Subgroups — #34258882

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	#23774000	C₂	1	1	yes	maximal, characteristic
2	#23772369	C₂	1	1	yes	maximal, characteristic
3	#23772335	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762294	C₂	1	2	yes	maximal, complemented
5	#23762287	C₂	1	2	yes	maximal, complemented
6	#23762216	C₂	1	2	yes	maximal, complemented
7	#23762215	C₂	1	2	yes	maximal, complemented
8	#23762168	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761866	C₂	1	1	yes	maximal, characteristic
10	#23761681	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1497	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099097	C₂²	1	1	yes	characteristic
13	#19098969	C₄	1	1	yes	characteristic
14	#19098955	C₄	1	1	yes	characteristic
15	#19098931	C₄	1	1	yes	characteristic
16	#19098925	C₄	1	1	yes	characteristic
17	#19098819	C₄	1	2	yes	—
18	#19098811	C₄	1	2	yes	—
19	#19098694	—	2	1	no	—
20	#19098694	C₂²	1	2	yes	—
21	#19098690	C₂²	1	1	yes	characteristic
22	Q₈×C₇₉⋊C₈	—	2	1	no	—
23	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	—
24	#19098687	C₂²	1	1	yes	characteristic
25	C₄×#11929614	C₂²	1	2	yes	—
26	C₄×#11929611	C₂²	1	2	yes	—
27	#19098640	C₂²	1	1	yes	characteristic
28	#19098631	—	2	1	no	—
29	#19098628	C₂²	1	1	yes	characteristic
30	(C₂²⋊D₇₉)⋊C₈	—	2	1	no	—
31	#19098625	—	2	1	no	—
32	#19098590	—	2	1	no	—
33	#19098587	C₂²	1	1	yes	characteristic
34	#19098520	—	2	1	no	—
35	#19098519	—	2	1	no	—
36	C₄×#11929608	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
38	#19098315	C₂²	1	2	yes	—
39	#19098313	C₂²	1	2	yes	—
40	#19098295	C₂²	1	2	yes	—
41	#19098292	C₂²	1	2	yes	—
42	#19098285	C₂²	1	2	yes	—
43	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
44	#533×C₇₉	C₂²	1	1	yes	characteristic
45	#432×C₇₉	C₂²	1	1	yes	characteristic
46	#431×C₇₉	C₂²	1	1	yes	characteristic
47	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
48	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
49	C₂×#11929614	C₂×C₄	1	2	yes	—
50	C₂×#11929611	C₂×C₄	1	2	yes	—
51	C₂×#11929608	—	2	1	no	—
52	C₂×#11929608	C₂×C₄	1	2	yes	—
53	C₂×#11929607	—	2	1	no	—
54	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
55	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
56	C₂×C₈×D₇₉	—	2	1	no	—
57	#14579155	—	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	C₂×C₄	1	1	yes	characteristic
62	#14579135	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
64	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₇₉	—	2	1	no	—
66	#14579118	—	2	1	no	—
67	#14579094	C₂×C₄	1	2	yes	—
68	#14579092	C₂×C₄	1	2	yes	—
69	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
71	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
72	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
73	Dic₇₉⋊C₈	—	2	1	no	—
74	Dic₇₉⋊C₈	—	2	1	no	—
75	#14579085	C₂×C₄	1	2	yes	—
76	#14579085	C₂×C₄	1	2	yes	—
77	#14579084	C₂×C₄	1	2	yes	—
78	#14579081	C₂×C₄	1	2	yes	—
79	(C₂×D₇₉)⋊C₈	—	2	1	no	—
80	(C₂×D₇₉)⋊C₈	—	2	1	no	—
81	#14579072	—	2	2	no	—
82	#14579072	C₂×C₄	1	1	yes	characteristic
83	#14579072	C₂×C₄	1	1	yes	characteristic
84	#14579071	—	2	1	no	—
85	C₄×C₇₉⋊C₈	—	2	2	no	—
86	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
87	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
88	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
89	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
90	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
91	C₈×Dic₇₉	—	2	1	no	—
92	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
93	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
94	#125×C₇₉	—	2	1	no	—
95	C₂²⋊Q₈×C₇₉	—	2	1	no	—
96	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₇₉	—	2	1	no	—
98	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
99	#117×C₇₉	—	2	1	no	—
100	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₇₉	—	2	1	no	—
102	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
104	C₂²⋊C₈×C₇₉	—	2	1	no	—
105	C₂²⋊C₈×C₇₉	—	2	1	no	—
106	#97×C₇₉	—	2	1	no	—
107	C₄×C₈×C₇₉	C₂³	1	2	yes	—
108	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₇₉	—	2	1	no	—
111	C₂×C₄×D₇₉	—	2	1	no	—
112	#11929614	—	2	4	no	—
113	#11929611	—	2	4	no	—
114	#11929608	—	2	4	no	—
115	#11929608	—	4	2	no	—
116	#11929607	—	4	2	no	—
117	C₂×C₇₉⋊C₈	—	2	2	no	—
118	C₂×C₇₉⋊C₈	—	2	2	no	—
119	C₂×C₇₉⋊C₈	—	4	1	no	—
120	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
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	C₈×D₇₉	—	4	2	no	—
127	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
129	Dic₇₉⋊C₄	—	2	1	no	—
130	Dic₇₉⋊C₄	—	2	1	no	—
131	Dic₇₉⋊C₄	—	2	1	no	—
132	Dic₇₉⋊C₄	—	2	1	no	—
133	C₂²⋊Dic₇₉	—	2	1	no	—
134	(C₂×D₇₉)⋊C₄	—	2	1	no	—
135	(C₂×D₇₉)⋊C₄	—	2	1	no	—
136	(C₂×D₇₉)⋊C₄	—	2	1	no	—
137	(C₂×D₇₉)⋊C₄	—	2	1	no	—
138	C₄×Dic₇₉	—	2	1	no	—
139	C₂×Q₈×C₇₉	—	2	1	no	—
140	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
144	C₂×C₈×C₇₉	—	2	1	no	—
145	C₂×C₈×C₇₉	—	2	1	no	—
146	C₂×C₈×C₇₉	—	2	2	no	—
147	C₄⋊C₄×C₇₉	—	2	1	no	—
148	C₄⋊C₄×C₇₉	—	2	1	no	—
149	C₄⋊C₄×C₇₉	—	2	1	no	—
150	C₄⋊C₄×C₇₉	—	2	2	no	—
151	C₄⋊C₄×C₇₉	—	2	2	no	—
152	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₇₉	—	2	2	no	—
154	C₄²×C₇₉	—	2	2	no	—
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	Q₈×C₇₉	—	2	2	no	—
162	Q₈×C₇₉	—	2	2	no	—
163	Q₈×C₇₉	—	4	2	no	—
164	C₂×C₄×C₇₉	—	2	2	no	—
165	C₂×C₄×C₇₉	—	2	1	no	—
166	C₂×C₄×C₇₉	—	2	1	no	—
167	C₂×C₄×C₇₉	—	2	2	no	—
168	C₂×C₄×C₇₉	—	2	2	no	—
169	C₂×C₄×C₇₉	—	4	1	no	—
170	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₇₉	—	4	2	no	—
177	C₂×Dic₇₉	—	2	1	no	—
178	C₂×Dic₇₉	—	2	1	no	—
179	C₂×Dic₇₉	—	2	1	no	—
180	D₃₁₆	—	2	2	no	—
181	C₄×D₇₉	—	4	1	no	—
182	C₄×D₇₉	—	4	1	no	—
183	Dic₁₅₈	—	2	2	no	—
184	C₈×C₇₉	—	4	2	no	—
185	C₈×C₇₉	—	4	1	no	—
186	C₈×C₇₉	—	4	1	no	—
187	C₇₉⋊C₈	—	2	2	no	—
188	C₇₉⋊C₈	—	2	1	no	—
189	C₇₉⋊C₈	—	2	1	no	—
190	C₇₉⋊C₈	—	2	1	no	—
191	C₇₉⋊C₈	—	4	2	no	—
192	C₇₉⋊C₈	#131	1	4	yes	—
193	C₇₉⋊C₈	#137	1	2	yes	—
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	—	4	2	no	—
206	C₄×C₇₉	—	4	2	no	—
207	C₄×C₇₉	C₂×#131	1	2	yes	—
208	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
209	C₄×C₇₉	#575	1	1	yes	characteristic
210	Dic₇₉	—	4	1	no	—
211	Dic₇₉	—	4	1	no	—
212	Dic₇₉	—	4	1	no	—
213	#17967	—	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	#1591	—	79	2	no	—
223	#1590	—	79	2	no	—
224	#1579	—	79	2	no	—
225	SD₁₆⋊C₈	—	79	2	no	—
226	#1569	—	79	1	no	—
227	#1497	D₇₉	1	1	yes	characteristic, complemented
228	#1495	—	79	1	no	—
229	C₈×M₁₆	—	79	1	no	—
230	C₇₉	#17967	1	1	yes	characteristic, complemented, Sylow
231	#533	C₂×D₇₉	1	1	yes	characteristic
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	C₂×D₇₉	1	1	yes	characteristic
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	—	79	1	no	—
259	C₂×C₄×C₈	—	79	1	no	—
260	#335	—	79	2	no	—
261	#334	—	79	2	no	—
262	Q₈⋊C₈	—	79	2	no	—
263	Q₈⋊C₈	C₂×D₇₉	1	2	yes	—
264	Q₈⋊C₈	C₂×D₇₉	1	2	yes	—
265	D₄⋊C₈	—	79	2	no	—
266	#322	—	79	2	no	—
267	C₈²	—	79	2	no	—
268	C₂×Q₁₆	—	79	2	no	—
269	C₂×SD₁₆	—	79	2	no	—
270	C₂×M₁₆	—	79	2	no	—
271	C₂×M₁₆	—	158	1	no	—
272	C₂×M₁₆	—	158	1	no	—
273	C₂²×C₈	—	79	1	no	—
274	C₂²×C₈	—	79	1	no	—
275	C₂²×C₈	—	158	1	no	—
276	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
277	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
278	#126	—	158	1	no	—
279	#125	—	2	1	no	—
280	#125	—	79	1	no	—
281	#124	—	79	1	no	—
282	#123	—	158	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	79	1	no	—
285	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
286	#121	—	79	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	79	1	no	—
289	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
290	C₄×D₄	—	79	1	no	—
291	C₄×D₄	—	158	1	no	—
292	#117	—	2	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	—	158	2	no	—
300	C₄⋊C₈	—	158	2	no	—
301	C₄⋊C₈	—	158	1	no	—
302	C₄⋊C₈	—	158	1	no	—
303	C₄⋊C₈	—	158	1	no	—
304	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
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	—	2	1	no	—
312	C₂²⋊C₈	—	158	1	no	—
313	C₂²⋊C₈	—	158	1	no	—
314	#97	—	2	1	no	—
315	#97	—	79	1	no	—
316	#97	—	79	1	no	—
317	#97	—	158	2	no	—
318	#97	—	158	1	no	—
319	C₄×C₈	—	79	1	no	—
320	C₄×C₈	—	79	1	no	—
321	C₄×C₈	—	79	1	no	—
322	C₄×C₈	—	79	2	no	—
323	C₄×C₈	—	79	1	no	—
324	C₄×C₈	—	158	2	no	—
325	C₄×C₈	—	158	1	no	—
326	C₄×C₈	C₂²×D₇₉	1	2	yes	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	79	1	no	—
329	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
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	D₄×D₇₉	1	1	yes	characteristic
335	C₂²×C₄	#11929623	1	1	yes	characteristic
336	Q₁₆	—	158	4	no	—
337	SD₁₆	—	158	4	no	—
338	M₁₆	—	316	2	no	—
339	M₁₆	—	316	2	no	—
340	M₁₆	—	158	4	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	316	2	no	—
345	C₂×C₈	—	316	1	no	—
346	C₂×C₈	—	79	2	no	—
347	C₂×C₈	—	79	1	no	—
348	C₂×C₈	—	79	2	no	—
349	C₂×C₈	—	79	1	no	—
350	C₂×C₈	—	79	1	no	—
351	C₂×C₈	—	79	1	no	—
352	C₂×C₈	—	158	2	no	—
353	C₂×C₈	—	158	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	79	1	no	—
360	C₄⋊C₄	—	79	1	no	—
361	C₄⋊C₄	—	158	1	no	—
362	C₄⋊C₄	—	158	1	no	—
363	C₄⋊C₄	—	158	1	no	—
364	C₄⋊C₄	—	158	1	no	—
365	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
366	C₂²⋊C₄	—	2	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	—	2	2	no	—
373	C₄²	—	158	1	no	—
374	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
375	C₄²	D₄×D₇₉	1	1	yes	characteristic
376	C₄²	#11929623	1	1	yes	characteristic
377	C₄²	C₂³×D₇₉	1	1	yes	characteristic
378	C₂³	—	158	1	no	—
379	C₂³	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	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	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	316	1	no	—
393	C₂×C₄	—	316	1	no	—
394	C₂×C₄	—	158	1	no	—
395	C₂×C₄	—	158	1	no	—
396	C₂×C₄	—	158	1	no	—
397	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
398	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
399	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
402	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	316	2	no	—
407	C₈	—	79	4	no	—
408	C₈	—	79	2	no	—
409	C₈	—	158	2	no	—
410	C₈	—	158	1	no	—
411	C₈	—	158	1	no	—
412	C₈	—	158	1	no	—
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×(C₂²⋊D₇₉)⋊C₄	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	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	316	1	no	—
427	C₄	—	316	1	no	—
428	C₄	—	316	1	no	—
429	C₄	#131×D₇₉	1	2	yes	—
430	C₄	#137×D₇₉	1	1	yes	characteristic
431	C₄	#19099362	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	632	1	no	—
434	C₂	#23772108	1	1	yes	characteristic
435	C₂	#23772215	1	1	yes	characteristic
436	C₂	#23772299	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1497	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#14579135	C₂×C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1497	D₇₉
hypocenter	C₇₉	#17967
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1497

Complements

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

N	H ≅ G/N	type
3. #23772335	C₂	semidirect
4. #23762294	C₂	semidirect
5. #23762287	C₂	semidirect
6. #23762216	C₂	semidirect
7. #23762215	C₂	semidirect
8. #23762168	C₂	semidirect
10. #23761681	C₂	semidirect
11. C₇₉×#1497	C₂	semidirect
227. #1497	D₇₉	semidirect
230. C₇₉	#17967	semidirect

Maximal subgroups

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

subgroup	index
#23774000	2
#23772369	2
#23772335	2
#23762294	2
#23762287	2
#23762216	2
#23762215	2
#23762168	2
#23761866	2
#23761681	2
C₇₉×#1497	2
#17967	79