Subgroups — #31815696

Order 17792.

700 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17984889	C₂	1	1	yes	maximal, characteristic
2	C₂×#17984871	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Q₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581526	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581116	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581115	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581112	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581111	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581110	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581108	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581107	C₂	1	1	yes	maximal, characteristic, complemented
12	#22580960	C₂	1	1	yes	maximal, characteristic, complemented
13	#22580946	C₂	1	1	yes	maximal, characteristic, complemented
14	#22580918	C₂	1	1	yes	maximal, characteristic, complemented
15	#452×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#17984889	—	2	4	no	—
17	#17984889	—	2	4	no	—
18	C₂×#14555785	—	2	1	no	—
19	C₂×#14555785	C₂²	1	1	yes	characteristic
20	C₂×#14555784	—	2	1	no	—
21	C₂×#14555784	—	2	1	no	—
22	C₂×#14555784	C₂²	1	1	yes	characteristic
23	C₂×#14555784	C₂²	1	1	yes	characteristic
24	C₂²×Dic₂₇₈	—	2	1	no	—
25	C₂²×Dic₂₇₈	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic
29	#17984871	—	2	4	no	—
30	C₂×Dic₅₅₆	C₂²	1	1	yes	characteristic
31	C₂×Dic₅₅₆	C₂²	1	1	yes	characteristic
32	C₂×#14555775	C₂²	1	1	yes	characteristic
33	C₂×#14555775	C₂²	1	1	yes	characteristic
34	C₂×#14555775	C₂²	1	1	yes	characteristic
35	Q₁₆×D₁₃₉	—	2	4	no	—
36	C₂×#14555773	C₂²	1	1	yes	characteristic
37	C₂×#14555768	C₂²	1	1	yes	characteristic
38	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic
39	#17984841	—	2	1	no	—
40	#17984828	—	2	1	no	—
41	#17984827	—	2	1	no	—
42	#17984824	—	2	1	no	—
43	#17984822	C₂²	1	1	yes	characteristic
44	#17984821	C₂²	1	1	yes	characteristic
45	#17984818	C₂²	1	1	yes	characteristic
46	#17984800	C₂²	1	1	yes	characteristic
47	#17984767	C₂²	1	1	yes	characteristic
48	#17984767	C₂²	1	1	yes	characteristic
49	#17984766	C₂²	1	1	yes	characteristic
50	#17984765	C₂²	1	1	yes	characteristic
51	#17984765	C₂²	1	1	yes	characteristic
52	#17984763	C₂²	1	1	yes	characteristic
53	C₂²⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic
54	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic
55	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×#41×C₁₃₉	C₂²	1	1	yes	characteristic
57	C₂×Q₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
58	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
59	C₂²⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
60	#103×C₁₃₉	C₂²	1	1	yes	characteristic
61	#102×C₁₃₉	C₂²	1	1	yes	characteristic
62	C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
63	#14555785	—	2	8	no	—
64	#14555785	—	2	2	no	—
65	#14555785	—	2	2	no	—
66	#14555784	—	2	8	no	—
67	#14555784	—	2	8	no	—
68	#14555784	—	2	2	no	—
69	#14555784	—	2	2	no	—
70	#14555784	—	2	2	no	—
71	#14555784	D₄	1	4	yes	—
72	C₂×Dic₂₇₈	—	2	8	no	—
73	C₂×Dic₂₇₈	—	2	2	no	—
74	C₂×Dic₂₇₈	—	2	2	no	—
75	C₂×Dic₂₇₈	—	2	1	no	—
76	C₂×Dic₂₇₈	—	2	1	no	—
77	C₂×Dic₂₇₈	—	2	1	no	—
78	C₂×Dic₂₇₈	—	2	1	no	—
79	C₂×Dic₂₇₈	D₄	1	1	yes	characteristic
80	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
81	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
82	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
83	Q₈×D₁₃₉	—	2	2	no	—
84	Q₈×D₁₃₉	—	2	2	no	—
85	Q₈×D₁₃₉	—	2	2	no	—
86	Q₈×D₁₃₉	—	2	2	no	—
87	Q₈×D₁₃₉	—	2	2	no	—
88	Q₈×D₁₃₉	D₄	1	4	yes	—
89	C₂×D₅₅₆	D₄	1	1	yes	characteristic
90	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
91	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
92	C₂×C₂²⋊D₁₃₉	D₄	1	1	yes	characteristic
93	C₂×C₂²⋊D₁₃₉	D₄	1	1	yes	characteristic
94	C₂²×Dic₁₃₉	—	2	1	no	—
95	C₂²×Dic₁₃₉	—	2	1	no	—
96	C₂²×Dic₁₃₉	—	2	1	no	—
97	C₂×C₄×D₁₃₉	—	2	1	no	—
98	C₂×C₄×D₁₃₉	—	2	1	no	—
99	C₂×C₄×D₁₃₉	—	2	1	no	—
100	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
102	Dic₅₅₆	—	2	2	no	—
103	Dic₅₅₆	—	2	2	no	—
104	#14555775	—	2	2	no	—
105	#14555775	—	2	2	no	—
106	#14555775	—	2	2	no	—
107	#14555773	—	2	2	no	—
108	#14555768	—	2	2	no	—
109	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
111	C₈×D₁₃₉	—	2	2	no	—
112	C₄⋊Dic₁₃₉	—	2	1	no	—
113	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
114	Dic₁₃₉⋊C₄	—	2	1	no	—
115	Dic₁₃₉⋊C₄	—	2	1	no	—
116	C₂²⋊Dic₁₃₉	—	2	1	no	—
117	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
118	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
119	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
120	C₄×Dic₁₃₉	—	2	1	no	—
121	#41×C₁₃₉	—	2	2	no	—
122	#41×C₁₃₉	—	2	2	no	—
123	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₃₉	—	2	1	no	—
126	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃₉	—	2	1	no	—
128	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
129	Q₁₆×C₁₃₉	—	2	2	no	—
130	SD₁₆×C₁₃₉	—	2	2	no	—
131	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
132	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₄×C₁₃₉	—	2	1	no	—
134	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
136	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
138	Dic₂₇₈	—	2	4	no	—
139	Dic₂₇₈	—	2	4	no	—
140	Dic₂₇₈	—	2	1	no	—
141	Dic₂₇₈	—	2	1	no	—
142	Dic₂₇₈	—	2	4	no	—
143	Dic₂₇₈	—	2	2	no	—
144	Dic₂₇₈	—	2	1	no	—
145	Dic₂₇₈	—	2	1	no	—
146	Dic₂₇₈	—	4	2	no	—
147	Dic₂₇₈	C₂×D₄	1	2	yes	—
148	Dic₂₇₈	C₂×D₄	1	2	yes	—
149	D₅₅₆	—	2	2	no	—
150	C₂²⋊D₁₃₉	—	2	4	no	—
151	C₂²⋊D₁₃₉	—	2	4	no	—
152	C₂²⋊D₁₃₉	—	2	2	no	—
153	C₂²⋊D₁₃₉	—	2	2	no	—
154	C₂×Dic₁₃₉	—	2	4	no	—
155	C₂×Dic₁₃₉	—	2	4	no	—
156	C₂×Dic₁₃₉	—	2	1	no	—
157	C₂×Dic₁₃₉	—	2	1	no	—
158	C₂×Dic₁₃₉	—	2	4	no	—
159	C₂×Dic₁₃₉	—	2	1	no	—
160	C₂×Dic₁₃₉	—	2	1	no	—
161	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
162	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
163	C₄×D₁₃₉	—	2	4	no	—
164	C₄×D₁₃₉	—	2	4	no	—
165	C₄×D₁₃₉	—	2	1	no	—
166	C₄×D₁₃₉	—	2	1	no	—
167	C₄×D₁₃₉	—	4	2	no	—
168	C₄×D₁₃₉	C₂×D₄	1	2	yes	—
169	C₄×D₁₃₉	C₂×D₄	1	2	yes	—
170	C₁₃₉⋊C₈	—	2	1	no	—
171	C₁₃₉⋊C₈	—	2	1	no	—
172	C₂³×C₁₃₉	—	2	1	no	—
173	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
174	Q₈×C₁₃₉	—	2	1	no	—
175	Q₈×C₁₃₉	—	2	1	no	—
176	Q₈×C₁₃₉	—	2	1	no	—
177	Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
178	D₄×C₁₃₉	—	2	4	no	—
179	D₄×C₁₃₉	—	2	1	no	—
180	D₄×C₁₃₉	C₂×D₄	1	2	yes	—
181	C₂×C₄×C₁₃₉	—	2	4	no	—
182	C₂×C₄×C₁₃₉	—	2	1	no	—
183	C₂×C₄×C₁₃₉	—	2	1	no	—
184	C₂×C₄×C₁₃₉	—	2	1	no	—
185	C₂×C₄×C₁₃₉	—	2	1	no	—
186	C₂×C₄×C₁₃₉	—	2	1	no	—
187	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
189	C₈×C₁₃₉	—	2	1	no	—
190	C₈×C₁₃₉	—	2	1	no	—
191	C₂²×C₁₃₉	—	2	1	no	—
192	C₂²×C₁₃₉	—	2	2	no	—
193	C₂²×C₁₃₉	—	2	1	no	—
194	C₂²×C₁₃₉	—	2	1	no	—
195	C₂²×C₁₃₉	—	4	1	no	—
196	C₂²×C₁₃₉	—	4	1	no	—
197	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×D₁₃₉	—	2	1	no	—
199	C₂×D₁₃₉	—	2	1	no	—
200	C₂×D₁₃₉	—	2	1	no	—
201	C₂×D₁₃₉	—	2	1	no	—
202	C₂×D₁₃₉	—	2	1	no	—
203	C₂×D₁₃₉	#120	1	2	yes	—
204	C₄×C₁₃₉	—	2	1	no	—
205	C₄×C₁₃₉	—	2	2	no	—
206	C₄×C₁₃₉	—	4	1	no	—
207	C₄×C₁₃₉	—	4	1	no	—
208	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
209	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
210	Dic₁₃₉	—	2	2	no	—
211	Dic₁₃₉	—	2	2	no	—
212	Dic₁₃₉	—	2	1	no	—
213	Dic₁₃₉	—	4	1	no	—
214	Dic₁₃₉	—	4	1	no	—
215	Dic₁₃₉	#120	1	2	yes	—
216	C₂×C₁₃₉	—	4	1	no	—
217	C₂×C₁₃₉	—	4	2	no	—
218	C₂×C₁₃₉	C₂×#120	1	1	yes	characteristic
219	C₂×C₁₃₉	#578	1	1	yes	characteristic
220	C₂×C₁₃₉	#578	1	1	yes	characteristic
221	D₁₃₉	—	2	2	no	—
222	D₁₃₉	—	4	1	no	—
223	C₁₃₉	#3011	1	1	yes	characteristic, complemented, Sylow
224	#3011	—	139	1	no	maximal, Sylow
225	C₂×2₋¹⁺⁴	—	139	1	no	—
226	C₂×#137	—	139	1	no	—
227	C₂²×Q₁₆	—	139	1	no	—
228	#536	—	139	1	no	—
229	#452	—	139	1	no	—
230	#452	—	139	1	no	—
231	#452	—	139	1	no	—
232	#452	D₁₃₉	1	1	yes	characteristic, complemented
233	#451	—	139	1	no	—
234	#451	—	139	1	no	—
235	#451	—	139	1	no	—
236	#451	—	139	1	no	—
237	#419	—	139	1	no	—
238	#416	—	139	1	no	—
239	#408	—	139	1	no	—
240	2₋¹⁺⁴	—	278	4	no	—
241	2₋¹⁺⁴	—	278	4	no	—
242	C₂×#41	—	278	1	no	—
243	C₂×#41	—	278	1	no	—
244	C₂×#41	—	278	1	no	—
245	C₂×#41	—	139	1	no	—
246	C₂×#41	—	139	1	no	—
247	C₂×#41	—	139	1	no	—
248	C₂×#41	C₂×D₁₃₉	1	1	yes	characteristic
249	C₂²×Q₈	—	278	1	no	—
250	C₂²×Q₈	—	139	1	no	—
251	C₂²×Q₈	—	139	1	no	—
252	C₂²×Q₈	—	139	1	no	—
253	C₂²×Q₈	—	139	1	no	—
254	#137	—	278	4	no	—
255	C₂×Q₁₆	—	278	4	no	—
256	C₂×Q₁₆	—	139	1	no	—
257	C₂×Q₁₆	—	139	1	no	—
258	C₂×Q₁₆	—	139	1	no	—
259	C₂×Q₁₆	—	139	1	no	—
260	C₂×Q₁₆	—	139	1	no	—
261	C₂×Q₁₆	C₂×D₁₃₉	1	1	yes	characteristic
262	C₂×SD₁₆	—	139	1	no	—
263	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic
264	C₂×M₁₆	—	139	1	no	—
265	C₂²×C₈	—	139	1	no	—
266	C₄⋊Q₈	—	278	1	no	—
267	#124	—	278	1	no	—
268	#123	—	278	1	no	—
269	#123	—	278	1	no	—
270	C₂²⋊Q₈	—	139	1	no	—
271	C₂²⋊Q₈	—	139	1	no	—
272	C₂²⋊Q₈	—	139	1	no	—
273	C₂²⋊Q₈	C₂×D₁₃₉	1	1	yes	characteristic
274	#117	—	139	1	no	—
275	#103	—	139	1	no	—
276	#103	—	139	1	no	—
277	#103	—	139	1	no	—
278	#103	—	139	1	no	—
279	#103	—	139	1	no	—
280	#103	C₂×D₁₃₉	1	1	yes	characteristic
281	#102	—	139	1	no	—
282	#102	C₂×D₁₃₉	1	1	yes	characteristic
283	C₂²⋊C₈	—	139	1	no	—
284	C₂²⋊C₈	—	139	1	no	—
285	C₂²⋊C₈	—	139	1	no	—
286	C₂²⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic
287	#41	—	2	2	no	—
288	#41	—	2	2	no	—
289	#41	—	278	8	no	—
290	#41	—	278	2	no	—
291	#41	—	278	2	no	—
292	#41	—	278	8	no	—
293	#41	—	278	8	no	—
294	#41	—	278	2	no	—
295	#41	—	278	2	no	—
296	#41	—	278	2	no	—
297	#41	—	139	4	no	—
298	C₂×Q₈	—	278	8	no	—
299	C₂×Q₈	—	278	2	no	—
300	C₂×Q₈	—	278	2	no	—
301	C₂×Q₈	—	278	1	no	—
302	C₂×Q₈	—	278	1	no	—
303	C₂×Q₈	—	278	1	no	—
304	C₂×Q₈	—	278	2	no	—
305	C₂×Q₈	—	278	2	no	—
306	C₂×Q₈	—	278	2	no	—
307	C₂×Q₈	—	278	1	no	—
308	C₂×Q₈	—	278	2	no	—
309	C₂×Q₈	—	278	2	no	—
310	C₂×Q₈	—	139	4	no	—
311	C₂×Q₈	—	139	1	no	—
312	C₂×Q₈	—	139	1	no	—
313	C₂×Q₈	—	139	1	no	—
314	C₂×Q₈	—	139	1	no	—
315	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
316	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	278	1	no	—
319	C₂×D₄	—	278	1	no	—
320	C₂×D₄	—	139	1	no	—
321	C₂×D₄	—	139	1	no	—
322	C₂×D₄	—	139	1	no	—
323	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	278	1	no	—
326	C₂²×C₄	—	278	1	no	—
327	C₂²×C₄	—	278	1	no	—
328	C₂²×C₄	—	278	1	no	—
329	C₂²×C₄	—	278	1	no	—
330	C₂²×C₄	—	278	1	no	—
331	C₂²×C₄	—	139	1	no	—
332	C₂²×C₄	—	139	1	no	—
333	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
334	Q₁₆	—	2	2	no	—
335	Q₁₆	—	278	2	no	—
336	Q₁₆	—	278	2	no	—
337	Q₁₆	—	278	2	no	—
338	Q₁₆	—	278	2	no	—
339	Q₁₆	—	278	2	no	—
340	SD₁₆	—	2	2	no	—
341	SD₁₆	—	278	2	no	—
342	M₁₆	—	278	2	no	—
343	C₂×C₈	—	278	2	no	—
344	C₂×C₈	—	139	1	no	—
345	C₂×C₈	—	139	1	no	—
346	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
347	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	278	1	no	—
350	C₄⋊C₄	—	278	1	no	—
351	C₄⋊C₄	—	278	1	no	—
352	C₄⋊C₄	—	139	1	no	—
353	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	278	1	no	—
356	C₂²⋊C₄	—	278	1	no	—
357	C₂²⋊C₄	—	278	1	no	—
358	C₂²⋊C₄	—	278	1	no	—
359	C₄²	—	278	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	139	1	no	—
362	C₂³	—	139	1	no	—
363	C₂³	D₄×D₁₃₉	1	1	yes	characteristic
364	Q₈	—	2	1	no	—
365	Q₈	—	2	1	no	—
366	Q₈	—	2	1	no	—
367	Q₈	—	278	4	no	—
368	Q₈	—	278	4	no	—
369	Q₈	—	278	2	no	—
370	Q₈	—	278	4	no	—
371	Q₈	—	278	1	no	—
372	Q₈	—	278	1	no	—
373	Q₈	—	278	1	no	—
374	Q₈	—	278	1	no	—
375	Q₈	—	556	2	no	—
376	Q₈	—	139	2	no	—
377	Q₈	—	139	2	no	—
378	Q₈	D₄×D₁₃₉	1	2	yes	—
379	D₄	—	2	4	no	—
380	D₄	—	2	1	no	—
381	D₄	—	278	2	no	—
382	D₄	—	278	4	no	—
383	D₄	—	278	4	no	—
384	D₄	—	278	2	no	—
385	D₄	—	278	2	no	—
386	D₄	D₄×D₁₃₉	1	2	yes	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	278	4	no	—
394	C₂×C₄	—	278	4	no	—
395	C₂×C₄	—	278	4	no	—
396	C₂×C₄	—	278	4	no	—
397	C₂×C₄	—	278	1	no	—
398	C₂×C₄	—	278	1	no	—
399	C₂×C₄	—	278	4	no	—
400	C₂×C₄	—	278	1	no	—
401	C₂×C₄	—	278	1	no	—
402	C₂×C₄	—	278	1	no	—
403	C₂×C₄	—	278	1	no	—
404	C₂×C₄	—	556	2	no	—
405	C₂×C₄	—	139	1	no	—
406	C₂×C₄	—	139	1	no	—
407	C₂×C₄	—	139	2	no	—
408	C₂×C₄	—	139	2	no	—
409	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
410	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	278	1	no	—
414	C₈	—	278	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	278	1	no	—
422	C₂²	—	278	1	no	—
423	C₂²	—	278	1	no	—
424	C₂²	—	278	1	no	—
425	C₂²	—	278	1	no	—
426	C₂²	—	139	2	no	—
427	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	278	2	no	—
433	C₄	—	278	2	no	—
434	C₄	—	278	1	no	—
435	C₄	—	556	1	no	—
436	C₄	—	556	1	no	—
437	C₄	—	139	2	no	—
438	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
439	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
440	C₂	—	4	1	no	—
441	C₂	—	4	2	no	—
442	C₂	—	278	2	no	—
443	C₂	—	556	1	no	—
444	C₂	#120×D₁₃₉	1	1	yes	characteristic
445	C₂	#22581767	1	1	yes	characteristic
446	C₂	#22581769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#452×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
prime radical	C₂×#17984889	C₂
hypercenter	#452	D₁₃₉
hypocenter	C₁₃₉	#3011
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #452

Complements

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

N	H ≅ G/N	type
2. C₂×#17984871	C₂	semidirect
3. C₂×Q₁₆×D₁₃₉	C₂	semidirect
4. #22581526	C₂	semidirect
5. #22581116	C₂	semidirect
6. #22581115	C₂	semidirect
7. #22581112	C₂	semidirect
8. #22581111	C₂	semidirect
9. #22581110	C₂	semidirect
10. #22581108	C₂	semidirect
11. #22581107	C₂	semidirect
12. #22580960	C₂	semidirect
13. #22580946	C₂	semidirect
14. #22580918	C₂	semidirect
15. #452×C₁₃₉	C₂	semidirect
223. C₁₃₉	#3011	semidirect
232. #452	D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17984889	2
C₂×#17984871	2
C₂×Q₁₆×D₁₃₉	2
#22581526	2
#22581116	2
#22581115	2
#22581112	2
#22581111	2
#22581110	2
#22581108	2
#22581107	2
#22580960	2
#22580946	2
#22580918	2
#452×C₁₃₉	2
#3011	139