Subgroups — C₇₃×#18814 #32928218

Order 18688.

1262 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1642	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1639	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1621	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1619	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1555	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1488	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₇₃	—	2	1	no	—
13	#550×C₇₃	—	2	1	no	—
14	#550×C₇₃	C₂²	1	2	yes	—
15	D₄²×C₇₃	—	2	2	no	—
16	D₄²×C₇₃	—	2	2	no	—
17	D₄²×C₇₃	—	2	1	no	—
18	D₄²×C₇₃	C₂²	1	2	yes	—
19	#535×C₇₃	—	2	2	no	—
20	#535×C₇₃	—	2	1	no	—
21	#532×C₇₃	—	2	1	no	—
22	#532×C₇₃	C₂²	1	1	yes	characteristic
23	#532×C₇₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×#127×C₇₃	—	2	1	no	—
25	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
26	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
27	#496×C₇₃	—	2	1	no	—
28	#493×C₇₃	C₂²	1	2	yes	complemented
29	#489×C₇₃	—	2	1	no	—
30	#486×C₇₃	C₂²	1	2	yes	complemented
31	#482×C₇₃	—	2	1	no	—
32	#475×C₇₃	C₂²	1	1	yes	characteristic, complemented
33	#474×C₇₃	C₂²	1	1	yes	characteristic, complemented
34	#461×C₇₃	C₂²	1	2	yes	complemented
35	#460×C₇₃	C₂²	1	1	yes	characteristic, complemented
36	#459×C₇₃	—	2	2	no	—
37	#459×C₇₃	C₂²	1	2	yes	complemented
38	#459×C₇₃	C₂²	1	1	yes	characteristic, complemented
39	#449×C₇₃	—	2	1	no	—
40	#449×C₇₃	—	2	2	no	—
41	#447×C₇₃	—	2	2	no	—
42	#442×C₇₃	—	2	1	no	—
43	#440×C₇₃	—	2	1	no	—
44	#432×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	#432×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	#431×C₇₃	C₂²	1	1	yes	characteristic, complemented
47	#331×C₇₃	C₂²	1	2	yes	complemented
48	#331×C₇₃	C₂²	1	2	yes	complemented
49	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	complemented
50	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
51	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
52	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
53	H(5,𝔽₂)×C₇₃	—	4	4	no	—
54	H(5,𝔽₂)×C₇₃	—	4	4	no	—
55	C₂×#41×C₇₃	—	2	2	no	—
56	C₂×#41×C₇₃	—	2	2	no	—
57	C₂×#41×C₇₃	—	2	1	no	—
58	C₂×#41×C₇₃	—	2	1	no	—
59	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₇₃	—	2	2	no	—
61	C₂²×D₄×C₇₃	—	2	4	no	—
62	C₂²×D₄×C₇₃	—	2	2	no	—
63	C₂²×D₄×C₇₃	—	2	2	no	—
64	C₂²×D₄×C₇₃	—	2	2	no	—
65	C₂²×D₄×C₇₃	—	2	1	no	—
66	C₂²×D₄×C₇₃	—	2	1	no	—
67	C₂²×D₄×C₇₃	D₄	1	2	yes	—
68	C₂×SD₁₆×C₇₃	—	2	1	no	—
69	C₂×SD₁₆×C₇₃	—	2	2	no	—
70	C₂×D₈×C₇₃	—	2	1	no	—
71	C₂×D₈×C₇₃	—	2	4	no	—
72	C₂×D₈×C₇₃	—	2	2	no	—
73	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
75	#127×C₇₃	—	2	2	no	—
76	#127×C₇₃	—	2	2	no	—
77	#127×C₇₃	—	2	2	no	—
78	#127×C₇₃	—	2	1	no	—
79	#127×C₇₃	—	2	1	no	—
80	#127×C₇₃	D₄	1	2	yes	—
81	#127×C₇₃	D₄	1	1	yes	characteristic
82	#127×C₇₃	C₂³	1	1	yes	characteristic
83	#127×C₇₃	C₂³	1	2	yes	—
84	#124×C₇₃	—	2	2	no	—
85	#124×C₇₃	—	2	1	no	—
86	#124×C₇₃	—	2	1	no	—
87	#121×C₇₃	—	2	2	no	—
88	#121×C₇₃	—	2	4	no	—
89	#121×C₇₃	—	2	4	no	—
90	#121×C₇₃	—	2	1	no	—
91	#121×C₇₃	—	2	2	no	—
92	#121×C₇₃	—	2	2	no	—
93	#121×C₇₃	—	2	2	no	—
94	#121×C₇₃	—	2	1	no	—
95	#121×C₇₃	—	2	1	no	—
96	#121×C₇₃	D₄	1	2	yes	—
97	#120×C₇₃	—	2	4	no	—
98	#120×C₇₃	—	2	4	no	—
99	#120×C₇₃	—	2	4	no	—
100	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
101	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₇₃	—	2	2	no	—
103	C₄×D₄×C₇₃	—	2	1	no	—
104	C₄×D₄×C₇₃	—	2	1	no	—
105	C₄×D₄×C₇₃	—	2	2	no	—
106	C₄×D₄×C₇₃	—	2	1	no	—
107	C₄×D₄×C₇₃	—	2	1	no	—
108	C₄×D₄×C₇₃	—	2	1	no	—
109	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
110	C₄×D₄×C₇₃	C₂³	1	2	yes	—
111	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
112	#117×C₇₃	—	2	1	no	—
113	#117×C₇₃	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₇₃	—	2	1	no	—
115	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
116	#107×C₇₃	—	2	1	no	—
117	#106×C₇₃	—	2	1	no	—
118	C₄⋊C₈×C₇₃	—	2	1	no	—
119	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
120	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
121	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
122	#103×C₇₃	—	2	1	no	—
123	#103×C₇₃	—	2	2	no	—
124	#102×C₇₃	—	2	1	no	—
125	#102×C₇₃	—	2	4	no	—
126	#102×C₇₃	—	2	1	no	—
127	#102×C₇₃	—	2	1	no	—
128	#102×C₇₃	—	2	2	no	—
129	C₂²⋊C₈×C₇₃	—	2	1	no	—
130	C₂²⋊C₈×C₇₃	—	2	1	no	—
131	C₂²⋊C₈×C₇₃	—	2	1	no	—
132	#97×C₇₃	—	2	1	no	—
133	#97×C₇₃	—	2	1	no	—
134	C₄×C₈×C₇₃	C₂³	1	2	yes	—
135	C₂⁴×C₇₃	—	2	4	no	—
136	C₂⁴×C₇₃	—	2	2	no	—
137	#41×C₇₃	—	2	2	no	—
138	#41×C₇₃	—	2	2	no	—
139	#41×C₇₃	—	4	8	no	—
140	#41×C₇₃	—	4	2	no	—
141	#41×C₇₃	—	4	2	no	—
142	#41×C₇₃	—	4	4	no	—
143	#41×C₇₃	—	4	4	no	—
144	#41×C₇₃	—	8	2	no	—
145	C₂×Q₈×C₇₃	—	2	1	no	—
146	C₂×Q₈×C₇₃	—	2	1	no	—
147	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₇₃	—	2	1	no	—
149	C₂×D₄×C₇₃	—	2	4	no	—
150	C₂×D₄×C₇₃	—	2	4	no	—
151	C₂×D₄×C₇₃	—	2	2	no	—
152	C₂×D₄×C₇₃	—	2	4	no	—
153	C₂×D₄×C₇₃	—	2	4	no	—
154	C₂×D₄×C₇₃	—	2	2	no	—
155	C₂×D₄×C₇₃	—	2	1	no	—
156	C₂×D₄×C₇₃	—	2	2	no	—
157	C₂×D₄×C₇₃	—	2	1	no	—
158	C₂×D₄×C₇₃	—	2	2	no	—
159	C₂×D₄×C₇₃	—	2	2	no	—
160	C₂×D₄×C₇₃	—	2	2	no	—
161	C₂×D₄×C₇₃	—	2	1	no	—
162	C₂×D₄×C₇₃	—	2	1	no	—
163	C₂×D₄×C₇₃	—	2	1	no	—
164	C₂×D₄×C₇₃	—	4	8	no	—
165	C₂×D₄×C₇₃	—	4	2	no	—
166	C₂×D₄×C₇₃	—	4	2	no	—
167	C₂×D₄×C₇₃	—	4	16	no	—
168	C₂×D₄×C₇₃	—	4	4	no	—
169	C₂×D₄×C₇₃	—	4	4	no	—
170	C₂×D₄×C₇₃	—	4	1	no	—
171	C₂×D₄×C₇₃	—	8	2	no	—
172	C₂×D₄×C₇₃	—	8	2	no	—
173	C₂×D₄×C₇₃	—	8	2	no	—
174	C₂×D₄×C₇₃	—	8	2	no	—
175	C₂×D₄×C₇₃	—	8	4	no	—
176	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
177	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
178	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₇₃	—	2	1	no	—
180	C₂²×C₄×C₇₃	—	2	4	no	—
181	C₂²×C₄×C₇₃	—	2	1	no	—
182	C₂²×C₄×C₇₃	—	2	1	no	—
183	C₂²×C₄×C₇₃	—	2	2	no	—
184	C₂²×C₄×C₇₃	—	4	1	no	—
185	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
188	SD₁₆×C₇₃	—	4	2	no	—
189	SD₁₆×C₇₃	—	8	2	no	—
190	D₈×C₇₃	—	4	2	no	—
191	D₈×C₇₃	—	8	2	no	—
192	D₈×C₇₃	—	8	4	no	—
193	C₂×C₈×C₇₃	—	2	2	no	—
194	C₂×C₈×C₇₃	—	2	1	no	—
195	C₂×C₈×C₇₃	—	2	1	no	—
196	C₂×C₈×C₇₃	—	2	2	no	—
197	C₄⋊C₄×C₇₃	—	2	1	no	—
198	C₄⋊C₄×C₇₃	—	2	1	no	—
199	C₄⋊C₄×C₇₃	—	2	1	no	—
200	C₄⋊C₄×C₇₃	—	2	1	no	—
201	C₄⋊C₄×C₇₃	—	2	1	no	—
202	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
203	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₇₃	—	2	4	no	—
206	C₂²⋊C₄×C₇₃	—	2	4	no	—
207	C₂²⋊C₄×C₇₃	—	2	1	no	—
208	C₂²⋊C₄×C₇₃	—	2	1	no	—
209	C₂²⋊C₄×C₇₃	—	2	2	no	—
210	C₂²⋊C₄×C₇₃	—	2	1	no	—
211	C₂²⋊C₄×C₇₃	—	2	2	no	—
212	C₂²⋊C₄×C₇₃	—	4	1	no	—
213	C₂²⋊C₄×C₇₃	—	4	1	no	—
214	C₄²×C₇₃	—	2	1	no	—
215	C₄²×C₇₃	—	2	1	no	—
216	C₄²×C₇₃	—	2	1	no	—
217	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
221	C₂³×C₇₃	—	2	1	no	—
222	C₂³×C₇₃	—	2	2	no	—
223	C₂³×C₇₃	—	2	4	no	—
224	C₂³×C₇₃	—	4	4	no	—
225	C₂³×C₇₃	—	4	8	no	—
226	C₂³×C₇₃	—	4	1	no	—
227	C₂³×C₇₃	—	8	2	no	—
228	C₂³×C₇₃	—	8	2	no	—
229	C₂³×C₇₃	—	8	4	no	—
230	C₂³×C₇₃	—	8	4	no	—
231	C₂³×C₇₃	#120	1	1	yes	characteristic
232	Q₈×C₇₃	—	2	1	no	—
233	Q₈×C₇₃	—	4	2	no	—
234	Q₈×C₇₃	—	4	2	no	—
235	Q₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
236	D₄×C₇₃	—	2	4	no	—
237	D₄×C₇₃	—	2	1	no	—
238	D₄×C₇₃	—	2	2	no	—
239	D₄×C₇₃	—	2	2	no	—
240	D₄×C₇₃	—	4	4	no	—
241	D₄×C₇₃	—	4	4	no	—
242	D₄×C₇₃	—	4	2	no	—
243	D₄×C₇₃	—	4	8	no	—
244	D₄×C₇₃	—	4	4	no	—
245	D₄×C₇₃	—	4	2	no	—
246	D₄×C₇₃	—	4	2	no	—
247	D₄×C₇₃	—	4	4	no	—
248	D₄×C₇₃	—	4	8	no	—
249	D₄×C₇₃	—	4	2	no	—
250	D₄×C₇₃	—	4	2	no	—
251	D₄×C₇₃	—	4	1	no	—
252	D₄×C₇₃	—	4	1	no	—
253	D₄×C₇₃	—	4	2	no	—
254	D₄×C₇₃	—	4	2	no	—
255	D₄×C₇₃	—	4	2	no	—
256	D₄×C₇₃	—	8	2	no	—
257	D₄×C₇₃	—	8	4	no	—
258	D₄×C₇₃	—	8	4	no	—
259	D₄×C₇₃	—	8	2	no	—
260	D₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
261	C₂×C₄×C₇₃	—	2	4	no	—
262	C₂×C₄×C₇₃	—	2	1	no	—
263	C₂×C₄×C₇₃	—	2	1	no	—
264	C₂×C₄×C₇₃	—	2	1	no	—
265	C₂×C₄×C₇₃	—	2	2	no	—
266	C₂×C₄×C₇₃	—	2	1	no	—
267	C₂×C₄×C₇₃	—	2	1	no	—
268	C₂×C₄×C₇₃	—	2	2	no	—
269	C₂×C₄×C₇₃	—	4	1	no	—
270	C₂×C₄×C₇₃	—	4	8	no	—
271	C₂×C₄×C₇₃	—	4	2	no	—
272	C₂×C₄×C₇₃	—	4	2	no	—
273	C₂×C₄×C₇₃	—	4	2	no	—
274	C₂×C₄×C₇₃	—	4	2	no	—
275	C₂×C₄×C₇₃	—	4	1	no	—
276	C₂×C₄×C₇₃	—	8	2	no	—
277	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
278	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
279	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
280	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
283	C₈×C₇₃	—	4	2	no	—
284	C₈×C₇₃	—	4	1	no	—
285	C₈×C₇₃	—	4	1	no	—
286	C₈×C₇₃	—	4	2	no	—
287	C₂²×C₇₃	—	2	1	no	—
288	C₂²×C₇₃	—	2	2	no	—
289	C₂²×C₇₃	—	2	1	no	—
290	C₂²×C₇₃	—	2	1	no	—
291	C₂²×C₇₃	—	4	1	no	—
292	C₂²×C₇₃	—	4	1	no	—
293	C₂²×C₇₃	—	4	4	no	—
294	C₂²×C₇₃	—	4	2	no	—
295	C₂²×C₇₃	—	4	2	no	—
296	C₂²×C₇₃	—	4	4	no	—
297	C₂²×C₇₃	—	4	4	no	—
298	C₂²×C₇₃	—	4	2	no	—
299	C₂²×C₇₃	—	8	1	no	—
300	C₂²×C₇₃	—	8	1	no	—
301	C₂²×C₇₃	—	8	1	no	—
302	C₂²×C₇₃	—	16	4	no	—
303	C₂²×C₇₃	—	16	8	no	—
304	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
305	C₄×C₇₃	—	2	1	no	—
306	C₄×C₇₃	—	2	2	no	—
307	C₄×C₇₃	—	2	1	no	—
308	C₄×C₇₃	—	2	1	no	—
309	C₄×C₇₃	—	2	1	no	—
310	C₄×C₇₃	—	4	2	no	—
311	C₄×C₇₃	—	4	1	no	—
312	C₄×C₇₃	—	4	1	no	—
313	C₄×C₇₃	—	8	1	no	—
314	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
315	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
316	C₄×C₇₃	#576	1	2	yes	—
317	#18814	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
318	C₂×C₇₃	—	4	1	no	—
319	C₂×C₇₃	—	4	2	no	—
320	C₂×C₇₃	—	8	2	no	—
321	C₂×C₇₃	—	8	4	no	—
322	C₂×C₇₃	—	16	1	no	—
323	C₂×C₇₃	#3003	1	1	yes	characteristic
324	C₂×C₇₃	#3008	1	1	yes	characteristic
325	C₂×C₇₃	#3019	1	1	yes	characteristic
326	#3498	C₂×C₇₃	1	1	yes	characteristic, complemented
327	#3214	C₂×C₇₃	1	1	yes	characteristic, complemented
328	#3205	C₂×C₇₃	1	1	yes	characteristic, complemented
329	#3115	C₂×C₇₃	1	1	yes	characteristic, complemented
330	#1642	C₂×C₇₃	1	2	yes	complemented
331	#1639	C₂×C₇₃	1	2	yes	complemented
332	#1621	C₂×C₇₃	1	2	yes	complemented
333	#1619	C₂×C₇₃	1	2	yes	complemented
334	#1555	C₂×C₇₃	1	1	yes	characteristic, complemented
335	#1496	C₂×C₇₃	1	1	yes	characteristic, complemented
336	#1488	C₂×C₇₃	1	1	yes	characteristic, complemented
337	C₇₃	#18814	1	1	yes	characteristic, direct product factor, Sylow
338	C₂×H(5,𝔽₂)	—	2	1	no	—
339	#550	—	2	1	no	—
340	#550	C₂²×C₇₃	1	2	yes	—
341	D₄²	—	2	2	no	—
342	D₄²	—	2	2	no	—
343	D₄²	—	2	1	no	—
344	D₄²	C₂²×C₇₃	1	2	yes	—
345	#535	—	2	2	no	—
346	#535	—	2	1	no	—
347	#532	—	2	1	no	—
348	#532	C₂²×C₇₃	1	1	yes	characteristic
349	#532	C₂²×C₇₃	1	1	yes	characteristic, complemented
350	C₂×#127	—	2	1	no	—
351	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
352	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
353	#496	—	2	1	no	—
354	#493	C₂²×C₇₃	1	2	yes	complemented
355	#489	—	2	1	no	—
356	#486	C₂²×C₇₃	1	2	yes	complemented
357	#482	—	2	1	no	—
358	#475	C₂²×C₇₃	1	1	yes	characteristic, complemented
359	#474	C₂²×C₇₃	1	1	yes	characteristic, complemented
360	#461	C₂²×C₇₃	1	2	yes	complemented
361	#460	C₂²×C₇₃	1	1	yes	characteristic, complemented
362	#459	—	2	2	no	—
363	#459	C₂²×C₇₃	1	1	yes	characteristic, complemented
364	#459	C₂²×C₇₃	1	2	yes	complemented
365	#449	—	2	1	no	—
366	#449	—	2	2	no	—
367	#447	—	2	2	no	—
368	#442	—	2	1	no	—
369	#440	—	2	1	no	—
370	#432	C₂²×C₇₃	1	1	yes	characteristic, complemented
371	#432	C₂²×C₇₃	1	1	yes	characteristic, complemented
372	#431	C₂²×C₇₃	1	1	yes	characteristic, complemented
373	#331	C₂²×C₇₃	1	2	yes	complemented
374	#331	C₂²×C₇₃	1	2	yes	complemented
375	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
376	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
377	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
378	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
379	H(5,𝔽₂)	—	4	4	no	—
380	H(5,𝔽₂)	—	4	4	no	—
381	C₂×#41	—	2	2	no	—
382	C₂×#41	—	2	2	no	—
383	C₂×#41	—	2	1	no	—
384	C₂×#41	—	2	1	no	—
385	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
386	C₂²×D₄	—	2	2	no	—
387	C₂²×D₄	—	2	4	no	—
388	C₂²×D₄	—	2	2	no	—
389	C₂²×D₄	—	2	2	no	—
390	C₂²×D₄	—	2	2	no	—
391	C₂²×D₄	—	2	1	no	—
392	C₂²×D₄	—	2	1	no	—
393	C₂²×D₄	D₄×C₇₃	1	2	yes	—
394	C₂×SD₁₆	—	2	1	no	—
395	C₂×SD₁₆	—	2	2	no	—
396	C₂×D₈	—	2	1	no	—
397	C₂×D₈	—	2	4	no	—
398	C₂×D₈	—	2	2	no	—
399	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
400	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
401	#127	—	2	2	no	—
402	#127	—	2	2	no	—
403	#127	—	2	2	no	—
404	#127	—	2	1	no	—
405	#127	—	2	1	no	—
406	#127	D₄×C₇₃	1	1	yes	characteristic
407	#127	D₄×C₇₃	1	2	yes	—
408	#127	C₂³×C₇₃	1	1	yes	characteristic
409	#127	C₂³×C₇₃	1	2	yes	—
410	#124	—	2	2	no	—
411	#124	—	2	1	no	—
412	#124	—	2	1	no	—
413	#121	—	2	2	no	—
414	#121	—	2	4	no	—
415	#121	—	2	4	no	—
416	#121	—	2	1	no	—
417	#121	—	2	2	no	—
418	#121	—	2	2	no	—
419	#121	—	2	2	no	—
420	#121	—	2	1	no	—
421	#121	—	2	1	no	—
422	#121	D₄×C₇₃	1	2	yes	—
423	#120	—	2	4	no	—
424	#120	—	2	4	no	—
425	#120	—	2	4	no	—
426	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
427	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	—	2	1	no	—
435	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
436	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
437	C₄×D₄	C₂³×C₇₃	1	2	yes	—
438	#117	—	2	1	no	—
439	#117	D₄×C₇₃	1	1	yes	characteristic
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
442	#107	—	2	1	no	—
443	#106	—	2	1	no	—
444	C₄⋊C₈	—	2	1	no	—
445	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
446	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
447	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
448	#103	—	2	1	no	—
449	#103	—	2	2	no	—
450	#102	—	2	1	no	—
451	#102	—	2	4	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	—	2	2	no	—
455	C₂²⋊C₈	—	2	1	no	—
456	C₂²⋊C₈	—	2	1	no	—
457	C₂²⋊C₈	—	2	1	no	—
458	#97	—	2	1	no	—
459	#97	—	2	1	no	—
460	C₄×C₈	C₂³×C₇₃	1	2	yes	—
461	C₂⁴	—	2	4	no	—
462	C₂⁴	—	2	2	no	—
463	#41	—	2	2	no	—
464	#41	—	2	2	no	—
465	#41	—	4	8	no	—
466	#41	—	4	2	no	—
467	#41	—	4	2	no	—
468	#41	—	4	4	no	—
469	#41	—	4	4	no	—
470	#41	—	8	2	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	2	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	4	8	no	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	—	4	2	no	—
493	C₂×D₄	—	4	16	no	—
494	C₂×D₄	—	4	4	no	—
495	C₂×D₄	—	4	4	no	—
496	C₂×D₄	—	4	1	no	—
497	C₂×D₄	—	8	2	no	—
498	C₂×D₄	—	8	2	no	—
499	C₂×D₄	—	8	2	no	—
500	C₂×D₄	—	8	2	no	—
501	C₂×D₄	—	8	4	no	—
502	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
503	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
504	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	4	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	4	1	no	—
511	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
514	SD₁₆	—	4	2	no	—
515	SD₁₆	—	8	2	no	—
516	D₈	—	4	2	no	—
517	D₈	—	8	2	no	—
518	D₈	—	8	4	no	—
519	C₂×C₈	—	2	2	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	2	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
529	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
530	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
531	C₂²⋊C₄	—	2	4	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	1	no	—
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	1	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
544	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
545	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
546	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
547	C₂³	—	2	1	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	4	4	no	—
551	C₂³	—	4	8	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	8	2	no	—
554	C₂³	—	8	2	no	—
555	C₂³	—	8	4	no	—
556	C₂³	—	8	4	no	—
557	C₂³	#120×C₇₃	1	1	yes	characteristic
558	Q₈	—	2	1	no	—
559	Q₈	—	4	2	no	—
560	Q₈	—	4	2	no	—
561	Q₈	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
562	D₄	—	2	4	no	—
563	D₄	—	2	1	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	4	4	no	—
567	D₄	—	4	4	no	—
568	D₄	—	4	2	no	—
569	D₄	—	4	8	no	—
570	D₄	—	4	4	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	4	4	no	—
574	D₄	—	4	8	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	8	2	no	—
583	D₄	—	8	4	no	—
584	D₄	—	8	4	no	—
585	D₄	—	8	2	no	—
586	D₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	8	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	8	2	no	—
603	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
604	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
605	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
609	C₈	—	4	2	no	—
610	C₈	—	4	1	no	—
611	C₈	—	4	1	no	—
612	C₈	—	4	2	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	4	4	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	16	4	no	—
629	C₂²	—	16	8	no	—
630	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	8	1	no	—
640	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
641	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
642	C₄	#576×C₇₃	1	2	yes	—
643	C₂	—	4	1	no	—
644	C₂	—	4	2	no	—
645	C₂	—	8	2	no	—
646	C₂	—	8	4	no	—
647	C₂	—	16	1	no	—
648	C₂	C₇₃×#3003	1	1	yes	characteristic
649	C₂	C₇₃×#3008	1	1	yes	characteristic
650	C₂	C₇₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3498	C₂	semidirect
2. C₇₃×#3214	C₂	semidirect
3. C₇₃×#3205	C₂	semidirect
4. C₇₃×#3115	C₂	semidirect
5. C₇₃×#1642	C₂	semidirect
6. C₇₃×#1639	C₂	semidirect
7. C₇₃×#1621	C₂	semidirect
8. C₇₃×#1619	C₂	semidirect
9. C₇₃×#1555	C₂	semidirect
10. C₇₃×#1496	C₂	semidirect
11. C₇₃×#1488	C₂	semidirect
23. #532×C₇₃	C₂²	semidirect
28. #493×C₇₃	C₂²	semidirect
30. #486×C₇₃	C₂²	semidirect
32. #475×C₇₃	C₂²	semidirect
33. #474×C₇₃	C₂²	semidirect
34. #461×C₇₃	C₂²	semidirect
35. #460×C₇₃	C₂²	semidirect
37. #459×C₇₃	C₂²	semidirect
38. #459×C₇₃	C₂²	semidirect
44. #432×C₇₃	C₂²	semidirect
45. #432×C₇₃	C₂²	semidirect
46. #431×C₇₃	C₂²	semidirect
47. #331×C₇₃	C₂²	semidirect
48. #331×C₇₃	C₂²	semidirect
49. Q₈⋊C₈×C₇₃	C₂²	semidirect
50. D₄⋊C₈×C₇₃	C₂²	semidirect
51. D₄⋊C₈×C₇₃	C₂²	semidirect
52. D₄⋊C₈×C₇₃	C₂²	semidirect
317. #18814	C₇₃	direct (N × H)
326. #3498	C₂×C₇₃	semidirect
327. #3214	C₂×C₇₃	semidirect
328. #3205	C₂×C₇₃	semidirect
329. #3115	C₂×C₇₃	semidirect
330. #1642	C₂×C₇₃	semidirect
331. #1639	C₂×C₇₃	semidirect
332. #1621	C₂×C₇₃	semidirect
333. #1619	C₂×C₇₃	semidirect
334. #1555	C₂×C₇₃	semidirect
335. #1496	C₂×C₇₃	semidirect
336. #1488	C₂×C₇₃	semidirect
337. C₇₃	#18814	direct (N × H)
349. #532	C₂²×C₇₃	semidirect
354. #493	C₂²×C₇₃	semidirect
356. #486	C₂²×C₇₃	semidirect
358. #475	C₂²×C₇₃	semidirect
359. #474	C₂²×C₇₃	semidirect
360. #461	C₂²×C₇₃	semidirect
361. #460	C₂²×C₇₃	semidirect
363. #459	C₂²×C₇₃	semidirect
364. #459	C₂²×C₇₃	semidirect
370. #432	C₂²×C₇₃	semidirect
371. #432	C₂²×C₇₃	semidirect
372. #431	C₂²×C₇₃	semidirect
373. #331	C₂²×C₇₃	semidirect
374. #331	C₂²×C₇₃	semidirect
375. Q₈⋊C₈	C₂²×C₇₃	semidirect
376. D₄⋊C₈	C₂²×C₇₃	semidirect
377. D₄⋊C₈	C₂²×C₇₃	semidirect
378. D₄⋊C₈	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3498	2
C₇₃×#3214	2
C₇₃×#3205	2
C₇₃×#3115	2
C₇₃×#1642	2
C₇₃×#1639	2
C₇₃×#1621	2
C₇₃×#1619	2
C₇₃×#1555	2
C₇₃×#1496	2
C₇₃×#1488	2
#18814	73

Subgroups — C73×#18814 #32928218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18814 #32928218