Subgroups — C₇₃×#32797 #32942201

Order 18688.

868 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2860	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2042	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2012	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2012	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2011	C₂	1	1	yes	maximal, characteristic
11	C₇₃×#1839	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#126×C₇₃	—	2	1	no	—
17	C₂×#124×C₇₃	C₂²	1	2	yes	—
18	C₂×#124×C₇₃	C₂²	1	2	yes	—
19	C₂×#103×C₇₃	C₂²	1	2	yes	—
20	C₂×#103×C₇₃	C₂²	1	2	yes	—
21	C₂×#103×C₇₃	C₂²	1	2	yes	—
22	C₂×#102×C₇₃	C₂²	1	2	yes	—
23	C₂×#102×C₇₃	C₂²	1	2	yes	—
24	C₂×#102×C₇₃	C₂²	1	2	yes	—
25	#390×C₇₃	—	2	1	no	—
26	#390×C₇₃	—	2	1	no	—
27	#390×C₇₃	—	2	1	no	—
28	#390×C₇₃	—	2	1	no	—
29	#390×C₇₃	C₂²	1	1	yes	characteristic
30	#390×C₇₃	C₂²	1	1	yes	characteristic
31	#390×C₇₃	C₂²	1	1	yes	characteristic
32	#389×C₇₃	C₂²	1	1	yes	characteristic
33	#389×C₇₃	C₂²	1	1	yes	characteristic
34	#389×C₇₃	C₂²	1	1	yes	characteristic
35	#388×C₇₃	—	2	1	no	—
36	#388×C₇₃	—	2	1	no	—
37	#388×C₇₃	—	2	1	no	—
38	C₄³×C₇₃	C₂²	1	1	yes	characteristic
39	#336×C₇₃	C₂²	1	1	yes	characteristic
40	#336×C₇₃	C₂²	1	2	yes	—
41	#336×C₇₃	C₂²	1	2	yes	—
42	#336×C₇₃	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₇₃	—	2	1	no	—
45	C₂²×D₄×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
48	C₂×SD₁₆×C₇₃	—	4	2	no	—
49	C₂×SD₁₆×C₇₃	—	4	2	no	—
50	C₂×SD₁₆×C₇₃	—	4	2	no	—
51	C₂×D₈×C₇₃	—	4	2	no	—
52	C₂×D₈×C₇₃	—	4	2	no	—
53	C₂×D₈×C₇₃	—	4	2	no	—
54	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₇₃	—	4	2	no	—
57	#127×C₇₃	—	4	2	no	—
58	#126×C₇₃	—	4	4	no	—
59	#124×C₇₃	—	4	2	no	—
60	#124×C₇₃	—	4	2	no	—
61	#124×C₇₃	—	4	2	no	—
62	#124×C₇₃	—	4	2	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
81	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
88	#103×C₇₃	—	4	2	no	—
89	#103×C₇₃	—	4	2	no	—
90	#103×C₇₃	—	4	2	no	—
91	#102×C₇₃	—	4	2	no	—
92	#102×C₇₃	—	4	2	no	—
93	#102×C₇₃	—	4	2	no	—
94	#95×C₇₃	—	2	1	no	—
95	#95×C₇₃	—	2	1	no	—
96	#95×C₇₃	—	2	1	no	—
97	C₂⁴×C₇₃	—	2	1	no	—
98	C₂⁴×C₇₃	—	2	2	no	—
99	C₂×Q₈×C₇₃	—	2	2	no	—
100	C₂×Q₈×C₇₃	—	2	2	no	—
101	C₂×Q₈×C₇₃	—	2	2	no	—
102	C₂×Q₈×C₇₃	—	2	2	no	—
103	C₂×Q₈×C₇₃	—	2	2	no	—
104	C₂×Q₈×C₇₃	—	2	2	no	—
105	C₂×D₄×C₇₃	—	2	2	no	—
106	C₂×D₄×C₇₃	—	2	2	no	—
107	C₂×D₄×C₇₃	—	2	2	no	—
108	C₂×D₄×C₇₃	—	2	2	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	1	no	—
112	C₂×D₄×C₇₃	—	2	2	no	—
113	C₂×D₄×C₇₃	—	2	2	no	—
114	C₂×D₄×C₇₃	—	2	1	no	—
115	C₂×D₄×C₇₃	—	4	2	no	—
116	C₂×D₄×C₇₃	—	4	2	no	—
117	C₂×D₄×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	—	4	2	no	—
119	C₂×D₄×C₇₃	—	4	2	no	—
120	C₂×D₄×C₇₃	—	4	2	no	—
121	C₂²×C₄×C₇₃	—	2	1	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	1	no	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
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	SD₁₆×C₇₃	—	4	8	no	—
133	D₈×C₇₃	—	4	8	no	—
134	C₂×C₈×C₇₃	—	2	2	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	C₂×C₈×C₇₃	—	2	2	no	—
140	C₄⋊C₄×C₇₃	—	2	1	no	—
141	C₄⋊C₄×C₇₃	—	2	2	no	—
142	C₄⋊C₄×C₇₃	—	2	2	no	—
143	C₄⋊C₄×C₇₃	—	2	1	no	—
144	C₄⋊C₄×C₇₃	—	4	2	no	—
145	C₄⋊C₄×C₇₃	—	4	2	no	—
146	C₄⋊C₄×C₇₃	—	4	2	no	—
147	C₄⋊C₄×C₇₃	—	4	2	no	—
148	C₄⋊C₄×C₇₃	—	4	2	no	—
149	C₂²⋊C₄×C₇₃	—	4	2	no	—
150	C₂²⋊C₄×C₇₃	—	4	2	no	—
151	C₂²⋊C₄×C₇₃	—	4	4	no	—
152	C₂²⋊C₄×C₇₃	—	4	4	no	—
153	C₂²⋊C₄×C₇₃	—	4	4	no	—
154	C₂²⋊C₄×C₇₃	—	4	4	no	—
155	C₂²⋊C₄×C₇₃	—	4	2	no	—
156	C₂²⋊C₄×C₇₃	—	4	2	no	—
157	C₂²⋊C₄×C₇₃	—	4	2	no	—
158	C₂²⋊C₄×C₇₃	—	4	2	no	—
159	C₄²×C₇₃	—	2	2	no	—
160	C₄²×C₇₃	—	2	2	no	—
161	C₄²×C₇₃	—	2	2	no	—
162	C₄²×C₇₃	—	2	1	no	—
163	C₄²×C₇₃	—	2	1	no	—
164	C₄²×C₇₃	—	2	2	no	—
165	C₄²×C₇₃	—	4	1	no	—
166	C₄²×C₇₃	—	4	1	no	—
167	C₂³×C₇₃	—	4	2	no	—
168	C₂³×C₇₃	—	4	2	no	—
169	C₂³×C₇₃	—	4	2	no	—
170	C₂³×C₇₃	—	4	1	no	—
171	C₂³×C₇₃	—	4	1	no	—
172	C₂³×C₇₃	—	4	1	no	—
173	C₂³×C₇₃	—	4	1	no	—
174	C₂³×C₇₃	—	4	2	no	—
175	C₂³×C₇₃	—	4	1	no	—
176	C₂³×C₇₃	—	4	2	no	—
177	C₂³×C₇₃	—	4	1	no	—
178	C₂³×C₇₃	—	4	1	no	—
179	C₂³×C₇₃	—	4	2	no	—
180	C₂³×C₇₃	—	4	2	no	—
181	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₇₃	—	4	2	no	—
183	Q₈×C₇₃	—	4	2	no	—
184	Q₈×C₇₃	—	4	2	no	—
185	Q₈×C₇₃	—	4	2	no	—
186	D₄×C₇₃	—	4	2	no	—
187	D₄×C₇₃	—	4	2	no	—
188	D₄×C₇₃	—	4	2	no	—
189	D₄×C₇₃	—	4	2	no	—
190	D₄×C₇₃	—	4	2	no	—
191	D₄×C₇₃	—	4	2	no	—
192	D₄×C₇₃	—	8	4	no	—
193	D₄×C₇₃	—	8	4	no	—
194	C₂×C₄×C₇₃	—	2	1	no	—
195	C₂×C₄×C₇₃	—	2	1	no	—
196	C₂×C₄×C₇₃	—	2	1	no	—
197	C₂×C₄×C₇₃	—	2	1	no	—
198	C₂×C₄×C₇₃	—	2	1	no	—
199	C₂×C₄×C₇₃	—	2	1	no	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	2	1	no	—
202	C₂×C₄×C₇₃	—	2	1	no	—
203	C₂×C₄×C₇₃	—	2	1	no	—
204	C₂×C₄×C₇₃	—	2	1	no	—
205	C₂×C₄×C₇₃	—	2	1	no	—
206	C₂×C₄×C₇₃	—	2	1	no	—
207	C₂×C₄×C₇₃	—	2	1	no	—
208	C₂×C₄×C₇₃	—	2	1	no	—
209	C₂×C₄×C₇₃	—	2	1	no	—
210	C₂×C₄×C₇₃	—	4	2	no	—
211	C₂×C₄×C₇₃	—	4	2	no	—
212	C₂×C₄×C₇₃	—	4	1	no	—
213	C₂×C₄×C₇₃	—	4	1	no	—
214	C₂×C₄×C₇₃	—	4	1	no	—
215	C₂×C₄×C₇₃	—	4	2	no	—
216	C₂×C₄×C₇₃	—	4	1	no	—
217	C₂×C₄×C₇₃	—	4	1	no	—
218	C₂×C₄×C₇₃	—	4	1	no	—
219	C₂×C₄×C₇₃	—	4	1	no	—
220	C₂×C₄×C₇₃	—	4	1	no	—
221	C₂×C₄×C₇₃	—	4	1	no	—
222	C₂×C₄×C₇₃	#135	1	2	yes	—
223	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
225	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
228	C₈×C₇₃	—	4	2	no	—
229	C₈×C₇₃	—	4	2	no	—
230	C₂²×C₇₃	—	8	1	no	—
231	C₂²×C₇₃	—	8	2	no	—
232	C₂²×C₇₃	—	8	2	no	—
233	C₂²×C₇₃	—	8	1	no	—
234	C₂²×C₇₃	—	8	2	no	—
235	C₂²×C₇₃	—	8	1	no	—
236	C₂²×C₇₃	—	8	2	no	—
237	C₂²×C₇₃	—	8	1	no	—
238	C₂²×C₇₃	—	8	2	no	—
239	C₂²×C₇₃	—	8	1	no	—
240	C₂²×C₇₃	—	8	2	no	—
241	C₂²×C₇₃	—	8	1	no	—
242	C₂²×C₇₃	—	8	2	no	—
243	C₂²×C₇₃	—	8	1	no	—
244	C₂²×C₇₃	#535	1	1	yes	characteristic
245	C₂²×C₇₃	#535	1	1	yes	characteristic
246	C₂²×C₇₃	#535	1	1	yes	characteristic
247	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
248	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂²×C₇₃	#575	1	1	yes	characteristic
250	C₂²×C₇₃	#575	1	1	yes	characteristic
251	C₄×C₇₃	—	2	2	no	—
252	C₄×C₇₃	—	2	2	no	—
253	C₄×C₇₃	—	4	1	no	—
254	C₄×C₇₃	—	4	1	no	—
255	C₄×C₇₃	—	4	1	no	—
256	C₄×C₇₃	—	4	1	no	—
257	C₄×C₇₃	—	8	2	no	—
258	C₄×C₇₃	—	8	1	no	—
259	C₄×C₇₃	—	8	1	no	—
260	C₄×C₇₃	—	8	1	no	—
261	C₄×C₇₃	#560	1	2	yes	—
262	C₄×C₇₃	#560	1	2	yes	—
263	#32797	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
264	C₂×C₇₃	—	16	2	no	—
265	C₂×C₇₃	—	16	1	no	—
266	C₂×C₇₃	#2818	1	1	yes	characteristic
267	C₂×C₇₃	#3207	1	1	yes	characteristic
268	C₂×C₇₃	#3211	1	1	yes	characteristic
269	C₂×C₇₃	#3212	1	1	yes	characteristic
270	C₂×C₇₃	#3213	1	1	yes	characteristic
271	C₂×C₇₃	#3214	1	1	yes	characteristic
272	C₂×C₇₃	#3219	1	1	yes	characteristic
273	#2860	C₂×C₇₃	1	1	yes	characteristic, complemented
274	#2858	C₂×C₇₃	1	1	yes	characteristic, complemented
275	#2043	C₂×C₇₃	1	1	yes	characteristic, complemented
276	#2042	C₂×C₇₃	1	2	yes	complemented
277	#2042	C₂×C₇₃	1	2	yes	complemented
278	#2041	C₂×C₇₃	1	1	yes	characteristic, complemented
279	#2013	C₂×C₇₃	1	1	yes	characteristic, complemented
280	#2012	C₂×C₇₃	1	2	yes	complemented
281	#2012	C₂×C₇₃	1	2	yes	complemented
282	#2011	C₂×C₇₃	1	1	yes	characteristic
283	#1839	C₂×C₇₃	1	1	yes	characteristic, complemented
284	C₇₃	#32797	1	1	yes	characteristic, direct product factor, Sylow
285	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
286	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
287	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
288	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
289	C₂×#126	—	2	1	no	—
290	C₂×#124	C₂²×C₇₃	1	2	yes	—
291	C₂×#124	C₂²×C₇₃	1	2	yes	—
292	C₂×#103	C₂²×C₇₃	1	2	yes	—
293	C₂×#103	C₂²×C₇₃	1	2	yes	—
294	C₂×#103	C₂²×C₇₃	1	2	yes	—
295	C₂×#102	C₂²×C₇₃	1	2	yes	—
296	C₂×#102	C₂²×C₇₃	1	2	yes	—
297	C₂×#102	C₂²×C₇₃	1	2	yes	—
298	#390	—	2	1	no	—
299	#390	—	2	1	no	—
300	#390	—	2	1	no	—
301	#390	—	2	1	no	—
302	#390	C₂²×C₇₃	1	1	yes	characteristic
303	#390	C₂²×C₇₃	1	1	yes	characteristic
304	#390	C₂²×C₇₃	1	1	yes	characteristic
305	#389	C₂²×C₇₃	1	1	yes	characteristic
306	#389	C₂²×C₇₃	1	1	yes	characteristic
307	#389	C₂²×C₇₃	1	1	yes	characteristic
308	#388	—	2	1	no	—
309	#388	—	2	1	no	—
310	#388	—	2	1	no	—
311	C₄³	C₂²×C₇₃	1	1	yes	characteristic
312	#336	C₂²×C₇₃	1	1	yes	characteristic
313	#336	C₂²×C₇₃	1	2	yes	—
314	#336	C₂²×C₇₃	1	2	yes	—
315	#336	C₂²×C₇₃	1	1	yes	characteristic
316	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
320	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
321	C₂×SD₁₆	—	4	2	no	—
322	C₂×SD₁₆	—	4	2	no	—
323	C₂×SD₁₆	—	4	2	no	—
324	C₂×D₈	—	4	2	no	—
325	C₂×D₈	—	4	2	no	—
326	C₂×D₈	—	4	2	no	—
327	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
328	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
329	C₄⋊Q₈	—	4	2	no	—
330	#127	—	4	2	no	—
331	#126	—	4	4	no	—
332	#124	—	4	2	no	—
333	#124	—	4	2	no	—
334	#124	—	4	2	no	—
335	#124	—	4	2	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
355	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
356	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
357	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
361	#103	—	4	2	no	—
362	#103	—	4	2	no	—
363	#103	—	4	2	no	—
364	#102	—	4	2	no	—
365	#102	—	4	2	no	—
366	#102	—	4	2	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	C₂⁴	—	2	1	no	—
371	C₂⁴	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	4	2	no	—
390	C₂×D₄	—	4	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
405	SD₁₆	—	4	8	no	—
406	D₈	—	4	8	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₂²⋊C₄	—	4	4	no	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂²⋊C₄	—	4	2	no	—
430	C₂²⋊C₄	—	4	2	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	4	1	no	—
439	C₄²	—	4	1	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	4	1	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	1	no	—
451	C₂³	—	4	1	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	2	no	—
465	D₄	—	8	4	no	—
466	D₄	—	8	4	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	#135×C₇₃	1	2	yes	—
496	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
497	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
498	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
499	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
500	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
501	C₈	—	4	2	no	—
502	C₈	—	4	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	1	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	1	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	1	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	1	no	—
515	C₂²	—	8	1	no	—
516	C₂²	—	8	2	no	—
517	C₂²	#535×C₇₃	1	1	yes	characteristic
518	C₂²	#535×C₇₃	1	1	yes	characteristic
519	C₂²	#535×C₇₃	1	1	yes	characteristic
520	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
521	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
522	C₂²	#575×C₇₃	1	1	yes	characteristic
523	C₂²	#575×C₇₃	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	2	2	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	8	1	no	—
531	C₄	—	8	1	no	—
532	C₄	—	8	1	no	—
533	C₄	—	8	2	no	—
534	C₄	#560×C₇₃	1	2	yes	—
535	C₄	#560×C₇₃	1	2	yes	—
536	C₂	—	16	2	no	—
537	C₂	—	16	1	no	—
538	C₂	C₇₃×#2818	1	1	yes	characteristic
539	C₂	C₇₃×#3207	1	1	yes	characteristic
540	C₂	C₇₃×#3211	1	1	yes	characteristic
541	C₂	C₇₃×#3212	1	1	yes	characteristic
542	C₂	C₇₃×#3213	1	1	yes	characteristic
543	C₂	C₇₃×#3214	1	1	yes	characteristic
544	C₂	C₇₃×#3219	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2860	C₂	semidirect
2. C₇₃×#2858	C₂	semidirect
3. C₇₃×#2043	C₂	semidirect
4. C₇₃×#2042	C₂	semidirect
5. C₇₃×#2042	C₂	semidirect
6. C₇₃×#2041	C₂	semidirect
7. C₇₃×#2013	C₂	semidirect
8. C₇₃×#2012	C₂	semidirect
9. C₇₃×#2012	C₂	semidirect
11. C₇₃×#1839	C₂	semidirect
263. #32797	C₇₃	direct (N × H)
273. #2860	C₂×C₇₃	semidirect
274. #2858	C₂×C₇₃	semidirect
275. #2043	C₂×C₇₃	semidirect
276. #2042	C₂×C₇₃	semidirect
277. #2042	C₂×C₇₃	semidirect
278. #2041	C₂×C₇₃	semidirect
279. #2013	C₂×C₇₃	semidirect
280. #2012	C₂×C₇₃	semidirect
281. #2012	C₂×C₇₃	semidirect
283. #1839	C₂×C₇₃	semidirect
284. C₇₃	#32797	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#2860	2
C₇₃×#2858	2
C₇₃×#2043	2
C₇₃×#2042	2
C₇₃×#2041	2
C₇₃×#2013	2
C₇₃×#2012	2
C₇₃×#2011	2
C₇₃×#1839	2
#32797	73

Subgroups — C73×#32797 #32942201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#32797 #32942201