Subgroups — C₇₃×#32783 #32942187

Order 18688.

686 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2629	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2620	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2083	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2036	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2033	C₂	1	2	yes	maximal
9	C₇₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#107×C₇₃	C₂²	1	2	yes	—
18	C₂×#107×C₇₃	C₂²	1	2	yes	—
19	C₂×#103×C₇₃	C₂²	1	2	yes	—
20	C₂×#103×C₇₃	C₂²	1	2	yes	—
21	C₂×#102×C₇₃	C₂²	1	2	yes	—
22	C₂×#102×C₇₃	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
24	#398×C₇₃	—	2	2	no	—
25	#396×C₇₃	—	2	2	no	—
26	#396×C₇₃	—	2	2	no	—
27	#394×C₇₃	—	2	2	no	—
28	#391×C₇₃	C₂²	1	1	yes	characteristic
29	#390×C₇₃	C₂²	1	1	yes	characteristic
30	#389×C₇₃	C₂²	1	2	yes	—
31	#384×C₇₃	C₂²	1	1	yes	characteristic
32	#384×C₇₃	C₂²	1	1	yes	characteristic
33	#380×C₇₃	C₂²	1	2	yes	—
34	#340×C₇₃	C₂²	1	2	yes	—
35	#340×C₇₃	C₂²	1	2	yes	—
36	#336×C₇₃	C₂²	1	1	yes	characteristic
37	#336×C₇₃	C₂²	1	1	yes	characteristic
38	#336×C₇₃	C₂²	1	2	yes	—
39	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₇₃	—	2	1	no	—
41	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
45	#125×C₇₃	—	4	2	no	—
46	#124×C₇₃	—	4	2	no	—
47	C₂²⋊Q₈×C₇₃	—	4	2	no	—
48	#121×C₇₃	—	4	2	no	—
49	#117×C₇₃	—	4	2	no	—
50	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
51	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
53	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
54	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
66	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
68	#107×C₇₃	—	4	2	no	—
69	#107×C₇₃	—	4	2	no	—
70	#103×C₇₃	—	4	2	no	—
71	#103×C₇₃	—	4	2	no	—
72	#102×C₇₃	—	4	2	no	—
73	#102×C₇₃	—	4	2	no	—
74	C₂²⋊C₈×C₇₃	—	4	2	no	—
75	#95×C₇₃	—	2	2	no	—
76	#95×C₇₃	—	2	2	no	—
77	#95×C₇₃	—	2	2	no	—
78	C₂⁴×C₇₃	—	2	1	no	—
79	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
80	C₂×Q₈×C₇₃	—	2	2	no	—
81	C₂×Q₈×C₇₃	—	2	2	no	—
82	C₂×Q₈×C₇₃	—	2	1	no	—
83	C₂×Q₈×C₇₃	—	2	1	no	—
84	C₂×D₄×C₇₃	—	2	2	no	—
85	C₂×D₄×C₇₃	—	2	2	no	—
86	C₂×D₄×C₇₃	—	2	1	no	—
87	C₂×D₄×C₇₃	—	2	1	no	—
88	C₂×D₄×C₇₃	—	4	2	no	—
89	C₂×D₄×C₇₃	—	8	2	no	—
90	C₂²×C₄×C₇₃	—	2	2	no	—
91	C₂²×C₄×C₇₃	—	2	2	no	—
92	C₂²×C₄×C₇₃	—	2	1	no	—
93	C₂²×C₄×C₇₃	—	2	1	no	—
94	C₂²×C₄×C₇₃	—	2	1	no	—
95	C₂²×C₄×C₇₃	—	2	2	no	—
96	C₂²×C₄×C₇₃	—	2	2	no	—
97	C₂²×C₄×C₇₃	—	2	1	no	—
98	C₂²×C₄×C₇₃	—	2	1	no	—
99	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₇₃	—	2	2	no	—
104	C₂×C₈×C₇₃	—	2	2	no	—
105	C₂×C₈×C₇₃	—	2	2	no	—
106	C₂×C₈×C₇₃	—	2	2	no	—
107	C₂×C₈×C₇₃	—	2	2	no	—
108	C₂×C₈×C₇₃	—	2	2	no	—
109	C₄⋊C₄×C₇₃	—	2	2	no	—
110	C₄⋊C₄×C₇₃	—	2	2	no	—
111	C₄⋊C₄×C₇₃	—	2	2	no	—
112	C₄⋊C₄×C₇₃	—	2	2	no	—
113	C₄⋊C₄×C₇₃	—	2	2	no	—
114	C₄⋊C₄×C₇₃	—	2	2	no	—
115	C₄⋊C₄×C₇₃	—	4	2	no	—
116	C₄⋊C₄×C₇₃	—	4	2	no	—
117	C₄⋊C₄×C₇₃	—	4	4	no	—
118	C₄⋊C₄×C₇₃	—	8	2	no	—
119	C₄⋊C₄×C₇₃	—	8	2	no	—
120	C₄⋊C₄×C₇₃	—	8	2	no	—
121	C₂²⋊C₄×C₇₃	—	4	2	no	—
122	C₂²⋊C₄×C₇₃	—	4	2	no	—
123	C₂²⋊C₄×C₇₃	—	4	4	no	—
124	C₂²⋊C₄×C₇₃	—	4	2	no	—
125	C₂²⋊C₄×C₇₃	—	8	2	no	—
126	C₂²⋊C₄×C₇₃	—	8	2	no	—
127	C₄²×C₇₃	—	2	2	no	—
128	C₄²×C₇₃	—	2	2	no	—
129	C₂³×C₇₃	—	2	1	no	—
130	C₂³×C₇₃	—	2	1	no	—
131	C₂³×C₇₃	—	2	1	no	—
132	C₂³×C₇₃	—	2	2	no	—
133	C₂³×C₇₃	—	2	2	no	—
134	C₂³×C₇₃	—	4	1	no	—
135	C₂³×C₇₃	—	4	1	no	—
136	C₂³×C₇₃	—	4	1	no	—
137	C₂³×C₇₃	—	4	2	no	—
138	C₂³×C₇₃	—	4	2	no	—
139	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₇₃	—	4	2	no	—
141	Q₈×C₇₃	—	4	2	no	—
142	D₄×C₇₃	—	4	2	no	—
143	D₄×C₇₃	—	4	2	no	—
144	D₄×C₇₃	—	8	4	no	—
145	C₂×C₄×C₇₃	—	2	2	no	—
146	C₂×C₄×C₇₃	—	2	2	no	—
147	C₂×C₄×C₇₃	—	2	1	no	—
148	C₂×C₄×C₇₃	—	2	1	no	—
149	C₂×C₄×C₇₃	—	2	1	no	—
150	C₂×C₄×C₇₃	—	2	2	no	—
151	C₂×C₄×C₇₃	—	2	2	no	—
152	C₂×C₄×C₇₃	—	2	2	no	—
153	C₂×C₄×C₇₃	—	2	2	no	—
154	C₂×C₄×C₇₃	—	4	2	no	—
155	C₂×C₄×C₇₃	—	4	2	no	—
156	C₂×C₄×C₇₃	—	4	1	no	—
157	C₂×C₄×C₇₃	—	4	2	no	—
158	C₂×C₄×C₇₃	—	4	1	no	—
159	C₂×C₄×C₇₃	—	4	1	no	—
160	C₂×C₄×C₇₃	—	4	1	no	—
161	C₂×C₄×C₇₃	—	4	2	no	—
162	C₂×C₄×C₇₃	—	4	1	no	—
163	C₂×C₄×C₇₃	—	4	2	no	—
164	C₂×C₄×C₇₃	—	4	2	no	—
165	C₂×C₄×C₇₃	—	4	2	no	—
166	C₂×C₄×C₇₃	—	4	2	no	—
167	C₂×C₄×C₇₃	—	4	2	no	—
168	C₂×C₄×C₇₃	—	4	2	no	—
169	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
170	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
173	C₈×C₇₃	—	4	2	no	—
174	C₈×C₇₃	—	4	2	no	—
175	C₂²×C₇₃	—	4	1	no	—
176	C₂²×C₇₃	—	4	2	no	—
177	C₂²×C₇₃	—	4	1	no	—
178	C₂²×C₇₃	—	4	1	no	—
179	C₂²×C₇₃	—	4	2	no	—
180	C₂²×C₇₃	—	8	1	no	—
181	C₂²×C₇₃	—	8	2	no	—
182	C₂²×C₇₃	—	8	1	no	—
183	C₂²×C₇₃	—	8	1	no	—
184	C₂²×C₇₃	—	8	2	no	—
185	C₂²×C₇₃	#534	1	1	yes	characteristic
186	C₂²×C₇₃	#535	1	1	yes	characteristic
187	C₂²×C₇₃	#536	1	1	yes	characteristic
188	C₂²×C₇₃	#576	1	2	yes	—
189	C₂²×C₇₃	#578	1	2	yes	—
190	C₄×C₇₃	—	4	1	no	—
191	C₄×C₇₃	—	4	2	no	—
192	C₄×C₇₃	—	4	2	no	—
193	C₄×C₇₃	—	8	1	no	—
194	C₄×C₇₃	—	8	2	no	—
195	C₄×C₇₃	—	8	1	no	—
196	C₄×C₇₃	—	8	2	no	—
197	C₄×C₇₃	—	8	1	no	—
198	C₄×C₇₃	#562	1	2	yes	—
199	C₄×C₇₃	#562	1	2	yes	—
200	#32783	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂×C₇₃	—	8	1	no	—
202	C₂×C₇₃	—	16	1	no	—
203	C₂×C₇₃	#2816	1	1	yes	characteristic
204	C₂×C₇₃	#3203	1	2	yes	—
205	C₂×C₇₃	#3220	1	1	yes	characteristic
206	C₂×C₇₃	#3223	1	1	yes	characteristic
207	C₂×C₇₃	#3243	1	2	yes	—
208	#2629	C₂×C₇₃	1	1	yes	characteristic, complemented
209	#2620	C₂×C₇₃	1	1	yes	characteristic
210	#2095	C₂×C₇₃	1	1	yes	characteristic, complemented
211	#2093	C₂×C₇₃	1	1	yes	characteristic, complemented
212	#2083	C₂×C₇₃	1	2	yes	complemented
213	#2042	C₂×C₇₃	1	2	yes	complemented
214	#2036	C₂×C₇₃	1	2	yes	complemented
215	#2033	C₂×C₇₃	1	2	yes	—
216	#2026	C₂×C₇₃	1	1	yes	characteristic, complemented
217	#2025	C₂×C₇₃	1	1	yes	characteristic, complemented
218	#1818	C₂×C₇₃	1	1	yes	characteristic, complemented
219	C₇₃	#32783	1	1	yes	characteristic, direct product factor, Sylow
220	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
221	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
222	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
223	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
224	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
225	C₂×#107	C₂²×C₇₃	1	2	yes	—
226	C₂×#107	C₂²×C₇₃	1	2	yes	—
227	C₂×#103	C₂²×C₇₃	1	2	yes	—
228	C₂×#103	C₂²×C₇₃	1	2	yes	—
229	C₂×#102	C₂²×C₇₃	1	2	yes	—
230	C₂×#102	C₂²×C₇₃	1	2	yes	—
231	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
232	#398	—	2	2	no	—
233	#396	—	2	2	no	—
234	#396	—	2	2	no	—
235	#394	—	2	2	no	—
236	#391	C₂²×C₇₃	1	1	yes	characteristic
237	#390	C₂²×C₇₃	1	1	yes	characteristic
238	#389	C₂²×C₇₃	1	2	yes	—
239	#384	C₂²×C₇₃	1	1	yes	characteristic
240	#384	C₂²×C₇₃	1	1	yes	characteristic
241	#380	C₂²×C₇₃	1	2	yes	—
242	#340	C₂²×C₇₃	1	2	yes	—
243	#340	C₂²×C₇₃	1	2	yes	—
244	#336	C₂²×C₇₃	1	2	yes	—
245	#336	C₂²×C₇₃	1	1	yes	characteristic
246	#336	C₂²×C₇₃	1	1	yes	characteristic
247	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
252	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
253	#125	—	4	2	no	—
254	#124	—	4	2	no	—
255	C₂²⋊Q₈	—	4	2	no	—
256	#121	—	4	2	no	—
257	#117	—	4	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
274	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
276	#107	—	4	2	no	—
277	#107	—	4	2	no	—
278	#103	—	4	2	no	—
279	#103	—	4	2	no	—
280	#102	—	4	2	no	—
281	#102	—	4	2	no	—
282	C₂²⋊C₈	—	4	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	C₂⁴	—	2	1	no	—
287	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	8	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	—	8	2	no	—
328	C₄⋊C₄	—	8	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	4	4	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	8	2	no	—
334	C₂²⋊C₄	—	8	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	8	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
378	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
379	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
380	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	1	no	—
392	C₂²	—	8	2	no	—
393	C₂²	#534×C₇₃	1	1	yes	characteristic
394	C₂²	#535×C₇₃	1	1	yes	characteristic
395	C₂²	#536×C₇₃	1	1	yes	characteristic
396	C₂²	#576×C₇₃	1	2	yes	—
397	C₂²	#578×C₇₃	1	2	yes	—
398	C₄	—	4	1	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	1	no	—
405	C₄	—	8	2	no	—
406	C₄	#562×C₇₃	1	2	yes	—
407	C₄	#562×C₇₃	1	2	yes	—
408	C₂	—	8	1	no	—
409	C₂	—	16	1	no	—
410	C₂	C₇₃×#2816	1	1	yes	characteristic
411	C₂	C₇₃×#3203	1	2	yes	—
412	C₂	C₇₃×#3220	1	1	yes	characteristic
413	C₂	C₇₃×#3223	1	1	yes	characteristic
414	C₂	C₇₃×#3243	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#121×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2629	C₂	semidirect
3. C₇₃×#2095	C₂	semidirect
4. C₇₃×#2093	C₂	semidirect
5. C₇₃×#2083	C₂	semidirect
6. C₇₃×#2042	C₂	semidirect
7. C₇₃×#2036	C₂	semidirect
9. C₇₃×#2026	C₂	semidirect
10. C₇₃×#2025	C₂	semidirect
11. C₇₃×#1818	C₂	semidirect
200. #32783	C₇₃	direct (N × H)
208. #2629	C₂×C₇₃	semidirect
210. #2095	C₂×C₇₃	semidirect
211. #2093	C₂×C₇₃	semidirect
212. #2083	C₂×C₇₃	semidirect
213. #2042	C₂×C₇₃	semidirect
214. #2036	C₂×C₇₃	semidirect
216. #2026	C₂×C₇₃	semidirect
217. #2025	C₂×C₇₃	semidirect
218. #1818	C₂×C₇₃	semidirect
219. C₇₃	#32783	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×#2629	2
C₇₃×#2620	2
C₇₃×#2095	2
C₇₃×#2093	2
C₇₃×#2083	2
C₇₃×#2042	2
C₇₃×#2036	2
C₇₃×#2033	2
C₇₃×#2026	2
C₇₃×#2025	2
C₇₃×#1818	2
#32783	73

Subgroups — C73×#32783 #32942187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#32783 #32942187