Subgroups — #34307973

Order 20224.

710 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#135×Dic₇₉	C₂	1	1	yes	maximal, characteristic
2	#23772062	C₂	1	2	yes	maximal, complemented
3	#23764294	C₂	1	1	yes	maximal, characteristic
4	#23764051	C₂	1	2	yes	maximal, complemented
5	#23764045	C₂	1	2	yes	maximal, complemented
6	#23763570	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763418	C₂	1	2	yes	maximal, complemented
8	#23763287	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763284	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763268	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1975	C₂	1	1	yes	maximal, characteristic
12	#41×Dic₇₉	C₂²	1	2	yes	—
13	Q₁₆×Dic₇₉	C₄	1	1	yes	characteristic, complemented
14	Q₁₆×Dic₇₉	C₄	1	1	yes	characteristic, complemented
15	SD₁₆×Dic₇₉	C₄	1	2	yes	complemented
16	SD₁₆×Dic₇₉	C₄	1	2	yes	complemented
17	D₈×Dic₇₉	C₄	1	1	yes	characteristic, complemented
18	D₈×Dic₇₉	C₄	1	1	yes	characteristic, complemented
19	#19098621	—	2	2	no	—
20	#19098621	—	2	2	no	—
21	#19098617	—	2	2	no	—
22	#19098613	—	2	2	no	—
23	C₂×#14579097	C₂²	1	1	yes	characteristic
24	C₂×#14579096	C₂²	1	2	yes	—
25	#19098601	C₂²	1	1	yes	characteristic
26	#19098586	C₂²	1	2	yes	—
27	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×#14579088	C₂²	1	2	yes	—
29	#19098559	C₂²	1	2	yes	—
30	#19098530	C₂²	1	2	yes	—
31	#19098521	C₂²	1	2	yes	—
32	#19098518	C₂²	1	2	yes	—
33	C₂×#14579071	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
35	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
36	#19098324	C₂²	1	2	yes	—
37	#19098323	C₂²	1	2	yes	—
38	#19098318	C₂²	1	1	yes	characteristic
39	#19098317	C₂²	1	1	yes	characteristic
40	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#104×C₇₉	C₂²	1	2	yes	—
43	#408×C₇₉	C₂²	1	2	yes	—
44	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×#11929608	C₂³	1	2	yes	—
46	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
48	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
49	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
50	D₄×Dic₇₉	—	2	2	no	—
51	D₄×Dic₇₉	—	2	2	no	—
52	D₄×Dic₇₉	C₂×C₄	1	2	yes	—
53	D₄×Dic₇₉	C₂×C₄	1	2	yes	—
54	#14579120	—	2	2	no	—
55	#14579120	C₂³	1	2	yes	—
56	C₂×Dic₇₉⋊C₄	—	2	1	no	—
57	C₂×C₄×Dic₇₉	—	2	2	no	—
58	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
60	#14579097	—	2	2	no	—
61	#14579096	—	4	2	no	—
62	#14579095	C₂×C₄	1	1	yes	characteristic
63	#14579095	C₂×C₄	1	1	yes	characteristic
64	#14579093	C₂×C₄	1	2	yes	—
65	Dic₇₉⋊C₈	—	2	2	no	—
66	Dic₇₉⋊C₈	—	2	2	no	—
67	Dic₇₉⋊C₈	D₄	1	2	yes	—
68	Dic₇₉⋊C₈	D₄	1	2	yes	—
69	#14579088	—	4	2	no	—
70	#14579085	C₂×C₄	1	2	yes	—
71	#14579085	C₂×C₄	1	2	yes	—
72	#14579082	C₂×C₄	1	2	yes	—
73	#14579082	C₂×C₄	1	2	yes	—
74	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
75	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
76	#14579071	—	2	2	no	—
77	#14579071	—	2	2	no	—
78	#14579071	—	2	2	no	—
79	C₈×Dic₇₉	—	2	2	no	—
80	C₈×Dic₇₉	—	2	2	no	—
81	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
85	C₇₉⋊#95	—	2	1	no	—
86	C₂×#41×C₇₉	C₂³	1	2	yes	—
87	#135×C₇₉	—	2	2	no	—
88	#135×C₇₉	—	2	2	no	—
89	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
90	C₂×SD₁₆×C₇₉	C₂×C₄	1	2	yes	—
91	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
92	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
93	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
96	#108×C₇₉	—	2	2	no	—
97	#104×C₇₉	—	4	2	no	—
98	C₂²⋊C₈×C₇₉	—	2	2	no	—
99	C₂²⋊C₈×C₇₉	—	2	2	no	—
100	#97×C₇₉	—	2	2	no	—
101	C₂²×Dic₇₉	—	2	2	no	—
102	C₂²×Dic₇₉	—	2	2	no	—
103	C₂²×Dic₇₉	—	2	1	no	—
104	C₂²×Dic₇₉	#41	1	1	yes	characteristic
105	C₂²×Dic₇₉	#41	1	1	yes	characteristic
106	#11929608	—	2	2	no	—
107	#11929608	—	2	2	no	—
108	C₂×C₇₉⋊C₈	—	2	2	no	—
109	C₂×C₇₉⋊C₈	—	2	1	no	—
110	C₂×C₇₉⋊C₈	—	2	1	no	—
111	C₂×C₇₉⋊C₈	—	2	1	no	—
112	C₂×C₇₉⋊C₈	—	2	1	no	—
113	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
116	C₄⋊Dic₇₉	—	2	2	no	—
117	C₄⋊Dic₇₉	—	2	2	no	—
118	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
119	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
120	Dic₇₉⋊C₄	—	4	2	no	—
121	C₂²⋊Dic₇₉	—	2	2	no	—
122	C₂²⋊Dic₇₉	—	2	2	no	—
123	C₂²⋊Dic₇₉	—	2	2	no	—
124	C₄×Dic₇₉	—	2	2	no	—
125	C₄×Dic₇₉	—	2	2	no	—
126	C₄×Dic₇₉	—	2	2	no	—
127	C₄×Dic₇₉	—	2	1	no	—
128	C₄×Dic₇₉	—	2	1	no	—
129	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
132	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
133	#41×C₇₉	—	2	2	no	—
134	#41×C₇₉	—	2	2	no	—
135	#41×C₇₉	—	2	2	no	—
136	#41×C₇₉	—	2	2	no	—
137	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₇₉	—	2	2	no	—
139	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₇₉	—	2	2	no	—
141	C₂²×C₄×C₇₉	—	2	1	no	—
142	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
143	Q₁₆×C₇₉	—	2	2	no	—
144	SD₁₆×C₇₉	—	2	4	no	—
145	D₈×C₇₉	—	2	2	no	—
146	M₁₆×C₇₉	—	2	2	no	—
147	M₁₆×C₇₉	—	2	2	no	—
148	C₂×C₈×C₇₉	—	2	2	no	—
149	C₂×C₈×C₇₉	—	2	1	no	—
150	C₂×C₈×C₇₉	—	2	1	no	—
151	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₇₉	#41	1	2	yes	—
155	C₂×C₈×C₇₉	#41	1	2	yes	—
156	C₄²×C₇₉	—	2	1	no	—
157	C₄²×C₇₉	—	2	1	no	—
158	C₂³×C₇₉	—	2	2	no	—
159	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
160	Q₈×C₇₉	—	2	2	no	—
161	Q₈×C₇₉	—	2	2	no	—
162	D₄×C₇₉	—	2	2	no	—
163	D₄×C₇₉	—	2	2	no	—
164	D₄×C₇₉	—	4	2	no	—
165	D₄×C₇₉	—	4	2	no	—
166	C₂×C₄×C₇₉	—	2	2	no	—
167	C₂×C₄×C₇₉	—	4	2	no	—
168	C₂×C₄×C₇₉	—	4	2	no	—
169	C₂×C₄×C₇₉	—	4	1	no	—
170	C₂×C₄×C₇₉	—	4	1	no	—
171	C₂×C₄×C₇₉	—	4	1	no	—
172	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
178	C₂×Dic₇₉	—	2	2	no	—
179	C₂×Dic₇₉	—	2	2	no	—
180	C₂×Dic₇₉	—	2	2	no	—
181	C₂×Dic₇₉	—	4	1	no	—
182	C₂×Dic₇₉	—	4	4	no	—
183	C₂×Dic₇₉	—	4	1	no	—
184	C₂×Dic₇₉	—	4	1	no	—
185	C₂×Dic₇₉	—	4	1	no	—
186	C₂×Dic₇₉	—	8	2	no	—
187	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
188	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
189	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
190	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
191	C₈×C₇₉	—	2	2	no	—
192	C₈×C₇₉	—	4	2	no	—
193	C₈×C₇₉	#117	1	2	yes	—
194	C₈×C₇₉	#117	1	2	yes	—
195	C₇₉⋊C₈	—	2	1	no	—
196	C₇₉⋊C₈	—	2	1	no	—
197	C₇₉⋊C₈	—	2	2	no	—
198	C₇₉⋊C₈	—	4	2	no	—
199	C₂²×C₇₉	—	2	1	no	—
200	C₂²×C₇₉	—	2	1	no	—
201	C₂²×C₇₉	—	4	2	no	—
202	C₂²×C₇₉	—	4	2	no	—
203	C₂²×C₇₉	—	4	2	no	—
204	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₇₉	#555	1	1	yes	characteristic
206	C₂²×C₇₉	#556	1	1	yes	characteristic
207	C₄×C₇₉	—	4	2	no	—
208	C₄×C₇₉	—	8	1	no	—
209	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
210	C₄×C₇₉	#520	1	1	yes	characteristic
211	C₄×C₇₉	#547	1	1	yes	characteristic
212	C₄×C₇₉	#550	1	1	yes	characteristic
213	Dic₇₉	—	2	1	no	—
214	Dic₇₉	—	2	1	no	—
215	Dic₇₉	—	2	1	no	—
216	Dic₇₉	—	4	2	no	—
217	Dic₇₉	—	4	2	no	—
218	Dic₇₉	—	8	1	no	—
219	Dic₇₉	#444	1	2	yes	—
220	#22803	—	79	1	no	maximal, Sylow
221	C₂×C₇₉	—	2	1	no	—
222	C₂×C₇₉	—	2	1	no	—
223	C₂×C₇₉	—	8	2	no	—
224	C₂×C₇₉	#2354	1	1	yes	characteristic
225	C₂×C₇₉	C₂×#444	1	1	yes	characteristic
226	C₂×C₇₉	#2957	1	1	yes	characteristic
227	C₄×#135	—	79	1	no	—
228	#2925	—	79	2	no	—
229	#1975	—	79	1	no	—
230	#1975	D₇₉	1	1	yes	characteristic
231	#1929	—	79	2	no	—
232	#1929	—	79	2	no	—
233	#1848	—	79	1	no	—
234	#1806	—	79	2	no	—
235	#1773	—	79	1	no	—
236	#1773	—	79	1	no	—
237	#1770	—	79	1	no	—
238	C₇₉	#22803	1	1	yes	characteristic, complemented, Sylow
239	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
240	C₄×#41	—	79	2	no	—
241	C₄×Q₁₆	—	79	1	no	—
242	C₄×Q₁₆	—	79	1	no	—
243	C₄×SD₁₆	—	79	2	no	—
244	C₄×SD₁₆	—	79	2	no	—
245	C₄×D₈	—	79	1	no	—
246	C₄×D₈	—	79	1	no	—
247	#433	—	158	2	no	—
248	#433	—	158	2	no	—
249	#432	—	158	2	no	—
250	#431	—	158	2	no	—
251	C₂×#108	—	79	2	no	—
252	C₂×#108	—	79	1	no	—
253	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
254	#427	—	79	1	no	—
255	#423	—	79	2	no	—
256	C₂×C₄⋊C₈	—	79	1	no	—
257	C₂×#104	—	79	2	no	—
258	C₂×#104	C₂×D₇₉	1	2	yes	—
259	#416	—	79	2	no	—
260	#408	—	79	2	no	—
261	#408	C₂×D₇₉	1	2	yes	—
262	#405	—	79	2	no	—
263	#405	—	79	2	no	—
264	C₂×#97	—	79	1	no	—
265	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
266	C₂×C₄×C₈	—	79	1	no	—
267	C₄×C₄⋊C₄	—	79	1	no	—
268	#339	—	79	2	no	—
269	#339	—	79	2	no	—
270	#336	—	79	1	no	—
271	#336	—	79	1	no	—
272	C₂×#41	C₂²×D₇₉	1	2	yes	—
273	#135	—	2	2	no	—
274	#135	—	2	2	no	—
275	C₂×Q₁₆	C₄×D₇₉	1	1	yes	characteristic
276	C₂×SD₁₆	C₄×D₇₉	1	2	yes	—
277	C₂×D₈	C₄×D₇₉	1	1	yes	characteristic
278	C₂×M₁₆	—	79	2	no	—
279	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
280	C₂²×C₈	—	79	1	no	—
281	C₂²×C₈	—	79	1	no	—
282	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
284	C₄×Q₈	—	79	2	no	—
285	C₄×Q₈	—	79	2	no	—
286	C₄×D₄	—	79	2	no	—
287	C₄×D₄	—	79	2	no	—
288	C₄×D₄	—	158	2	no	—
289	C₄×D₄	—	158	2	no	—
290	#117	—	79	2	no	—
291	#117	—	158	2	no	—
292	C₂×C₄⋊C₄	—	158	1	no	—
293	C₂×C₄²	—	79	1	no	—
294	C₂×C₄²	—	79	1	no	—
295	C₂×C₄²	—	158	2	no	—
296	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
297	#108	—	2	2	no	—
298	#108	—	316	2	no	—
299	#108	—	158	2	no	—
300	#107	—	79	1	no	—
301	#107	—	79	1	no	—
302	#106	—	79	2	no	—
303	C₄⋊C₈	—	79	2	no	—
304	C₄⋊C₈	—	79	2	no	—
305	C₄⋊C₈	—	158	2	no	—
306	C₄⋊C₈	—	158	2	no	—
307	#104	—	4	2	no	—
308	#104	—	316	2	no	—
309	#103	—	79	2	no	—
310	#103	—	79	2	no	—
311	#102	—	79	2	no	—
312	#102	—	79	2	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	C₂²⋊C₈	—	158	2	no	—
316	C₂²⋊C₈	—	158	2	no	—
317	#97	—	2	2	no	—
318	#97	—	158	2	no	—
319	#97	—	158	2	no	—
320	#97	—	158	2	no	—
321	C₄×C₈	—	79	1	no	—
322	C₄×C₈	—	79	1	no	—
323	C₄×C₈	—	79	1	no	—
324	C₄×C₈	—	79	1	no	—
325	C₄×C₈	—	158	2	no	—
326	C₄×C₈	—	158	2	no	—
327	#95	—	158	1	no	—
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	79	1	no	—
338	C₂²×C₄	—	79	1	no	—
339	C₂²×C₄	—	158	1	no	—
340	C₂²×C₄	—	158	2	no	—
341	C₂²×C₄	—	158	2	no	—
342	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
343	Q₁₆	—	2	2	no	—
344	SD₁₆	—	2	4	no	—
345	D₈	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	158	2	no	—
349	M₁₆	—	158	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	79	1	no	—
354	C₂×C₈	—	79	1	no	—
355	C₂×C₈	—	79	2	no	—
356	C₂×C₈	—	158	2	no	—
357	C₂×C₈	—	158	1	no	—
358	C₂×C₈	—	158	1	no	—
359	C₂×C₈	—	158	1	no	—
360	C₂×C₈	—	158	1	no	—
361	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
362	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
363	C₂×C₈	D₄×D₇₉	1	2	yes	—
364	C₂×C₈	#11929623	1	2	yes	—
365	C₂×C₈	#11929623	1	2	yes	—
366	C₄⋊C₄	—	316	2	no	—
367	C₄⋊C₄	—	79	2	no	—
368	C₄⋊C₄	—	79	2	no	—
369	C₄⋊C₄	—	158	2	no	—
370	C₄⋊C₄	—	158	2	no	—
371	C₂²⋊C₄	—	158	2	no	—
372	C₂²⋊C₄	—	158	2	no	—
373	C₂²⋊C₄	—	158	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	79	1	no	—
377	C₄²	—	79	1	no	—
378	C₄²	—	79	1	no	—
379	C₄²	—	79	1	no	—
380	C₄²	—	158	2	no	—
381	C₄²	—	158	2	no	—
382	C₄²	—	158	1	no	—
383	C₄²	—	158	1	no	—
384	C₄²	—	158	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	#41×D₇₉	1	1	yes	characteristic
387	Q₈	—	2	2	no	—
388	Q₈	—	2	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	316	4	no	—
400	C₂×C₄	—	316	1	no	—
401	C₂×C₄	—	316	1	no	—
402	C₂×C₄	—	316	1	no	—
403	C₂×C₄	—	316	1	no	—
404	C₂×C₄	—	79	1	no	—
405	C₂×C₄	—	79	1	no	—
406	C₂×C₄	—	79	1	no	—
407	C₂×C₄	—	79	1	no	—
408	C₂×C₄	—	632	2	no	—
409	C₂×C₄	—	158	2	no	—
410	C₂×C₄	—	158	2	no	—
411	C₂×C₄	—	158	2	no	—
412	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
414	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
415	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
416	C₂×C₄	#14579206	1	1	yes	characteristic
417	C₂×C₄	#14579208	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	316	2	no	—
421	C₈	—	158	2	no	—
422	C₈	—	158	1	no	—
423	C₈	—	158	1	no	—
424	C₈	#14579117	1	2	yes	—
425	C₈	#14579117	1	2	yes	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
432	C₂²	#19099277	1	1	yes	characteristic
433	C₂²	#19099282	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	8	1	no	—
436	C₄	—	316	2	no	—
437	C₄	—	316	2	no	—
438	C₄	—	79	2	no	—
439	C₄	—	632	1	no	—
440	C₄	—	158	1	no	—
441	C₄	—	158	1	no	—
442	C₄	—	158	1	no	—
443	C₄	C₂×#14579117	1	1	yes	characteristic
444	C₄	#19099042	1	1	yes	characteristic
445	C₄	#19099213	1	1	yes	characteristic
446	C₄	#19099233	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	8	2	no	—
450	C₂	#23766348	1	1	yes	characteristic
451	C₂	#444×D₇₉	1	1	yes	characteristic
452	C₂	#23772314	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1975	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#135×C₇₉	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1975	D₇₉
hypocenter	C₇₉	#22803
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1975

Complements

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

N	H ≅ G/N	type
2. #23772062	C₂	semidirect
4. #23764051	C₂	semidirect
5. #23764045	C₂	semidirect
6. #23763570	C₂	semidirect
7. #23763418	C₂	semidirect
8. #23763287	C₂	semidirect
9. #23763284	C₂	semidirect
10. #23763268	C₂	semidirect
13. Q₁₆×Dic₇₉	C₄	semidirect
14. Q₁₆×Dic₇₉	C₄	semidirect
15. SD₁₆×Dic₇₉	C₄	semidirect
16. SD₁₆×Dic₇₉	C₄	semidirect
17. D₈×Dic₇₉	C₄	semidirect
18. D₈×Dic₇₉	C₄	semidirect
238. C₇₉	#22803	semidirect

Maximal subgroups

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

subgroup	index
#135×Dic₇₉	2
#23772062	2
#23764294	2
#23764051	2
#23764045	2
#23763570	2
#23763418	2
#23763287	2
#23763284	2
#23763268	2
C₇₉×#1975	2
#22803	79