Subgroups — #31815685

Order 17792.

732 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17984890	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17984869	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×SD₁₆×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#22581519	C₂	1	1	yes	maximal, characteristic, complemented
5	#22581101	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581100	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581097	C₂	1	1	yes	maximal, characteristic, complemented
8	#22581096	C₂	1	1	yes	maximal, characteristic, complemented
9	#22581093	C₂	1	1	yes	maximal, characteristic, complemented
10	#22581092	C₂	1	1	yes	maximal, characteristic, complemented
11	#22581090	C₂	1	1	yes	maximal, characteristic, complemented
12	#22580960	C₂	1	1	yes	maximal, characteristic, complemented
13	#22580948	C₂	1	1	yes	maximal, characteristic, complemented
14	#22580918	C₂	1	1	yes	maximal, characteristic, complemented
15	#448×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#17984890	—	2	4	no	—
17	#17984890	—	2	4	no	—
18	C₂×#14555786	—	2	1	no	—
19	C₂×#14555786	C₂²	1	1	yes	characteristic
20	C₂×#14555786	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14555785	—	2	1	no	—
22	C₂×#14555785	—	2	1	no	—
23	C₂×#14555785	C₂²	1	1	yes	characteristic
24	C₂×#14555785	C₂²	1	1	yes	characteristic, complemented
25	C₂×Q₈×D₁₃₉	—	2	1	no	—
26	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₁₃₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₄×D₁₃₉	C₂²	1	1	yes	characteristic
29	#17984869	—	2	4	no	—
30	C₂×#14555774	C₂²	1	1	yes	characteristic
31	C₂×#14555773	C₂²	1	1	yes	characteristic
32	C₂×#14555772	C₂²	1	1	yes	characteristic
33	C₂×#14555772	C₂²	1	1	yes	characteristic
34	SD₁₆×D₁₃₉	—	2	4	no	—
35	C₂×D₁₁₁₂	C₂²	1	1	yes	characteristic
36	C₂×#14555770	C₂²	1	1	yes	characteristic
37	C₂×#14555768	C₂²	1	1	yes	characteristic
38	C₂×C₈×D₁₃₉	C₂²	1	1	yes	characteristic
39	#17984838	—	2	1	no	—
40	#17984828	—	2	1	no	—
41	#17984817	C₂²	1	1	yes	characteristic
42	#17984816	C₂²	1	1	yes	characteristic
43	#17984813	C₂²	1	1	yes	characteristic
44	#17984812	—	2	1	no	—
45	#17984810	—	2	1	no	—
46	#17984800	C₂²	1	1	yes	characteristic
47	#17984767	C₂²	1	1	yes	characteristic, complemented
48	#17984766	C₂²	1	1	yes	characteristic, complemented
49	#17984766	C₂²	1	1	yes	characteristic, complemented
50	#17984765	C₂²	1	1	yes	characteristic, complemented
51	#17984764	C₂²	1	1	yes	characteristic, complemented
52	#17984762	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	(C₂×D₁₃₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	C₂²×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
57	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
58	C₂×SD₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
59	#121×C₁₃₉	C₂²	1	1	yes	characteristic
60	#103×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
61	#103×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
62	C₂²⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₁₃₉	—	2	1	no	—
64	#14555786	—	2	8	no	—
65	#14555786	—	2	2	no	—
66	#14555786	—	2	2	no	—
67	#14555786	—	2	2	no	—
68	#14555786	D₄	1	4	yes	complemented
69	#14555785	—	2	8	no	—
70	#14555785	—	2	8	no	—
71	#14555785	—	2	2	no	—
72	#14555785	—	2	2	no	—
73	#14555785	—	2	2	no	—
74	#14555785	—	2	2	no	—
75	C₂×Dic₂₇₈	—	2	1	no	—
76	C₂×Dic₂₇₈	—	2	1	no	—
77	C₂×Dic₂₇₈	D₄	1	1	yes	characteristic
78	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
79	Q₈×D₁₃₉	—	2	8	no	—
80	Q₈×D₁₃₉	—	2	2	no	—
81	Q₈×D₁₃₉	—	2	2	no	—
82	Q₈×D₁₃₉	—	2	2	no	—
83	Q₈×D₁₃₉	D₄	1	4	yes	complemented
84	C₂×D₅₅₆	—	2	1	no	—
85	C₂×D₅₅₆	—	2	1	no	—
86	C₂×D₅₅₆	—	2	1	no	—
87	C₂×D₅₅₆	D₄	1	1	yes	characteristic
88	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
89	C₂×D₅₅₆	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
91	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
92	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
93	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
94	C₂×C₂²⋊D₁₃₉	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊D₁₃₉	D₄	1	1	yes	characteristic
96	D₄×D₁₃₉	—	2	2	no	—
97	D₄×D₁₃₉	—	2	2	no	—
98	C₂×C₄×D₁₃₉	—	2	1	no	—
99	C₂×C₄×D₁₃₉	—	2	1	no	—
100	C₂×C₄×D₁₃₉	—	2	1	no	—
101	C₂×C₄×D₁₃₉	—	2	1	no	—
102	C₂×C₄×D₁₃₉	—	2	1	no	—
103	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
104	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
105	#14555774	—	2	2	no	—
106	#14555773	—	2	2	no	—
107	#14555772	—	2	2	no	—
108	#14555772	—	2	2	no	—
109	D₁₁₁₂	—	2	2	no	—
110	#14555770	—	2	2	no	—
111	#14555768	—	2	2	no	—
112	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
113	C₂×C₁₃₉⋊C₈	C₂³	1	1	yes	characteristic
114	C₈×D₁₃₉	—	2	2	no	—
115	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
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	C₂×Q₈×C₁₃₉	—	2	2	no	—
122	C₂×Q₈×C₁₃₉	—	2	2	no	—
123	C₂×Q₈×C₁₃₉	—	2	1	no	—
124	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃₉	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃₉	—	2	1	no	—
127	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃₉	—	2	1	no	—
129	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
130	SD₁₆×C₁₃₉	—	2	2	no	—
131	SD₁₆×C₁₃₉	—	2	2	no	—
132	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
133	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
134	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
135	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
136	C₂²×D₁₃₉	—	2	1	no	—
137	C₂²×D₁₃₉	—	2	1	no	—
138	C₂²×D₁₃₉	—	4	2	no	—
139	C₂²×D₁₃₉	—	8	1	no	—
140	C₂²×D₁₃₉	—	8	1	no	—
141	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
143	Dic₂₇₈	—	2	4	no	—
144	Dic₂₇₈	—	2	1	no	—
145	Dic₂₇₈	—	2	2	no	—
146	Dic₂₇₈	—	2	4	no	—
147	Dic₂₇₈	C₂×D₄	1	2	yes	—
148	D₅₅₆	—	2	4	no	—
149	D₅₅₆	—	2	4	no	—
150	D₅₅₆	—	2	2	no	—
151	D₅₅₆	—	2	1	no	—
152	D₅₅₆	—	2	1	no	—
153	D₅₅₆	—	2	1	no	—
154	D₅₅₆	—	8	1	no	—
155	D₅₅₆	C₂×D₄	1	2	yes	—
156	C₂²⋊D₁₃₉	—	2	4	no	—
157	C₂²⋊D₁₃₉	—	2	2	no	—
158	C₂²⋊D₁₃₉	—	2	2	no	—
159	C₂²⋊D₁₃₉	—	4	2	no	—
160	C₂²⋊D₁₃₉	—	8	1	no	—
161	C₂²⋊D₁₃₉	—	8	1	no	—
162	C₂×Dic₁₃₉	—	2	1	no	—
163	C₂×Dic₁₃₉	—	2	1	no	—
164	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
165	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
166	C₄×D₁₃₉	—	2	4	no	—
167	C₄×D₁₃₉	—	2	4	no	—
168	C₄×D₁₃₉	—	2	4	no	—
169	C₄×D₁₃₉	—	2	4	no	—
170	C₄×D₁₃₉	—	2	1	no	—
171	C₄×D₁₃₉	—	2	1	no	—
172	C₄×D₁₃₉	—	2	4	no	—
173	C₄×D₁₃₉	C₂×D₄	1	2	yes	—
174	C₄×D₁₃₉	C₂×D₄	1	2	yes	—
175	C₁₃₉⋊C₈	—	2	1	no	—
176	C₁₃₉⋊C₈	—	2	1	no	—
177	C₂³×C₁₃₉	—	2	1	no	—
178	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
179	Q₈×C₁₃₉	—	2	4	no	—
180	Q₈×C₁₃₉	—	2	1	no	—
181	Q₈×C₁₃₉	—	2	1	no	—
182	Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
183	Q₈×C₁₃₉	C₂×D₄	1	2	yes	—
184	D₄×C₁₃₉	—	2	1	no	—
185	D₄×C₁₃₉	—	2	1	no	—
186	D₄×C₁₃₉	—	8	1	no	—
187	C₂×C₄×C₁₃₉	—	2	4	no	—
188	C₂×C₄×C₁₃₉	—	2	1	no	—
189	C₂×C₄×C₁₃₉	—	2	1	no	—
190	C₂×C₄×C₁₃₉	—	2	1	no	—
191	C₂×C₄×C₁₃₉	—	2	1	no	—
192	C₂×C₄×C₁₃₉	—	2	1	no	—
193	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
195	C₈×C₁₃₉	—	2	1	no	—
196	C₈×C₁₃₉	—	2	1	no	—
197	C₂²×C₁₃₉	—	2	1	no	—
198	C₂²×C₁₃₉	—	2	1	no	—
199	C₂²×C₁₃₉	—	2	1	no	—
200	C₂²×C₁₃₉	—	4	1	no	—
201	C₂²×C₁₃₉	—	4	1	no	—
202	C₂²×C₁₃₉	—	4	1	no	—
203	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×D₁₃₉	—	2	1	no	—
205	C₂×D₁₃₉	—	2	1	no	—
206	C₂×D₁₃₉	—	2	1	no	—
207	C₂×D₁₃₉	—	2	2	no	—
208	C₂×D₁₃₉	—	2	1	no	—
209	C₂×D₁₃₉	—	2	1	no	—
210	C₂×D₁₃₉	—	4	1	no	—
211	C₂×D₁₃₉	—	4	1	no	—
212	C₂×D₁₃₉	—	4	1	no	—
213	C₂×D₁₃₉	—	4	1	no	—
214	C₂×D₁₃₉	—	4	1	no	—
215	C₂×D₁₃₉	—	8	4	no	—
216	C₂×D₁₃₉	#120	1	2	yes	—
217	C₄×C₁₃₉	—	2	2	no	—
218	C₄×C₁₃₉	—	2	2	no	—
219	C₄×C₁₃₉	—	2	1	no	—
220	C₄×C₁₃₉	—	4	1	no	—
221	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
222	C₄×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
223	Dic₁₃₉	—	2	2	no	—
224	Dic₁₃₉	—	2	1	no	—
225	Dic₁₃₉	—	4	1	no	—
226	Dic₁₃₉	#120	1	2	yes	—
227	C₂×C₁₃₉	—	4	1	no	—
228	C₂×C₁₃₉	—	8	1	no	—
229	C₂×C₁₃₉	C₂×#120	1	1	yes	characteristic
230	C₂×C₁₃₉	#577	1	1	yes	characteristic
231	C₂×C₁₃₉	#577	1	1	yes	characteristic
232	D₁₃₉	—	2	2	no	—
233	D₁₃₉	—	4	1	no	—
234	D₁₃₉	—	4	2	no	—
235	D₁₃₉	—	8	1	no	—
236	C₁₃₉	#3010	1	1	yes	characteristic, complemented, Sylow
237	#3010	—	139	1	no	maximal, Sylow
238	C₂×2₋¹⁺⁴	—	139	1	no	—
239	C₂×AGL(1,ℤ/8)	—	139	1	no	—
240	C₂²×SD₁₆	—	139	1	no	—
241	#535	—	139	1	no	—
242	#449	—	139	1	no	—
243	#449	—	139	1	no	—
244	#449	—	139	1	no	—
245	#449	—	139	1	no	—
246	#448	—	139	1	no	—
247	#448	—	139	1	no	—
248	#448	—	139	1	no	—
249	#448	D₁₃₉	1	1	yes	characteristic, complemented
250	#419	—	139	1	no	—
251	#416	—	139	1	no	—
252	#408	—	139	1	no	—
253	2₋¹⁺⁴	—	278	4	no	—
254	2₋¹⁺⁴	—	278	4	no	—
255	C₂×#41	—	278	1	no	—
256	C₂×#41	—	278	1	no	—
257	C₂×#41	—	278	1	no	—
258	C₂×#41	—	139	1	no	—
259	C₂×#41	—	139	1	no	—
260	C₂×#41	—	139	1	no	—
261	C₂×#41	—	139	1	no	—
262	C₂²×Q₈	—	278	1	no	—
263	C₂²×Q₈	—	139	1	no	—
264	C₂²×Q₈	—	139	1	no	—
265	C₂²×Q₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
266	C₂²×D₄	—	139	1	no	—
267	AGL(1,ℤ/8)	—	278	4	no	—
268	C₂×SD₁₆	—	278	4	no	—
269	C₂×SD₁₆	—	139	1	no	—
270	C₂×SD₁₆	—	139	1	no	—
271	C₂×SD₁₆	—	139	1	no	—
272	C₂×SD₁₆	—	139	1	no	—
273	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic
274	C₂×SD₁₆	C₂×D₁₃₉	1	1	yes	characteristic
275	C₂×D₈	—	139	1	no	—
276	C₂×D₈	—	139	1	no	—
277	C₂×M₁₆	—	139	1	no	—
278	C₂²×C₈	—	139	1	no	—
279	#127	—	278	1	no	—
280	#124	—	278	1	no	—
281	#121	—	139	1	no	—
282	#121	—	139	1	no	—
283	#121	—	139	1	no	—
284	#121	C₂×D₁₃₉	1	1	yes	characteristic
285	#120	—	278	1	no	—
286	#120	—	278	1	no	—
287	#117	—	139	1	no	—
288	#103	—	139	1	no	—
289	#103	—	139	1	no	—
290	#103	—	139	1	no	—
291	#103	—	139	1	no	—
292	#103	C₂×D₁₃₉	1	1	yes	characteristic, complemented
293	#103	C₂×D₁₃₉	1	1	yes	characteristic, complemented
294	#102	—	139	1	no	—
295	#102	—	139	1	no	—
296	C₂²⋊C₈	—	139	1	no	—
297	C₂²⋊C₈	—	139	1	no	—
298	C₂²⋊C₈	—	139	1	no	—
299	C₂²⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic, complemented
300	C₂⁴	—	278	1	no	—
301	#41	—	278	8	no	—
302	#41	—	278	8	no	—
303	#41	—	278	2	no	—
304	#41	—	278	2	no	—
305	#41	—	278	2	no	—
306	#41	—	278	2	no	—
307	#41	—	278	8	no	—
308	#41	—	278	2	no	—
309	#41	—	278	2	no	—
310	#41	—	278	2	no	—
311	#41	—	139	4	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	278	1	no	—
316	C₂×Q₈	—	278	1	no	—
317	C₂×Q₈	—	278	8	no	—
318	C₂×Q₈	—	278	2	no	—
319	C₂×Q₈	—	278	2	no	—
320	C₂×Q₈	—	278	2	no	—
321	C₂×Q₈	—	139	4	no	—
322	C₂×Q₈	—	139	1	no	—
323	C₂×Q₈	—	139	1	no	—
324	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
325	C₂×Q₈	C₂²×D₁₃₉	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	278	1	no	—
328	C₂×D₄	—	278	1	no	—
329	C₂×D₄	—	278	1	no	—
330	C₂×D₄	—	278	1	no	—
331	C₂×D₄	—	278	1	no	—
332	C₂×D₄	—	278	1	no	—
333	C₂×D₄	—	278	2	no	—
334	C₂×D₄	—	278	2	no	—
335	C₂×D₄	—	278	1	no	—
336	C₂×D₄	—	139	1	no	—
337	C₂×D₄	—	139	1	no	—
338	C₂×D₄	—	139	1	no	—
339	C₂×D₄	—	139	1	no	—
340	C₂×D₄	—	139	1	no	—
341	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	278	1	no	—
344	C₂²×C₄	—	278	1	no	—
345	C₂²×C₄	—	278	1	no	—
346	C₂²×C₄	—	278	1	no	—
347	C₂²×C₄	—	278	1	no	—
348	C₂²×C₄	—	139	1	no	—
349	C₂²×C₄	—	139	1	no	—
350	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
351	SD₁₆	—	2	2	no	—
352	SD₁₆	—	2	2	no	—
353	SD₁₆	—	278	2	no	—
354	SD₁₆	—	278	2	no	—
355	SD₁₆	—	278	2	no	—
356	SD₁₆	—	278	2	no	—
357	D₈	—	278	2	no	—
358	D₈	—	278	2	no	—
359	M₁₆	—	278	2	no	—
360	C₂×C₈	—	278	2	no	—
361	C₂×C₈	—	139	1	no	—
362	C₂×C₈	—	139	1	no	—
363	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
364	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
365	C₄⋊C₄	—	139	1	no	—
366	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	278	1	no	—
369	C₂²⋊C₄	—	278	1	no	—
370	C₂²⋊C₄	—	278	1	no	—
371	C₂²⋊C₄	—	278	1	no	—
372	C₄²	—	278	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	278	1	no	—
375	C₂³	—	278	1	no	—
376	C₂³	—	556	2	no	—
377	C₂³	—	1112	1	no	—
378	C₂³	—	1112	1	no	—
379	C₂³	—	139	1	no	—
380	C₂³	—	139	1	no	—
381	C₂³	D₄×D₁₃₉	1	1	yes	characteristic
382	Q₈	—	2	4	no	—
383	Q₈	—	2	1	no	—
384	Q₈	—	2	1	no	—
385	Q₈	—	278	4	no	—
386	Q₈	—	278	4	no	—
387	Q₈	—	278	2	no	—
388	Q₈	—	278	1	no	—
389	Q₈	—	139	2	no	—
390	Q₈	D₄×D₁₃₉	1	2	yes	—
391	Q₈	D₄×D₁₃₉	1	2	yes	—
392	D₄	—	2	1	no	—
393	D₄	—	2	1	no	—
394	D₄	—	8	1	no	—
395	D₄	—	278	4	no	—
396	D₄	—	278	4	no	—
397	D₄	—	278	2	no	—
398	D₄	—	278	4	no	—
399	D₄	—	278	2	no	—
400	D₄	—	278	2	no	—
401	D₄	—	278	1	no	—
402	D₄	—	278	1	no	—
403	D₄	—	278	1	no	—
404	D₄	—	556	2	no	—
405	D₄	—	1112	1	no	—
406	D₄	—	1112	1	no	—
407	D₄	—	1112	1	no	—
408	D₄	—	139	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	278	4	no	—
416	C₂×C₄	—	278	4	no	—
417	C₂×C₄	—	278	4	no	—
418	C₂×C₄	—	278	4	no	—
419	C₂×C₄	—	278	4	no	—
420	C₂×C₄	—	278	1	no	—
421	C₂×C₄	—	278	1	no	—
422	C₂×C₄	—	278	1	no	—
423	C₂×C₄	—	278	1	no	—
424	C₂×C₄	—	139	1	no	—
425	C₂×C₄	—	139	1	no	—
426	C₂×C₄	—	139	2	no	—
427	C₂×C₄	—	139	2	no	—
428	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
429	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	278	1	no	—
433	C₈	—	278	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	278	1	no	—
441	C₂²	—	278	1	no	—
442	C₂²	—	278	1	no	—
443	C₂²	—	278	1	no	—
444	C₂²	—	278	2	no	—
445	C₂²	—	278	1	no	—
446	C₂²	—	556	1	no	—
447	C₂²	—	556	1	no	—
448	C₂²	—	556	1	no	—
449	C₂²	—	556	1	no	—
450	C₂²	—	556	1	no	—
451	C₂²	—	1112	4	no	—
452	C₂²	—	139	2	no	—
453	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	278	2	no	—
459	C₄	—	278	1	no	—
460	C₄	—	556	1	no	—
461	C₄	—	139	2	no	—
462	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
463	C₄	C₂×D₄×D₁₃₉	1	1	yes	characteristic
464	C₂	—	4	1	no	—
465	C₂	—	8	1	no	—
466	C₂	—	278	2	no	—
467	C₂	—	556	1	no	—
468	C₂	—	556	2	no	—
469	C₂	—	1112	1	no	—
470	C₂	#120×D₁₃₉	1	1	yes	characteristic
471	C₂	#22581759	1	1	yes	characteristic
472	C₂	#22581762	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#448×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
hypercenter	#448	D₁₃₉
hypocenter	C₁₃₉	#3010
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #448

Complements

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

N	H ≅ G/N	type
1. C₂×#17984890	C₂	semidirect
2. C₂×#17984869	C₂	semidirect
3. C₂×SD₁₆×D₁₃₉	C₂	semidirect
4. #22581519	C₂	semidirect
5. #22581101	C₂	semidirect
6. #22581100	C₂	semidirect
7. #22581097	C₂	semidirect
8. #22581096	C₂	semidirect
9. #22581093	C₂	semidirect
10. #22581092	C₂	semidirect
11. #22581090	C₂	semidirect
12. #22580960	C₂	semidirect
13. #22580948	C₂	semidirect
14. #22580918	C₂	semidirect
15. #448×C₁₃₉	C₂	semidirect
20. C₂×#14555786	C₂²	semidirect
24. C₂×#14555785	C₂²	semidirect
27. C₂×Q₈×D₁₃₉	C₂²	semidirect
47. #17984767	C₂²	semidirect
48. #17984766	C₂²	semidirect
49. #17984766	C₂²	semidirect
50. #17984765	C₂²	semidirect
51. #17984764	C₂²	semidirect
52. #17984762	C₂²	semidirect
53. C₂²⋊(C₁₃₉⋊C₈)	C₂²	semidirect
54. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
55. (C₂×D₁₃₉)⋊C₈	C₂²	semidirect
56. C₂²×Q₈×C₁₃₉	C₂²	semidirect
60. #103×C₁₃₉	C₂²	semidirect
61. #103×C₁₃₉	C₂²	semidirect
62. C₂²⋊C₈×C₁₃₉	C₂²	semidirect
68. #14555786	D₄	semidirect
83. Q₈×D₁₃₉	D₄	semidirect
236. C₁₃₉	#3010	semidirect
249. #448	D₁₃₉	semidirect
265. C₂²×Q₈	C₂×D₁₃₉	semidirect
292. #103	C₂×D₁₃₉	semidirect
293. #103	C₂×D₁₃₉	semidirect
299. C₂²⋊C₈	C₂×D₁₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17984890	2
C₂×#17984869	2
C₂×SD₁₆×D₁₃₉	2
#22581519	2
#22581101	2
#22581100	2
#22581097	2
#22581096	2
#22581093	2
#22581092	2
#22581090	2
#22580960	2
#22580948	2
#22580918	2
#448×C₁₃₉	2
#3010	139