Subgroups — #34183026

Order 20224.

592 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	C₂×#19098850	C₂	1	1	yes	maximal, characteristic
2	#23766347	C₂	1	1	yes	maximal, characteristic
3	#23764203	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19098290	C₂	1	1	yes	maximal, characteristic
5	#23761284	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761241	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
9	C₂×#14579119	—	2	1	no	—
10	#19098850	—	2	2	no	—
11	#19098850	C₄	1	4	yes	complemented
12	C₂×#14579092	—	2	1	no	—
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#14579085	—	2	2	no	—
15	C₂×#14579081	—	2	1	no	—
16	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
17	#19098465	—	2	1	no	—
18	#19098455	—	2	2	no	—
19	#19098433	C₂²	1	1	yes	characteristic
20	#19098420	—	2	1	no	—
21	C₄×C₄⋊Dic₇₉	—	2	1	no	—
22	#19098290	—	2	2	no	—
23	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
26	#340×C₇₉	—	2	1	no	—
27	#340×C₇₉	—	2	1	no	—
28	C₂²×D₃₁₆	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₇₉	—	2	1	no	—
30	C₂²×C₇₉⋊C₈	—	2	1	no	—
31	C₂²×C₇₉⋊C₈	—	2	1	no	—
32	C₄×D₃₁₆	—	2	1	no	—
33	C₄×D₃₁₆	—	2	1	no	—
34	C₄×D₃₁₆	C₂×C₄	1	2	yes	—
35	C₄×D₃₁₆	D₄	1	2	yes	—
36	#14579119	—	4	2	no	—
37	#14579119	—	4	2	no	—
38	C₂×C₄⋊Dic₇₉	—	2	1	no	—
39	C₂×C₄⋊Dic₇₉	—	2	1	no	—
40	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
42	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
43	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
44	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
45	C₂×C₄×Dic₇₉	—	2	2	no	—
46	#14579092	—	2	4	no	—
47	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
48	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
49	#14579085	—	4	4	no	—
50	#14579081	—	2	4	no	—
51	C₄×C₇₉⋊C₈	—	2	1	no	—
52	C₄×C₇₉⋊C₈	—	2	1	no	—
53	C₇₉⋊#95	—	2	2	no	—
54	C₂²×Q₈×C₇₉	—	2	1	no	—
55	C₂²×C₈×C₇₉	—	2	1	no	—
56	C₄⋊Q₈×C₇₉	—	2	1	no	—
57	C₄⋊Q₈×C₇₉	—	2	1	no	—
58	C₄⋊Q₈×C₇₉	—	2	1	no	—
59	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₇₉	—	2	1	no	—
65	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₇₉	—	2	1	no	—
67	C₄⋊C₈×C₇₉	—	2	1	no	—
68	#95×C₇₉	—	2	1	no	—
69	C₂³×D₇₉	—	2	1	no	—
70	C₂×D₃₁₆	—	2	1	no	—
71	C₂×D₃₁₆	—	2	1	no	—
72	C₂×D₃₁₆	—	2	1	no	—
73	C₂×D₃₁₆	—	2	1	no	—
74	C₂×D₃₁₆	—	2	1	no	—
75	C₂×D₃₁₆	C₂²⋊C₄	1	2	yes	—
76	C₂²×Dic₇₉	—	2	1	no	—
77	C₂²×Dic₇₉	—	2	2	no	—
78	C₂×C₄×D₇₉	—	2	2	no	—
79	C₂×C₄×D₇₉	—	2	2	no	—
80	C₂×C₄×D₇₉	—	4	1	no	—
81	C₂×C₄×D₇₉	—	4	1	no	—
82	C₂×C₄×D₇₉	—	4	1	no	—
83	C₂×C₄×D₇₉	—	4	1	no	—
84	C₂×C₇₉⋊C₈	—	2	2	no	—
85	C₂×C₇₉⋊C₈	—	2	2	no	—
86	C₂×C₇₉⋊C₈	—	4	1	no	—
87	C₂×C₇₉⋊C₈	—	4	1	no	—
88	C₂×C₇₉⋊C₈	—	4	1	no	—
89	C₂×C₇₉⋊C₈	—	4	1	no	—
90	C₄⋊Dic₇₉	—	2	1	no	—
91	C₄⋊Dic₇₉	—	4	2	no	—
92	C₄⋊Dic₇₉	—	4	1	no	—
93	C₄⋊Dic₇₉	—	4	1	no	—
94	C₄⋊Dic₇₉	—	4	1	no	—
95	C₄⋊Dic₇₉	—	4	1	no	—
96	C₄⋊Dic₇₉	C₂²⋊C₄	1	2	yes	—
97	(C₂×D₇₉)⋊C₄	—	2	2	no	—
98	(C₂×D₇₉)⋊C₄	—	2	2	no	—
99	(C₂×D₇₉)⋊C₄	—	4	4	no	—
100	(C₂×D₇₉)⋊C₄	—	8	2	no	—
101	C₄×Dic₇₉	—	4	4	no	—
102	C₂×Q₈×C₇₉	—	2	2	no	—
103	C₂×Q₈×C₇₉	—	4	2	no	—
104	C₂×Q₈×C₇₉	—	4	2	no	—
105	C₂×Q₈×C₇₉	—	4	1	no	—
106	C₂²×C₄×C₇₉	—	2	1	no	—
107	C₂²×C₄×C₇₉	—	2	1	no	—
108	C₂²×C₄×C₇₉	—	4	1	no	—
109	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₇₉	—	4	1	no	—
113	C₂×C₈×C₇₉	—	4	1	no	—
114	C₂×C₈×C₇₉	—	4	1	no	—
115	C₄⋊C₄×C₇₉	—	2	1	no	—
116	C₄⋊C₄×C₇₉	—	2	2	no	—
117	C₄⋊C₄×C₇₉	—	2	2	no	—
118	C₄⋊C₄×C₇₉	—	2	1	no	—
119	C₄⋊C₄×C₇₉	—	2	1	no	—
120	C₄⋊C₄×C₇₉	—	4	1	no	—
121	C₄⋊C₄×C₇₉	—	4	1	no	—
122	C₄⋊C₄×C₇₉	SD₁₆	1	2	yes	—
123	C₄²×C₇₉	—	4	1	no	—
124	C₄²×C₇₉	—	4	1	no	—
125	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₇₉	#41	1	1	yes	characteristic
128	C₄²×C₇₉	#41	1	1	yes	characteristic
129	C₂³×C₇₉	#120	1	1	yes	characteristic
130	C₂²×D₇₉	—	2	2	no	—
131	C₂²×D₇₉	—	4	1	no	—
132	C₂²×D₇₉	—	4	1	no	—
133	C₂²×D₇₉	—	4	1	no	—
134	C₂²×D₇₉	—	4	1	no	—
135	C₂²×D₇₉	—	4	1	no	—
136	C₂²×D₇₉	—	4	1	no	—
137	Q₈×C₇₉	—	4	4	no	—
138	Q₈×C₇₉	—	8	2	no	—
139	C₂×C₄×C₇₉	—	2	1	no	—
140	C₂×C₄×C₇₉	—	2	1	no	—
141	C₂×C₄×C₇₉	—	2	2	no	—
142	C₂×C₄×C₇₉	—	4	1	no	—
143	C₂×C₄×C₇₉	—	4	1	no	—
144	C₂×C₄×C₇₉	—	4	2	no	—
145	C₂×C₄×C₇₉	—	4	1	no	—
146	C₂×C₄×C₇₉	—	4	1	no	—
147	C₂×C₄×C₇₉	—	4	1	no	—
148	C₂×C₄×C₇₉	—	8	1	no	—
149	C₂×C₄×C₇₉	—	8	1	no	—
150	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
158	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
159	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
160	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
162	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
163	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
164	C₂×Dic₇₉	—	2	2	no	—
165	C₂×Dic₇₉	—	4	1	no	—
166	C₂×Dic₇₉	—	4	1	no	—
167	C₂×Dic₇₉	—	4	2	no	—
168	C₂×Dic₇₉	—	4	2	no	—
169	C₂×Dic₇₉	—	4	2	no	—
170	D₃₁₆	—	2	2	no	—
171	D₃₁₆	—	2	2	no	—
172	D₃₁₆	—	4	1	no	—
173	D₃₁₆	—	4	1	no	—
174	C₄×D₇₉	—	4	2	no	—
175	C₄×D₇₉	—	4	2	no	—
176	C₄×D₇₉	—	4	2	no	—
177	C₄×D₇₉	—	4	2	no	—
178	C₈×C₇₉	—	8	1	no	—
179	C₇₉⋊C₈	—	4	2	no	—
180	C₇₉⋊C₈	—	4	2	no	—
181	C₂²×C₇₉	#386	1	1	yes	characteristic
182	C₂²×C₇₉	#450	1	1	yes	characteristic
183	C₂²×C₇₉	#452	1	1	yes	characteristic
184	C₂²×C₇₉	#452	1	1	yes	characteristic
185	C₂²×C₇₉	#452	1	1	yes	characteristic
186	C₂²×C₇₉	#453	1	1	yes	characteristic
187	C₂²×C₇₉	#454	1	1	yes	characteristic
188	C₂×D₇₉	—	4	2	no	—
189	C₂×D₇₉	—	4	2	no	—
190	C₂×D₇₉	—	4	2	no	—
191	C₂×D₇₉	—	8	1	no	—
192	C₂×D₇₉	—	8	1	no	—
193	C₂×D₇₉	—	8	1	no	—
194	C₂×D₇₉	—	8	1	no	—
195	C₄×C₇₉	—	2	1	no	—
196	C₄×C₇₉	—	2	1	no	—
197	C₄×C₇₉	—	4	2	no	—
198	C₄×C₇₉	—	8	2	no	—
199	C₄×C₇₉	—	8	1	no	—
200	C₄×C₇₉	#416	1	1	yes	characteristic
201	C₄×C₇₉	#419	1	1	yes	characteristic
202	C₄×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
203	C₄×C₇₉	#440	1	1	yes	characteristic
204	C₄×C₇₉	#461	1	1	yes	characteristic
205	C₄×C₇₉	#463	1	1	yes	characteristic
206	C₄×C₇₉	#485	1	1	yes	characteristic
207	C₄×C₇₉	#485	1	1	yes	characteristic
208	Dic₇₉	—	4	2	no	—
209	Dic₇₉	—	8	2	no	—
210	#8976	—	79	1	no	maximal, Sylow
211	C₂×C₇₉	#1631	1	1	yes	characteristic
212	C₂×C₇₉	#1634	1	1	yes	characteristic
213	C₂×C₇₉	#1635	1	1	yes	characteristic
214	C₂×C₇₉	#1638	1	1	yes	characteristic
215	C₂×C₇₉	#1873	1	1	yes	characteristic
216	C₂×C₇₉	#1877	1	1	yes	characteristic
217	C₂×C₇₉	#1883	1	1	yes	characteristic
218	D₇₉	—	8	2	no	—
219	C₂×#476	—	79	1	no	—
220	#2354	—	79	1	no	—
221	#1987	D₇₉	1	1	yes	characteristic, complemented
222	#1956	—	79	1	no	—
223	C₂×D₄⋊C₈	—	79	1	no	—
224	#1296	—	79	1	no	—
225	#1279	—	79	1	no	—
226	C₇₉	#8976	1	1	yes	characteristic, complemented, Sylow
227	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
228	C₂×C₄×D₄	—	79	1	no	—
229	C₂×#117	—	158	1	no	—
230	#476	—	79	4	no	—
231	#476	—	158	2	no	—
232	C₂×#106	—	158	1	no	—
233	C₂×C₄⋊C₈	—	79	1	no	—
234	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
235	C₂×#103	—	158	2	no	—
236	C₂×#102	—	158	1	no	—
237	C₂×C₄×C₈	—	79	1	no	—
238	#390	—	158	1	no	—
239	#388	—	158	2	no	—
240	#384	—	79	1	no	—
241	#380	—	158	1	no	—
242	C₄×C₄⋊C₄	—	158	1	no	—
243	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
244	#340	—	2	1	no	—
245	#340	—	2	1	no	—
246	D₄⋊C₈	—	158	2	no	—
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×D₄	—	79	1	no	—
249	C₂³×C₄	—	158	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	158	1	no	—
252	C₂²×C₈	—	158	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	C₄×D₇₉	1	2	yes	—
257	C₄×D₄	—	79	2	no	—
258	C₄×D₄	—	79	2	no	—
259	C₄×D₄	—	158	1	no	—
260	C₄×D₄	—	158	1	no	—
261	#117	—	316	2	no	—
262	#117	—	316	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	79	2	no	—
266	C₂×C₄⋊C₄	—	79	1	no	—
267	C₂×C₄⋊C₄	—	158	1	no	—
268	C₂×C₄⋊C₄	—	158	1	no	—
269	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	—	158	2	no	—
272	C₂×C₂²⋊C₄	—	158	2	no	—
273	C₂×C₂²⋊C₄	—	158	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	—	158	2	no	—
276	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
277	#106	—	158	4	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	79	2	no	—
281	C₄⋊C₈	—	158	1	no	—
282	#103	—	316	4	no	—
283	#102	—	158	4	no	—
284	C₄×C₈	—	158	1	no	—
285	C₄×C₈	—	158	1	no	—
286	#95	—	2	1	no	—
287	#95	—	158	2	no	—
288	C₂⁴	—	158	1	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×D₄	—	79	2	no	—
294	C₂×D₄	—	158	1	no	—
295	C₂×D₄	—	158	1	no	—
296	C₂×D₄	—	158	1	no	—
297	C₂×D₄	—	158	1	no	—
298	C₂×D₄	—	158	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	316	1	no	—
303	C₂²×C₄	—	316	1	no	—
304	C₂²×C₄	—	316	1	no	—
305	C₂²×C₄	—	316	1	no	—
306	C₂²×C₄	—	158	2	no	—
307	C₂²×C₄	—	158	1	no	—
308	C₂²×C₄	—	158	2	no	—
309	C₂²×C₄	—	158	2	no	—
310	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	316	1	no	—
317	C₂×C₈	—	316	1	no	—
318	C₂×C₈	—	316	1	no	—
319	C₂×C₈	—	316	1	no	—
320	C₂×C₈	—	158	2	no	—
321	C₂×C₈	—	158	2	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	316	2	no	—
330	C₄⋊C₄	—	316	1	no	—
331	C₄⋊C₄	—	316	1	no	—
332	C₄⋊C₄	—	316	1	no	—
333	C₄⋊C₄	—	316	1	no	—
334	C₄⋊C₄	—	79	2	no	—
335	C₄⋊C₄	—	158	1	no	—
336	C₄⋊C₄	#11929611	1	2	yes	—
337	C₂²⋊C₄	—	316	4	no	—
338	C₂²⋊C₄	—	632	2	no	—
339	C₂²⋊C₄	—	158	2	no	—
340	C₂²⋊C₄	—	158	2	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	316	4	no	—
344	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
345	C₄²	D₄×D₇₉	1	1	yes	characteristic
346	C₄²	#11929623	1	1	yes	characteristic
347	C₄²	#11929624	1	1	yes	characteristic
348	C₂³	—	316	1	no	—
349	C₂³	—	316	1	no	—
350	C₂³	—	316	1	no	—
351	C₂³	—	316	1	no	—
352	C₂³	—	316	1	no	—
353	C₂³	—	316	1	no	—
354	C₂³	—	158	2	no	—
355	C₂³	#14579129	1	1	yes	characteristic
356	Q₈	—	4	4	no	—
357	Q₈	—	8	2	no	—
358	D₄	—	316	1	no	—
359	D₄	—	316	1	no	—
360	D₄	—	158	2	no	—
361	D₄	—	158	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	—	316	1	no	—
374	C₂×C₄	—	316	1	no	—
375	C₂×C₄	—	316	2	no	—
376	C₂×C₄	—	316	2	no	—
377	C₂×C₄	—	316	2	no	—
378	C₂×C₄	—	316	2	no	—
379	C₂×C₄	—	316	2	no	—
380	C₂×C₄	—	316	2	no	—
381	C₂×C₄	—	316	2	no	—
382	C₂×C₄	—	158	2	no	—
383	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
384	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
385	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
386	C₂×C₄	#14579132	1	1	yes	characteristic
387	C₂×C₄	#14579134	1	1	yes	characteristic
388	C₂×C₄	#14579143	1	1	yes	characteristic
389	C₂×C₄	C₂×#11929611	1	1	yes	characteristic
390	C₂×C₄	#14579181	1	1	yes	characteristic
391	C₂×C₄	#14579182	1	1	yes	characteristic
392	C₂×C₄	#14579184	1	1	yes	characteristic
393	C₂×C₄	#14579186	1	1	yes	characteristic
394	C₂×C₄	#14579190	1	1	yes	characteristic
395	C₂×C₄	#14579192	1	1	yes	characteristic
396	C₂×C₄	#14579193	1	1	yes	characteristic
397	C₈	—	8	1	no	—
398	C₈	—	316	2	no	—
399	C₈	—	316	2	no	—
400	C₂²	—	316	2	no	—
401	C₂²	—	316	2	no	—
402	C₂²	—	316	2	no	—
403	C₂²	—	632	1	no	—
404	C₂²	—	632	1	no	—
405	C₂²	—	632	1	no	—
406	C₂²	—	632	1	no	—
407	C₂²	#19098439	1	1	yes	characteristic
408	C₂²	#19098713	1	1	yes	characteristic
409	C₂²	#19098722	1	1	yes	characteristic
410	C₂²	#19098723	1	1	yes	characteristic
411	C₂²	#19098724	1	1	yes	characteristic
412	C₂²	#19098729	1	1	yes	characteristic
413	C₂²	#19098734	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	8	1	no	—
419	C₄	—	316	2	no	—
420	C₄	—	632	2	no	—
421	C₄	#19098558	1	1	yes	characteristic
422	C₄	#19098570	1	1	yes	characteristic
423	C₄	C₄×#11929611	1	1	yes	characteristic
424	C₄	#19098661	1	1	yes	characteristic
425	C₄	#19098765	1	1	yes	characteristic
426	C₄	#19098775	1	1	yes	characteristic
427	C₄	#19098902	1	1	yes	characteristic
428	C₄	#19098903	1	1	yes	characteristic
429	C₂	—	632	2	no	—
430	C₂	#23762525	1	1	yes	characteristic
431	C₂	#23762544	1	1	yes	characteristic
432	C₂	#23762549	1	1	yes	characteristic
433	C₂	#23762571	1	1	yes	characteristic
434	C₂	#23763709	1	1	yes	characteristic
435	C₂	#23763737	1	1	yes	characteristic
436	C₂	#23763773	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579129
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1987	C₂
socle	C₂³×C₇₉	#120
prime radical	C₂²×D₃₁₆	D₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1987	D₇₉
hypocenter	C₇₉	#8976
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1987

Complements

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

N	H ≅ G/N	type
3. #23764203	C₂	semidirect
5. #23761284	C₂	semidirect
6. #23761241	C₂	semidirect
7. C₇₉×#1987	C₂	semidirect
11. #19098850	C₄	semidirect
221. #1987	D₇₉	semidirect
226. C₇₉	#8976	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098850	2
#23766347	2
#23764203	2
C₂×#19098290	2
#23761284	2
#23761241	2
C₇₉×#1987	2
#8976	79