Subgroups — #34258868

Order 20224.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23774006	C₂	1	1	yes	maximal, characteristic
2	#23772375	C₂	1	1	yes	maximal, characteristic
3	#23772334	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762310	C₂	1	2	yes	maximal, complemented
5	#23762304	C₂	1	2	yes	maximal, complemented
6	C₈×Dic₃₁₆	C₂	1	2	yes	maximal, complemented
7	C₈×#11929613	C₂	1	2	yes	maximal, complemented
8	#23762167	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761874	C₂	1	1	yes	maximal, characteristic, complemented
10	#23761866	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099120	C₂²	1	1	yes	characteristic
13	#19099097	C₂²	1	1	yes	characteristic
14	#19098972	C₄	1	1	yes	characteristic
15	#19098957	C₄	1	1	yes	characteristic
16	#19098932	C₄	1	1	yes	characteristic
17	#19098923	C₄	1	1	yes	characteristic
18	#19098821	C₄	1	2	yes	—
19	#19098809	C₄	1	2	yes	—
20	#19098693	—	2	1	no	—
21	#19098693	C₂²	1	2	yes	—
22	#19098693	C₂²	1	1	yes	characteristic
23	C₈×Dic₁₅₈	—	2	1	no	—
24	C₈×Dic₁₅₈	C₂²	1	2	yes	—
25	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
26	C₄×Dic₃₁₆	C₂²	1	2	yes	—
27	C₄×#11929613	C₂²	1	2	yes	—
28	#19098642	C₂²	1	1	yes	characteristic
29	#19098634	—	2	1	no	—
30	C₈×D₃₁₆	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₇₉	—	2	1	no	—
32	#19098622	—	2	1	no	—
33	#19098620	C₂²	1	1	yes	characteristic
34	#19098589	—	2	1	no	—
35	#19098587	C₂²	1	1	yes	characteristic
36	#19098518	—	2	1	no	—
37	#19098517	—	2	1	no	—
38	#19098316	C₂²	1	2	yes	—
39	#19098314	C₂²	1	2	yes	—
40	#19098295	C₂²	1	2	yes	—
41	#19098295	C₂²	1	2	yes	—
42	#19098295	C₂²	1	2	yes	—
43	#19098292	C₂²	1	2	yes	—
44	#431×C₇₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
47	#322×C₇₉	C₂²	1	2	yes	—
48	C₈²×C₇₉	C₂²	1	2	yes	—
49	C₂×Dic₃₁₆	C₂×C₄	1	2	yes	—
50	C₂×#11929613	C₂×C₄	1	2	yes	—
51	C₂×#11929608	—	2	1	no	—
52	C₂×#11929607	—	2	1	no	—
53	C₂×C₈×D₇₉	—	2	1	no	—
54	#14579161	C₂×C₄	1	1	yes	characteristic
55	#14579161	C₂×C₄	1	1	yes	characteristic
56	#14579155	—	2	1	no	—
57	#14579153	—	2	1	no	—
58	#14579153	C₂×C₄	1	1	yes	characteristic
59	#14579149	C₂×C₄	1	1	yes	characteristic
60	#14579144	—	2	1	no	—
61	#14579140	—	2	1	no	—
62	#14579140	C₂×C₄	1	2	yes	—
63	#14579140	C₂×C₄	1	1	yes	characteristic
64	#14579135	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₁₅₈	—	2	1	no	—
66	C₄×Dic₁₅₈	C₂³	1	2	yes	—
67	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
68	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₇₉	—	2	1	no	—
70	#14579120	—	2	1	no	—
71	#14579118	—	2	1	no	—
72	#14579095	C₂×C₄	1	2	yes	—
73	#14579093	C₂×C₄	1	2	yes	—
74	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
78	Dic₇₉⋊C₈	—	2	1	no	—
79	Dic₇₉⋊C₈	—	2	1	no	—
80	Dic₇₉⋊C₈	—	2	2	no	—
81	Dic₇₉⋊C₈	—	2	2	no	—
82	#14579086	C₂×C₄	1	2	yes	—
83	#14579086	C₂×C₄	1	2	yes	—
84	#14579086	C₂×C₄	1	2	yes	—
85	#14579083	C₂×C₄	1	2	yes	—
86	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
87	(C₂×D₇₉)⋊C₈	—	2	1	no	—
88	(C₂×D₇₉)⋊C₈	—	2	1	no	—
89	#14579072	—	2	1	no	—
90	#14579071	—	2	1	no	—
91	#14579071	—	2	2	no	—
92	C₈×Dic₇₉	—	2	1	no	—
93	C₈×Dic₇₉	—	2	2	no	—
94	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
95	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₉	—	2	1	no	—
99	C₂²⋊C₈×C₇₉	—	2	1	no	—
100	#97×C₇₉	C₂×C₄	1	1	yes	characteristic
101	#97×C₇₉	C₂×C₄	1	1	yes	characteristic
102	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
103	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
104	C₄×C₈×C₇₉	C₂³	1	2	yes	—
105	C₄×C₈×C₇₉	C₂³	1	2	yes	—
106	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
108	C₂×Dic₁₅₈	—	2	1	no	—
109	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
110	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
111	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₇₉	—	2	1	no	—
113	C₂×C₄×D₇₉	—	2	1	no	—
114	Dic₃₁₆	—	2	4	no	—
115	#11929613	—	2	4	no	—
116	#11929608	—	4	2	no	—
117	#11929607	—	4	2	no	—
118	C₂×C₇₉⋊C₈	—	2	2	no	—
119	C₂×C₇₉⋊C₈	—	2	1	no	—
120	C₂×C₇₉⋊C₈	—	2	1	no	—
121	C₈×D₇₉	—	4	2	no	—
122	C₄⋊Dic₇₉	—	2	1	no	—
123	C₄⋊Dic₇₉	—	2	1	no	—
124	C₄⋊Dic₇₉	—	2	1	no	—
125	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
126	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
127	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
128	Dic₇₉⋊C₄	—	2	1	no	—
129	Dic₇₉⋊C₄	—	2	1	no	—
130	Dic₇₉⋊C₄	—	2	1	no	—
131	Dic₇₉⋊C₄	—	2	2	no	—
132	Dic₇₉⋊C₄	—	2	2	no	—
133	Dic₇₉⋊C₄	—	2	1	no	—
134	C₂²⋊Dic₇₉	—	2	2	no	—
135	C₂²⋊Dic₇₉	—	2	1	no	—
136	(C₂×D₇₉)⋊C₄	—	2	1	no	—
137	(C₂×D₇₉)⋊C₄	—	2	1	no	—
138	(C₂×D₇₉)⋊C₄	—	2	1	no	—
139	(C₂×D₇₉)⋊C₄	—	2	1	no	—
140	C₄×Dic₇₉	—	2	1	no	—
141	C₄×Dic₇₉	—	2	2	no	—
142	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
145	M₁₆×C₇₉	—	2	4	no	—
146	C₂×C₈×C₇₉	—	2	2	no	—
147	C₂×C₈×C₇₉	—	2	2	no	—
148	C₂×C₈×C₇₉	—	4	1	no	—
149	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₇₉	#41	1	1	yes	characteristic
158	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
159	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₇₉	—	2	1	no	—
161	C₂×C₄×C₇₉	—	2	2	no	—
162	C₂×C₄×C₇₉	—	2	1	no	—
163	C₂×C₄×C₇₉	—	2	1	no	—
164	C₂×C₄×C₇₉	—	4	1	no	—
165	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
171	C₂²⋊D₇₉	—	4	2	no	—
172	C₂×Dic₇₉	—	2	1	no	—
173	C₂×Dic₇₉	—	2	1	no	—
174	C₂×Dic₇₉	—	2	2	no	—
175	C₂×Dic₇₉	—	2	2	no	—
176	C₂×Dic₇₉	—	2	1	no	—
177	D₃₁₆	—	2	2	no	—
178	C₄×D₇₉	—	4	1	no	—
179	C₄×D₇₉	—	4	1	no	—
180	Dic₁₅₈	—	2	2	no	—
181	Dic₁₅₈	—	2	2	no	—
182	Dic₁₅₈	—	2	2	no	—
183	Dic₁₅₈	—	4	2	no	—
184	C₈×C₇₉	—	2	2	no	—
185	C₈×C₇₉	—	2	1	no	—
186	C₈×C₇₉	—	2	1	no	—
187	C₈×C₇₉	—	2	1	no	—
188	C₈×C₇₉	—	4	2	no	—
189	C₈×C₇₉	#131	1	4	yes	—
190	C₈×C₇₉	#137	1	2	yes	—
191	C₇₉⋊C₈	—	4	1	no	—
192	C₇₉⋊C₈	—	4	1	no	—
193	C₇₉⋊C₈	—	4	2	no	—
194	C₂²×C₇₉	—	2	1	no	—
195	C₂²×C₇₉	—	2	1	no	—
196	C₂²×C₇₉	—	2	1	no	—
197	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×D₇₉	—	4	1	no	—
199	C₂×D₇₉	—	4	1	no	—
200	C₂×D₇₉	—	4	1	no	—
201	C₄×C₇₉	—	2	1	no	—
202	C₄×C₇₉	—	2	1	no	—
203	C₄×C₇₉	—	2	1	no	—
204	C₄×C₇₉	—	2	1	no	—
205	C₄×C₇₉	C₂×#131	1	2	yes	—
206	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
207	C₄×C₇₉	#575	1	1	yes	characteristic
208	Dic₇₉	—	4	2	no	—
209	Dic₇₉	—	4	1	no	—
210	Dic₇₉	—	4	1	no	—
211	Dic₇₉	—	4	1	no	—
212	Dic₇₉	—	4	2	no	—
213	#17965	—	79	1	no	maximal, Sylow
214	C₂×C₇₉	—	4	1	no	—
215	C₂×C₇₉	#2931	1	1	yes	characteristic
216	C₂×C₇₉	C₄×#137	1	1	yes	characteristic
217	C₂×C₇₉	#2955	1	1	yes	characteristic
218	D₇₉	—	8	1	no	—
219	#3172	—	79	1	no	—
220	#2966	—	79	1	no	—
221	#2960	—	79	1	no	—
222	#1593	—	79	2	no	—
223	#1592	—	79	2	no	—
224	C₈×Q₁₆	—	79	2	no	—
225	C₈×SD₁₆	—	79	2	no	—
226	#1569	—	79	1	no	—
227	#1497	—	79	1	no	—
228	#1495	—	79	1	no	—
229	C₈×M₁₆	D₇₉	1	1	yes	characteristic, complemented
230	C₇₉	#17965	1	1	yes	characteristic, complemented, Sylow
231	#533	—	79	1	no	—
232	#529	—	79	1	no	—
233	#501	—	79	1	no	—
234	#497	—	79	1	no	—
235	#491	—	79	1	no	—
236	#489	—	79	1	no	—
237	#470	—	79	2	no	—
238	#468	—	79	2	no	—
239	#446	—	79	2	no	—
240	#446	—	79	1	no	—
241	#446	—	158	1	no	—
242	C₈×Q₈	—	79	2	no	—
243	C₈×Q₈	—	79	1	no	—
244	C₈×Q₈	—	158	1	no	—
245	C₄×Q₁₆	—	79	2	no	—
246	C₄×SD₁₆	—	79	2	no	—
247	#436	—	79	1	no	—
248	#435	—	158	1	no	—
249	C₈×D₄	—	79	1	no	—
250	C₈×D₄	—	158	1	no	—
251	#433	—	158	1	no	—
252	#432	—	79	1	no	—
253	#431	C₂×D₇₉	1	1	yes	characteristic
254	#424	—	158	1	no	—
255	#423	—	79	1	no	—
256	#405	—	158	1	no	—
257	#405	—	158	1	no	—
258	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
260	#335	—	79	2	no	—
261	#334	—	79	2	no	—
262	Q₈⋊C₈	—	79	2	no	—
263	Q₈⋊C₈	—	79	2	no	—
264	Q₈⋊C₈	—	79	2	no	—
265	D₄⋊C₈	—	79	2	no	—
266	#322	C₂×D₇₉	1	2	yes	—
267	C₈²	C₂×D₇₉	1	2	yes	—
268	C₂×Q₁₆	—	79	2	no	—
269	C₂×SD₁₆	—	79	2	no	—
270	C₂×M₁₆	—	158	1	no	—
271	C₂×M₁₆	—	158	1	no	—
272	C₂×M₁₆	C₄×D₇₉	1	2	yes	—
273	C₂²×C₈	—	158	1	no	—
274	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
275	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
276	C₄⋊Q₈	—	79	1	no	—
277	C₄⋊Q₈	—	79	1	no	—
278	#126	—	158	1	no	—
279	#125	—	79	1	no	—
280	#125	—	158	1	no	—
281	#124	—	79	1	no	—
282	#123	—	158	1	no	—
283	C₂²⋊Q₈	—	79	1	no	—
284	C₂²⋊Q₈	—	79	2	no	—
285	C₂²⋊Q₈	—	158	1	no	—
286	#121	—	79	1	no	—
287	C₄×Q₈	—	79	1	no	—
288	C₄×Q₈	—	79	2	no	—
289	C₄×Q₈	—	158	1	no	—
290	C₄×D₄	—	79	1	no	—
291	C₄×D₄	—	158	1	no	—
292	#117	—	158	1	no	—
293	#117	—	158	1	no	—
294	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
295	#107	—	79	2	no	—
296	#106	—	79	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	79	2	no	—
299	C₄⋊C₈	—	79	1	no	—
300	C₄⋊C₈	—	79	1	no	—
301	C₄⋊C₈	—	158	2	no	—
302	C₄⋊C₈	—	158	2	no	—
303	C₄⋊C₈	—	158	1	no	—
304	C₄⋊C₈	—	158	1	no	—
305	C₄⋊C₈	—	158	1	no	—
306	#103	—	79	2	no	—
307	#103	—	79	2	no	—
308	#103	—	79	2	no	—
309	#102	—	79	2	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	158	1	no	—
312	C₂²⋊C₈	—	158	1	no	—
313	C₂²⋊C₈	—	158	1	no	—
314	#97	—	158	1	no	—
315	#97	—	158	2	no	—
316	#97	—	158	1	no	—
317	#97	C₄×D₇₉	1	1	yes	characteristic
318	#97	C₄×D₇₉	1	1	yes	characteristic
319	C₄×C₈	—	158	1	no	—
320	C₄×C₈	—	158	2	no	—
321	C₄×C₈	D₃₁₆	1	1	yes	characteristic
322	C₄×C₈	D₃₁₆	1	1	yes	characteristic
323	C₄×C₈	C₂²×D₇₉	1	2	yes	—
324	C₄×C₈	C₂²×D₇₉	1	2	yes	—
325	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
327	C₂×Q₈	—	79	1	no	—
328	C₂×Q₈	—	79	2	no	—
329	C₂×Q₈	—	158	1	no	—
330	C₂×D₄	—	79	1	no	—
331	C₂×D₄	—	158	1	no	—
332	C₂²×C₄	—	158	1	no	—
333	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
335	C₂²×C₄	#11929624	1	1	yes	characteristic
336	Q₁₆	—	158	4	no	—
337	SD₁₆	—	158	4	no	—
338	M₁₆	—	2	4	no	—
339	M₁₆	—	316	2	no	—
340	M₁₆	—	316	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	316	2	no	—
345	C₂×C₈	—	158	1	no	—
346	C₂×C₈	—	158	2	no	—
347	C₂×C₈	—	158	1	no	—
348	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
349	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
350	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
351	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
352	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
353	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
354	C₄⋊C₄	—	79	2	no	—
355	C₄⋊C₄	—	79	1	no	—
356	C₄⋊C₄	—	79	1	no	—
357	C₄⋊C₄	—	158	2	no	—
358	C₄⋊C₄	—	158	1	no	—
359	C₄⋊C₄	—	158	1	no	—
360	C₄⋊C₄	—	158	1	no	—
361	C₄⋊C₄	—	158	1	no	—
362	C₄⋊C₄	—	158	2	no	—
363	C₄⋊C₄	—	158	1	no	—
364	C₄⋊C₄	—	158	1	no	—
365	C₄⋊C₄	—	158	1	no	—
366	C₂²⋊C₄	—	158	2	no	—
367	C₂²⋊C₄	—	158	1	no	—
368	C₂²⋊C₄	—	158	1	no	—
369	C₂²⋊C₄	—	158	1	no	—
370	C₂²⋊C₄	—	158	1	no	—
371	C₂²⋊C₄	—	158	1	no	—
372	C₄²	—	158	1	no	—
373	C₄²	—	158	2	no	—
374	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
375	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
376	C₄²	#11929624	1	1	yes	characteristic
377	C₄²	C₂³×D₇₉	1	1	yes	characteristic
378	C₂³	—	158	1	no	—
379	C₂³	C₄×D₃₁₆	1	1	yes	characteristic
380	Q₈	—	316	2	no	—
381	Q₈	—	158	2	no	—
382	Q₈	—	158	2	no	—
383	Q₈	—	158	2	no	—
384	D₄	—	316	2	no	—
385	D₄	—	158	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	316	1	no	—
391	C₂×C₄	—	316	1	no	—
392	C₂×C₄	—	158	1	no	—
393	C₂×C₄	—	158	1	no	—
394	C₂×C₄	—	158	2	no	—
395	C₂×C₄	—	158	2	no	—
396	C₂×C₄	—	158	1	no	—
397	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
398	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
399	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
402	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	2	1	no	—
407	C₈	—	4	2	no	—
408	C₈	—	316	1	no	—
409	C₈	—	316	1	no	—
410	C₈	—	316	2	no	—
411	C₈	#14579167	1	4	yes	—
412	C₈	#14579194	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	316	1	no	—
417	C₂²	—	316	1	no	—
418	C₂²	—	316	1	no	—
419	C₂²	C₂×C₄×D₃₁₆	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	316	1	no	—
425	C₄	—	316	1	no	—
426	C₄	—	316	2	no	—
427	C₄	—	316	1	no	—
428	C₄	—	316	2	no	—
429	C₄	C₂×#14579167	1	2	yes	—
430	C₄	C₂×#14579194	1	1	yes	characteristic
431	C₄	#19099363	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	632	1	no	—
434	C₂	#23772113	1	1	yes	characteristic
435	C₂	C₄×#14579194	1	1	yes	characteristic
436	C₂	#23772304	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₈×M₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#14579135	C₂×C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	C₈×M₁₆	D₇₉
hypocenter	C₇₉	#17965
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
3. #23772334	C₂	semidirect
4. #23762310	C₂	semidirect
5. #23762304	C₂	semidirect
6. C₈×Dic₃₁₆	C₂	semidirect
7. C₈×#11929613	C₂	semidirect
8. #23762167	C₂	semidirect
9. #23761874	C₂	semidirect
11. C₈×M₁₆×C₇₉	C₂	semidirect
229. C₈×M₁₆	D₇₉	semidirect
230. C₇₉	#17965	semidirect

Maximal subgroups

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

subgroup	index
#23774006	2
#23772375	2
#23772334	2
#23762310	2
#23762304	2
C₈×Dic₃₁₆	2
C₈×#11929613	2
#23762167	2
#23761874	2
#23761866	2
C₈×M₁₆×C₇₉	2
#17965	79