
155	C₂×Q₈×C₁₃₉	—	2	4	no	—
156	C₂×Q₈×C₁₃₉	—	2	4	no	—
157	C₂×Q₈×C₁₃₉	—	4	4	no	—
158	C₂×Q₈×C₁₃₉	—	4	32	no	—
159	C₂×Q₈×C₁₃₉	C₂×D₄	1	8	yes	—
160	C₂×D₄×C₁₃₉	—	2	4	no	—
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	8	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	8	no	—
169	C₂×D₄×C₁₃₉	—	2	4	no	—
170	C₂×D₄×C₁₃₉	—	2	8	no	—
171	C₂×D₄×C₁₃₉	—	4	4	no	—
172	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₁₃₉	—	2	4	no	—
174	C₂²×C₄×C₁₃₉	—	2	2	no	—
175	C₂²×C₄×C₁₃₉	—	2	2	no	—
176	C₂²×C₄×C₁₃₉	—	2	2	no	—
177	C₂²×C₄×C₁₃₉	—	2	2	no	—
178	C₂²×C₄×C₁₃₉	—	2	4	no	—
179	C₂²×C₄×C₁₃₉	—	2	8	no	—
180	C₂²×C₄×C₁₃₉	—	2	4	no	—
181	C₂²×C₄×C₁₃₉	—	2	8	no	—
182	C₂²×C₄×C₁₃₉	—	2	8	no	—
183	C₂²×C₄×C₁₃₉	—	2	8	no	—
184	C₂²×C₄×C₁₃₉	—	2	4	no	—
185	C₂²×C₄×C₁₃₉	—	2	4	no	—
186	C₂²×C₄×C₁₃₉	—	4	4	no	—
187	C₂²×C₄×C₁₃₉	—	4	4	no	—
188	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₁₃₉	#41	1	8	yes	complemented
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	4	yes	—
195	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
203	C₄⋊C₄×C₁₃₉	—	2	16	no	—
204	C₄⋊C₄×C₁₃₉	—	2	8	no	—
205	C₄⋊C₄×C₁₃₉	—	2	8	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	—	2	8	no	—
210	C₄⋊C₄×C₁₃₉	C₂×D₄	1	16	yes	—
211	C₄⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
212	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
213	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
214	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
215	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
216	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
217	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
218	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
219	C₂²⋊C₄×C₁₃₉	—	2	16	no	—
220	C₂²⋊C₄×C₁₃₉	—	4	8	no	—
221	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
222	C₂²⋊C₄×C₁₃₉	C₂×D₄	1	4	yes	—
223	C₄²×C₁₃₉	—	2	4	no	—
224	C₄²×C₁₃₉	—	2	2	no	—
225	C₄²×C₁₃₉	—	2	2	no	—
226	C₄²×C₁₃₉	—	2	4	no	—
227	C₄²×C₁₃₉	—	2	8	no	—
228	C₄²×C₁₃₉	—	2	4	no	—
229	C₄²×C₁₃₉	—	2	2	no	—
230	C₄²×C₁₃₉	—	2	4	no	—
231	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
232	C₄²×C₁₃₉	C₂×D₄	1	4	yes	—
233	C₂³×C₁₃₉	—	2	1	no	—
234	C₂³×C₁₃₉	—	2	1	no	—
235	C₂³×C₁₃₉	—	2	2	no	—
236	C₂³×C₁₃₉	—	2	1	no	—
237	C₂³×C₁₃₉	—	2	2	no	—
238	C₂³×C₁₃₉	—	2	1	no	—
239	C₂³×C₁₃₉	—	2	2	no	—
240	C₂³×C₁₃₉	—	2	4	no	—
241	C₂³×C₁₃₉	—	2	4	no	—
242	C₂³×C₁₃₉	—	2	8	no	—
243	C₂³×C₁₃₉	—	2	4	no	—
244	C₂³×C₁₃₉	—	2	8	no	—
245	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
246	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
247	C₂³×C₁₃₉	C₂×#41	1	4	yes	—
248	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
249	Q₈×C₁₃₉	—	2	16	no	—
250	Q₈×C₁₃₉	—	4	16	no	—
251	Q₈×C₁₃₉	—	4	8	no	—
252	D₄×C₁₃₉	—	2	8	no	—
253	D₄×C₁₃₉	—	4	16	no	—
254	D₄×C₁₃₉	—	4	16	no	—
255	D₄×C₁₃₉	—	4	8	no	—
256	D₄×C₁₃₉	—	4	16	no	—
257	C₂×C₄×C₁₃₉	—	2	2	no	—
258	C₂×C₄×C₁₃₉	—	2	1	no	—
259	C₂×C₄×C₁₃₉	—	2	1	no	—
260	C₂×C₄×C₁₃₉	—	2	4	no	—
261	C₂×C₄×C₁₃₉	—	2	2	no	—
262	C₂×C₄×C₁₃₉	—	2	1	no	—
263	C₂×C₄×C₁₃₉	—	2	1	no	—
264	C₂×C₄×C₁₃₉	—	2	4	no	—
265	C₂×C₄×C₁₃₉	—	2	2	no	—
266	C₂×C₄×C₁₃₉	—	2	2	no	—
267	C₂×C₄×C₁₃₉	—	2	8	no	—
268	C₂×C₄×C₁₃₉	—	2	8	no	—
269	C₂×C₄×C₁₃₉	—	2	16	no	—
270	C₂×C₄×C₁₃₉	—	2	2	no	—
271	C₂×C₄×C₁₃₉	—	2	4	no	—
272	C₂×C₄×C₁₃₉	—	2	4	no	—
273	C₂×C₄×C₁₃₉	—	2	4	no	—
274	C₂×C₄×C₁₃₉	—	2	2	no	—
275	C₂×C₄×C₁₃₉	—	2	2	no	—
276	C₂×C₄×C₁₃₉	—	2	8	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	2	no	—
281	C₂×C₄×C₁₃₉	—	4	16	no	—
282	C₂×C₄×C₁₃₉	—	4	16	no	—
283	C₂×C₄×C₁₃₉	—	4	8	no	—
284	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₁₃₉	C₂²×D₄	1	8	yes	—
288	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	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	4	yes	—
292	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
293	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
294	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
295	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	4	yes	—
296	C₂²×C₁₃₉	—	2	2	no	—
297	C₂²×C₁₃₉	—	2	4	no	—
298	C₂²×C₁₃₉	—	2	2	no	—
299	C₂²×C₁₃₉	—	2	4	no	—
300	C₂²×C₁₃₉	—	2	2	no	—
301	C₂²×C₁₃₉	—	2	2	no	—
302	C₂²×C₁₃₉	—	2	2	no	—
303	C₂²×C₁₃₉	—	4	2	no	—
304	C₂²×C₁₃₉	—	4	2	no	—
305	C₂²×C₁₃₉	—	4	4	no	—
306	C₂²×C₁₃₉	—	4	4	no	—
307	C₂²×C₁₃₉	—	4	8	no	—
308	C₂²×C₁₃₉	—	4	4	no	—
309	C₂²×C₁₃₉	—	4	8	no	—
310	C₂²×C₁₃₉	#532	1	4	yes	complemented
311	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
312	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
313	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
314	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	2	yes	—
316	C₄×C₁₃₉	—	2	2	no	—
317	C₄×C₁₃₉	—	2	2	no	—
318	C₄×C₁₃₉	—	2	2	no	—
319	C₄×C₁₃₉	—	2	8	no	—
320	C₄×C₁₃₉	—	2	4	no	—
321	C₄×C₁₃₉	—	2	2	no	—
322	C₄×C₁₃₉	—	4	4	no	—
323	C₄×C₁₃₉	—	4	4	no	—
324	C₄×C₁₃₉	—	4	2	no	—
325	C₄×C₁₃₉	—	4	2	no	—
326	C₄×C₁₃₉	D₄²	1	4	yes	—
327	C₄×C₁₃₉	#548	1	8	yes	complemented
328	C₂×C₁₃₉	—	2	4	no	—
329	C₂×C₁₃₉	—	4	2	no	—
330	C₂×C₁₃₉	—	8	4	no	—
331	C₂×C₁₃₉	C₂×#532	1	1	yes	characteristic
332	C₂×C₁₃₉	C₂×D₄²	1	1	yes	characteristic
333	C₂×C₁₃₉	C₂×#548	1	2	yes	—
334	C₂×C₁₃₉	#3499	1	1	yes	characteristic
335	C₂×C₁₃₉	#3511	1	2	yes	—
336	#36122	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
337	C₁₃₉	#36122	1	1	yes	characteristic, direct product factor, Sylow
338	C₂×#548	C₂×C₁₃₉	1	2	yes	complemented
339	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic, complemented
340	C₂²×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
341	#2858	C₂×C₁₃₉	1	1	yes	characteristic, complemented
342	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
343	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
344	#2545	C₂×C₁₃₉	1	2	yes	complemented
345	#2491	C₂×C₁₃₉	1	4	yes	complemented
346	#2452	C₂×C₁₃₉	1	4	yes	complemented
347	#2436	C₂×C₁₃₉	1	2	yes	complemented
348	#2432	C₂×C₁₃₉	1	2	yes	complemented
349	#2416	C₂×C₁₃₉	1	4	yes	complemented
350	#2361	C₂×C₁₃₉	1	4	yes	complemented
351	C₄×C₄⋊Q₈	C₂×C₁₃₉	1	1	yes	characteristic, complemented
352	C₄²×D₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
353	C₂²×#41	C₂²×C₁₃₉	1	2	yes	—
354	C₂³×Q₈	C₂²×C₁₃₉	1	2	yes	—
355	#548	—	2	16	no	—
356	#532	—	2	8	no	—
357	C₂×C₄⋊Q₈	—	2	8	no	—
358	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
359	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
360	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
361	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
362	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
363	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
364	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
365	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
366	C₂×#124	C₂²×C₁₃₉	1	2	yes	—
367	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
368	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	4	yes	—
369	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
370	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
371	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
372	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
373	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
374	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
375	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
376	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
377	C₂×C₄×D₄	C₂²×C₁₃₉	1	1	yes	characteristic
378	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
379	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
380	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
381	#396	C₂²×C₁₃₉	1	8	yes	—
382	#394	C₂²×C₁₃₉	1	8	yes	—
383	#393	C₂²×C₁₃₉	1	8	yes	—
384	#391	C₂²×C₁₃₉	1	2	yes	—
385	#391	C₂²×C₁₃₉	1	2	yes	—
386	#390	C₂²×C₁₃₉	1	2	yes	—
387	#390	C₂²×C₁₃₉	1	4	yes	—
388	#390	C₂²×C₁₃₉	1	4	yes	—
389	#390	C₂²×C₁₃₉	1	4	yes	—
390	#389	C₂²×C₁₃₉	1	4	yes	—
391	#389	C₂²×C₁₃₉	1	4	yes	—
392	#388	C₂²×C₁₃₉	1	8	yes	—
393	#386	C₂²×C₁₃₉	1	8	yes	—
394	#385	C₂²×C₁₃₉	1	8	yes	—
395	#384	C₂²×C₁₃₉	1	1	yes	characteristic
396	#380	C₂²×C₁₃₉	1	4	yes	—
397	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
398	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
399	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
400	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
401	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
402	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	1	yes	characteristic
403	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
404	C₄³	C₂²×C₁₃₉	1	1	yes	characteristic
405	C₂×#41	—	2	8	no	—
406	C₂×#41	—	2	8	no	—
407	C₂×#41	—	4	4	no	—
408	C₂²×Q₈	—	2	8	no	—
409	C₂²×Q₈	—	2	8	no	—
410	C₂²×Q₈	—	4	4	no	—
411	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
412	C₂²×Q₈	C₂³×C₁₃₉	1	4	yes	—
413	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
414	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
415	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
416	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
417	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
418	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
420	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
421	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
422	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
425	C₄⋊Q₈	—	2	8	no	—
426	C₄⋊Q₈	—	2	16	no	—
427	C₄⋊Q₈	—	2	4	no	—
428	C₄⋊Q₈	D₄×C₁₃₉	1	8	yes	complemented
429	#127	—	2	4	no	—
430	#124	—	2	8	no	—
431	#124	—	2	16	no	—
432	#124	—	2	8	no	—
433	#124	—	4	4	no	—
434	C₂²⋊Q₈	—	2	8	no	—
435	C₂²⋊Q₈	—	2	16	no	—
436	#121	—	2	16	no	—
437	#121	—	2	8	no	—
438	#121	—	2	16	no	—
439	#121	—	2	16	no	—
440	C₄×Q₈	—	2	8	no	—
441	C₄×D₄	—	2	8	no	—
442	C₄×D₄	—	2	16	no	—
443	C₄×D₄	—	2	16	no	—
444	C₄×D₄	D₄×C₁₃₉	1	8	yes	complemented
445	C₂×C₄⋊C₄	—	2	16	no	—
446	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	8	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	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	8	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
465	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
466	C₂×C₄²	—	2	4	no	—
467	C₂×C₄²	—	2	4	no	—
468	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
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	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
474	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
478	#95	C₂³×C₁₃₉	1	2	yes	—
479	#95	C₂³×C₁₃₉	1	2	yes	—
480	#95	C₂³×C₁₃₉	1	2	yes	—
481	#95	C₂³×C₁₃₉	1	8	yes	—
482	#95	C₂³×C₁₃₉	1	8	yes	—
483	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
484	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
485	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
486	#41	—	4	32	no	—
487	C₂×Q₈	—	2	4	no	—
488	C₂×Q₈	—	2	8	no	—
489	C₂×Q₈	—	2	4	no	—
490	C₂×Q₈	—	2	8	no	—
491	C₂×Q₈	—	2	4	no	—
492	C₂×Q₈	—	2	4	no	—
493	C₂×Q₈	—	2	4	no	—
494	C₂×Q₈	—	4	4	no	—
495	C₂×Q₈	—	4	32	no	—
496	C₂×Q₈	C₂×D₄×C₁₃₉	1	8	yes	—
497	C₂×D₄	—	2	4	no	—
498	C₂×D₄	—	2	8	no	—
499	C₂×D₄	—	2	8	no	—
500	C₂×D₄	—	2	16	no	—
501	C₂×D₄	—	2	8	no	—
502	C₂×D₄	—	2	8	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	8	no	—
506	C₂×D₄	—	2	4	no	—
507	C₂×D₄	—	2	8	no	—
508	C₂×D₄	—	4	4	no	—
509	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	8	no	—
517	C₂²×C₄	—	2	4	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	4	no	—
523	C₂²×C₄	—	4	4	no	—
524	C₂²×C₄	—	4	4	no	—
525	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
526	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
527	C₂²×C₄	#41×C₁₃₉	1	8	yes	complemented
528	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
536	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
538	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
540	C₄⋊C₄	—	2	16	no	—
541	C₄⋊C₄	—	2	8	no	—
542	C₄⋊C₄	—	2	8	no	—
543	C₄⋊C₄	—	2	8	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	8	no	—
547	C₄⋊C₄	C₂×D₄×C₁₃₉	1	16	yes	—
548	C₄⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	16	no	—
552	C₂²⋊C₄	—	2	8	no	—
553	C₂²⋊C₄	—	2	8	no	—
554	C₂²⋊C₄	—	2	8	no	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	—	2	16	no	—
557	C₂²⋊C₄	—	4	8	no	—
558	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
559	C₂²⋊C₄	C₂×D₄×C₁₃₉	1	4	yes	—
560	C₄²	—	2	4	no	—
561	C₄²	—	2	2	no	—
562	C₄²	—	2	2	no	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	8	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	4	no	—
568	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
569	C₄²	C₂×D₄×C₁₃₉	1	4	yes	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	4	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	8	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	8	no	—
582	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
583	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
584	C₂³	C₂×#41×C₁₃₉	1	4	yes	—
585	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
586	Q₈	—	2	16	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	16	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	8	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	16	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	8	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	4	16	no	—
619	C₂×C₄	—	4	16	no	—
620	C₂×C₄	—	4	8	no	—
621	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
622	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
623	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
624	C₂×C₄	C₂²×D₄×C₁₃₉	1	8	yes	—
625	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
626	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
628	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
629	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
630	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
631	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
632	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	4	yes	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	4	no	—
644	C₂²	—	4	8	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	4	8	no	—
647	C₂²	#532×C₁₃₉	1	4	yes	complemented
648	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
649	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
650	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
651	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
652	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	2	yes	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	8	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	2	no	—
659	C₄	—	4	4	no	—
660	C₄	—	4	4	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	D₄²×C₁₃₉	1	4	yes	—
664	C₄	#548×C₁₃₉	1	8	yes	complemented
665	C₂	—	2	4	no	—
666	C₂	—	4	2	no	—
667	C₂	—	8	4	no	—
668	C₂	C₂×#532×C₁₃₉	1	1	yes	characteristic
669	C₂	C₂×D₄²×C₁₃₉	1	1	yes	characteristic
670	C₂	C₂×#548×C₁₃₉	1	2	yes	—
671	C₂	#3499×C₁₃₉	1	1	yes	characteristic
672	C₂	#3511×C₁₃₉	1	2	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×#548×C₁₃₉	C₂	semidirect
2. C₂×#532×C₁₃₉	C₂	semidirect
3. C₂²×C₄⋊Q₈×C₁₃₉	C₂	semidirect
4. #2858×C₁₃₉	C₂	semidirect
5. #2857×C₁₃₉	C₂	semidirect
6. #2856×C₁₃₉	C₂	semidirect
7. #2545×C₁₃₉	C₂	semidirect
8. #2491×C₁₃₉	C₂	semidirect
9. #2452×C₁₃₉	C₂	semidirect
10. #2436×C₁₃₉	C₂	semidirect
11. #2432×C₁₃₉	C₂	semidirect
12. #2416×C₁₃₉	C₂	semidirect
13. #2361×C₁₃₉	C₂	semidirect
14. C₄×C₄⋊Q₈×C₁₃₉	C₂	semidirect
15. C₄²×D₄×C₁₃₉	C₂	semidirect
91. C₄⋊Q₈×C₁₃₉	D₄	semidirect
107. C₄×D₄×C₁₃₉	D₄	semidirect
190. C₂²×C₄×C₁₃₉	#41	semidirect
310. C₂²×C₁₃₉	#532	semidirect
327. C₄×C₁₃₉	#548	semidirect
336. #36122	C₁₃₉	direct (N × H)
337. C₁₃₉	#36122	direct (N × H)
338. C₂×#548	C₂×C₁₃₉	semidirect
339. C₂×#532	C₂×C₁₃₉	semidirect
340. C₂²×C₄⋊Q₈	C₂×C₁₃₉	semidirect
341. #2858	C₂×C₁₃₉	semidirect
342. #2857	C₂×C₁₃₉	semidirect
343. #2856	C₂×C₁₃₉	semidirect
344. #2545	C₂×C₁₃₉	semidirect
345. #2491	C₂×C₁₃₉	semidirect
346. #2452	C₂×C₁₃₉	semidirect
347. #2436	C₂×C₁₃₉	semidirect
348. #2432	C₂×C₁₃₉	semidirect
349. #2416	C₂×C₁₃₉	semidirect
350. #2361	C₂×C₁₃₉	semidirect
351. C₄×C₄⋊Q₈	C₂×C₁₃₉	semidirect
352. C₄²×D₄	C₂×C₁₃₉	semidirect
428. C₄⋊Q₈	D₄×C₁₃₉	semidirect
444. C₄×D₄	D₄×C₁₃₉	semidirect
527. C₂²×C₄	#41×C₁₃₉	semidirect
647. C₂²	#532×C₁₃₉	semidirect
664. C₄	#548×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#548×C₁₃₉	2
C₂×#532×C₁₃₉	2
C₂²×C₄⋊Q₈×C₁₃₉	2
#2858×C₁₃₉	2
#2857×C₁₃₉	2
#2856×C₁₃₉	2
#2545×C₁₃₉	2
#2491×C₁₃₉	2
#2452×C₁₃₉	2
#2436×C₁₃₉	2
#2432×C₁₃₉	2
#2416×C₁₃₉	2
#2361×C₁₃₉	2
C₄×C₄⋊Q₈×C₁₃₉	2
C₄²×D₄×C₁₃₉	2
#36122	139

Subgroups — C139×#36122 #48030718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#36122 #48030718