Subgroups — C₁₃₉×#34744 #48029340

Order 35584.

2662 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#2448×C₁₃₉	C₂	1	2	yes	maximal, complemented
4	#2447×C₁₃₉	C₂	1	2	yes	maximal, complemented
5	#2446×C₁₃₉	C₂	1	2	yes	maximal, complemented
6	#2445×C₁₃₉	C₂	1	2	yes	maximal, complemented
7	#2444×C₁₃₉	C₂	1	4	yes	maximal, complemented
8	#2443×C₁₃₉	C₂	1	4	yes	maximal, complemented
9	#2395×C₁₃₉	C₂	1	4	yes	maximal, complemented
10	C₄×#123×C₁₃₉	C₂	1	4	yes	maximal, complemented
11	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#2297×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#2296×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₁₃₉	C₂²	1	1	yes	characteristic
18	#532×C₁₃₉	—	2	8	no	—
19	C₂×C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×#127×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₁₃₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₁₃₉	C₂²	1	4	yes	—
24	C₂×#121×C₁₃₉	C₂²	1	4	yes	—
25	C₄×#41×C₁₃₉	—	2	8	no	—
26	C₂×C₄×Q₈×C₁₃₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
28	C₂×C₄×D₄×C₁₃₉	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₁₃₉	C₂²	1	2	yes	—
30	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₁₃₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₁₃₉	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₁₃₉	C₂²	1	2	yes	—
38	#400×C₁₃₉	C₂²	1	4	yes	—
39	#399×C₁₃₉	C₂²	1	4	yes	—
40	#398×C₁₃₉	C₂²	1	4	yes	—
41	#397×C₁₃₉	C₂²	1	4	yes	—
42	#397×C₁₃₉	C₂²	1	4	yes	—
43	#397×C₁₃₉	C₂²	1	4	yes	—
44	#394×C₁₃₉	C₂²	1	4	yes	—
45	#394×C₁₃₉	C₂²	1	4	yes	—
46	#391×C₁₃₉	C₂²	1	2	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	2	yes	—
51	#390×C₁₃₉	C₂²	1	2	yes	—
52	#389×C₁₃₉	C₂²	1	2	yes	—
53	#389×C₁₃₉	C₂²	1	2	yes	—
54	#388×C₁₃₉	C₂²	1	4	yes	—
55	#388×C₁₃₉	C₂²	1	4	yes	—
56	#387×C₁₃₉	C₂²	1	4	yes	—
57	#387×C₁₃₉	C₂²	1	4	yes	—
58	#386×C₁₃₉	C₂²	1	2	yes	—
59	#386×C₁₃₉	C₂²	1	2	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	#381×C₁₃₉	C₂²	1	4	yes	—
67	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
72	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
74	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	4	yes	—
75	C₄×C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
76	C₂×#95×C₁₃₉	C₂²	1	2	yes	—
77	C₂×#41×C₁₃₉	—	2	4	no	—
78	C₂×#41×C₁₃₉	—	2	4	no	—
79	C₂×#41×C₁₃₉	—	2	4	no	—
80	C₂×#41×C₁₃₉	—	2	4	no	—
81	C₂×#41×C₁₃₉	—	2	4	no	—
82	C₂×#41×C₁₃₉	D₄	1	8	yes	—
83	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₁₃₉	C₂³	1	4	yes	—
88	C₂²×D₄×C₁₃₉	C₂³	1	2	yes	—
89	C₂²×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃₉	C₂³	1	4	yes	—
95	C₂³×C₄×C₁₃₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₁₃₉	—	2	4	no	—
99	#127×C₁₃₉	—	2	4	no	—
100	#124×C₁₃₉	—	2	4	no	—
101	#124×C₁₃₉	—	2	4	no	—
102	#123×C₁₃₉	—	2	16	no	—
103	#121×C₁₃₉	—	2	16	no	—
104	C₄×Q₈×C₁₃₉	—	2	8	no	—
105	C₄×D₄×C₁₃₉	—	2	16	no	—
106	C₄×D₄×C₁₃₉	—	2	8	no	—
107	C₄×D₄×C₁₃₉	—	2	16	no	—
108	#117×C₁₃₉	—	2	8	no	—
109	#117×C₁₃₉	—	2	4	no	—
110	#117×C₁₃₉	—	2	4	no	—
111	C₂×C₄⋊C₄×C₁₃₉	—	2	8	no	—
112	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	2	yes	—
118	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₁₃₉	C₂³	1	2	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	4	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	2	yes	—
128	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₁₃₉	C₂³	1	4	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×C₄²×C₁₃₉	—	2	8	no	—
134	C₂×C₄²×C₁₃₉	—	2	4	no	—
135	C₂×C₄²×C₁₃₉	—	2	4	no	—
136	C₂×C₄²×C₁₃₉	—	2	4	no	—
137	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₃₉	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
146	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₁₃₉	C₂³	1	2	yes	—
148	#95×C₁₃₉	C₂³	1	2	yes	—
149	#95×C₁₃₉	C₂³	1	4	yes	—
150	#95×C₁₃₉	C₂³	1	4	yes	—
151	#95×C₁₃₉	C₂³	1	4	yes	—
152	#95×C₁₃₉	C₂³	1	4	yes	—
153	#95×C₁₃₉	C₂³	1	4	yes	—
154	#95×C₁₃₉	C₂³	1	4	yes	—
155	#95×C₁₃₉	C₂³	1	2	yes	—
156	#95×C₁₃₉	C₂³	1	4	yes	—
157	#95×C₁₃₉	C₂³	1	2	yes	—
158	#95×C₁₃₉	C₂³	1	2	yes	—
159	#95×C₁₃₉	C₂³	1	4	yes	—
160	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
161	C₂⁴×C₁₃₉	C₂⁴	1	2	yes	—
162	C₂⁴×C₁₃₉	C₂⁴	1	1	yes	characteristic
163	#41×C₁₃₉	—	2	32	no	—
164	#41×C₁₃₉	—	4	16	no	—
165	C₂×Q₈×C₁₃₉	—	2	2	no	—
166	C₂×Q₈×C₁₃₉	—	2	2	no	—
167	C₂×Q₈×C₁₃₉	—	2	2	no	—
168	C₂×Q₈×C₁₃₉	—	2	2	no	—
169	C₂×Q₈×C₁₃₉	—	2	2	no	—
170	C₂×Q₈×C₁₃₉	C₂×D₄	1	4	yes	—
171	C₂×D₄×C₁₃₉	—	2	4	no	—
172	C₂×D₄×C₁₃₉	—	2	4	no	—
173	C₂×D₄×C₁₃₉	—	2	8	no	—
174	C₂×D₄×C₁₃₉	—	2	4	no	—
175	C₂×D₄×C₁₃₉	—	2	4	no	—
176	C₂×D₄×C₁₃₉	—	2	4	no	—
177	C₂×D₄×C₁₃₉	—	2	2	no	—
178	C₂×D₄×C₁₃₉	—	2	2	no	—
179	C₂×D₄×C₁₃₉	—	2	2	no	—
180	C₂×D₄×C₁₃₉	—	2	8	no	—
181	C₂×D₄×C₁₃₉	—	2	2	no	—
182	C₂×D₄×C₁₃₉	—	2	2	no	—
183	C₂×D₄×C₁₃₉	—	4	4	no	—
184	C₂×D₄×C₁₃₉	C₂×D₄	1	8	yes	—
185	C₂×D₄×C₁₃₉	C₂×D₄	1	4	yes	—
186	C₂²×C₄×C₁₃₉	—	2	2	no	—
187	C₂²×C₄×C₁₃₉	—	2	4	no	—
188	C₂²×C₄×C₁₃₉	—	2	4	no	—
189	C₂²×C₄×C₁₃₉	—	2	4	no	—
190	C₂²×C₄×C₁₃₉	—	2	8	no	—
191	C₂²×C₄×C₁₃₉	—	2	4	no	—
192	C₂²×C₄×C₁₃₉	—	2	4	no	—
193	C₂²×C₄×C₁₃₉	—	2	2	no	—
194	C₂²×C₄×C₁₃₉	—	2	4	no	—
195	C₂²×C₄×C₁₃₉	—	2	4	no	—
196	C₂²×C₄×C₁₃₉	—	2	4	no	—
197	C₂²×C₄×C₁₃₉	—	2	8	no	—
198	C₂²×C₄×C₁₃₉	—	2	4	no	—
199	C₂²×C₄×C₁₃₉	—	2	4	no	—
200	C₂²×C₄×C₁₃₉	—	4	2	no	—
201	C₂²×C₄×C₁₃₉	—	4	4	no	—
202	C₂²×C₄×C₁₃₉	—	4	2	no	—
203	C₂²×C₄×C₁₃₉	—	4	2	no	—
204	C₂²×C₄×C₁₃₉	C₂×D₄	1	8	yes	—
205	C₂²×C₄×C₁₃₉	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
207	C₂²×C₄×C₁₃₉	#41	1	4	yes	—
208	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃₉	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
220	C₄⋊C₄×C₁₃₉	—	2	8	no	—
221	C₄⋊C₄×C₁₃₉	—	2	4	no	—
222	C₄⋊C₄×C₁₃₉	—	2	8	no	—
223	C₄⋊C₄×C₁₃₉	—	2	4	no	—
224	C₄⋊C₄×C₁₃₉	—	2	4	no	—
225	C₄⋊C₄×C₁₃₉	—	2	4	no	—
226	C₄⋊C₄×C₁₃₉	—	2	4	no	—
227	C₄⋊C₄×C₁₃₉	—	2	8	no	—
228	C₄⋊C₄×C₁₃₉	—	4	4	no	—
229	C₄⋊C₄×C₁₃₉	#41	1	8	yes	complemented
230	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
231	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
232	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
233	C₂²⋊C₄×C₁₃₉	—	2	4	no	—
234	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
235	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
236	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
237	C₂²⋊C₄×C₁₃₉	—	2	8	no	—
238	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
239	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
240	C₂²⋊C₄×C₁₃₉	—	4	4	no	—
241	C₄²×C₁₃₉	—	2	2	no	—
242	C₄²×C₁₃₉	—	2	4	no	—
243	C₄²×C₁₃₉	—	2	2	no	—
244	C₄²×C₁₃₉	—	2	4	no	—
245	C₄²×C₁₃₉	—	2	8	no	—
246	C₄²×C₁₃₉	—	2	4	no	—
247	C₄²×C₁₃₉	—	2	2	no	—
248	C₄²×C₁₃₉	—	2	2	no	—
249	C₄²×C₁₃₉	—	2	4	no	—
250	C₄²×C₁₃₉	—	2	4	no	—
251	C₄²×C₁₃₉	—	2	4	no	—
252	C₂³×C₁₃₉	—	2	2	no	—
253	C₂³×C₁₃₉	—	2	2	no	—
254	C₂³×C₁₃₉	—	2	4	no	—
255	C₂³×C₁₃₉	—	2	2	no	—
256	C₂³×C₁₃₉	—	2	2	no	—
257	C₂³×C₁₃₉	—	2	4	no	—
258	C₂³×C₁₃₉	—	2	2	no	—
259	C₂³×C₁₃₉	—	2	4	no	—
260	C₂³×C₁₃₉	—	2	2	no	—
261	C₂³×C₁₃₉	—	2	2	no	—
262	C₂³×C₁₃₉	—	2	4	no	—
263	C₂³×C₁₃₉	C₂²×D₄	1	4	yes	—
264	C₂³×C₁₃₉	C₂²×D₄	1	2	yes	—
265	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
266	C₂³×C₁₃₉	C₂×#41	1	2	yes	—
267	C₂³×C₁₃₉	C₂⁵	1	1	yes	characteristic
268	Q₈×C₁₃₉	—	2	8	no	—
269	Q₈×C₁₃₉	—	4	4	no	—
270	D₄×C₁₃₉	—	2	16	no	—
271	D₄×C₁₃₉	—	2	8	no	—
272	D₄×C₁₃₉	—	4	16	no	—
273	D₄×C₁₃₉	—	4	8	no	—
274	D₄×C₁₃₉	—	4	4	no	—
275	C₂×C₄×C₁₃₉	—	2	8	no	—
276	C₂×C₄×C₁₃₉	—	2	2	no	—
277	C₂×C₄×C₁₃₉	—	2	2	no	—
278	C₂×C₄×C₁₃₉	—	2	2	no	—
279	C₂×C₄×C₁₃₉	—	2	2	no	—
280	C₂×C₄×C₁₃₉	—	2	2	no	—
281	C₂×C₄×C₁₃₉	—	2	2	no	—
282	C₂×C₄×C₁₃₉	—	2	2	no	—
283	C₂×C₄×C₁₃₉	—	2	2	no	—
284	C₂×C₄×C₁₃₉	—	2	16	no	—
285	C₂×C₄×C₁₃₉	—	2	2	no	—
286	C₂×C₄×C₁₃₉	—	2	4	no	—
287	C₂×C₄×C₁₃₉	—	2	2	no	—
288	C₂×C₄×C₁₃₉	—	2	2	no	—
289	C₂×C₄×C₁₃₉	—	2	2	no	—
290	C₂×C₄×C₁₃₉	—	2	4	no	—
291	C₂×C₄×C₁₃₉	—	2	4	no	—
292	C₂×C₄×C₁₃₉	—	2	4	no	—
293	C₂×C₄×C₁₃₉	—	2	2	no	—
294	C₂×C₄×C₁₃₉	—	2	2	no	—
295	C₂×C₄×C₁₃₉	—	2	2	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	2	no	—
300	C₂×C₄×C₁₃₉	—	2	2	no	—
301	C₂×C₄×C₁₃₉	—	2	4	no	—
302	C₂×C₄×C₁₃₉	—	2	2	no	—
303	C₂×C₄×C₁₃₉	—	4	8	no	—
304	C₂×C₄×C₁₃₉	—	4	16	no	—
305	C₂×C₄×C₁₃₉	—	4	8	no	—
306	C₂×C₄×C₁₃₉	—	4	4	no	—
307	C₂×C₄×C₁₃₉	—	4	8	no	—
308	C₂×C₄×C₁₃₉	#123	1	16	yes	complemented
309	C₂×C₄×C₁₃₉	C₂²×D₄	1	4	yes	—
310	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₁₃₉	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
313	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
314	C₂×C₄×C₁₃₉	C₂×#41	1	4	yes	—
315	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
316	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
317	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
318	C₂×C₄×C₁₃₉	C₂×#41	1	2	yes	—
319	C₂²×C₁₃₉	—	2	2	no	—
320	C₂²×C₁₃₉	—	2	2	no	—
321	C₂²×C₁₃₉	—	2	4	no	—
322	C₂²×C₁₃₉	—	2	4	no	—
323	C₂²×C₁₃₉	—	2	4	no	—
324	C₂²×C₁₃₉	—	2	8	no	—
325	C₂²×C₁₃₉	—	4	2	no	—
326	C₂²×C₁₃₉	—	4	2	no	—
327	C₂²×C₁₃₉	—	4	4	no	—
328	C₂²×C₁₃₉	—	4	2	no	—
329	C₂²×C₁₃₉	—	4	2	no	—
330	C₂²×C₁₃₉	—	4	2	no	—
331	C₂²×C₁₃₉	—	4	4	no	—
332	C₂²×C₁₃₉	—	4	4	no	—
333	C₂²×C₁₃₉	C₂×#123	1	4	yes	—
334	C₂²×C₁₃₉	C₂³×D₄	1	1	yes	characteristic
335	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
336	C₂²×C₁₃₉	C₂²×#41	1	1	yes	characteristic
337	C₂²×C₁₃₉	C₂²×#41	1	2	yes	—
338	C₂²×C₁₃₉	#585	1	2	yes	—
339	C₄×C₁₃₉	—	2	4	no	—
340	C₄×C₁₃₉	—	2	4	no	—
341	C₄×C₁₃₉	—	2	4	no	—
342	C₄×C₁₃₉	—	2	4	no	—
343	C₄×C₁₃₉	—	4	2	no	—
344	C₄×C₁₃₉	—	4	2	no	—
345	C₄×C₁₃₉	—	4	2	no	—
346	C₄×C₁₃₉	—	4	4	no	—
347	C₄×C₁₃₉	—	4	2	no	—
348	C₄×C₁₃₉	—	4	4	no	—
349	C₄×C₁₃₉	C₂×#123	1	4	yes	—
350	C₄×C₁₃₉	C₂×#123	1	4	yes	—
351	C₂×C₁₃₉	—	2	4	no	—
352	C₂×C₁₃₉	—	4	4	no	—
353	C₂×C₁₃₉	—	8	2	no	—
354	C₂×C₁₃₉	C₂²×#123	1	1	yes	characteristic
355	C₂×C₁₃₉	#3444	1	1	yes	characteristic
356	C₂×C₁₃₉	#3455	1	1	yes	characteristic
357	C₂×C₁₃₉	D₄×#41	1	2	yes	—
358	C₂×C₁₃₉	#3480	1	2	yes	—
359	#34744	C₁₃₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
360	C₁₃₉	#34744	1	1	yes	characteristic, direct product factor, Sylow
361	C₂×#532	C₂×C₁₃₉	1	1	yes	characteristic
362	C₂×C₄×#41	C₂×C₁₃₉	1	1	yes	characteristic, complemented
363	#2448	C₂×C₁₃₉	1	2	yes	complemented
364	#2447	C₂×C₁₃₉	1	2	yes	complemented
365	#2446	C₂×C₁₃₉	1	2	yes	complemented
366	#2445	C₂×C₁₃₉	1	2	yes	complemented
367	#2444	C₂×C₁₃₉	1	4	yes	complemented
368	#2443	C₂×C₁₃₉	1	4	yes	complemented
369	#2395	C₂×C₁₃₉	1	4	yes	complemented
370	C₄×#123	C₂×C₁₃₉	1	4	yes	complemented
371	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
372	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
373	#2297	C₂×C₁₃₉	1	1	yes	characteristic, complemented
374	#2296	C₂×C₁₃₉	1	1	yes	characteristic, complemented
375	C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	1	1	yes	characteristic, complemented
376	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
377	C₂²×#41	C₂²×C₁₃₉	1	1	yes	characteristic
378	#532	—	2	8	no	—
379	C₂×C₄⋊Q₈	C₂²×C₁₃₉	1	1	yes	characteristic
380	C₂×#127	C₂²×C₁₃₉	1	1	yes	characteristic
381	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
382	C₂×#124	C₂²×C₁₃₉	1	1	yes	characteristic
383	C₂×#123	C₂²×C₁₃₉	1	4	yes	—
384	C₂×#121	C₂²×C₁₃₉	1	4	yes	—
385	C₄×#41	—	2	8	no	—
386	C₂×C₄×Q₈	C₂²×C₁₃₉	1	2	yes	—
387	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
388	C₂×C₄×D₄	C₂²×C₁₃₉	1	4	yes	—
389	C₂×C₄×D₄	C₂²×C₁₃₉	1	2	yes	—
390	C₂×#117	C₂²×C₁₃₉	1	2	yes	—
391	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
392	C₂×#117	C₂²×C₁₃₉	1	1	yes	characteristic
393	C₂²×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
394	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
395	C₂²×C₄²	C₂²×C₁₃₉	1	2	yes	—
396	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
397	C₂²×C₄²	C₂²×C₁₃₉	1	1	yes	characteristic
398	#400	C₂²×C₁₃₉	1	4	yes	—
399	#399	C₂²×C₁₃₉	1	4	yes	—
400	#398	C₂²×C₁₃₉	1	4	yes	—
401	#397	C₂²×C₁₃₉	1	4	yes	—
402	#397	C₂²×C₁₃₉	1	4	yes	—
403	#397	C₂²×C₁₃₉	1	4	yes	—
404	#394	C₂²×C₁₃₉	1	4	yes	—
405	#394	C₂²×C₁₃₉	1	4	yes	—
406	#391	C₂²×C₁₃₉	1	2	yes	—
407	#391	C₂²×C₁₃₉	1	2	yes	—
408	#391	C₂²×C₁₃₉	1	2	yes	—
409	#390	C₂²×C₁₃₉	1	2	yes	—
410	#390	C₂²×C₁₃₉	1	2	yes	—
411	#390	C₂²×C₁₃₉	1	2	yes	—
412	#389	C₂²×C₁₃₉	1	2	yes	—
413	#389	C₂²×C₁₃₉	1	2	yes	—
414	#388	C₂²×C₁₃₉	1	4	yes	—
415	#388	C₂²×C₁₃₉	1	4	yes	—
416	#387	C₂²×C₁₃₉	1	4	yes	—
417	#387	C₂²×C₁₃₉	1	4	yes	—
418	#386	C₂²×C₁₃₉	1	2	yes	—
419	#386	C₂²×C₁₃₉	1	2	yes	—
420	#386	C₂²×C₁₃₉	1	4	yes	—
421	#386	C₂²×C₁₃₉	1	2	yes	—
422	#386	C₂²×C₁₃₉	1	2	yes	—
423	#386	C₂²×C₁₃₉	1	4	yes	—
424	#385	C₂²×C₁₃₉	1	4	yes	—
425	#385	C₂²×C₁₃₉	1	4	yes	—
426	#381	C₂²×C₁₃₉	1	4	yes	—
427	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
428	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	4	yes	—
429	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
430	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
431	C₄×C₄⋊C₄	C₂²×C₁₃₉	1	2	yes	—
432	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
433	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
434	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	4	yes	—
435	C₄×C₂²⋊C₄	C₂²×C₁₃₉	1	2	yes	—
436	C₂×#95	C₂²×C₁₃₉	1	2	yes	—
437	C₂×#41	—	2	4	no	—
438	C₂×#41	—	2	4	no	—
439	C₂×#41	—	2	4	no	—
440	C₂×#41	—	2	4	no	—
441	C₂×#41	—	2	4	no	—
442	C₂×#41	D₄×C₁₃₉	1	8	yes	—
443	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
444	C₂²×Q₈	C₂³×C₁₃₉	1	1	yes	characteristic
445	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
446	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
447	C₂²×D₄	C₂³×C₁₃₉	1	4	yes	—
448	C₂²×D₄	C₂³×C₁₃₉	1	2	yes	—
449	C₂²×D₄	C₂³×C₁₃₉	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
452	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
453	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
454	C₂³×C₄	C₂³×C₁₃₉	1	4	yes	—
455	C₂³×C₄	C₂³×C₁₃₉	1	2	yes	—
456	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
457	C₂³×C₄	C₂³×C₁₃₉	1	1	yes	characteristic
458	C₄⋊Q₈	—	2	4	no	—
459	#127	—	2	4	no	—
460	#124	—	2	4	no	—
461	#124	—	2	4	no	—
462	#123	—	2	16	no	—
463	#121	—	2	16	no	—
464	C₄×Q₈	—	2	8	no	—
465	C₄×D₄	—	2	16	no	—
466	C₄×D₄	—	2	8	no	—
467	C₄×D₄	—	2	16	no	—
468	#117	—	2	8	no	—
469	#117	—	2	4	no	—
470	#117	—	2	4	no	—
471	C₂×C₄⋊C₄	—	2	8	no	—
472	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
477	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
479	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
480	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	4	yes	—
481	C₂×C₄⋊C₄	C₂³×C₁₃₉	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	2	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₁₃₉	1	4	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	4	yes	—
493	C₂×C₄²	—	2	8	no	—
494	C₂×C₄²	—	2	4	no	—
495	C₂×C₄²	—	2	4	no	—
496	C₂×C₄²	—	2	4	no	—
497	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
499	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
500	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
501	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
502	C₂×C₄²	C₂³×C₁₃₉	1	4	yes	—
503	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
504	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
506	C₂×C₄²	C₂³×C₁₃₉	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₁₃₉	1	2	yes	—
508	#95	C₂³×C₁₃₉	1	2	yes	—
509	#95	C₂³×C₁₃₉	1	2	yes	—
510	#95	C₂³×C₁₃₉	1	2	yes	—
511	#95	C₂³×C₁₃₉	1	2	yes	—
512	#95	C₂³×C₁₃₉	1	4	yes	—
513	#95	C₂³×C₁₃₉	1	4	yes	—
514	#95	C₂³×C₁₃₉	1	4	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	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
521	C₂⁴	C₂⁴×C₁₃₉	1	2	yes	—
522	C₂⁴	C₂⁴×C₁₃₉	1	1	yes	characteristic
523	#41	—	2	32	no	—
524	#41	—	4	16	no	—
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	C₂×D₄×C₁₃₉	1	4	yes	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	8	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	8	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	C₂×D₄×C₁₃₉	1	8	yes	—
545	C₂×D₄	C₂×D₄×C₁₃₉	1	4	yes	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	8	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	8	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	4	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	C₂×D₄×C₁₃₉	1	8	yes	—
565	C₂²×C₄	C₂×D₄×C₁₃₉	1	4	yes	—
566	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
567	C₂²×C₄	#41×C₁₃₉	1	4	yes	—
568	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
570	C₂²×C₄	C₂⁴×C₁₃₉	1	4	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	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₁₃₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₁₃₉	1	1	yes	characteristic
580	C₄⋊C₄	—	2	8	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	8	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	8	no	—
588	C₄⋊C₄	—	4	4	no	—
589	C₄⋊C₄	#41×C₁₃₉	1	8	yes	complemented
590	C₂²⋊C₄	—	2	8	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	—	2	8	no	—
593	C₂²⋊C₄	—	2	4	no	—
594	C₂²⋊C₄	—	2	8	no	—
595	C₂²⋊C₄	—	2	8	no	—
596	C₂²⋊C₄	—	2	8	no	—
597	C₂²⋊C₄	—	2	8	no	—
598	C₂²⋊C₄	—	4	4	no	—
599	C₂²⋊C₄	—	4	4	no	—
600	C₂²⋊C₄	—	4	4	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	4	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	4	no	—
605	C₄²	—	2	8	no	—
606	C₄²	—	2	4	no	—
607	C₄²	—	2	2	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	2	4	no	—
611	C₄²	—	2	4	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	4	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	4	no	—
623	C₂³	C₂²×D₄×C₁₃₉	1	4	yes	—
624	C₂³	C₂²×D₄×C₁₃₉	1	2	yes	—
625	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
626	C₂³	C₂×#41×C₁₃₉	1	2	yes	—
627	C₂³	C₂⁵×C₁₃₉	1	1	yes	characteristic
628	Q₈	—	2	8	no	—
629	Q₈	—	4	4	no	—
630	D₄	—	2	16	no	—
631	D₄	—	2	8	no	—
632	D₄	—	4	16	no	—
633	D₄	—	4	8	no	—
634	D₄	—	4	4	no	—
635	C₂×C₄	—	2	8	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	16	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	4	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	4	8	no	—
664	C₂×C₄	—	4	16	no	—
665	C₂×C₄	—	4	8	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	#123×C₁₃₉	1	16	yes	complemented
669	C₂×C₄	C₂²×D₄×C₁₃₉	1	4	yes	—
670	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₁₃₉	1	2	yes	—
672	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
673	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
674	C₂×C₄	C₂×#41×C₁₃₉	1	4	yes	—
675	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
676	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
677	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
678	C₂×C₄	C₂×#41×C₁₃₉	1	2	yes	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	4	no	—
684	C₂²	—	2	8	no	—
685	C₂²	—	4	2	no	—
686	C₂²	—	4	2	no	—
687	C₂²	—	4	4	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	4	no	—
692	C₂²	—	4	4	no	—
693	C₂²	C₂×#123×C₁₃₉	1	4	yes	—
694	C₂²	C₂³×D₄×C₁₃₉	1	1	yes	characteristic
695	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
696	C₂²	C₂²×#41×C₁₃₉	1	1	yes	characteristic
697	C₂²	C₂²×#41×C₁₃₉	1	2	yes	—
698	C₂²	#585×C₁₃₉	1	2	yes	—
699	C₄	—	2	4	no	—
700	C₄	—	2	4	no	—
701	C₄	—	2	4	no	—
702	C₄	—	2	4	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	2	no	—
705	C₄	—	4	2	no	—
706	C₄	—	4	4	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	4	no	—
709	C₄	C₂×#123×C₁₃₉	1	4	yes	—
710	C₄	C₂×#123×C₁₃₉	1	4	yes	—
711	C₂	—	2	4	no	—
712	C₂	—	4	4	no	—
713	C₂	—	8	2	no	—
714	C₂	C₂²×#123×C₁₃₉	1	1	yes	characteristic
715	C₂	#3444×C₁₃₉	1	1	yes	characteristic
716	C₂	#3455×C₁₃₉	1	1	yes	characteristic
717	C₂	D₄×#41×C₁₃₉	1	2	yes	—
718	C₂	#3480×C₁₃₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃₉
socle	C₂³×C₁₃₉	C₂⁵
prime radical	C₂×#532×C₁₃₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₁₃₉	C₂	semidirect
3. #2448×C₁₃₉	C₂	semidirect
4. #2447×C₁₃₉	C₂	semidirect
5. #2446×C₁₃₉	C₂	semidirect
6. #2445×C₁₃₉	C₂	semidirect
7. #2444×C₁₃₉	C₂	semidirect
8. #2443×C₁₃₉	C₂	semidirect
9. #2395×C₁₃₉	C₂	semidirect
10. C₄×#123×C₁₃₉	C₂	semidirect
11. #2297×C₁₃₉	C₂	semidirect
12. #2297×C₁₃₉	C₂	semidirect
13. #2297×C₁₃₉	C₂	semidirect
14. #2296×C₁₃₉	C₂	semidirect
15. C₂×C₄×C₄⋊C₄×C₁₃₉	C₂	semidirect
229. C₄⋊C₄×C₁₃₉	#41	semidirect
308. C₂×C₄×C₁₃₉	#123	semidirect
359. #34744	C₁₃₉	direct (N × H)
360. C₁₃₉	#34744	direct (N × H)
362. C₂×C₄×#41	C₂×C₁₃₉	semidirect
363. #2448	C₂×C₁₃₉	semidirect
364. #2447	C₂×C₁₃₉	semidirect
365. #2446	C₂×C₁₃₉	semidirect
366. #2445	C₂×C₁₃₉	semidirect
367. #2444	C₂×C₁₃₉	semidirect
368. #2443	C₂×C₁₃₉	semidirect
369. #2395	C₂×C₁₃₉	semidirect
370. C₄×#123	C₂×C₁₃₉	semidirect
371. #2297	C₂×C₁₃₉	semidirect
372. #2297	C₂×C₁₃₉	semidirect
373. #2297	C₂×C₁₃₉	semidirect
374. #2296	C₂×C₁₃₉	semidirect
375. C₂×C₄×C₄⋊C₄	C₂×C₁₃₉	semidirect
589. C₄⋊C₄	#41×C₁₃₉	semidirect
668. C₂×C₄	#123×C₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₁₃₉	2
C₂×C₄×#41×C₁₃₉	2
#2448×C₁₃₉	2
#2447×C₁₃₉	2
#2446×C₁₃₉	2
#2445×C₁₃₉	2
#2444×C₁₃₉	2
#2443×C₁₃₉	2
#2395×C₁₃₉	2
C₄×#123×C₁₃₉	2
#2297×C₁₃₉	2
#2296×C₁₃₉	2
C₂×C₄×C₄⋊C₄×C₁₃₉	2
#34744	139

Subgroups — C139×#34744 #48029340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₉×#34744 #48029340