Subgroups — C₁₃₉×#37316 #48031912

Order 35584.

2102 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2857×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#2856×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2808×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2804×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2733×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2703×C₁₃₉	C₂	1	4	yes	maximal, complemented
7	#2682×C₁₃₉	C₂	1	2	yes	maximal, complemented
8	#2676×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2615×C₁₃₉	C₂	1	2	yes	maximal, complemented
10	#2497×C₁₃₉	C₂	1	2	yes	maximal, complemented
11	#2491×C₁₃₉	C₂	1	2	yes	maximal, complemented
12	#2428×C₁₃₉	C₂	1	2	yes	maximal, complemented
13	#2422×C₁₃₉	C₂	1	2	yes	maximal, complemented
14	#2324×C₁₃₉	C₂	1	2	yes	maximal, complemented
15	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×#124×C₁₃₉	C₂²	1	4	yes	—
20	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
21	C₂×C₂²⋊Q₈×C₁₃₉	C₂²	1	2	yes	—
22	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
23	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
25	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₃₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
29	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
31	#400×C₁₃₉	C₂²	1	4	yes	—
32	#397×C₁₃₉	C₂²	1	4	yes	—
33	#396×C₁₃₉	C₂²	1	4	yes	—
34	#394×C₁₃₉	C₂²	1	4	yes	—
35	#394×C₁₃₉	C₂²	1	4	yes	—
36	#394×C₁₃₉	C₂²	1	4	yes	—
37	#393×C₁₃₉	C₂²	1	4	yes	—
38	#393×C₁₃₉	C₂²	1	4	yes	—
39	#392×C₁₃₉	C₂²	1	4	yes	—
40	#392×C₁₃₉	C₂²	1	4	yes	—
41	#392×C₁₃₉	C₂²	1	4	yes	—
42	#392×C₁₃₉	C₂²	1	4	yes	—
43	#391×C₁₃₉	C₂²	1	1	yes	characteristic
44	#391×C₁₃₉	C₂²	1	2	yes	—
45	#391×C₁₃₉	C₂²	1	1	yes	characteristic
46	#390×C₁₃₉	C₂²	1	2	yes	—
47	#390×C₁₃₉	C₂²	1	2	yes	—
48	#390×C₁₃₉	C₂²	1	1	yes	characteristic
49	#390×C₁₃₉	C₂²	1	1	yes	characteristic
50	#390×C₁₃₉	C₂²	1	4	yes	—
51	#390×C₁₃₉	C₂²	1	2	yes	—
52	#390×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#389×C₁₃₉	C₂²	1	2	yes	—
55	#389×C₁₃₉	C₂²	1	2	yes	—
56	#388×C₁₃₉	C₂²	1	4	yes	—
57	#388×C₁₃₉	C₂²	1	4	yes	—
58	#388×C₁₃₉	C₂²	1	4	yes	—
59	#387×C₁₃₉	C₂²	1	4	yes	—
60	#386×C₁₃₉	C₂²	1	4	yes	—
61	#386×C₁₃₉	C₂²	1	2	yes	—
62	#386×C₁₃₉	C₂²	1	2	yes	—
63	#386×C₁₃₉	C₂²	1	4	yes	—
64	#385×C₁₃₉	C₂²	1	4	yes	—
65	#385×C₁₃₉	C₂²	1	4	yes	—
66	#384×C₁₃₉	C₂²	1	1	yes	characteristic
67	#384×C₁₃₉	C₂²	1	1	yes	characteristic
68	#380×C₁₃₉	C₂²	1	2	yes	—
69	#380×C₁₃₉	C₂²	1	2	yes	—
70	#380×C₁₃₉	C₂²	1	2	yes	—
71	#380×C₁₃₉	C₂²	1	2	yes	—
72	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
75	C₂×#41×C₁₃₉	—	2	4	no	—
76	C₂×#41×C₁₃₉	—	4	2	no	—
77	C₂×#41×C₁₃₉	—	4	2	no	—
78	C₂²×Q₈×C₁₃₉	C₂³	1	2	yes	—
79	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
83	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
84	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
87	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
93	C₄⋊Q₈×C₁₃₉	—	4	2	no	—
94	#127×C₁₃₉	—	4	2	no	—
95	#124×C₁₃₉	—	4	8	no	—
96	#123×C₁₃₉	—	4	8	no	—
97	C₂²⋊Q₈×C₁₃₉	—	4	4	no	—
98	#121×C₁₃₉	—	2	8	no	—
99	#121×C₁₃₉	—	4	4	no	—
100	#121×C₁₃₉	—	4	4	no	—
101	#121×C₁₃₉	—	4	8	no	—
102	#121×C₁₃₉	—	4	4	no	—
103	#121×C₁₃₉	—	4	4	no	—
104	C₄×D₄×C₁₃₉	—	4	4	no	—
105	#117×C₁₃₉	—	4	2	no	—
106	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
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	4	yes	—
113	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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	2	yes	—
125	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	yes	—
134	C₂×C₄²×C₁₃₉	—	4	2	no	—
135	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
141	#95×C₁₃₉	C₂³	1	4	yes	—
142	#95×C₁₃₉	C₂³	1	2	yes	—
143	#95×C₁₃₉	C₂³	1	4	yes	—
144	#95×C₁₃₉	C₂³	1	4	yes	—
145	#95×C₁₃₉	C₂³	1	2	yes	—
146	#95×C₁₃₉	C₂³	1	4	yes	—
147	#95×C₁₃₉	C₂³	1	4	yes	—
148	#95×C₁₃₉	C₂³	1	2	yes	—
149	#95×C₁₃₉	C₂³	1	2	yes	—
150	#95×C₁₃₉	C₂³	1	4	yes	—
151	C₂⁴×C₁₃₉	C₂⁴	1	4	yes	—
152	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
153	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
154	#41×C₁₃₉	—	4	16	no	—
155	C₂×Q₈×C₁₃₉	—	2	2	no	—
156	C₂×Q₈×C₁₃₉	—	2	4	no	—
157	C₂×Q₈×C₁₃₉	—	4	1	no	—
158	C₂×Q₈×C₁₃₉	—	4	1	no	—
159	C₂×Q₈×C₁₃₉	—	4	2	no	—
160	C₂×Q₈×C₁₃₉	—	4	2	no	—
161	C₂×D₄×C₁₃₉	—	2	4	no	—
162	C₂×D₄×C₁₃₉	—	2	8	no	—
163	C₂×D₄×C₁₃₉	—	2	4	no	—
164	C₂×D₄×C₁₃₉	—	2	2	no	—
165	C₂×D₄×C₁₃₉	—	2	4	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	—	4	1	no	—
170	C₂×D₄×C₁₃₉	—	4	1	no	—
171	C₂×D₄×C₁₃₉	—	4	2	no	—
172	C₂×D₄×C₁₃₉	—	4	2	no	—
173	C₂×D₄×C₁₃₉	—	4	2	no	—
174	C₂×D₄×C₁₃₉	—	4	2	no	—
175	C₂×D₄×C₁₃₉	—	4	4	no	—
176	C₂×D₄×C₁₃₉	—	4	4	no	—
177	C₂×D₄×C₁₃₉	—	4	4	no	—
178	C₂×D₄×C₁₃₉	—	4	4	no	—
179	C₂×D₄×C₁₃₉	—	4	4	no	—
180	C₂×D₄×C₁₃₉	—	4	4	no	—
181	C₂×D₄×C₁₃₉	—	4	4	no	—
182	C₂×D₄×C₁₃₉	—	4	4	no	—
183	C₂×D₄×C₁₃₉	—	4	2	no	—
184	C₂×D₄×C₁₃₉	—	4	2	no	—
185	C₂²×C₄×C₁₃₉	—	2	2	no	—
186	C₂²×C₄×C₁₃₉	—	2	2	no	—
187	C₂²×C₄×C₁₃₉	—	2	4	no	—
188	C₂²×C₄×C₁₃₉	—	2	2	no	—
189	C₂²×C₄×C₁₃₉	—	2	2	no	—
190	C₂²×C₄×C₁₃₉	—	2	4	no	—
191	C₂²×C₄×C₁₃₉	—	2	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	2	no	—
193	C₂²×C₄×C₁₃₉	—	2	2	no	—
194	C₂²×C₄×C₁₃₉	—	4	1	no	—
195	C₂²×C₄×C₁₃₉	—	4	1	no	—
196	C₂²×C₄×C₁₃₉	—	4	4	no	—
197	C₂²×C₄×C₁₃₉	—	4	4	no	—
198	C₂²×C₄×C₁₃₉	—	4	4	no	—
199	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
200	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
212	C₄⋊C₄×C₁₃₉	—	2	4	no	—
213	C₄⋊C₄×C₁₃₉	—	2	4	no	—
214	C₄⋊C₄×C₁₃₉	—	2	8	no	—
215	C₄⋊C₄×C₁₃₉	—	2	4	no	—
216	C₄⋊C₄×C₁₃₉	—	2	4	no	—
217	C₄⋊C₄×C₁₃₉	—	4	1	no	—
218	C₄⋊C₄×C₁₃₉	—	4	1	no	—
219	C₄⋊C₄×C₁₃₉	—	4	2	no	—
220	C₄⋊C₄×C₁₃₉	—	4	2	no	—
221	C₄⋊C₄×C₁₃₉	—	4	2	no	—
222	C₄⋊C₄×C₁₃₉	—	4	4	no	—
223	C₄⋊C₄×C₁₃₉	—	4	2	no	—
224	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
225	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
226	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
227	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
228	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
229	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
230	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
231	C₂²⋊C₄×C₁₃₉	—	4	2	no	—
232	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
233	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
234	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
235	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
236	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
237	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
238	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
239	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
240	C₄²×C₁₃₉	—	2	2	no	—
241	C₄²×C₁₃₉	—	2	2	no	—
242	C₄²×C₁₃₉	—	2	4	no	—
243	C₄²×C₁₃₉	—	4	1	no	—
244	C₄²×C₁₃₉	—	4	1	no	—
245	C₄²×C₁₃₉	—	4	4	no	—
246	C₂³×C₁₃₉	—	2	1	no	—
247	C₂³×C₁₃₉	—	2	1	no	—
248	C₂³×C₁₃₉	—	2	1	no	—
249	C₂³×C₁₃₉	—	2	1	no	—
250	C₂³×C₁₃₉	—	2	1	no	—
251	C₂³×C₁₃₉	—	2	1	no	—
252	C₂³×C₁₃₉	—	2	4	no	—
253	C₂³×C₁₃₉	—	2	2	no	—
254	C₂³×C₁₃₉	—	2	2	no	—
255	C₂³×C₁₃₉	—	2	2	no	—
256	C₂³×C₁₃₉	—	2	4	no	—
257	C₂³×C₁₃₉	—	2	4	no	—
258	C₂³×C₁₃₉	—	2	2	no	—
259	C₂³×C₁₃₉	—	2	4	no	—
260	C₂³×C₁₃₉	—	2	4	no	—
261	C₂³×C₁₃₉	—	2	4	no	—
262	C₂³×C₁₃₉	—	2	2	no	—
263	C₂³×C₁₃₉	—	2	2	no	—
264	C₂³×C₁₃₉	—	2	2	no	—
265	C₂³×C₁₃₉	—	2	4	no	—
266	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
267	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
268	Q₈×C₁₃₉	—	4	4	no	—
269	Q₈×C₁₃₉	—	8	4	no	—
270	D₄×C₁₃₉	—	4	4	no	—
271	D₄×C₁₃₉	—	4	8	no	—
272	D₄×C₁₃₉	—	4	8	no	—
273	D₄×C₁₃₉	—	8	4	no	—
274	D₄×C₁₃₉	—	8	4	no	—
275	D₄×C₁₃₉	—	8	8	no	—
276	D₄×C₁₃₉	—	8	8	no	—
277	D₄×C₁₃₉	—	8	8	no	—
278	C₂×C₄×C₁₃₉	—	2	1	no	—
279	C₂×C₄×C₁₃₉	—	2	1	no	—
280	C₂×C₄×C₁₃₉	—	2	1	no	—
281	C₂×C₄×C₁₃₉	—	2	1	no	—
282	C₂×C₄×C₁₃₉	—	2	1	no	—
283	C₂×C₄×C₁₃₉	—	2	1	no	—
284	C₂×C₄×C₁₃₉	—	2	1	no	—
285	C₂×C₄×C₁₃₉	—	2	1	no	—
286	C₂×C₄×C₁₃₉	—	2	1	no	—
287	C₂×C₄×C₁₃₉	—	2	1	no	—
288	C₂×C₄×C₁₃₉	—	2	8	no	—
289	C₂×C₄×C₁₃₉	—	2	4	no	—
290	C₂×C₄×C₁₃₉	—	2	2	no	—
291	C₂×C₄×C₁₃₉	—	2	2	no	—
292	C₂×C₄×C₁₃₉	—	2	2	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	4	no	—
295	C₂×C₄×C₁₃₉	—	2	4	no	—
296	C₂×C₄×C₁₃₉	—	2	2	no	—
297	C₂×C₄×C₁₃₉	—	2	4	no	—
298	C₂×C₄×C₁₃₉	—	2	2	no	—
299	C₂×C₄×C₁₃₉	—	2	4	no	—
300	C₂×C₄×C₁₃₉	—	2	4	no	—
301	C₂×C₄×C₁₃₉	—	2	2	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	2	4	no	—
304	C₂×C₄×C₁₃₉	—	2	4	no	—
305	C₂×C₄×C₁₃₉	—	2	4	no	—
306	C₂×C₄×C₁₃₉	—	2	2	no	—
307	C₂×C₄×C₁₃₉	—	4	4	no	—
308	C₂×C₄×C₁₃₉	—	4	4	no	—
309	C₂×C₄×C₁₃₉	—	4	8	no	—
310	C₂×C₄×C₁₃₉	—	8	8	no	—
311	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
312	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
313	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
314	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
315	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
316	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
317	C₂×C₄×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
318	C₂×C₄×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
319	C₂²×C₁₃₉	—	2	2	no	—
320	C₂²×C₁₃₉	—	2	2	no	—
321	C₂²×C₁₃₉	—	2	2	no	—
322	C₂²×C₁₃₉	—	4	1	no	—
323	C₂²×C₁₃₉	—	4	1	no	—
324	C₂²×C₁₃₉	—	4	1	no	—
325	C₂²×C₁₃₉	—	4	1	no	—
326	C₂²×C₁₃₉	—	4	2	no	—
327	C₂²×C₁₃₉	—	4	4	no	—
328	C₂²×C₁₃₉	—	4	4	no	—
329	C₂²×C₁₃₉	—	4	2	no	—
330	C₂²×C₁₃₉	—	4	4	no	—
331	C₂²×C₁₃₉	—	4	2	no	—
332	C₂²×C₁₃₉	—	4	4	no	—
333	C₂²×C₁₃₉	—	4	2	no	—
334	C₂²×C₁₃₉	—	4	4	no	—
335	C₂²×C₁₃₉	—	4	2	no	—
336	C₂²×C₁₃₉	—	4	2	no	—
337	C₂²×C₁₃₉	—	4	4	no	—
338	C₂²×C₁₃₉	—	4	4	no	—
339	C₂²×C₁₃₉	—	4	2	no	—
340	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
341	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
343	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂²×C₁₃₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂²×C₁₃₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
347	C₄×C₁₃₉	—	2	2	no	—
348	C₄×C₁₃₉	—	2	2	no	—
349	C₄×C₁₃₉	—	2	2	no	—
350	C₄×C₁₃₉	—	2	2	no	—
351	C₄×C₁₃₉	—	2	2	no	—
352	C₄×C₁₃₉	—	4	2	no	—
353	C₄×C₁₃₉	—	4	4	no	—
354	C₄×C₁₃₉	—	4	4	no	—
355	C₄×C₁₃₉	—	4	2	no	—
356	C₄×C₁₃₉	—	4	2	no	—
357	C₄×C₁₃₉	—	4	4	no	—
358	C₄×C₁₃₉	#538	1	4	yes	—
359	C₂×C₁₃₉	—	4	2	no	—
360	C₂×C₁₃₉	—	8	2	no	—
361	C₂×C₁₃₉	—	8	4	no	—
362	C₂×C₁₃₉	C₂×#538	1	1	yes	characteristic
363	C₂×C₁₃₉	#3508	1	1	yes	characteristic
364	C₂×C₁₃₉	#3511	1	1	yes	characteristic
365	C₂×C₁₃₉	#3536	1	1	yes	characteristic
366	C₂×C₁₃₉	#3537	1	1	yes	characteristic
367	C₂×C₁₃₉	#3548	1	1	yes	characteristic
368	C₂×C₁₃₉	#3549	1	1	yes	characteristic
369	#37316	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
370	C₁₃₉	#37316	1	1	yes	characteristic, direct product factor, Sylow
371	#2857	C₂×C₁₃₉	1	1	yes	characteristic, complemented
372	#2856	C₂×C₁₃₉	1	1	yes	characteristic, complemented
373	#2808	C₂×C₁₃₉	1	2	yes	complemented
374	#2804	C₂×C₁₃₉	1	2	yes	complemented
375	#2733	C₂×C₁₃₉	1	2	yes	complemented
376	#2703	C₂×C₁₃₉	1	4	yes	complemented
377	#2682	C₂×C₁₃₉	1	2	yes	complemented
378	#2676	C₂×C₁₃₉	1	4	yes	complemented
379	#2615	C₂×C₁₃₉	1	2	yes	complemented
380	#2497	C₂×C₁₃₉	1	2	yes	complemented
381	#2491	C₂×C₁₃₉	1	2	yes	complemented
382	#2428	C₂×C₁₃₉	1	2	yes	complemented
383	#2422	C₂×C₁₃₉	1	2	yes	complemented
384	#2324	C₂×C₁₃₉	1	2	yes	complemented
385	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
386	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
387	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
388	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
389	C₂×#124	C₂²×C₁₃₉	1	4	yes	—
390	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₁₃₉	1	2	yes	—
392	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
393	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
394	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
395	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
396	C₂×#121	C₂²×C₁₃₉	1	2	yes	—
397	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
398	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
399	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
400	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
401	#400	C₂²×C₁₃₉	1	4	yes	—
402	#397	C₂²×C₁₃₉	1	4	yes	—
403	#396	C₂²×C₁₃₉	1	4	yes	—
404	#394	C₂²×C₁₃₉	1	4	yes	—
405	#394	C₂²×C₁₃₉	1	4	yes	—
406	#394	C₂²×C₁₃₉	1	4	yes	—
407	#393	C₂²×C₁₃₉	1	4	yes	—
408	#393	C₂²×C₁₃₉	1	4	yes	—
409	#392	C₂²×C₁₃₉	1	4	yes	—
410	#392	C₂²×C₁₃₉	1	4	yes	—
411	#392	C₂²×C₁₃₉	1	4	yes	—
412	#392	C₂²×C₁₃₉	1	4	yes	—
413	#391	C₂²×C₁₃₉	1	2	yes	—
414	#391	C₂²×C₁₃₉	1	1	yes	characteristic
415	#391	C₂²×C₁₃₉	1	1	yes	characteristic
416	#390	C₂²×C₁₃₉	1	4	yes	—
417	#390	C₂²×C₁₃₉	1	2	yes	—
418	#390	C₂²×C₁₃₉	1	2	yes	—
419	#390	C₂²×C₁₃₉	1	2	yes	—
420	#390	C₂²×C₁₃₉	1	2	yes	—
421	#390	C₂²×C₁₃₉	1	1	yes	characteristic
422	#390	C₂²×C₁₃₉	1	1	yes	characteristic
423	#389	C₂²×C₁₃₉	1	2	yes	—
424	#389	C₂²×C₁₃₉	1	2	yes	—
425	#389	C₂²×C₁₃₉	1	2	yes	—
426	#388	C₂²×C₁₃₉	1	4	yes	—
427	#388	C₂²×C₁₃₉	1	4	yes	—
428	#388	C₂²×C₁₃₉	1	4	yes	—
429	#387	C₂²×C₁₃₉	1	4	yes	—
430	#386	C₂²×C₁₃₉	1	4	yes	—
431	#386	C₂²×C₁₃₉	1	2	yes	—
432	#386	C₂²×C₁₃₉	1	4	yes	—
433	#386	C₂²×C₁₃₉	1	2	yes	—
434	#385	C₂²×C₁₃₉	1	4	yes	—
435	#385	C₂²×C₁₃₉	1	4	yes	—
436	#384	C₂²×C₁₃₉	1	1	yes	characteristic
437	#384	C₂²×C₁₃₉	1	1	yes	characteristic
438	#380	C₂²×C₁₃₉	1	2	yes	—
439	#380	C₂²×C₁₃₉	1	2	yes	—
440	#380	C₂²×C₁₃₉	1	2	yes	—
441	#380	C₂²×C₁₃₉	1	2	yes	—
442	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
443	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
444	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
445	C₂×#41	—	2	4	no	—
446	C₂×#41	—	4	2	no	—
447	C₂×#41	—	4	2	no	—
448	C₂²×Q₈	C₂³×C₁₃₉	1	2	yes	—
449	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
450	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
451	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
453	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
454	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
455	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
456	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
457	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
458	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
459	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
463	C₄⋊Q₈	—	4	2	no	—
464	#127	—	4	2	no	—
465	#124	—	4	8	no	—
466	#123	—	4	8	no	—
467	C₂²⋊Q₈	—	4	4	no	—
468	#121	—	2	8	no	—
469	#121	—	4	4	no	—
470	#121	—	4	4	no	—
471	#121	—	4	8	no	—
472	#121	—	4	4	no	—
473	#121	—	4	4	no	—
474	C₄×D₄	—	4	4	no	—
475	#117	—	4	2	no	—
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
482	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
490	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
491	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
493	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
494	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
504	C₂×C₄²	—	4	2	no	—
505	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
509	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
511	#95	C₂³×C₁₃₉	1	2	yes	—
512	#95	C₂³×C₁₃₉	1	2	yes	—
513	#95	C₂³×C₁₃₉	1	2	yes	—
514	#95	C₂³×C₁₃₉	1	2	yes	—
515	#95	C₂³×C₁₃₉	1	4	yes	—
516	#95	C₂³×C₁₃₉	1	4	yes	—
517	#95	C₂³×C₁₃₉	1	4	yes	—
518	#95	C₂³×C₁₃₉	1	4	yes	—
519	#95	C₂³×C₁₃₉	1	4	yes	—
520	#95	C₂³×C₁₃₉	1	4	yes	—
521	C₂⁴	C₂⁴×C₁₃₉	1	4	yes	—
522	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
523	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
524	#41	—	4	16	no	—
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	2	4	no	—
527	C₂×Q₈	—	4	1	no	—
528	C₂×Q₈	—	4	1	no	—
529	C₂×Q₈	—	4	2	no	—
530	C₂×Q₈	—	4	2	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	4	no	—
539	C₂×D₄	—	4	1	no	—
540	C₂×D₄	—	4	1	no	—
541	C₂×D₄	—	4	2	no	—
542	C₂×D₄	—	4	2	no	—
543	C₂×D₄	—	4	2	no	—
544	C₂×D₄	—	4	2	no	—
545	C₂×D₄	—	4	4	no	—
546	C₂×D₄	—	4	4	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	—	4	4	no	—
549	C₂×D₄	—	4	4	no	—
550	C₂×D₄	—	4	4	no	—
551	C₂×D₄	—	4	4	no	—
552	C₂×D₄	—	4	4	no	—
553	C₂×D₄	—	4	2	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	—	4	1	no	—
566	C₂²×C₄	—	4	4	no	—
567	C₂²×C₄	—	4	4	no	—
568	C₂²×C₄	—	4	4	no	—
569	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
575	C₂²×C₄	C₂⁴×C₁₃₉	1	4	yes	—
576	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	8	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	4	1	no	—
588	C₄⋊C₄	—	4	1	no	—
589	C₄⋊C₄	—	4	2	no	—
590	C₄⋊C₄	—	4	2	no	—
591	C₄⋊C₄	—	4	2	no	—
592	C₄⋊C₄	—	4	4	no	—
593	C₄⋊C₄	—	4	2	no	—
594	C₂²⋊C₄	—	2	8	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	2	8	no	—
598	C₂²⋊C₄	—	2	4	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	4	2	no	—
602	C₂²⋊C₄	—	4	4	no	—
603	C₂²⋊C₄	—	4	4	no	—
604	C₂²⋊C₄	—	4	4	no	—
605	C₂²⋊C₄	—	4	4	no	—
606	C₂²⋊C₄	—	4	4	no	—
607	C₂²⋊C₄	—	4	4	no	—
608	C₂²⋊C₄	—	4	4	no	—
609	C₂²⋊C₄	—	4	4	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	4	no	—
613	C₄²	—	4	1	no	—
614	C₄²	—	4	1	no	—
615	C₄²	—	4	4	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	1	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	4	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	4	no	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	2	4	no	—
631	C₂³	—	2	4	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	4	no	—
636	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
637	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
638	Q₈	—	4	4	no	—
639	Q₈	—	8	4	no	—
640	D₄	—	4	4	no	—
641	D₄	—	4	8	no	—
642	D₄	—	4	8	no	—
643	D₄	—	8	4	no	—
644	D₄	—	8	4	no	—
645	D₄	—	8	8	no	—
646	D₄	—	8	8	no	—
647	D₄	—	8	8	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	8	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	4	4	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	4	8	no	—
680	C₂×C₄	—	8	8	no	—
681	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
682	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
683	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
684	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
685	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
686	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
687	C₂×C₄	H(5,𝔽₂)×C₁₃₉	1	2	yes	—
688	C₂×C₄	2₋¹⁺⁴×C₁₃₉	1	2	yes	—
689	C₂²	—	2	2	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	4	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	4	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
711	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
712	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
713	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
714	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
715	C₂²	C₂×H(5,𝔽₂)×C₁₃₉	1	1	yes	characteristic
716	C₂²	C₂×2₋¹⁺⁴×C₁₃₉	1	1	yes	characteristic
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	4	4	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	4	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	4	no	—
728	C₄	#538×C₁₃₉	1	4	yes	—
729	C₂	—	4	2	no	—
730	C₂	—	8	4	no	—
731	C₂	—	8	2	no	—
732	C₂	C₂×#538×C₁₃₉	1	1	yes	characteristic
733	C₂	#3508×C₁₃₉	1	1	yes	characteristic
734	C₂	#3511×C₁₃₉	1	1	yes	characteristic
735	C₂	#3536×C₁₃₉	1	1	yes	characteristic
736	C₂	#3537×C₁₃₉	1	1	yes	characteristic
737	C₂	#3548×C₁₃₉	1	1	yes	characteristic
738	C₂	#3549×C₁₃₉	1	1	yes	characteristic

	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. #2857×C₁₃₉	C₂	semidirect
2. #2856×C₁₃₉	C₂	semidirect
3. #2808×C₁₃₉	C₂	semidirect
4. #2804×C₁₃₉	C₂	semidirect
5. #2733×C₁₃₉	C₂	semidirect
6. #2703×C₁₃₉	C₂	semidirect
7. #2682×C₁₃₉	C₂	semidirect
8. #2676×C₁₃₉	C₂	semidirect
9. #2615×C₁₃₉	C₂	semidirect
10. #2497×C₁₃₉	C₂	semidirect
11. #2491×C₁₃₉	C₂	semidirect
12. #2428×C₁₃₉	C₂	semidirect
13. #2422×C₁₃₉	C₂	semidirect
14. #2324×C₁₃₉	C₂	semidirect
15. #2297×C₁₃₉	C₂	semidirect
369. #37316	C₁₃₉	direct (N × H)
370. C₁₃₉	#37316	direct (N × H)
371. #2857	C₂×C₁₃₉	semidirect
372. #2856	C₂×C₁₃₉	semidirect
373. #2808	C₂×C₁₃₉	semidirect
374. #2804	C₂×C₁₃₉	semidirect
375. #2733	C₂×C₁₃₉	semidirect
376. #2703	C₂×C₁₃₉	semidirect
377. #2682	C₂×C₁₃₉	semidirect
378. #2676	C₂×C₁₃₉	semidirect
379. #2615	C₂×C₁₃₉	semidirect
380. #2497	C₂×C₁₃₉	semidirect
381. #2491	C₂×C₁₃₉	semidirect
382. #2428	C₂×C₁₃₉	semidirect
383. #2422	C₂×C₁₃₉	semidirect
384. #2324	C₂×C₁₃₉	semidirect
385. #2297	C₂×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
#2857×C₁₃₉	2
#2856×C₁₃₉	2
#2808×C₁₃₉	2
#2804×C₁₃₉	2
#2733×C₁₃₉	2
#2703×C₁₃₉	2
#2682×C₁₃₉	2
#2676×C₁₃₉	2
#2615×C₁₃₉	2
#2497×C₁₃₉	2
#2491×C₁₃₉	2
#2428×C₁₃₉	2
#2422×C₁₃₉	2
#2324×C₁₃₉	2
#2297×C₁₃₉	2
#37316	139

Subgroups — C139×#37316 #48031912

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#37316 #48031912