Subgroups — #34272063

Order 20224.

690 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773982	C₂	1	1	yes	maximal, characteristic, complemented
2	#23773197	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#23762853	C₂	1	2	yes	maximal, complemented
5	#23762849	C₂	1	2	yes	maximal, complemented
6	#23762797	C₂	1	2	yes	maximal, complemented
7	#23762763	C₂	1	2	yes	maximal, complemented
8	#23762158	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762091	C₂	1	1	yes	maximal, characteristic, complemented
10	#23762090	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3077	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₇₉⋊C₈	—	2	1	no	—
13	#19099120	C₂²	1	1	yes	characteristic
14	#19098966	C₂²	1	1	yes	characteristic, complemented
15	#19098942	C₂²	1	1	yes	characteristic, complemented
16	#19098915	C₂²	1	1	yes	characteristic, complemented
17	#19098913	C₂²	1	1	yes	characteristic, complemented
18	#19098863	—	2	2	no	—
19	#19098853	C₂²	1	2	yes	—
20	#19098843	C₂²	1	2	yes	—
21	#19098802	—	2	1	no	—
22	#19098802	—	2	1	no	—
23	C₄×#11929614	—	2	1	no	—
24	C₄×#11929614	—	2	1	no	—
25	D₄×C₇₉⋊C₈	—	2	1	no	—
26	D₄×C₇₉⋊C₈	—	2	1	no	—
27	D₄×C₇₉⋊C₈	C₂²	1	2	yes	—
28	D₄×C₇₉⋊C₈	C₂²	1	2	yes	—
29	#19098603	—	2	1	no	—
30	#19098587	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
32	#19098568	—	2	1	no	—
33	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
34	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
35	#19098315	C₂²	1	2	yes	complemented
36	#19098315	C₂²	1	2	yes	complemented
37	#19098312	C₂²	1	2	yes	complemented
38	#19098311	C₂²	1	2	yes	complemented
39	#19098309	C₂²	1	2	yes	complemented
40	#19098308	C₂²	1	2	yes	complemented
41	#533×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
43	#478×C₇₉	—	2	2	no	—
44	#476×C₇₉	C₂²	1	2	yes	—
45	#474×C₇₉	C₂²	1	2	yes	—
46	#428×C₇₉	—	2	1	no	—
47	#423×C₇₉	C₂²	1	1	yes	characteristic
48	#418×C₇₉	—	2	1	no	—
49	C₂×#11929614	—	2	1	no	—
50	C₂×#11929614	—	2	1	no	—
51	C₂×#11929608	—	2	1	no	—
52	C₂²×C₇₉⋊C₈	—	2	1	no	—
53	C₂²×C₇₉⋊C₈	—	2	2	no	—
54	C₂²×C₇₉⋊C₈	—	2	2	no	—
55	C₂²×C₇₉⋊C₈	—	4	4	no	—
56	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
58	#14579161	C₂³	1	1	yes	characteristic
59	#14579161	C₂³	1	1	yes	characteristic
60	#14579153	—	2	1	no	—
61	#14579140	—	2	1	no	—
62	#14579140	—	2	1	no	—
63	C₄×Dic₁₅₈	—	2	1	no	—
64	C₄×Dic₁₅₈	—	2	1	no	—
65	#14579120	—	2	1	no	—
66	#14579094	—	2	2	no	—
67	#14579094	—	2	1	no	—
68	#14579094	—	2	1	no	—
69	#14579092	—	2	2	no	—
70	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
73	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
74	#14579085	—	2	1	no	—
75	#14579085	—	2	1	no	—
76	#14579084	—	2	1	no	—
77	#14579084	—	2	1	no	—
78	#14579082	—	2	2	no	—
79	#14579082	—	2	2	no	—
80	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
81	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
82	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
84	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₇₉	—	2	1	no	—
88	C₂×M₁₆×C₇₉	—	2	1	no	—
89	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
91	#125×C₇₉	—	2	1	no	—
92	C₂²⋊Q₈×C₇₉	—	2	1	no	—
93	C₂²⋊Q₈×C₇₉	—	2	1	no	—
94	C₄×Q₈×C₇₉	—	2	1	no	—
95	C₄×Q₈×C₇₉	—	2	1	no	—
96	C₄×D₄×C₇₉	—	2	1	no	—
97	C₄×D₄×C₇₉	—	2	1	no	—
98	C₄×D₄×C₇₉	D₄	1	2	yes	—
99	C₄×D₄×C₇₉	C₂³	1	2	yes	—
100	#117×C₇₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
103	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
104	#107×C₇₉	—	2	2	no	—
105	#106×C₇₉	—	2	2	no	—
106	C₄⋊C₈×C₇₉	—	2	1	no	—
107	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
108	#102×C₇₉	—	2	2	no	—
109	#102×C₇₉	—	2	2	no	—
110	C₂×Dic₁₅₈	—	2	1	no	—
111	C₂×Dic₁₅₈	—	2	1	no	—
112	#11929614	—	4	2	no	—
113	#11929614	—	4	2	no	—
114	#11929608	—	4	2	no	—
115	C₂×C₇₉⋊C₈	—	2	2	no	—
116	C₂×C₇₉⋊C₈	—	2	2	no	—
117	C₂×C₇₉⋊C₈	—	2	2	no	—
118	C₂×C₇₉⋊C₈	—	4	1	no	—
119	C₂×C₇₉⋊C₈	—	4	2	no	—
120	C₂×C₇₉⋊C₈	—	4	4	no	—
121	C₂×C₇₉⋊C₈	—	4	4	no	—
122	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
124	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
126	C₄⋊Dic₇₉	—	2	1	no	—
127	C₄⋊Dic₇₉	—	2	1	no	—
128	C₄⋊Dic₇₉	—	2	1	no	—
129	C₄⋊Dic₇₉	—	2	1	no	—
130	Dic₇₉⋊C₄	—	4	1	no	—
131	Dic₇₉⋊C₄	—	4	1	no	—
132	C₂²⋊Dic₇₉	—	4	1	no	—
133	C₄×Dic₇₉	—	4	1	no	—
134	C₂⁴×C₇₉	—	2	1	no	—
135	C₂×Q₈×C₇₉	—	2	1	no	—
136	C₂×Q₈×C₇₉	—	2	1	no	—
137	C₂×D₄×C₇₉	—	2	1	no	—
138	C₂×D₄×C₇₉	—	2	2	no	—
139	C₂×D₄×C₇₉	Q₁₆	1	4	yes	complemented
140	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₇₉	—	2	1	no	—
142	C₂²×C₄×C₇₉	—	2	2	no	—
143	C₂²×C₄×C₇₉	—	2	2	no	—
144	C₂²×C₄×C₇₉	—	4	2	no	—
145	C₂²×C₄×C₇₉	—	4	2	no	—
146	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
149	M₁₆×C₇₉	—	4	2	no	—
150	C₂×C₈×C₇₉	—	2	2	no	—
151	C₄⋊C₄×C₇₉	—	2	1	no	—
152	C₄⋊C₄×C₇₉	—	2	1	no	—
153	C₄⋊C₄×C₇₉	—	2	1	no	—
154	C₄⋊C₄×C₇₉	—	2	1	no	—
155	C₄⋊C₄×C₇₉	—	2	1	no	—
156	C₄⋊C₄×C₇₉	—	4	1	no	—
157	C₄⋊C₄×C₇₉	—	4	1	no	—
158	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
159	C₂²⋊C₄×C₇₉	—	2	2	no	—
160	C₂²⋊C₄×C₇₉	—	2	2	no	—
161	C₂²⋊C₄×C₇₉	—	4	1	no	—
162	C₄²×C₇₉	—	4	1	no	—
163	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₇₉	#41	1	1	yes	characteristic
166	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
167	C₂³×C₇₉	—	2	2	no	—
168	C₂³×C₇₉	—	2	4	no	—
169	C₂³×C₇₉	—	4	2	no	—
170	C₂³×C₇₉	—	4	2	no	—
171	C₂³×C₇₉	#121	1	1	yes	characteristic
172	Q₈×C₇₉	—	4	1	no	—
173	Q₈×C₇₉	—	4	1	no	—
174	Q₈×C₇₉	—	8	1	no	—
175	D₄×C₇₉	—	2	2	no	—
176	D₄×C₇₉	—	2	4	no	—
177	D₄×C₇₉	C₂×Q₁₆	1	4	yes	—
178	C₂×C₄×C₇₉	—	2	1	no	—
179	C₂×C₄×C₇₉	—	2	1	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	4	1	no	—
182	C₂×C₄×C₇₉	—	4	4	no	—
183	C₂×C₄×C₇₉	—	4	2	no	—
184	C₂×C₄×C₇₉	—	4	2	no	—
185	C₂×C₄×C₇₉	—	4	2	no	—
186	C₂×C₄×C₇₉	—	4	1	no	—
187	C₂×C₄×C₇₉	—	4	1	no	—
188	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
190	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
192	C₂×C₄×C₇₉	#135	1	2	yes	—
193	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
196	C₂×Dic₇₉	—	4	1	no	—
197	C₂×Dic₇₉	—	4	1	no	—
198	Dic₁₅₈	—	4	1	no	—
199	Dic₁₅₈	—	4	1	no	—
200	Dic₁₅₈	—	8	1	no	—
201	C₈×C₇₉	—	4	2	no	—
202	C₇₉⋊C₈	—	2	1	no	—
203	C₇₉⋊C₈	—	2	1	no	—
204	C₇₉⋊C₈	—	2	1	no	—
205	C₇₉⋊C₈	—	4	2	no	—
206	C₇₉⋊C₈	—	4	2	no	—
207	C₇₉⋊C₈	AGL(1,ℤ/8)	1	2	yes	—
208	C₂²×C₇₉	—	2	1	no	—
209	C₂²×C₇₉	—	2	1	no	—
210	C₂²×C₇₉	—	2	4	no	—
211	C₂²×C₇₉	—	4	8	no	—
212	C₂²×C₇₉	—	4	2	no	—
213	C₂²×C₇₉	—	4	2	no	—
214	C₂²×C₇₉	#467	1	2	yes	—
215	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
216	C₄×C₇₉	—	2	1	no	—
217	C₄×C₇₉	—	2	1	no	—
218	C₄×C₇₉	—	2	1	no	—
219	C₄×C₇₉	—	4	2	no	—
220	C₄×C₇₉	—	8	1	no	—
221	C₄×C₇₉	—	8	1	no	—
222	C₄×C₇₉	#467	1	2	yes	—
223	C₄×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
224	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
225	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₄×C₇₉	#575	1	1	yes	characteristic
227	Dic₇₉	—	8	1	no	—
228	Dic₇₉	—	8	1	no	—
229	#19256	—	79	1	no	maximal, Sylow
230	C₂×C₇₉	—	2	2	no	—
231	C₂×C₇₉	—	4	4	no	—
232	C₂×C₇₉	#3036	1	1	yes	characteristic
233	C₂×C₇₉	C₂×#467	1	1	yes	characteristic
234	C₂×C₇₉	#3067	1	1	yes	characteristic
235	#3170	—	79	1	no	—
236	#3077	—	79	1	no	—
237	#3077	D₇₉	1	1	yes	characteristic
238	C₂×C₈×D₄	—	79	1	no	—
239	#1683	—	79	2	no	—
240	#1683	—	79	2	no	—
241	#1675	—	79	2	no	—
242	#1669	—	79	2	no	—
243	#1567	—	79	1	no	—
244	#1550	—	79	1	no	—
245	#1550	—	79	1	no	—
246	C₇₉	#19256	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₈	—	158	1	no	—
248	#533	—	79	1	no	—
249	#533	C₂×D₇₉	1	1	yes	characteristic
250	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
251	#500	—	79	1	no	—
252	#494	—	79	1	no	—
253	#487	—	79	1	no	—
254	#487	—	79	1	no	—
255	#478	—	2	2	no	—
256	#478	—	158	2	no	—
257	#476	—	79	2	no	—
258	#476	C₂×D₇₉	1	2	yes	—
259	#474	—	79	2	no	—
260	#474	C₂×D₇₉	1	2	yes	—
261	#467	—	158	1	no	—
262	#467	—	158	1	no	—
263	C₄×Q₁₆	—	158	1	no	—
264	C₄×Q₁₆	—	158	1	no	—
265	C₈×D₄	—	79	2	no	—
266	C₈×D₄	—	79	2	no	—
267	C₈×D₄	—	158	1	no	—
268	C₈×D₄	—	158	1	no	—
269	#428	—	2	1	no	—
270	#428	—	158	1	no	—
271	#423	—	79	1	no	—
272	#423	C₂×D₇₉	1	1	yes	characteristic
273	C₂×C₄⋊C₈	—	79	1	no	—
274	#418	—	2	1	no	—
275	#418	—	158	1	no	—
276	C₂×C₂²⋊C₈	—	158	1	no	—
277	C₂×C₄×C₈	—	79	1	no	—
278	#335	—	79	2	no	—
279	#335	—	79	2	no	—
280	#333	—	79	2	no	—
281	#333	—	79	2	no	—
282	#332	—	79	2	no	—
283	#332	—	79	2	no	—
284	C₂²×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂×Q₁₆	—	158	1	no	—
287	C₂×Q₁₆	—	158	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	158	1	no	—
290	C₂²×C₈	—	316	4	no	—
291	C₂²×C₈	—	79	1	no	—
292	C₂²×C₈	—	79	1	no	—
293	C₂²×C₈	—	158	2	no	—
294	C₂²×C₈	—	158	2	no	—
295	C₂²×C₈	—	158	1	no	—
296	C₄⋊Q₈	—	79	1	no	—
297	C₄⋊Q₈	—	79	1	no	—
298	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
299	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
300	#125	—	2	1	no	—
301	#125	—	158	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	C₂²⋊Q₈	—	158	1	no	—
305	C₂²⋊Q₈	—	158	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	158	1	no	—
309	C₄×Q₈	—	158	1	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	C₂²⋊D₇₉	1	2	yes	—
313	C₄×D₄	C₂²×D₇₉	1	2	yes	—
314	#117	—	2	1	no	—
315	#117	—	158	1	no	—
316	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
319	#107	—	2	2	no	—
320	#107	—	158	1	no	—
321	#107	—	158	1	no	—
322	#107	—	158	2	no	—
323	#106	—	2	2	no	—
324	#106	—	158	2	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	79	2	no	—
327	C₄⋊C₈	—	79	2	no	—
328	C₄⋊C₈	—	158	1	no	—
329	C₄⋊C₈	—	158	1	no	—
330	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
331	#103	—	158	1	no	—
332	#103	—	158	1	no	—
333	#103	—	158	1	no	—
334	#103	—	158	1	no	—
335	#102	—	2	2	no	—
336	#102	—	2	2	no	—
337	#102	—	158	2	no	—
338	#102	—	158	2	no	—
339	C₂²⋊C₈	—	158	2	no	—
340	C₂²⋊C₈	—	158	2	no	—
341	C₄×C₈	—	79	1	no	—
342	C₄×C₈	—	79	1	no	—
343	C₄×C₈	—	79	1	no	—
344	C₄×C₈	—	79	1	no	—
345	C₂⁴	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	158	1	no	—
349	C₂×Q₈	—	158	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	#11929614	1	4	yes	complemented
353	C₂×D₄	C₂×C₂²⋊D₇₉	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
361	C₂²×C₄	#11929623	1	1	yes	characteristic
362	Q₁₆	—	316	2	no	—
363	Q₁₆	—	316	2	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	—	316	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	316	2	no	—
368	C₂×C₈	—	316	4	no	—
369	C₂×C₈	—	316	4	no	—
370	C₂×C₈	—	316	1	no	—
371	C₂×C₈	—	79	1	no	—
372	C₂×C₈	—	79	1	no	—
373	C₂×C₈	—	79	1	no	—
374	C₂×C₈	—	79	1	no	—
375	C₂×C₈	—	158	2	no	—
376	C₂×C₈	—	158	2	no	—
377	C₂×C₈	—	158	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	—	316	1	no	—
386	C₄⋊C₄	—	316	1	no	—
387	C₄⋊C₄	—	158	1	no	—
388	C₄⋊C₄	—	158	1	no	—
389	C₄⋊C₄	—	158	1	no	—
390	C₄⋊C₄	—	158	1	no	—
391	C₄⋊C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₂²⋊C₄	—	316	1	no	—
396	C₄²	—	4	1	no	—
397	C₄²	—	316	1	no	—
398	C₄²	D₄×D₇₉	1	1	yes	characteristic
399	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
400	C₄²	#11929623	1	1	yes	characteristic
401	C₄²	C₂³×D₇₉	1	1	yes	characteristic
402	C₂³	—	2	2	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	#14579133	1	1	yes	characteristic
407	Q₈	—	4	1	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	8	1	no	—
410	Q₈	—	316	1	no	—
411	Q₈	—	316	1	no	—
412	Q₈	—	632	1	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	2	no	—
415	D₄	C₂×#11929614	1	4	yes	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	316	1	no	—
427	C₂×C₄	—	316	1	no	—
428	C₂×C₄	#14579133	1	1	yes	characteristic
429	C₂×C₄	#14579133	1	1	yes	characteristic
430	C₂×C₄	#14579133	1	1	yes	characteristic
431	C₂×C₄	C₂×#11929614	1	2	yes	—
432	C₂×C₄	#14579181	1	2	yes	—
433	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
435	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
436	C₈	—	4	2	no	—
437	C₈	—	316	2	no	—
438	C₈	—	316	2	no	—
439	C₈	—	79	2	no	—
440	C₈	—	158	1	no	—
441	C₈	—	158	1	no	—
442	C₈	—	158	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	4	8	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	#19098802	1	2	yes	—
450	C₂²	C₂×#14579133	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	—	632	1	no	—
458	C₄	—	632	1	no	—
459	C₄	#19098802	1	2	yes	—
460	C₄	C₂²×#11929614	1	1	yes	characteristic
461	C₄	C₂×#14579181	1	1	yes	characteristic
462	C₄	AGL(1,ℤ/8)×D₇₉	1	1	yes	characteristic
463	C₄	#19099359	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	4	4	no	—
466	C₂	#23772861	1	1	yes	characteristic
467	C₂	C₂×#19098802	1	1	yes	characteristic
468	C₂	#23773117	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14579133
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3077	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	C₂²×D₄×C₇₉	D₄
hypercenter	#3077	D₇₉
hypocenter	C₇₉	#19256
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3077

Complements

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

N	H ≅ G/N	type
1. #23773982	C₂	semidirect
4. #23762853	C₂	semidirect
5. #23762849	C₂	semidirect
6. #23762797	C₂	semidirect
7. #23762763	C₂	semidirect
8. #23762158	C₂	semidirect
9. #23762091	C₂	semidirect
10. #23762090	C₂	semidirect
14. #19098966	C₂²	semidirect
15. #19098942	C₂²	semidirect
16. #19098915	C₂²	semidirect
17. #19098913	C₂²	semidirect
35. #19098315	C₂²	semidirect
36. #19098315	C₂²	semidirect
37. #19098312	C₂²	semidirect
38. #19098311	C₂²	semidirect
39. #19098309	C₂²	semidirect
40. #19098308	C₂²	semidirect
139. C₂×D₄×C₇₉	Q₁₆	semidirect
246. C₇₉	#19256	semidirect
352. C₂×D₄	#11929614	semidirect

Maximal subgroups

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

subgroup	index
#23773982	2
#23773197	2
C₂×D₄×C₇₉⋊C₈	2
#23762853	2
#23762849	2
#23762797	2
#23762763	2
#23762158	2
#23762091	2
#23762090	2
C₇₉×#3077	2
#19256	79