Subgroups — #34257468

Order 20224.

616 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772032	C₂	1	1	yes	maximal, characteristic
2	#23772028	C₂	1	1	yes	maximal, characteristic
3	#23772028	C₂	1	1	yes	maximal, characteristic
4	#23762191	C₂	1	1	yes	maximal, characteristic, complemented
5	#23762189	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762188	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762179	C₂	1	2	yes	maximal, complemented
8	#23762177	C₂	1	2	yes	maximal, complemented
9	#23762166	C₂	1	2	yes	maximal, complemented
10	#23762164	C₂	1	2	yes	maximal, complemented
11	C₇₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
13	#19098619	—	2	1	no	—
14	#19098619	C₄	1	2	yes	—
15	#19098619	C₂²	1	1	yes	characteristic
16	#19098619	C₂²	1	1	yes	characteristic
17	#19098619	C₂²	1	2	yes	—
18	#19098617	—	2	1	no	—
19	#19098617	C₄	1	2	yes	—
20	#19098616	C₂²	1	1	yes	characteristic
21	#19098616	C₂²	1	1	yes	characteristic
22	#19098615	—	2	1	no	—
23	#19098615	C₂²	1	2	yes	—
24	#19098614	—	2	1	no	—
25	#19098614	C₂²	1	2	yes	—
26	#19098587	C₂²	1	1	yes	characteristic
27	#19098585	C₄	1	2	yes	—
28	#19098585	C₂²	1	1	yes	characteristic
29	#19098585	C₂²	1	1	yes	characteristic
30	#19098526	—	2	1	no	—
31	#19098525	—	2	1	no	—
32	#19098525	C₄	1	2	yes	—
33	M₁₆×Dic₇₉	—	2	1	no	—
34	C₄×#11929607	—	2	1	no	—
35	C₄×#11929607	C₂²	1	2	yes	—
36	#19098316	C₂²	1	2	yes	complemented
37	#19098315	C₂²	1	2	yes	complemented
38	#19098315	C₂²	1	2	yes	complemented
39	#19098314	C₂²	1	2	yes	complemented
40	#19098313	C₂²	1	2	yes	complemented
41	#19098313	C₂²	1	2	yes	complemented
42	#431×C₇₉	C₂²	1	1	yes	characteristic
43	#431×C₇₉	C₂²	1	1	yes	characteristic
44	#423×C₇₉	C₂²	1	1	yes	characteristic
45	#335×C₇₉	C₂²	1	2	yes	complemented
46	#334×C₇₉	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₇₉	Q₈	1	1	yes	characteristic
50	C₂×#11929608	—	2	1	no	—
51	C₂×#11929607	—	2	1	no	—
52	C₂×#11929607	—	2	1	no	—
53	C₂×#11929607	C₂×C₄	1	4	yes	—
54	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₇₉	Q₈	1	1	yes	characteristic
57	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₇₉	D₄	1	1	yes	characteristic
60	C₄²×D₇₉	D₄	1	1	yes	characteristic
61	C₄²×D₇₉	Q₈	1	1	yes	characteristic
62	C₄²×D₇₉	Q₈	1	1	yes	characteristic
63	C₄²×D₇₉	C₂³	1	1	yes	characteristic
64	C₄²×D₇₉	C₂³	1	1	yes	characteristic
65	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
67	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
69	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
70	Dic₇₉⋊C₈	—	2	1	no	—
71	Dic₇₉⋊C₈	—	2	1	no	—
72	Dic₇₉⋊C₈	C₂×C₄	1	4	yes	—
73	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
75	(C₂×D₇₉)⋊C₈	—	2	1	no	—
76	(C₂×D₇₉)⋊C₈	—	2	1	no	—
77	(C₂×D₇₉)⋊C₈	—	2	2	no	—
78	(C₂×D₇₉)⋊C₈	—	2	2	no	—
79	(C₂×D₇₉)⋊C₈	C₂×C₄	1	4	yes	—
80	#14579071	—	2	1	no	—
81	#14579071	—	2	1	no	—
82	#14579071	—	2	2	no	—
83	#14579071	C₂×C₄	1	4	yes	—
84	C₄×C₇₉⋊C₈	—	2	1	no	—
85	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
86	C₈×Dic₇₉	—	2	2	no	—
87	C₂×M₁₆×C₇₉	—	2	1	no	—
88	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₇₉	—	2	1	no	—
90	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
91	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
92	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
94	C₂²⋊C₈×C₇₉	—	2	1	no	—
95	C₂²⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
96	C₄×C₈×C₇₉	—	2	1	no	—
97	C₄×C₈×C₇₉	C₂³	1	2	yes	—
98	C₂³×D₇₉	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₇₉	—	4	2	no	—
103	C₂×C₄×D₇₉	—	4	1	no	—
104	C₂×C₄×D₇₉	—	4	1	no	—
105	C₂×C₄×D₇₉	—	4	2	no	—
106	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₇₉	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₄×D₇₉	C₂×Q₈	1	1	yes	characteristic
118	#11929608	—	4	2	no	—
119	#11929607	—	4	4	no	—
120	#11929607	—	4	2	no	—
121	#11929607	—	4	2	no	—
122	C₂×C₇₉⋊C₈	—	2	2	no	—
123	C₂×C₇₉⋊C₈	—	2	1	no	—
124	C₂×C₇₉⋊C₈	—	2	1	no	—
125	C₂×C₇₉⋊C₈	C₂²×C₄	1	4	yes	—
126	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₇₉	C₂×Q₈	1	1	yes	characteristic
137	C₄×Dic₇₉	C₂×Q₈	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
141	M₁₆×C₇₉	—	4	2	no	—
142	C₂×C₈×C₇₉	—	2	1	no	—
143	C₂×C₈×C₇₉	—	2	1	no	—
144	C₂×C₈×C₇₉	—	2	2	no	—
145	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
146	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
149	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
150	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂²×D₇₉	—	4	1	no	—
152	C₂²×D₇₉	—	4	1	no	—
153	C₂²×D₇₉	—	4	1	no	—
154	C₂²×D₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂²×D₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₇₉	—	2	2	no	—
157	C₂×C₄×C₇₉	—	2	1	no	—
158	C₂×C₄×C₇₉	—	2	1	no	—
159	C₂×C₄×C₇₉	—	2	2	no	—
160	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
166	C₂×Dic₇₉	—	4	1	no	—
167	C₂×Dic₇₉	—	4	1	no	—
168	C₂×Dic₇₉	—	4	1	no	—
169	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₄×D₇₉	—	2	2	no	—
176	C₄×D₇₉	—	2	2	no	—
177	C₄×D₇₉	—	2	1	no	—
178	C₄×D₇₉	—	2	1	no	—
179	C₄×D₇₉	—	2	1	no	—
180	C₄×D₇₉	—	2	1	no	—
181	C₄×D₇₉	—	2	2	no	—
182	C₄×D₇₉	—	2	2	no	—
183	C₄×D₇₉	—	4	1	no	—
184	C₄×D₇₉	—	4	1	no	—
185	C₄×D₇₉	—	4	1	no	—
186	C₄×D₇₉	—	4	1	no	—
187	C₄×D₇₉	—	4	1	no	—
188	C₄×D₇₉	—	4	1	no	—
189	C₈×C₇₉	—	2	4	no	—
190	C₈×C₇₉	—	4	1	no	—
191	C₈×C₇₉	—	4	1	no	—
192	C₈×C₇₉	—	4	2	no	—
193	C₇₉⋊C₈	—	2	4	no	—
194	C₇₉⋊C₈	—	4	1	no	—
195	C₇₉⋊C₈	—	4	1	no	—
196	C₇₉⋊C₈	—	4	2	no	—
197	C₂²×C₇₉	—	2	1	no	—
198	C₂²×C₇₉	—	2	1	no	—
199	C₂²×C₇₉	—	2	1	no	—
200	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
201	C₂×D₇₉	—	2	1	no	—
202	C₂×D₇₉	—	2	1	no	—
203	C₂×D₇₉	—	2	1	no	—
204	C₂×D₇₉	—	2	1	no	—
205	C₂×D₇₉	—	2	1	no	—
206	C₂×D₇₉	—	2	1	no	—
207	C₂×D₇₉	—	4	4	no	—
208	C₄×C₇₉	—	2	1	no	—
209	C₄×C₇₉	—	2	1	no	—
210	C₄×C₇₉	—	2	1	no	—
211	C₄×C₇₉	#430	1	2	yes	—
212	C₄×C₇₉	#568	1	2	yes	—
213	C₄×C₇₉	#575	1	1	yes	characteristic
214	C₄×C₇₉	#575	1	1	yes	characteristic
215	Dic₇₉	—	2	1	no	—
216	Dic₇₉	—	2	1	no	—
217	Dic₇₉	—	2	1	no	—
218	Dic₇₉	—	2	1	no	—
219	Dic₇₉	—	2	1	no	—
220	Dic₇₉	—	2	1	no	—
221	#17823	—	79	1	no	maximal, Sylow
222	C₂×C₇₉	—	4	1	no	—
223	C₂×C₇₉	#2905	1	1	yes	characteristic
224	C₂×C₇₉	#2911	1	1	yes	characteristic
225	C₂×C₇₉	C₂×#430	1	1	yes	characteristic
226	D₇₉	—	4	1	no	—
227	D₇₉	—	4	1	no	—
228	#2920	—	79	1	no	—
229	#2920	—	79	1	no	—
230	#2920	—	79	1	no	—
231	#1574	—	79	1	no	—
232	#1574	—	79	1	no	—
233	#1574	—	79	1	no	—
234	#1574	D₇₉	1	1	yes	characteristic, complemented
235	#1572	—	79	2	no	—
236	#1572	—	79	2	no	—
237	#1569	—	79	2	no	—
238	#1569	—	79	2	no	—
239	C₇₉	#17823	1	1	yes	characteristic, complemented, Sylow
240	C₂²×C₄²	—	79	1	no	—
241	#432	—	79	2	no	—
242	#432	—	79	2	no	—
243	#432	—	79	2	no	—
244	#432	—	79	1	no	—
245	#432	—	79	1	no	—
246	#432	—	158	1	no	—
247	#432	—	158	1	no	—
248	#431	—	79	1	no	—
249	#431	—	79	2	no	—
250	#431	—	79	1	no	—
251	#431	—	79	2	no	—
252	#431	—	158	1	no	—
253	#431	—	158	1	no	—
254	#431	C₂×D₇₉	1	1	yes	characteristic
255	#431	C₂×D₇₉	1	1	yes	characteristic
256	#423	—	79	2	no	—
257	#423	—	79	1	no	—
258	#423	—	79	1	no	—
259	#423	—	79	1	no	—
260	#423	C₂×D₇₉	1	1	yes	characteristic
261	#407	—	79	2	no	—
262	#407	—	158	1	no	—
263	#407	—	158	1	no	—
264	C₄×M₁₆	—	79	2	no	—
265	C₄×M₁₆	—	158	1	no	—
266	C₄×M₁₆	—	158	1	no	—
267	#335	—	79	2	no	—
268	#335	—	79	2	no	—
269	#335	—	79	2	no	—
270	#335	C₂×D₇₉	1	2	yes	complemented
271	#334	—	79	2	no	—
272	#334	—	79	2	no	—
273	#334	—	79	2	no	—
274	#334	C₂×D₇₉	1	2	yes	complemented
275	C₂³×C₄	—	79	1	no	—
276	C₂³×C₄	—	79	1	no	—
277	C₂³×C₄	—	79	1	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	79	4	no	—
280	C₂×M₁₆	—	158	1	no	—
281	C₂×M₁₆	—	158	1	no	—
282	C₂×M₁₆	—	158	1	no	—
283	C₂×C₄²	—	79	1	no	—
284	C₂×C₄²	—	79	1	no	—
285	C₂×C₄²	—	79	1	no	—
286	C₂×C₄²	—	79	1	no	—
287	C₂×C₄²	—	79	1	no	—
288	C₂×C₄²	—	79	1	no	—
289	C₂×C₄²	—	79	1	no	—
290	C₂×C₄²	—	79	1	no	—
291	C₂×C₄²	—	79	1	no	—
292	C₂×C₄²	—	79	1	no	—
293	C₂×C₄²	—	79	1	no	—
294	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	79	4	no	—
297	C₄⋊C₈	—	79	2	no	—
298	C₄⋊C₈	—	79	1	no	—
299	C₄⋊C₈	—	79	2	no	—
300	C₄⋊C₈	—	79	1	no	—
301	C₄⋊C₈	—	158	1	no	—
302	C₄⋊C₈	—	158	1	no	—
303	C₄⋊C₈	—	158	1	no	—
304	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
305	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
307	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	79	2	no	—
310	C₂²⋊C₈	—	79	4	no	—
311	C₂²⋊C₈	—	158	2	no	—
312	C₂²⋊C₈	—	158	1	no	—
313	C₂²⋊C₈	—	158	1	no	—
314	C₂²⋊C₈	—	158	2	no	—
315	C₂²⋊C₈	—	158	1	no	—
316	C₂²⋊C₈	C₄×D₇₉	1	2	yes	—
317	#97	—	79	4	no	—
318	#97	—	158	1	no	—
319	#97	—	158	1	no	—
320	#97	—	158	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	79	2	no	—
323	C₄×C₈	—	158	2	no	—
324	C₄×C₈	—	158	1	no	—
325	C₄×C₈	C₂²×D₇₉	1	2	yes	—
326	C₂⁴	—	79	1	no	—
327	C₂²×C₄	—	316	2	no	—
328	C₂²×C₄	—	316	1	no	—
329	C₂²×C₄	—	316	1	no	—
330	C₂²×C₄	—	316	2	no	—
331	C₂²×C₄	—	79	1	no	—
332	C₂²×C₄	—	79	1	no	—
333	C₂²×C₄	—	79	1	no	—
334	C₂²×C₄	—	79	1	no	—
335	C₂²×C₄	—	79	1	no	—
336	C₂²×C₄	—	79	1	no	—
337	C₂²×C₄	—	79	1	no	—
338	C₂²×C₄	—	79	1	no	—
339	C₂²×C₄	—	79	1	no	—
340	C₂²×C₄	—	79	1	no	—
341	C₂²×C₄	—	79	1	no	—
342	C₂²×C₄	—	79	1	no	—
343	C₂²×C₄	—	79	1	no	—
344	C₂²×C₄	—	79	1	no	—
345	C₂²×C₄	—	79	1	no	—
346	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
348	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
349	M₁₆	—	4	2	no	—
350	M₁₆	—	316	4	no	—
351	M₁₆	—	316	2	no	—
352	M₁₆	—	316	2	no	—
353	M₁₆	—	316	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	79	4	no	—
358	C₂×C₈	—	158	1	no	—
359	C₂×C₈	—	158	2	no	—
360	C₂×C₈	—	158	1	no	—
361	C₂×C₈	C₂×C₄×D₇₉	1	4	yes	—
362	C₄²	—	79	1	no	—
363	C₄²	—	79	1	no	—
364	C₄²	—	79	1	no	—
365	C₄²	—	79	1	no	—
366	C₄²	—	79	1	no	—
367	C₄²	—	79	1	no	—
368	C₄²	—	79	1	no	—
369	C₄²	—	79	1	no	—
370	C₄²	—	79	1	no	—
371	C₄²	—	79	1	no	—
372	C₄²	—	79	1	no	—
373	C₄²	—	79	1	no	—
374	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
375	C₄²	D₄×D₇₉	1	1	yes	characteristic
376	C₄²	Q₈×D₇₉	1	1	yes	characteristic
377	C₄²	C₂³×D₇₉	1	1	yes	characteristic
378	C₂³	—	316	1	no	—
379	C₂³	—	316	1	no	—
380	C₂³	—	316	1	no	—
381	C₂³	—	79	1	no	—
382	C₂³	—	79	1	no	—
383	C₂³	C₄⋊C₄×D₇₉	1	1	yes	characteristic
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	316	1	no	—
389	C₂×C₄	—	316	1	no	—
390	C₂×C₄	—	316	1	no	—
391	C₂×C₄	—	316	1	no	—
392	C₂×C₄	—	316	1	no	—
393	C₂×C₄	—	316	1	no	—
394	C₂×C₄	—	316	1	no	—
395	C₂×C₄	—	316	1	no	—
396	C₂×C₄	—	316	1	no	—
397	C₂×C₄	—	79	1	no	—
398	C₂×C₄	—	79	1	no	—
399	C₂×C₄	—	79	1	no	—
400	C₂×C₄	—	79	1	no	—
401	C₂×C₄	—	79	1	no	—
402	C₂×C₄	—	79	1	no	—
403	C₂×C₄	—	158	2	no	—
404	C₂×C₄	—	158	2	no	—
405	C₂×C₄	—	158	1	no	—
406	C₂×C₄	—	158	1	no	—
407	C₂×C₄	—	158	1	no	—
408	C₂×C₄	—	158	1	no	—
409	C₂×C₄	—	158	2	no	—
410	C₂×C₄	—	158	2	no	—
411	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
412	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
413	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
416	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	1	no	—
421	C₈	—	316	1	no	—
422	C₈	—	316	1	no	—
423	C₈	—	316	2	no	—
424	C₈	—	158	4	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	316	4	no	—
429	C₂²	—	158	1	no	—
430	C₂²	—	158	1	no	—
431	C₂²	—	158	1	no	—
432	C₂²	—	158	1	no	—
433	C₂²	—	158	1	no	—
434	C₂²	—	158	1	no	—
435	C₂²	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	158	1	no	—
440	C₄	—	158	1	no	—
441	C₄	—	158	1	no	—
442	C₄	—	158	1	no	—
443	C₄	—	158	1	no	—
444	C₄	—	158	1	no	—
445	C₄	#19098610	1	2	yes	—
446	C₄	#19099328	1	2	yes	—
447	C₄	#19099359	1	1	yes	characteristic
448	C₄	#19099362	1	1	yes	characteristic
449	C₂	—	4	1	no	—
450	C₂	—	316	1	no	—
451	C₂	—	316	1	no	—
452	C₂	#23771961	1	1	yes	characteristic
453	C₂	#23771987	1	1	yes	characteristic
454	C₂	C₂×#19098610	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×#1574	C₂
socle	C₂²×C₇₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₉	C₄⋊C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1574	D₇₉
hypocenter	C₇₉	#17823
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1574

Complements

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

N	H ≅ G/N	type
4. #23762191	C₂	semidirect
5. #23762189	C₂	semidirect
6. #23762188	C₂	semidirect
7. #23762179	C₂	semidirect
8. #23762177	C₂	semidirect
9. #23762166	C₂	semidirect
10. #23762164	C₂	semidirect
11. C₇₉×#1574	C₂	semidirect
36. #19098316	C₂²	semidirect
37. #19098315	C₂²	semidirect
38. #19098315	C₂²	semidirect
39. #19098314	C₂²	semidirect
40. #19098313	C₂²	semidirect
41. #19098313	C₂²	semidirect
45. #335×C₇₉	C₂²	semidirect
46. #334×C₇₉	C₂²	semidirect
234. #1574	D₇₉	semidirect
239. C₇₉	#17823	semidirect
270. #335	C₂×D₇₉	semidirect
274. #334	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23772032	2
#23772028	2
#23762191	2
#23762189	2
#23762188	2
#23762179	2
#23762177	2
#23762166	2
#23762164	2
C₇₉×#1574	2
#17823	79