Subgroups — C₄×#19098830 #34295143

Order 20224.

946 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098830	C₂	1	1	yes	maximal, characteristic
2	C₄×#14579187	C₂	1	2	yes	maximal, complemented
3	C₄×#14579167	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764311	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764183	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764059	C₂	1	2	yes	maximal, complemented
7	#23763911	C₂	1	2	yes	maximal, complemented
8	#23763465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#14579097	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14579078	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×D₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579187	C₂²	1	2	yes	—
13	C₂×#14579167	C₂²	1	1	yes	characteristic
14	C₂×#14579167	C₂²	1	1	yes	characteristic
15	C₄×#11929624	C₂²	1	1	yes	characteristic
16	#19098830	C₄	1	8	yes	direct product factor
17	#19098673	—	2	2	no	—
18	#19098663	—	2	2	no	—
19	C₄×#11929612	—	2	2	no	—
20	C₄×#11929609	—	2	2	no	—
21	C₂×#14579097	C₂²	1	1	yes	characteristic
22	C₂×#14579097	C₂²	1	1	yes	characteristic
23	#19098603	C₂²	1	2	yes	—
24	#19098568	C₂²	1	2	yes	—
25	#19098562	C₂²	1	2	yes	—
26	C₂×#14579078	C₂²	1	2	yes	—
27	C₂×#14579078	C₂²	1	2	yes	—
28	#19098518	C₂²	1	1	yes	characteristic
29	#19098518	C₂²	1	1	yes	characteristic
30	#19098517	—	2	1	no	—
31	#19098517	—	2	1	no	—
32	C₄×#11929608	C₂²	1	2	yes	—
33	C₄×#11929608	C₂²	1	1	yes	characteristic
34	C₄×#11929607	—	2	1	no	—
35	C₄×C₈×D₇₉	—	2	1	no	—
36	#19098332	C₂²	1	2	yes	—
37	#19098332	C₂²	1	2	yes	—
38	#19098328	C₂²	1	2	yes	—
39	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₇₉	C₂²	1	2	yes	—
41	C₄×D₈×C₇₉	—	2	1	no	—
42	C₄×D₈×C₇₉	—	2	1	no	—
43	C₄×D₈×C₇₉	—	2	1	no	—
44	C₄×D₈×C₇₉	—	2	1	no	—
45	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#102×C₇₉	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
48	C₂×#11929624	C₂³	1	1	yes	characteristic
49	#14579187	—	2	4	no	—
50	#14579187	C₂×C₄	1	8	yes	complemented
51	C₂×#11929612	—	2	2	no	—
52	C₂×#11929609	—	2	2	no	—
53	#14579167	—	2	2	no	—
54	#14579167	—	2	2	no	—
55	#14579167	—	2	2	no	—
56	#14579167	C₂×C₄	1	4	yes	complemented
57	C₂×#11929608	C₂³	1	2	yes	—
58	C₂×#11929608	C₂³	1	1	yes	characteristic
59	C₂×#11929608	C₂³	1	2	yes	—
60	C₂×#11929608	C₂³	1	1	yes	characteristic
61	C₂×#11929607	—	2	1	no	—
62	C₂×#11929607	—	2	1	no	—
63	C₂×C₈×D₇₉	—	2	1	no	—
64	C₂×C₈×D₇₉	—	2	1	no	—
65	C₄×Dic₁₅₈	D₄	1	1	yes	characteristic
66	C₄×Dic₁₅₈	D₄	1	1	yes	characteristic
67	C₄×D₃₁₆	D₄	1	1	yes	characteristic
68	C₄×D₃₁₆	D₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₇₉	—	2	1	no	—
70	C₄×C₂²⋊D₇₉	—	2	1	no	—
71	#14579120	C₂³	1	1	yes	characteristic
72	#14579118	—	2	1	no	—
73	C₄²×D₇₉	—	2	1	no	—
74	#14579097	—	2	2	no	—
75	#14579097	C₂×C₄	1	4	yes	complemented
76	#14579094	—	2	2	no	—
77	#14579092	—	2	2	no	—
78	#14579084	—	2	2	no	—
79	#14579082	—	2	2	no	—
80	#14579082	—	2	2	no	—
81	#14579081	—	2	2	no	—
82	#14579078	—	2	4	no	—
83	#14579078	C₂×C₄	1	8	yes	complemented
84	#14579072	—	2	2	no	—
85	#14579072	—	2	1	no	—
86	#14579071	—	2	1	no	—
87	#14579071	—	2	1	no	—
88	C₄×C₇₉⋊C₈	—	2	2	no	—
89	C₄×C₇₉⋊C₈	—	2	1	no	—
90	C₈×Dic₇₉	—	2	1	no	—
91	C₈×Dic₇₉	—	2	1	no	—
92	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₇₉	—	2	2	no	—
94	C₂×D₈×C₇₉	—	2	1	no	—
95	C₂×D₈×C₇₉	—	2	1	no	—
96	C₂×D₈×C₇₉	—	2	2	no	—
97	C₂×D₈×C₇₉	C₂×C₄	1	4	yes	complemented
98	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₇₉	—	2	2	no	—
101	C₄×D₄×C₇₉	—	2	2	no	—
102	C₄×D₄×C₇₉	—	2	2	no	—
103	C₄×D₄×C₇₉	—	2	2	no	—
104	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₇₉	—	2	2	no	—
106	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
107	#107×C₇₉	—	2	1	no	—
108	#107×C₇₉	—	2	1	no	—
109	#102×C₇₉	—	2	2	no	—
110	#102×C₇₉	—	2	2	no	—
111	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
112	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
113	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
114	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
115	#11929624	—	2	1	no	—
116	#11929624	—	2	1	no	—
117	#11929624	C₂²×C₄	1	2	yes	—
118	#11929624	#41	1	2	yes	—
119	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
120	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
121	C₂×C₂²⋊D₇₉	—	2	1	no	—
122	C₂×C₄×D₇₉	—	2	1	no	—
123	C₂×C₄×D₇₉	—	2	1	no	—
124	C₂×C₄×D₇₉	—	2	1	no	—
125	#11929612	—	2	8	no	—
126	#11929609	—	2	8	no	—
127	#11929608	—	2	1	no	—
128	#11929608	—	2	1	no	—
129	#11929608	—	2	2	no	—
130	#11929608	—	2	2	no	—
131	#11929608	—	2	2	no	—
132	#11929608	C₂²×C₄	1	2	yes	—
133	#11929608	C₂²×C₄	1	4	yes	—
134	#11929608	#41	1	2	yes	—
135	#11929607	—	2	4	no	—
136	#11929607	—	2	4	no	—
137	C₂×C₇₉⋊C₈	—	2	1	no	—
138	C₂×C₇₉⋊C₈	—	2	1	no	—
139	C₂×C₇₉⋊C₈	—	2	2	no	—
140	C₂×C₇₉⋊C₈	—	2	2	no	—
141	C₈×D₇₉	—	2	4	no	—
142	C₈×D₇₉	—	2	4	no	—
143	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
144	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
145	Dic₇₉⋊C₄	—	2	1	no	—
146	Dic₇₉⋊C₄	—	2	1	no	—
147	C₂²⋊Dic₇₉	—	2	1	no	—
148	(C₂×D₇₉)⋊C₄	—	2	1	no	—
149	(C₂×D₇₉)⋊C₄	—	2	1	no	—
150	C₄×Dic₇₉	—	2	1	no	—
151	C₄×Dic₇₉	—	2	1	no	—
152	C₄×Dic₇₉	—	2	1	no	—
153	C₂⁴×C₇₉	—	2	2	no	—
154	C₂×D₄×C₇₉	—	2	2	no	—
155	C₂×D₄×C₇₉	—	2	2	no	—
156	C₂×D₄×C₇₉	—	2	2	no	—
157	C₂×D₄×C₇₉	—	2	2	no	—
158	C₂×D₄×C₇₉	—	2	2	no	—
159	C₂×D₄×C₇₉	C₂²×C₄	1	4	yes	—
160	C₂²×C₄×C₇₉	—	2	2	no	—
161	C₂²×C₄×C₇₉	—	4	2	no	—
162	C₂²×C₄×C₇₉	—	4	2	no	—
163	C₂²×C₄×C₇₉	—	8	4	no	—
164	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
165	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
166	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
167	D₈×C₇₉	—	2	4	no	—
168	D₈×C₇₉	—	2	4	no	—
169	C₂×C₈×C₇₉	—	2	1	no	—
170	C₂×C₈×C₇₉	—	2	1	no	—
171	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
172	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₇₉	#41	1	2	yes	—
177	C₄⋊C₄×C₇₉	—	2	2	no	—
178	C₄⋊C₄×C₇₉	—	2	2	no	—
179	C₂²⋊C₄×C₇₉	—	4	2	no	—
180	C₂²⋊C₄×C₇₉	—	4	2	no	—
181	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
185	C₂³×C₇₉	—	2	4	no	—
186	C₂³×C₇₉	—	4	2	no	—
187	C₂³×C₇₉	—	4	2	no	—
188	C₂³×C₇₉	—	8	2	no	—
189	C₂³×C₇₉	—	8	2	no	—
190	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
191	C₂²×D₇₉	—	2	1	no	—
192	D₄×C₇₉	—	2	4	no	—
193	D₄×C₇₉	—	2	4	no	—
194	D₄×C₇₉	—	4	2	no	—
195	D₄×C₇₉	—	4	2	no	—
196	C₂×C₄×C₇₉	—	2	2	no	—
197	C₂×C₄×C₇₉	—	4	1	no	—
198	C₂×C₄×C₇₉	—	4	2	no	—
199	C₂×C₄×C₇₉	—	8	4	no	—
200	C₂×C₄×C₇₉	—	8	4	no	—
201	C₂×C₄×C₇₉	—	8	2	no	—
202	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
203	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
206	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
212	C₂²⋊D₇₉	—	2	2	no	—
213	C₂²⋊D₇₉	—	2	2	no	—
214	C₂×Dic₇₉	—	2	1	no	—
215	C₂×Dic₇₉	—	2	1	no	—
216	C₂×Dic₇₉	—	2	1	no	—
217	D₃₁₆	—	2	1	no	—
218	D₃₁₆	C₄×D₄	1	2	yes	—
219	C₄×D₇₉	—	2	2	no	—
220	C₄×D₇₉	—	2	2	no	—
221	C₄×D₇₉	—	4	2	no	—
222	C₄×D₇₉	—	4	2	no	—
223	Dic₁₅₈	—	2	1	no	—
224	Dic₁₅₈	C₄×D₄	1	2	yes	—
225	C₈×C₇₉	—	2	1	no	—
226	C₈×C₇₉	—	2	1	no	—
227	C₈×C₇₉	C₄×D₄	1	2	yes	—
228	C₈×C₇₉	C₄×D₄	1	2	yes	—
229	C₇₉⋊C₈	—	2	2	no	—
230	C₇₉⋊C₈	—	2	4	no	—
231	C₇₉⋊C₈	—	2	2	no	—
232	C₇₉⋊C₈	—	4	2	no	—
233	C₂²×C₇₉	—	2	1	no	—
234	C₂²×C₇₉	—	2	1	no	—
235	C₂²×C₇₉	—	4	4	no	—
236	C₂²×C₇₉	—	8	4	no	—
237	C₂²×C₇₉	—	8	4	no	—
238	C₂²×C₇₉	—	8	2	no	—
239	C₂²×C₇₉	—	8	2	no	—
240	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
241	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
242	C₂²×C₇₉	#529	1	1	yes	characteristic
243	C₂×D₇₉	—	2	2	no	—
244	C₂×D₇₉	—	4	1	no	—
245	C₂×D₇₉	—	4	1	no	—
246	C₄×C₇₉	—	2	1	no	—
247	C₄×C₇₉	—	2	1	no	—
248	C₄×C₇₉	—	2	1	no	—
249	C₄×C₇₉	—	8	2	no	—
250	C₄×C₇₉	#472	1	2	yes	complemented
251	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
252	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₇₉	#525	1	1	yes	characteristic
254	C₄×C₇₉	#532	1	1	yes	characteristic
255	Dic₇₉	—	2	2	no	—
256	Dic₇₉	—	4	1	no	—
257	Dic₇₉	—	4	1	no	—
258	C₄×#472	—	79	1	no	maximal, Sylow
259	C₂×C₇₉	—	2	1	no	—
260	C₂×C₇₉	—	2	1	no	—
261	C₂×C₇₉	—	8	4	no	—
262	C₂×C₇₉	C₄×#121	1	1	yes	characteristic
263	C₂×C₇₉	C₂×#472	1	1	yes	characteristic
264	C₂×C₇₉	#3067	1	1	yes	characteristic
265	D₇₉	—	4	2	no	—
266	C₂×#472	—	79	1	no	—
267	C₄×AGL(1,ℤ/8)	—	79	2	no	—
268	C₂×C₄×D₈	D₇₉	1	1	yes	characteristic, complemented
269	C₄×#131	—	79	1	no	—
270	#1978	—	79	1	no	—
271	#1952	—	79	1	no	—
272	#1931	—	79	2	no	—
273	#1907	—	79	2	no	—
274	#1816	—	79	1	no	—
275	C₄×#108	—	79	1	no	—
276	C₄×#100	—	79	2	no	—
277	C₇₉	C₄×#472	1	1	yes	characteristic, complemented, Sylow
278	C₂×AGL(1,ℤ/8)	—	79	2	no	—
279	C₂²×D₈	C₂×D₇₉	1	1	yes	characteristic
280	C₂×#131	—	79	1	no	—
281	C₂×#131	—	79	1	no	—
282	C₄×#41	—	79	1	no	—
283	C₂×C₄×D₄	C₂×D₇₉	1	2	yes	—
284	#472	—	79	8	no	—
285	#442	—	158	2	no	—
286	#440	—	158	2	no	—
287	C₄×SD₁₆	—	158	2	no	—
288	C₄×D₈	—	2	1	no	—
289	C₄×D₈	—	2	1	no	—
290	C₄×D₈	—	2	1	no	—
291	C₄×D₈	—	2	1	no	—
292	C₄×D₈	—	158	2	no	—
293	C₂×#108	—	79	1	no	—
294	C₂×#108	—	79	1	no	—
295	#428	—	79	2	no	—
296	C₂×#107	C₂×D₇₉	1	1	yes	characteristic
297	#418	—	79	2	no	—
298	#417	—	79	2	no	—
299	C₂×#102	C₂×D₇₉	1	2	yes	—
300	C₂×#100	—	79	2	no	—
301	C₂×#100	—	79	2	no	—
302	#405	—	79	1	no	—
303	#405	—	79	1	no	—
304	#405	—	158	1	no	—
305	#405	—	158	1	no	—
306	C₄×M₁₆	—	79	1	no	—
307	C₄×M₁₆	—	79	2	no	—
308	C₄×M₁₆	—	158	1	no	—
309	C₂×C₄×C₈	—	158	1	no	—
310	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
311	#343	—	79	2	no	—
312	#343	—	79	2	no	—
313	#341	—	79	2	no	—
314	C₂×#41	—	79	1	no	—
315	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
316	C₂³×C₄	—	2	2	no	—
317	AGL(1,ℤ/8)	—	79	8	no	—
318	AGL(1,ℤ/8)	—	158	4	no	—
319	C₂×SD₁₆	—	158	2	no	—
320	C₂×D₈	—	2	1	no	—
321	C₂×D₈	—	2	1	no	—
322	C₂×D₈	—	2	2	no	—
323	C₂×D₈	—	158	2	no	—
324	C₂×D₈	C₄×D₇₉	1	4	yes	complemented
325	#131	—	79	4	no	—
326	#131	—	158	2	no	—
327	#131	—	158	2	no	—
328	#131	—	158	2	no	—
329	C₂×M₁₆	—	79	1	no	—
330	C₂×M₁₆	—	79	1	no	—
331	C₂×M₁₆	—	79	2	no	—
332	C₂×M₁₆	—	79	2	no	—
333	C₂×M₁₆	—	158	1	no	—
334	C₂×M₁₆	—	158	1	no	—
335	C₂²×C₈	—	158	1	no	—
336	C₂²×C₈	—	158	1	no	—
337	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
338	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
339	C₄×Q₈	—	79	1	no	—
340	C₄×Q₈	—	79	1	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	79	1	no	—
346	C₄×D₄	—	79	1	no	—
347	C₄×D₄	—	158	1	no	—
348	C₄×D₄	—	158	1	no	—
349	#117	—	79	1	no	—
350	#117	—	158	1	no	—
351	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₄²	—	158	1	no	—
354	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
355	#108	—	79	4	no	—
356	#108	—	158	2	no	—
357	#107	—	2	1	no	—
358	#107	—	2	1	no	—
359	#107	—	158	2	no	—
360	#106	—	158	2	no	—
361	#103	—	158	2	no	—
362	#102	—	2	2	no	—
363	#102	—	2	2	no	—
364	#102	—	158	2	no	—
365	#102	—	158	2	no	—
366	#102	—	158	2	no	—
367	#100	—	79	8	no	—
368	#100	—	158	4	no	—
369	#97	—	158	1	no	—
370	#97	—	158	1	no	—
371	#97	—	158	2	no	—
372	#97	—	158	1	no	—
373	C₄×C₈	—	158	1	no	—
374	C₄×C₈	—	158	1	no	—
375	C₄×C₈	—	158	2	no	—
376	C₄×C₈	—	158	1	no	—
377	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
378	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
379	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
380	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
381	C₂⁴	—	2	2	no	—
382	#41	—	79	2	no	—
383	#41	—	79	2	no	—
384	#41	—	158	1	no	—
385	#41	—	158	1	no	—
386	C₂×Q₈	—	79	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	79	1	no	—
393	C₂×D₄	—	158	1	no	—
394	C₂×D₄	C₂×C₄×D₇₉	1	4	yes	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	8	4	no	—
399	C₂²×C₄	—	158	1	no	—
400	C₂²×C₄	—	158	1	no	—
401	C₂²×C₄	—	158	1	no	—
402	C₂²×C₄	#11929623	1	1	yes	characteristic
403	C₂²×C₄	#11929623	1	1	yes	characteristic
404	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
405	SD₁₆	—	158	8	no	—
406	D₈	—	2	4	no	—
407	D₈	—	2	4	no	—
408	D₈	—	158	8	no	—
409	M₁₆	—	79	2	no	—
410	M₁₆	—	79	2	no	—
411	M₁₆	—	79	4	no	—
412	M₁₆	—	158	4	no	—
413	M₁₆	—	158	2	no	—
414	M₁₆	—	158	2	no	—
415	M₁₆	—	158	1	no	—
416	M₁₆	—	158	2	no	—
417	M₁₆	—	158	1	no	—
418	M₁₆	—	158	4	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	158	4	no	—
422	C₂×C₈	—	158	2	no	—
423	C₂×C₈	—	158	2	no	—
424	C₂×C₈	—	158	1	no	—
425	C₂×C₈	—	158	1	no	—
426	C₂×C₈	—	158	4	no	—
427	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
428	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
429	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
430	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
431	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
432	C₂×C₈	#11929624	1	2	yes	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	79	1	no	—
436	C₄⋊C₄	—	79	1	no	—
437	C₄⋊C₄	—	158	1	no	—
438	C₄⋊C₄	—	158	1	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₂²⋊C₄	—	4	2	no	—
441	C₂²⋊C₄	—	158	1	no	—
442	C₂²⋊C₄	—	158	1	no	—
443	C₂²⋊C₄	—	158	1	no	—
444	C₄²	—	158	1	no	—
445	C₄²	—	158	1	no	—
446	C₄²	—	158	1	no	—
447	C₄²	D₄×D₇₉	1	1	yes	characteristic
448	C₄²	D₄×D₇₉	1	1	yes	characteristic
449	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
450	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
451	C₂³	—	2	4	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	158	1	no	—
457	C₂³	C₂×#11929623	1	1	yes	characteristic
458	Q₈	—	79	2	no	—
459	Q₈	—	158	1	no	—
460	D₄	—	2	4	no	—
461	D₄	—	2	4	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	79	2	no	—
465	D₄	—	158	2	no	—
466	D₄	—	158	2	no	—
467	D₄	—	158	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	8	4	no	—
472	C₂×C₄	—	8	4	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	—	316	2	no	—
475	C₂×C₄	—	316	2	no	—
476	C₂×C₄	—	158	1	no	—
477	C₂×C₄	—	158	1	no	—
478	C₂×C₄	—	158	1	no	—
479	C₂×C₄	—	158	2	no	—
480	C₂×C₄	—	158	2	no	—
481	C₂×C₄	#14579132	1	1	yes	characteristic
482	C₂×C₄	#14579132	1	1	yes	characteristic
483	C₂×C₄	#14579132	1	1	yes	characteristic
484	C₂×C₄	#14579132	1	1	yes	characteristic
485	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
486	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
487	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
488	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
489	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
490	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
491	C₈	—	2	1	no	—
492	C₈	—	2	1	no	—
493	C₈	—	316	2	no	—
494	C₈	—	158	4	no	—
495	C₈	—	158	2	no	—
496	C₈	—	158	2	no	—
497	C₈	C₄×C₂²⋊D₇₉	1	2	yes	—
498	C₈	C₄×C₂²⋊D₇₉	1	2	yes	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	8	4	no	—
503	C₂²	—	8	4	no	—
504	C₂²	—	8	2	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	316	1	no	—
507	C₂²	—	316	1	no	—
508	C₂²	—	158	2	no	—
509	C₂²	C₄×#11929623	1	1	yes	characteristic
510	C₂²	C₂×#14579132	1	1	yes	characteristic
511	C₂²	#19099095	1	1	yes	characteristic
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	8	2	no	—
516	C₄	—	316	1	no	—
517	C₄	—	316	1	no	—
518	C₄	—	158	2	no	—
519	C₄	#19098830	1	2	yes	direct product factor
520	C₄	C₄×D₄×D₇₉	1	1	yes	characteristic
521	C₄	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
522	C₄	#19099070	1	1	yes	characteristic
523	C₄	#19099110	1	1	yes	characteristic
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	8	4	no	—
527	C₂	—	316	2	no	—
528	C₂	C₄×#14579132	1	1	yes	characteristic
529	C₂	C₂×#19098830	1	1	yes	characteristic
530	C₂	#23773116	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14579132
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×C₄×D₈×C₇₉	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	C₂×#19098830	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×C₄×D₈	D₇₉
hypocenter	C₇₉	C₄×#472
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
2. C₄×#14579187	C₂	semidirect
3. C₄×#14579167	C₂	semidirect
4. #23764311	C₂	semidirect
5. #23764183	C₂	semidirect
6. #23764059	C₂	semidirect
7. #23763911	C₂	semidirect
8. #23763465	C₂	semidirect
9. C₄×#14579097	C₂	semidirect
10. C₄×#14579078	C₂	semidirect
11. C₂×C₄×D₈×C₇₉	C₂	semidirect
16. #19098830	C₄	direct (N × H)
50. #14579187	C₂×C₄	semidirect
56. #14579167	C₂×C₄	semidirect
75. #14579097	C₂×C₄	semidirect
83. #14579078	C₂×C₄	semidirect
97. C₂×D₈×C₇₉	C₂×C₄	semidirect
250. C₄×C₇₉	#472	semidirect
268. C₂×C₄×D₈	D₇₉	semidirect
277. C₇₉	C₄×#472	semidirect
324. C₂×D₈	C₄×D₇₉	semidirect
519. C₄	#19098830	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19098830	2
C₄×#14579187	2
C₄×#14579167	2
#23764311	2
#23764183	2
#23764059	2
#23763911	2
#23763465	2
C₄×#14579097	2
C₄×#14579078	2
C₂×C₄×D₈×C₇₉	2
C₄×#472	79

Subgroups — C4×#19098830 #34295143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19098830 #34295143