Subgroups — #34182706

Order 20224.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23766464	C₂	1	1	yes	maximal, characteristic
2	#23764205	C₂	1	1	yes	maximal, characteristic
3	#23764161	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19098306	C₂	1	1	yes	maximal, characteristic
5	#23761241	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761239	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14579158	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₃₁₆	—	2	1	no	—
10	C₂×#14579123	—	2	1	no	—
11	C₂×#14579092	—	2	1	no	—
12	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#14579081	—	2	2	no	—
14	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
15	#19098465	—	2	1	no	—
16	#19098464	—	2	1	no	—
17	#19098441	—	2	2	no	—
18	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
19	#19098325	—	2	1	no	—
20	#19098306	C₄	1	4	yes	complemented
21	C₂×#106×C₇₉	—	2	1	no	—
22	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
23	#384×C₇₉	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
25	#340×C₇₉	—	2	1	no	—
26	C₂²×D₃₁₆	—	2	1	no	—
27	C₂²×D₃₁₆	—	2	1	no	—
28	C₂²×D₃₁₆	D₄	1	2	yes	—
29	C₂²×C₄×D₇₉	—	2	2	no	—
30	C₂²×C₇₉⋊C₈	—	2	1	no	—
31	C₂²×C₇₉⋊C₈	—	2	1	no	—
32	#14579158	—	2	1	no	—
33	#14579158	—	2	1	no	—
34	#14579158	C₂×C₄	1	2	yes	—
35	#14579158	Q₈	1	2	yes	—
36	C₄×D₃₁₆	—	4	2	no	—
37	C₄×D₃₁₆	—	4	2	no	—
38	#14579123	—	4	2	no	—
39	#14579123	—	4	2	no	—
40	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
42	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
43	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
44	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
45	C₂×C₄×Dic₇₉	—	2	1	no	—
46	#14579092	—	4	2	no	—
47	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	complemented
49	#14579081	—	4	4	no	—
50	C₄×C₇₉⋊C₈	—	2	1	no	—
51	C₄×C₇₉⋊C₈	—	2	1	no	—
52	C₇₉⋊#95	—	2	1	no	—
53	C₂²×C₈×C₇₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₉	—	2	1	no	—
60	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
61	#106×C₇₉	—	4	2	no	—
62	C₄⋊C₈×C₇₉	—	2	1	no	—
63	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	complemented
64	#95×C₇₉	—	2	1	no	—
65	C₂³×D₇₉	—	2	2	no	—
66	C₂×D₃₁₆	—	2	2	no	—
67	C₂×D₃₁₆	—	2	2	no	—
68	C₂×D₃₁₆	—	2	2	no	—
69	C₂×D₃₁₆	—	2	2	no	—
70	C₂×D₃₁₆	—	2	2	no	—
71	C₂×D₃₁₆	—	4	2	no	—
72	C₂×D₃₁₆	—	4	2	no	—
73	C₂×D₃₁₆	—	4	1	no	—
74	C₂×D₃₁₆	—	4	1	no	—
75	C₂×D₃₁₆	—	4	1	no	—
76	C₂×D₃₁₆	—	4	1	no	—
77	C₂×D₃₁₆	—	4	1	no	—
78	C₂×D₃₁₆	—	4	1	no	—
79	C₂×D₃₁₆	—	4	1	no	—
80	C₂×D₃₁₆	—	4	1	no	—
81	C₂×D₃₁₆	C₄⋊C₄	1	4	yes	—
82	C₂²×Dic₇₉	—	2	1	no	—
83	C₂²×Dic₇₉	—	2	1	no	—
84	C₂×C₄×D₇₉	—	4	4	no	—
85	C₂×C₄×D₇₉	—	4	4	no	—
86	C₂×C₄×D₇₉	—	8	2	no	—
87	C₂×C₇₉⋊C₈	—	2	2	no	—
88	C₂×C₇₉⋊C₈	—	2	2	no	—
89	C₂×C₇₉⋊C₈	—	4	1	no	—
90	C₂×C₇₉⋊C₈	—	4	1	no	—
91	C₂×C₇₉⋊C₈	—	4	1	no	—
92	C₂×C₇₉⋊C₈	—	4	1	no	—
93	C₄⋊Dic₇₉	—	2	1	no	—
94	C₄⋊Dic₇₉	—	2	1	no	—
95	C₄⋊Dic₇₉	—	2	1	no	—
96	C₄⋊Dic₇₉	SD₁₆	1	2	yes	—
97	(C₂×D₇₉)⋊C₄	—	4	4	no	—
98	(C₂×D₇₉)⋊C₄	—	4	4	no	—
99	(C₂×D₇₉)⋊C₄	—	8	2	no	—
100	C₄×Dic₇₉	—	4	1	no	—
101	C₄×Dic₇₉	—	4	1	no	—
102	C₂²×C₄×C₇₉	—	2	1	no	—
103	C₂²×C₄×C₇₉	—	2	1	no	—
104	C₂²×C₄×C₇₉	—	4	1	no	—
105	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₇₉	—	2	2	no	—
109	C₂×C₈×C₇₉	—	4	1	no	—
110	C₂×C₈×C₇₉	—	4	1	no	—
111	C₄⋊C₄×C₇₉	—	2	1	no	—
112	C₄⋊C₄×C₇₉	—	2	1	no	—
113	C₄⋊C₄×C₇₉	—	2	1	no	—
114	C₄⋊C₄×C₇₉	—	4	2	no	—
115	C₄⋊C₄×C₇₉	—	4	1	no	—
116	C₄⋊C₄×C₇₉	—	4	1	no	—
117	C₄⋊C₄×C₇₉	—	4	1	no	—
118	C₄⋊C₄×C₇₉	—	4	1	no	—
119	C₄⋊C₄×C₇₉	SD₁₆	1	2	yes	—
120	C₄²×C₇₉	—	4	1	no	—
121	C₄²×C₇₉	—	4	1	no	—
122	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
124	C₄²×C₇₉	#41	1	1	yes	characteristic
125	C₄²×C₇₉	#41	1	1	yes	characteristic
126	C₂³×C₇₉	#120	1	1	yes	characteristic
127	C₂²×D₇₉	—	2	4	no	—
128	C₂²×D₇₉	—	4	2	no	—
129	C₂²×D₇₉	—	4	2	no	—
130	C₂²×D₇₉	—	4	2	no	—
131	C₂²×D₇₉	—	4	2	no	—
132	C₂²×D₇₉	—	4	2	no	—
133	C₂²×D₇₉	—	4	2	no	—
134	C₂×C₄×C₇₉	—	2	1	no	—
135	C₂×C₄×C₇₉	—	2	1	no	—
136	C₂×C₄×C₇₉	—	2	2	no	—
137	C₂×C₄×C₇₉	—	4	1	no	—
138	C₂×C₄×C₇₉	—	4	1	no	—
139	C₂×C₄×C₇₉	—	4	1	no	—
140	C₂×C₄×C₇₉	—	4	1	no	—
141	C₂×C₄×C₇₉	—	4	1	no	—
142	C₂×C₄×C₇₉	—	8	1	no	—
143	C₂×C₄×C₇₉	—	8	1	no	—
144	C₂×C₄×C₇₉	—	8	1	no	—
145	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂×C₄×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
154	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
155	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×Dic₇₉	—	2	2	no	—
160	C₂×Dic₇₉	—	4	1	no	—
161	C₂×Dic₇₉	—	4	1	no	—
162	C₂×Dic₇₉	—	4	1	no	—
163	C₂×Dic₇₉	—	4	1	no	—
164	C₂×Dic₇₉	—	4	1	no	—
165	D₃₁₆	—	4	4	no	—
166	D₃₁₆	—	4	2	no	—
167	D₃₁₆	—	4	2	no	—
168	D₃₁₆	—	4	2	no	—
169	D₃₁₆	—	4	2	no	—
170	D₃₁₆	—	4	2	no	—
171	D₃₁₆	—	4	2	no	—
172	D₃₁₆	—	4	2	no	—
173	D₃₁₆	—	4	2	no	—
174	D₃₁₆	—	8	2	no	—
175	C₄×D₇₉	—	8	8	no	—
176	C₈×C₇₉	—	4	2	no	—
177	C₇₉⋊C₈	—	4	2	no	—
178	C₇₉⋊C₈	—	4	2	no	—
179	C₂²×C₇₉	#385	1	1	yes	characteristic
180	C₂²×C₇₉	#449	1	1	yes	characteristic
181	C₂²×C₇₉	#449	1	1	yes	characteristic
182	C₂²×C₇₉	#450	1	1	yes	characteristic
183	C₂²×C₇₉	#450	1	1	yes	characteristic
184	C₂²×C₇₉	#453	1	1	yes	characteristic
185	C₂²×C₇₉	#455	1	1	yes	characteristic
186	C₂×D₇₉	—	4	4	no	—
187	C₂×D₇₉	—	4	4	no	—
188	C₂×D₇₉	—	4	4	no	—
189	C₂×D₇₉	—	8	2	no	—
190	C₂×D₇₉	—	8	2	no	—
191	C₂×D₇₉	—	8	2	no	—
192	C₂×D₇₉	—	8	2	no	—
193	C₄×C₇₉	—	2	1	no	—
194	C₄×C₇₉	—	2	1	no	—
195	C₄×C₇₉	—	4	2	no	—
196	C₄×C₇₉	—	8	1	no	—
197	C₄×C₇₉	—	16	1	no	—
198	C₄×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
199	C₄×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
200	C₄×C₇₉	#442	1	1	yes	characteristic
201	C₄×C₇₉	#442	1	1	yes	characteristic
202	C₄×C₇₉	#476	1	1	yes	characteristic
203	C₄×C₇₉	#476	1	1	yes	characteristic
204	C₄×C₇₉	#478	1	1	yes	characteristic
205	C₄×C₇₉	#478	1	1	yes	characteristic
206	Dic₇₉	—	4	2	no	—
207	Dic₇₉	—	8	1	no	—
208	#8924	—	79	1	no	maximal, Sylow
209	C₂×C₇₉	#1620	1	1	yes	characteristic
210	C₂×C₇₉	#1629	1	1	yes	characteristic
211	C₂×C₇₉	#1642	1	1	yes	characteristic
212	C₂×C₇₉	#1642	1	1	yes	characteristic
213	C₂×C₇₉	#1856	1	1	yes	characteristic
214	C₂×C₇₉	#1864	1	1	yes	characteristic
215	C₂×C₇₉	#1864	1	1	yes	characteristic
216	D₇₉	—	8	4	no	—
217	#2366	—	79	1	no	—
218	#1957	—	79	1	no	—
219	#1948	—	79	1	no	—
220	#1948	D₇₉	1	1	yes	characteristic, complemented
221	C₂×#331	—	79	1	no	—
222	#1279	—	79	1	no	—
223	#1279	—	79	1	no	—
224	C₇₉	#8924	1	1	yes	characteristic, complemented, Sylow
225	C₂×#127	—	79	1	no	—
226	C₂×C₄×D₄	—	158	1	no	—
227	C₂×C₄×D₄	—	158	1	no	—
228	C₂×#106	—	2	1	no	—
229	C₂×#106	—	158	1	no	—
230	C₂×C₄⋊C₈	—	79	1	no	—
231	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
232	C₂×#102	—	158	2	no	—
233	C₂×C₄×C₈	—	79	1	no	—
234	#390	—	158	1	no	—
235	#390	—	158	1	no	—
236	#386	—	158	2	no	—
237	#384	C₂×D₇₉	1	1	yes	characteristic
238	C₄×C₄⋊C₄	—	79	1	no	—
239	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
240	#340	—	2	1	no	—
241	#340	—	158	1	no	—
242	#331	—	79	4	no	—
243	C₂²×D₄	—	79	2	no	—
244	C₂²×D₄	—	158	1	no	—
245	C₂²×D₄	—	158	1	no	—
246	C₂³×C₄	—	158	2	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	158	1	no	—
249	C₂²×C₈	—	158	1	no	—
250	#127	—	79	2	no	—
251	#127	—	79	2	no	—
252	#127	—	158	1	no	—
253	#127	—	158	1	no	—
254	C₄×D₄	—	316	2	no	—
255	C₄×D₄	—	316	2	no	—
256	C₄×D₄	—	316	2	no	—
257	C₄×D₄	—	316	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	79	1	no	—
262	C₂×C₄⋊C₄	—	79	1	no	—
263	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	158	2	no	—
266	C₂×C₂²⋊C₄	—	158	2	no	—
267	C₂×C₂²⋊C₄	—	158	2	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	—	158	1	no	—
270	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
271	#106	—	4	2	no	—
272	#106	—	316	2	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	79	2	no	—
275	C₄⋊C₈	—	158	1	no	—
276	C₄⋊C₈	C₄×D₇₉	1	2	yes	complemented
277	#102	—	316	4	no	—
278	C₄×C₈	—	158	1	no	—
279	C₄×C₈	—	158	1	no	—
280	#95	—	2	1	no	—
281	#95	—	158	1	no	—
282	C₂⁴	—	158	2	no	—
283	C₂×D₄	—	316	2	no	—
284	C₂×D₄	—	316	2	no	—
285	C₂×D₄	—	316	1	no	—
286	C₂×D₄	—	316	1	no	—
287	C₂×D₄	—	316	1	no	—
288	C₂×D₄	—	316	1	no	—
289	C₂×D₄	—	316	1	no	—
290	C₂×D₄	—	316	1	no	—
291	C₂×D₄	—	316	1	no	—
292	C₂×D₄	—	316	1	no	—
293	C₂×D₄	—	79	4	no	—
294	C₂×D₄	—	158	2	no	—
295	C₂×D₄	—	158	2	no	—
296	C₂×D₄	—	158	2	no	—
297	C₂×D₄	—	158	2	no	—
298	C₂×D₄	—	158	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	316	4	no	—
303	C₂²×C₄	—	316	4	no	—
304	C₂²×C₄	—	632	2	no	—
305	C₂²×C₄	—	158	1	no	—
306	C₂²×C₄	—	158	1	no	—
307	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	316	1	no	—
314	C₂×C₈	—	316	1	no	—
315	C₂×C₈	—	316	1	no	—
316	C₂×C₈	—	316	1	no	—
317	C₂×C₈	—	158	2	no	—
318	C₂×C₈	—	158	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	79	2	no	—
328	C₄⋊C₄	—	158	1	no	—
329	C₄⋊C₄	—	158	1	no	—
330	C₄⋊C₄	—	158	1	no	—
331	C₄⋊C₄	#11929611	1	2	yes	—
332	C₂²⋊C₄	—	316	4	no	—
333	C₂²⋊C₄	—	316	4	no	—
334	C₂²⋊C₄	—	632	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	316	1	no	—
338	C₄²	—	316	1	no	—
339	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
340	C₄²	Q₈×D₇₉	1	1	yes	characteristic
341	C₄²	#11929624	1	1	yes	characteristic
342	C₄²	#11929625	1	1	yes	characteristic
343	C₂³	—	316	2	no	—
344	C₂³	—	316	2	no	—
345	C₂³	—	316	2	no	—
346	C₂³	—	316	2	no	—
347	C₂³	—	316	2	no	—
348	C₂³	—	316	2	no	—
349	C₂³	—	158	4	no	—
350	C₂³	#14579129	1	1	yes	characteristic
351	D₄	—	316	4	no	—
352	D₄	—	316	2	no	—
353	D₄	—	316	2	no	—
354	D₄	—	316	2	no	—
355	D₄	—	316	2	no	—
356	D₄	—	316	2	no	—
357	D₄	—	316	2	no	—
358	D₄	—	316	2	no	—
359	D₄	—	316	2	no	—
360	D₄	—	632	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	316	1	no	—
373	C₂×C₄	—	316	1	no	—
374	C₂×C₄	—	316	1	no	—
375	C₂×C₄	—	316	1	no	—
376	C₂×C₄	—	316	1	no	—
377	C₂×C₄	—	632	8	no	—
378	C₂×C₄	—	158	2	no	—
379	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
380	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
381	C₂×C₄	#14579123	1	1	yes	characteristic
382	C₂×C₄	#14579137	1	1	yes	characteristic
383	C₂×C₄	#14579139	1	1	yes	characteristic
384	C₂×C₄	#14579146	1	1	yes	characteristic
385	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
386	C₂×C₄	C₂×#11929611	1	1	yes	characteristic
387	C₂×C₄	#14579181	1	1	yes	characteristic
388	C₂×C₄	#14579182	1	1	yes	characteristic
389	C₂×C₄	#14579186	1	1	yes	characteristic
390	C₂×C₄	#14579187	1	1	yes	characteristic
391	C₂×C₄	#14579188	1	1	yes	characteristic
392	C₂×C₄	#14579188	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	316	2	no	—
395	C₈	—	316	2	no	—
396	C₂²	—	316	4	no	—
397	C₂²	—	316	4	no	—
398	C₂²	—	316	4	no	—
399	C₂²	—	632	2	no	—
400	C₂²	—	632	2	no	—
401	C₂²	—	632	2	no	—
402	C₂²	—	632	2	no	—
403	C₂²	#19098434	1	1	yes	characteristic
404	C₂²	#19098706	1	1	yes	characteristic
405	C₂²	#19098707	1	1	yes	characteristic
406	C₂²	#19098712	1	1	yes	characteristic
407	C₂²	#19098713	1	1	yes	characteristic
408	C₂²	#19098729	1	1	yes	characteristic
409	C₂²	#19098739	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	8	1	no	—
414	C₄	—	16	1	no	—
415	C₄	—	316	2	no	—
416	C₄	—	632	1	no	—
417	C₄	#19098650	1	1	yes	characteristic
418	C₄	C₄×#11929611	1	1	yes	characteristic
419	C₄	#19098673	1	1	yes	characteristic
420	C₄	#19098674	1	1	yes	characteristic
421	C₄	#19098850	1	1	yes	characteristic
422	C₄	#19098852	1	1	yes	characteristic
423	C₄	#19098860	1	1	yes	characteristic
424	C₄	#19098862	1	1	yes	characteristic
425	C₂	—	632	4	no	—
426	C₂	#23762458	1	1	yes	characteristic
427	C₂	#23762515	1	1	yes	characteristic
428	C₂	#23762598	1	1	yes	characteristic
429	C₂	#23762599	1	1	yes	characteristic
430	C₂	#23763608	1	1	yes	characteristic
431	C₂	#23763658	1	1	yes	characteristic
432	C₂	#23763660	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579129
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1948	C₂
socle	C₂³×C₇₉	#120
prime radical	C₂×#14579158	C₂²
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1948	D₇₉
hypocenter	C₇₉	#8924
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1948

Complements

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

N	H ≅ G/N	type
3. #23764161	C₂	semidirect
5. #23761241	C₂	semidirect
6. #23761239	C₂	semidirect
7. C₇₉×#1948	C₂	semidirect
20. #19098306	C₄	semidirect
48. C₄⋊(C₇₉⋊C₈)	C₂×C₄	semidirect
63. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
220. #1948	D₇₉	semidirect
224. C₇₉	#8924	semidirect
276. C₄⋊C₈	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23766464	2
#23764205	2
#23764161	2
C₂×#19098306	2
#23761241	2
#23761239	2
C₇₉×#1948	2
#8924	79