Subgroups — C₇₃×#25658 #32935062

Order 18688.

1076 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#490×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#479×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1982	C₂	1	1	yes	maximal, characteristic
9	C₇₃×#1864	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₇₃	—	2	4	no	—
13	#559×C₇₃	—	2	4	no	—
14	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₇₃	—	2	1	no	—
17	C₂×#124×C₇₃	C₂²	1	2	yes	—
18	C₂×#123×C₇₃	—	2	2	no	—
19	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₇₃	—	2	1	no	—
22	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
23	#490×C₇₃	—	2	4	no	—
24	#479×C₇₃	—	2	4	no	—
25	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#103×C₇₃	C₂²	1	2	yes	—
29	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#102×C₇₃	C₂²	1	2	yes	—
32	C₂×#102×C₇₃	C₂²	1	2	yes	—
33	C₂×#102×C₇₃	C₂²	1	2	yes	—
34	C₂×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
36	#398×C₇₃	—	2	1	no	—
37	#395×C₇₃	—	2	1	no	—
38	#389×C₇₃	—	2	2	no	—
39	#389×C₇₃	C₂²	1	2	yes	—
40	#389×C₇₃	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	#340×C₇₃	C₂²	1	2	yes	—
43	#336×C₇₃	C₂²	1	2	yes	—
44	#336×C₇₃	C₂²	1	2	yes	—
45	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₇₃	—	2	1	no	—
48	C₂²×D₄×C₇₃	—	2	1	no	—
49	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₇₃	—	2	2	no	—
51	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
54	#127×C₇₃	—	2	2	no	—
55	#127×C₇₃	D₄	1	4	yes	—
56	#125×C₇₃	—	2	2	no	—
57	#125×C₇₃	—	2	2	no	—
58	#124×C₇₃	—	2	8	no	—
59	#124×C₇₃	—	2	4	no	—
60	#124×C₇₃	—	2	4	no	—
61	#123×C₇₃	—	2	16	no	—
62	C₄×Q₈×C₇₃	—	2	2	no	—
63	C₄×Q₈×C₇₃	—	2	2	no	—
64	C₄×Q₈×C₇₃	—	2	2	no	—
65	C₄×Q₈×C₇₃	D₄	1	4	yes	—
66	C₄×D₄×C₇₃	—	2	8	no	—
67	C₄×D₄×C₇₃	—	2	4	no	—
68	C₄×D₄×C₇₃	—	2	4	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
83	C₂×C₄²×C₇₃	—	2	1	no	—
84	C₂×C₄²×C₇₃	—	2	1	no	—
85	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
87	#107×C₇₃	—	2	2	no	—
88	#106×C₇₃	—	2	2	no	—
89	C₄⋊C₈×C₇₃	—	2	2	no	—
90	#103×C₇₃	—	2	2	no	—
91	#103×C₇₃	—	2	2	no	—
92	#103×C₇₃	—	2	4	no	—
93	#102×C₇₃	—	2	4	no	—
94	#102×C₇₃	—	2	4	no	—
95	#102×C₇₃	—	2	4	no	—
96	#102×C₇₃	—	2	4	no	—
97	#97×C₇₃	—	2	2	no	—
98	#95×C₇₃	—	2	1	no	—
99	#95×C₇₃	—	2	2	no	—
100	#95×C₇₃	—	2	2	no	—
101	C₂⁴×C₇₃	—	2	2	no	—
102	C₂×Q₈×C₇₃	—	2	2	no	—
103	C₂×Q₈×C₇₃	—	2	1	no	—
104	C₂×Q₈×C₇₃	—	2	2	no	—
105	C₂×Q₈×C₇₃	—	2	2	no	—
106	C₂×Q₈×C₇₃	—	4	2	no	—
107	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₇₃	—	2	4	no	—
109	C₂×D₄×C₇₃	—	2	4	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	2	no	—
113	C₂×D₄×C₇₃	—	2	2	no	—
114	C₂×D₄×C₇₃	—	2	2	no	—
115	C₂×D₄×C₇₃	—	4	4	no	—
116	C₂×D₄×C₇₃	—	8	1	no	—
117	C₂×D₄×C₇₃	—	8	1	no	—
118	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₇₃	—	2	2	no	—
120	C₂²×C₄×C₇₃	—	2	1	no	—
121	C₂²×C₄×C₇₃	—	2	1	no	—
122	C₂²×C₄×C₇₃	—	2	8	no	—
123	C₂²×C₄×C₇₃	—	2	1	no	—
124	C₂²×C₄×C₇₃	—	2	1	no	—
125	C₂²×C₄×C₇₃	—	8	2	no	—
126	C₂²×C₄×C₇₃	—	8	2	no	—
127	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₇₃	—	2	2	no	—
133	C₂×C₈×C₇₃	—	2	1	no	—
134	C₂×C₈×C₇₃	—	2	1	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	—	2	2	no	—
138	C₂×C₈×C₇₃	—	2	2	no	—
139	C₄⋊C₄×C₇₃	—	2	4	no	—
140	C₄⋊C₄×C₇₃	—	2	2	no	—
141	C₄⋊C₄×C₇₃	—	2	4	no	—
142	C₄⋊C₄×C₇₃	—	2	1	no	—
143	C₄⋊C₄×C₇₃	—	2	2	no	—
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₄⋊C₄×C₇₃	—	2	1	no	—
146	C₄⋊C₄×C₇₃	—	2	1	no	—
147	C₄⋊C₄×C₇₃	—	2	1	no	—
148	C₄⋊C₄×C₇₃	—	4	4	no	—
149	C₄⋊C₄×C₇₃	—	4	2	no	—
150	C₄⋊C₄×C₇₃	—	4	2	no	—
151	C₄⋊C₄×C₇₃	—	8	2	no	—
152	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₇₃	#41	1	4	yes	—
154	C₂²⋊C₄×C₇₃	—	2	8	no	—
155	C₂²⋊C₄×C₇₃	—	2	8	no	—
156	C₂²⋊C₄×C₇₃	—	2	8	no	—
157	C₄²×C₇₃	—	2	4	no	—
158	C₄²×C₇₃	—	2	2	no	—
159	C₄²×C₇₃	—	2	2	no	—
160	C₄²×C₇₃	—	8	1	no	—
161	C₄²×C₇₃	C₂×D₄	1	2	yes	—
162	C₄²×C₇₃	C₂×D₄	1	2	yes	—
163	C₂³×C₇₃	—	2	4	no	—
164	C₂³×C₇₃	—	4	2	no	—
165	C₂³×C₇₃	—	4	2	no	—
166	C₂³×C₇₃	—	4	2	no	—
167	C₂³×C₇₃	—	4	2	no	—
168	C₂³×C₇₃	—	4	2	no	—
169	C₂³×C₇₃	—	4	2	no	—
170	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₇₃	—	2	2	no	—
172	Q₈×C₇₃	—	2	2	no	—
173	Q₈×C₇₃	—	4	4	no	—
174	Q₈×C₇₃	—	4	2	no	—
175	D₄×C₇₃	—	2	4	no	—
176	D₄×C₇₃	—	2	4	no	—
177	D₄×C₇₃	—	4	8	no	—
178	D₄×C₇₃	—	4	2	no	—
179	D₄×C₇₃	—	4	2	no	—
180	D₄×C₇₃	—	8	4	no	—
181	C₂×C₄×C₇₃	—	2	2	no	—
182	C₂×C₄×C₇₃	—	2	1	no	—
183	C₂×C₄×C₇₃	—	2	1	no	—
184	C₂×C₄×C₇₃	—	2	2	no	—
185	C₂×C₄×C₇₃	—	2	2	no	—
186	C₂×C₄×C₇₃	—	2	2	no	—
187	C₂×C₄×C₇₃	—	2	2	no	—
188	C₂×C₄×C₇₃	—	2	4	no	—
189	C₂×C₄×C₇₃	—	2	2	no	—
190	C₂×C₄×C₇₃	—	2	2	no	—
191	C₂×C₄×C₇₃	—	2	2	no	—
192	C₂×C₄×C₇₃	—	2	2	no	—
193	C₂×C₄×C₇₃	—	4	2	no	—
194	C₂×C₄×C₇₃	—	4	2	no	—
195	C₂×C₄×C₇₃	—	4	2	no	—
196	C₂×C₄×C₇₃	—	4	1	no	—
197	C₂×C₄×C₇₃	—	4	1	no	—
198	C₂×C₄×C₇₃	—	4	1	no	—
199	C₂×C₄×C₇₃	—	4	1	no	—
200	C₂×C₄×C₇₃	—	4	2	no	—
201	C₂×C₄×C₇₃	—	4	1	no	—
202	C₂×C₄×C₇₃	—	4	1	no	—
203	C₂×C₄×C₇₃	—	8	8	no	—
204	C₂×C₄×C₇₃	#120	1	2	yes	—
205	C₂×C₄×C₇₃	#120	1	2	yes	—
206	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
209	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
210	C₈×C₇₃	—	4	1	no	—
211	C₈×C₇₃	—	4	1	no	—
212	C₈×C₇₃	—	4	2	no	—
213	C₂²×C₇₃	—	4	4	no	—
214	C₂²×C₇₃	—	4	4	no	—
215	C₂²×C₇₃	—	4	4	no	—
216	C₂²×C₇₃	—	8	2	no	—
217	C₂²×C₇₃	—	8	2	no	—
218	C₂²×C₇₃	—	8	2	no	—
219	C₂²×C₇₃	—	8	2	no	—
220	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
221	C₂²×C₇₃	#548	1	2	yes	—
222	C₂²×C₇₃	#575	1	2	yes	—
223	C₂²×C₇₃	#576	1	1	yes	characteristic
224	C₂²×C₇₃	#577	1	1	yes	characteristic
225	C₄×C₇₃	—	2	2	no	—
226	C₄×C₇₃	—	2	2	no	—
227	C₄×C₇₃	—	4	4	no	—
228	C₄×C₇₃	—	4	2	no	—
229	C₄×C₇₃	—	4	2	no	—
230	C₄×C₇₃	—	4	2	no	—
231	C₄×C₇₃	—	4	2	no	—
232	C₄×C₇₃	—	8	1	no	—
233	C₄×C₇₃	—	8	1	no	—
234	C₄×C₇₃	#532	1	1	yes	characteristic
235	C₄×C₇₃	#536	1	1	yes	characteristic
236	C₄×C₇₃	#547	1	2	yes	—
237	#25658	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂×C₇₃	—	8	4	no	—
239	C₂×C₇₃	#2432	1	1	yes	characteristic
240	C₂×C₇₃	#3005	1	1	yes	characteristic
241	C₂×C₇₃	#3012	1	1	yes	characteristic
242	C₂×C₇₃	#3370	1	2	yes	—
243	C₂×C₇₃	#3371	1	2	yes	—
244	C₂×#559	C₂×C₇₃	1	1	yes	characteristic
245	C₂×#490	C₂×C₇₃	1	1	yes	characteristic
246	C₂×#479	C₂×C₇₃	1	1	yes	characteristic, complemented
247	#2584	C₂×C₇₃	1	1	yes	characteristic, complemented
248	#2042	C₂×C₇₃	1	2	yes	complemented
249	#2042	C₂×C₇₃	1	2	yes	complemented
250	#1985	C₂×C₇₃	1	1	yes	characteristic, complemented
251	#1982	C₂×C₇₃	1	1	yes	characteristic
252	#1864	C₂×C₇₃	1	2	yes	complemented
253	#1862	C₂×C₇₃	1	2	yes	complemented
254	#1763	C₂×C₇₃	1	1	yes	characteristic, complemented
255	C₇₃	#25658	1	1	yes	characteristic, direct product factor, Sylow
256	#559	—	2	4	no	—
257	#559	—	2	4	no	—
258	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
259	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
260	C₂×#124	—	2	1	no	—
261	C₂×#124	C₂²×C₇₃	1	2	yes	—
262	C₂×#123	—	2	2	no	—
263	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
265	C₂×C₄×D₄	—	2	1	no	—
266	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
267	#490	—	2	4	no	—
268	#479	—	2	4	no	—
269	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
270	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
272	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
273	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
274	C₂×#103	C₂²×C₇₃	1	2	yes	—
275	C₂×#102	C₂²×C₇₃	1	2	yes	—
276	C₂×#102	C₂²×C₇₃	1	2	yes	—
277	C₂×#102	C₂²×C₇₃	1	2	yes	—
278	C₂×#102	C₂²×C₇₃	1	2	yes	—
279	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
280	#398	—	2	1	no	—
281	#395	—	2	1	no	—
282	#389	—	2	2	no	—
283	#389	C₂²×C₇₃	1	2	yes	—
284	#389	C₂²×C₇₃	1	2	yes	—
285	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
286	#340	C₂²×C₇₃	1	2	yes	—
287	#336	C₂²×C₇₃	1	2	yes	—
288	#336	C₂²×C₇₃	1	2	yes	—
289	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
290	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
294	C₂³×C₄	—	2	2	no	—
295	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
296	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
298	#127	—	2	2	no	—
299	#127	D₄×C₇₃	1	4	yes	—
300	#125	—	2	2	no	—
301	#125	—	2	2	no	—
302	#124	—	2	8	no	—
303	#124	—	2	4	no	—
304	#124	—	2	4	no	—
305	#123	—	2	16	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	D₄×C₇₃	1	4	yes	—
310	C₄×D₄	—	2	8	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	4	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
330	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
331	#107	—	2	2	no	—
332	#106	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	#103	—	2	2	no	—
335	#103	—	2	2	no	—
336	#103	—	2	4	no	—
337	#102	—	2	4	no	—
338	#102	—	2	4	no	—
339	#102	—	2	4	no	—
340	#102	—	2	4	no	—
341	#97	—	2	2	no	—
342	#95	—	2	1	no	—
343	#95	—	2	2	no	—
344	#95	—	2	2	no	—
345	C₂⁴	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	8	1	no	—
361	C₂×D₄	—	8	1	no	—
362	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	8	2	no	—
370	C₂²×C₄	—	8	2	no	—
371	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
375	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	4	4	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	8	2	no	—
396	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
397	C₄⋊C₄	#41×C₇₃	1	4	yes	—
398	C₂²⋊C₄	—	2	8	no	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₄²	—	2	4	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	8	1	no	—
405	C₄²	C₂×D₄×C₇₃	1	2	yes	—
406	C₄²	C₂×D₄×C₇₃	1	2	yes	—
407	C₂³	—	2	4	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
415	Q₈	—	2	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	4	4	no	—
418	Q₈	—	4	2	no	—
419	D₄	—	2	4	no	—
420	D₄	—	2	4	no	—
421	D₄	—	4	8	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	8	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	8	8	no	—
448	C₂×C₄	#120×C₇₃	1	2	yes	—
449	C₂×C₄	#120×C₇₃	1	2	yes	—
450	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
453	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
454	C₈	—	4	1	no	—
455	C₈	—	4	1	no	—
456	C₈	—	4	2	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	—	8	2	no	—
463	C₂²	—	8	2	no	—
464	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
465	C₂²	#548×C₇₃	1	2	yes	—
466	C₂²	#575×C₇₃	1	2	yes	—
467	C₂²	#576×C₇₃	1	1	yes	characteristic
468	C₂²	#577×C₇₃	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	2	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	#532×C₇₃	1	1	yes	characteristic
479	C₄	#536×C₇₃	1	1	yes	characteristic
480	C₄	#547×C₇₃	1	2	yes	—
481	C₂	—	8	4	no	—
482	C₂	C₇₃×#2432	1	1	yes	characteristic
483	C₂	C₇₃×#3005	1	1	yes	characteristic
484	C₂	C₇₃×#3012	1	1	yes	characteristic
485	C₂	C₇₃×#3370	1	2	yes	—
486	C₂	C₇₃×#3371	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#127×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×Q₈×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#479×C₇₃	C₂	semidirect
4. C₇₃×#2584	C₂	semidirect
5. C₇₃×#2042	C₂	semidirect
6. C₇₃×#2042	C₂	semidirect
7. C₇₃×#1985	C₂	semidirect
9. C₇₃×#1864	C₂	semidirect
10. C₇₃×#1862	C₂	semidirect
11. C₇₃×#1763	C₂	semidirect
237. #25658	C₇₃	direct (N × H)
246. C₂×#479	C₂×C₇₃	semidirect
247. #2584	C₂×C₇₃	semidirect
248. #2042	C₂×C₇₃	semidirect
249. #2042	C₂×C₇₃	semidirect
250. #1985	C₂×C₇₃	semidirect
252. #1864	C₂×C₇₃	semidirect
253. #1862	C₂×C₇₃	semidirect
254. #1763	C₂×C₇₃	semidirect
255. C₇₃	#25658	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#559×C₇₃	2
C₂×#490×C₇₃	2
C₂×#479×C₇₃	2
C₇₃×#2584	2
C₇₃×#2042	2
C₇₃×#1985	2
C₇₃×#1982	2
C₇₃×#1864	2
C₇₃×#1862	2
C₇₃×#1763	2
#25658	73

Subgroups — C73×#25658 #32935062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25658 #32935062