Subgroups — C₇₃×#18820 #32928224

Order 18688.

940 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1646	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1643	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1624	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1622	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1558	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	#556×C₇₃	—	2	1	no	—
13	#555×C₇₃	C₂²	1	2	yes	—
14	#554×C₇₃	C₂²	1	2	yes	—
15	#553×C₇₃	—	2	2	no	—
16	#548×C₇₃	—	2	2	no	—
17	#547×C₇₃	—	2	1	no	—
18	#542×C₇₃	—	2	2	no	—
19	#537×C₇₃	—	2	1	no	—
20	#533×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
24	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	#520×C₇₃	—	2	1	no	—
26	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
27	#496×C₇₃	—	2	1	no	—
28	#492×C₇₃	C₂²	1	2	yes	—
29	#489×C₇₃	—	2	1	no	—
30	#487×C₇₃	C₂²	1	2	yes	—
31	#482×C₇₃	—	2	1	no	—
32	#475×C₇₃	C₂²	1	1	yes	characteristic
33	#474×C₇₃	C₂²	1	1	yes	characteristic
34	#461×C₇₃	—	2	2	no	—
35	#461×C₇₃	C₂²	1	2	yes	—
36	#460×C₇₃	C₂²	1	1	yes	characteristic
37	#459×C₇₃	C₂²	1	2	yes	—
38	#459×C₇₃	C₂²	1	1	yes	characteristic
39	#449×C₇₃	—	2	1	no	—
40	#449×C₇₃	—	2	2	no	—
41	#448×C₇₃	—	2	2	no	—
42	#442×C₇₃	—	2	1	no	—
43	#440×C₇₃	—	2	1	no	—
44	#432×C₇₃	C₂²	1	1	yes	characteristic
45	#432×C₇₃	C₂²	1	1	yes	characteristic
46	#431×C₇₃	C₂²	1	1	yes	characteristic
47	#333×C₇₃	C₂²	1	2	yes	—
48	#333×C₇₃	C₂²	1	2	yes	—
49	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	—
50	D₄⋊C₈×C₇₃	C₂²	1	2	yes	—
51	D₄⋊C₈×C₇₃	C₂²	1	2	yes	—
52	D₄⋊C₈×C₇₃	C₂²	1	2	yes	—
53	C₂×#41×C₇₃	—	2	2	no	—
54	C₂×#41×C₇₃	—	2	1	no	—
55	C₂×#41×C₇₃	—	2	1	no	—
56	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₇₃	D₄	1	2	yes	—
58	C₂×SD₁₆×C₇₃	—	2	1	no	—
59	C₂×SD₁₆×C₇₃	—	2	4	no	—
60	C₂×SD₁₆×C₇₃	—	2	2	no	—
61	C₂×D₈×C₇₃	—	2	1	no	—
62	C₂×D₈×C₇₃	—	2	2	no	—
63	C₄⋊Q₈×C₇₃	—	2	1	no	—
64	C₄⋊Q₈×C₇₃	—	2	1	no	—
65	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
66	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
69	#127×C₇₃	D₄	1	1	yes	characteristic
70	#127×C₇₃	C₂³	1	1	yes	characteristic
71	#126×C₇₃	—	2	4	no	—
72	#125×C₇₃	—	2	2	no	—
73	#124×C₇₃	—	2	2	no	—
74	#124×C₇₃	—	2	4	no	—
75	#124×C₇₃	—	2	1	no	—
76	#124×C₇₃	—	2	1	no	—
77	#123×C₇₃	—	2	4	no	—
78	C₂²⋊Q₈×C₇₃	—	2	2	no	—
79	C₂²⋊Q₈×C₇₃	—	2	2	no	—
80	C₂²⋊Q₈×C₇₃	—	2	2	no	—
81	C₂²⋊Q₈×C₇₃	—	2	4	no	—
82	#121×C₇₃	—	2	2	no	—
83	#121×C₇₃	—	2	4	no	—
84	#121×C₇₃	—	2	2	no	—
85	#121×C₇₃	—	2	2	no	—
86	#121×C₇₃	—	2	1	no	—
87	#121×C₇₃	—	2	1	no	—
88	#121×C₇₃	—	2	1	no	—
89	#121×C₇₃	D₄	1	2	yes	—
90	C₄×Q₈×C₇₃	—	2	2	no	—
91	C₄×Q₈×C₇₃	—	2	2	no	—
92	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
93	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₇₃	—	2	2	no	—
95	C₄×D₄×C₇₃	—	2	4	no	—
96	C₄×D₄×C₇₃	—	2	2	no	—
97	C₄×D₄×C₇₃	—	2	1	no	—
98	C₄×D₄×C₇₃	—	2	1	no	—
99	C₄×D₄×C₇₃	—	2	1	no	—
100	C₄×D₄×C₇₃	—	2	1	no	—
101	C₄×D₄×C₇₃	—	2	1	no	—
102	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
103	C₄×D₄×C₇₃	C₂³	1	2	yes	—
104	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
105	#117×C₇₃	—	2	2	no	—
106	#117×C₇₃	—	2	2	no	—
107	#117×C₇₃	—	2	1	no	—
108	#117×C₇₃	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
110	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
111	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
112	C₂×C₄²×C₇₃	—	2	1	no	—
113	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
114	#107×C₇₃	—	2	1	no	—
115	#106×C₇₃	—	2	1	no	—
116	C₄⋊C₈×C₇₃	—	2	1	no	—
117	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
118	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
119	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
120	#103×C₇₃	—	2	1	no	—
121	#103×C₇₃	—	2	4	no	—
122	#103×C₇₃	—	2	2	no	—
123	#102×C₇₃	—	2	1	no	—
124	#102×C₇₃	—	2	1	no	—
125	#102×C₇₃	—	2	1	no	—
126	#102×C₇₃	—	2	2	no	—
127	C₂²⋊C₈×C₇₃	—	2	1	no	—
128	C₂²⋊C₈×C₇₃	—	2	1	no	—
129	C₂²⋊C₈×C₇₃	—	2	1	no	—
130	#97×C₇₃	—	2	1	no	—
131	#97×C₇₃	—	2	1	no	—
132	C₄×C₈×C₇₃	C₂³	1	2	yes	—
133	#41×C₇₃	—	4	1	no	—
134	#41×C₇₃	—	4	1	no	—
135	#41×C₇₃	—	4	2	no	—
136	#41×C₇₃	—	4	2	no	—
137	#41×C₇₃	—	8	2	no	—
138	#41×C₇₃	—	8	4	no	—
139	C₂×Q₈×C₇₃	—	2	1	no	—
140	C₂×Q₈×C₇₃	—	2	2	no	—
141	C₂×Q₈×C₇₃	—	2	1	no	—
142	C₂×Q₈×C₇₃	—	8	2	no	—
143	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
145	C₂×D₄×C₇₃	—	2	1	no	—
146	C₂×D₄×C₇₃	—	2	2	no	—
147	C₂×D₄×C₇₃	—	2	4	no	—
148	C₂×D₄×C₇₃	—	2	1	no	—
149	C₂×D₄×C₇₃	—	2	1	no	—
150	C₂×D₄×C₇₃	—	2	1	no	—
151	C₂×D₄×C₇₃	—	2	1	no	—
152	C₂×D₄×C₇₃	—	2	1	no	—
153	C₂×D₄×C₇₃	—	4	1	no	—
154	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₇₃	—	2	4	no	—
157	C₂²×C₄×C₇₃	—	2	2	no	—
158	C₂²×C₄×C₇₃	—	2	1	no	—
159	C₂²×C₄×C₇₃	—	2	1	no	—
160	C₂²×C₄×C₇₃	—	2	1	no	—
161	C₂²×C₄×C₇₃	—	2	2	no	—
162	C₂²×C₄×C₇₃	—	4	1	no	—
163	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
166	SD₁₆×C₇₃	—	4	2	no	—
167	SD₁₆×C₇₃	—	8	2	no	—
168	SD₁₆×C₇₃	—	8	4	no	—
169	D₈×C₇₃	—	4	2	no	—
170	D₈×C₇₃	—	8	2	no	—
171	C₂×C₈×C₇₃	—	2	2	no	—
172	C₂×C₈×C₇₃	—	2	1	no	—
173	C₂×C₈×C₇₃	—	2	1	no	—
174	C₂×C₈×C₇₃	—	2	2	no	—
175	C₄⋊C₄×C₇₃	—	2	4	no	—
176	C₄⋊C₄×C₇₃	—	2	4	no	—
177	C₄⋊C₄×C₇₃	—	2	2	no	—
178	C₄⋊C₄×C₇₃	—	2	2	no	—
179	C₄⋊C₄×C₇₃	—	2	1	no	—
180	C₄⋊C₄×C₇₃	—	2	1	no	—
181	C₄⋊C₄×C₇₃	—	2	2	no	—
182	C₄⋊C₄×C₇₃	—	2	2	no	—
183	C₄⋊C₄×C₇₃	—	2	1	no	—
184	C₄⋊C₄×C₇₃	—	2	1	no	—
185	C₄⋊C₄×C₇₃	—	2	1	no	—
186	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
187	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
189	C₂²⋊C₄×C₇₃	—	2	4	no	—
190	C₂²⋊C₄×C₇₃	—	2	4	no	—
191	C₂²⋊C₄×C₇₃	—	2	4	no	—
192	C₂²⋊C₄×C₇₃	—	2	1	no	—
193	C₂²⋊C₄×C₇₃	—	2	1	no	—
194	C₂²⋊C₄×C₇₃	—	2	2	no	—
195	C₂²⋊C₄×C₇₃	—	2	1	no	—
196	C₂²⋊C₄×C₇₃	—	2	2	no	—
197	C₂²⋊C₄×C₇₃	—	4	1	no	—
198	C₂²⋊C₄×C₇₃	—	4	1	no	—
199	C₄²×C₇₃	—	2	4	no	—
200	C₄²×C₇₃	—	2	1	no	—
201	C₄²×C₇₃	—	2	1	no	—
202	C₄²×C₇₃	—	2	1	no	—
203	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
207	C₂³×C₇₃	—	2	1	no	—
208	C₂³×C₇₃	—	2	2	no	—
209	C₂³×C₇₃	—	4	1	no	—
210	C₂³×C₇₃	#120	1	1	yes	characteristic
211	Q₈×C₇₃	—	2	1	no	—
212	Q₈×C₇₃	—	2	1	no	—
213	Q₈×C₇₃	—	4	4	no	—
214	Q₈×C₇₃	—	4	4	no	—
215	Q₈×C₇₃	—	4	2	no	—
216	Q₈×C₇₃	—	4	2	no	—
217	D₄×C₇₃	—	2	1	no	—
218	D₄×C₇₃	—	2	1	no	—
219	D₄×C₇₃	—	2	2	no	—
220	D₄×C₇₃	—	2	2	no	—
221	D₄×C₇₃	—	4	2	no	—
222	D₄×C₇₃	—	4	2	no	—
223	D₄×C₇₃	—	4	2	no	—
224	D₄×C₇₃	—	4	2	no	—
225	D₄×C₇₃	—	4	4	no	—
226	D₄×C₇₃	—	4	1	no	—
227	D₄×C₇₃	—	4	1	no	—
228	D₄×C₇₃	—	4	2	no	—
229	D₄×C₇₃	—	8	4	no	—
230	D₄×C₇₃	—	8	2	no	—
231	C₂×C₄×C₇₃	—	2	1	no	—
232	C₂×C₄×C₇₃	—	2	1	no	—
233	C₂×C₄×C₇₃	—	2	2	no	—
234	C₂×C₄×C₇₃	—	2	1	no	—
235	C₂×C₄×C₇₃	—	2	1	no	—
236	C₂×C₄×C₇₃	—	2	2	no	—
237	C₂×C₄×C₇₃	—	2	1	no	—
238	C₂×C₄×C₇₃	—	2	4	no	—
239	C₂×C₄×C₇₃	—	4	1	no	—
240	C₂×C₄×C₇₃	—	4	2	no	—
241	C₂×C₄×C₇₃	—	4	2	no	—
242	C₂×C₄×C₇₃	—	4	2	no	—
243	C₂×C₄×C₇₃	—	4	2	no	—
244	C₂×C₄×C₇₃	—	4	2	no	—
245	C₂×C₄×C₇₃	—	4	1	no	—
246	C₂×C₄×C₇₃	—	8	2	no	—
247	C₂×C₄×C₇₃	—	8	2	no	—
248	C₂×C₄×C₇₃	—	8	4	no	—
249	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
250	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
251	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
252	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
255	C₈×C₇₃	—	4	2	no	—
256	C₈×C₇₃	—	4	1	no	—
257	C₈×C₇₃	—	4	1	no	—
258	C₈×C₇₃	—	4	2	no	—
259	C₂²×C₇₃	—	2	1	no	—
260	C₂²×C₇₃	—	2	1	no	—
261	C₂²×C₇₃	—	2	1	no	—
262	C₂²×C₇₃	—	4	1	no	—
263	C₂²×C₇₃	—	4	2	no	—
264	C₂²×C₇₃	—	4	1	no	—
265	C₂²×C₇₃	—	4	2	no	—
266	C₂²×C₇₃	—	4	1	no	—
267	C₂²×C₇₃	—	4	2	no	—
268	C₂²×C₇₃	—	8	1	no	—
269	C₂²×C₇₃	—	8	1	no	—
270	C₂²×C₇₃	—	8	1	no	—
271	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
272	C₄×C₇₃	—	2	1	no	—
273	C₄×C₇₃	—	2	1	no	—
274	C₄×C₇₃	—	2	1	no	—
275	C₄×C₇₃	—	2	1	no	—
276	C₄×C₇₃	—	4	1	no	—
277	C₄×C₇₃	—	4	2	no	—
278	C₄×C₇₃	—	4	1	no	—
279	C₄×C₇₃	—	4	1	no	—
280	C₄×C₇₃	—	4	4	no	—
281	C₄×C₇₃	—	8	1	no	—
282	C₄×C₇₃	#575	1	1	yes	characteristic
283	C₄×C₇₃	#575	1	1	yes	characteristic
284	C₄×C₇₃	#577	1	2	yes	—
285	#18820	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂×C₇₃	—	4	1	no	—
287	C₂×C₇₃	—	8	1	no	—
288	C₂×C₇₃	—	8	2	no	—
289	C₂×C₇₃	—	16	1	no	—
290	C₂×C₇₃	#3005	1	1	yes	characteristic
291	C₂×C₇₃	#3010	1	1	yes	characteristic
292	C₂×C₇₃	#3019	1	1	yes	characteristic
293	#3511	C₂×C₇₃	1	1	yes	characteristic, complemented
294	#3214	C₂×C₇₃	1	1	yes	characteristic, complemented
295	#3206	C₂×C₇₃	1	1	yes	characteristic, complemented
296	#3115	C₂×C₇₃	1	1	yes	characteristic, complemented
297	#1646	C₂×C₇₃	1	2	yes	complemented
298	#1643	C₂×C₇₃	1	2	yes	complemented
299	#1624	C₂×C₇₃	1	2	yes	complemented
300	#1622	C₂×C₇₃	1	2	yes	complemented
301	#1558	C₂×C₇₃	1	1	yes	characteristic, complemented
302	#1496	C₂×C₇₃	1	1	yes	characteristic, complemented
303	#1488	C₂×C₇₃	1	1	yes	characteristic, complemented
304	C₇₃	#18820	1	1	yes	characteristic, direct product factor, Sylow
305	#556	—	2	1	no	—
306	#555	C₂²×C₇₃	1	2	yes	—
307	#554	C₂²×C₇₃	1	2	yes	—
308	#553	—	2	2	no	—
309	#548	—	2	2	no	—
310	#547	—	2	1	no	—
311	#542	—	2	2	no	—
312	#537	—	2	1	no	—
313	#533	—	2	1	no	—
314	#532	—	2	1	no	—
315	#532	C₂²×C₇₃	1	1	yes	characteristic
316	#532	C₂²×C₇₃	1	1	yes	characteristic
317	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
318	#520	—	2	1	no	—
319	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
320	#496	—	2	1	no	—
321	#492	C₂²×C₇₃	1	2	yes	—
322	#489	—	2	1	no	—
323	#487	C₂²×C₇₃	1	2	yes	—
324	#482	—	2	1	no	—
325	#475	C₂²×C₇₃	1	1	yes	characteristic
326	#474	C₂²×C₇₃	1	1	yes	characteristic
327	#461	—	2	2	no	—
328	#461	C₂²×C₇₃	1	2	yes	—
329	#460	C₂²×C₇₃	1	1	yes	characteristic
330	#459	C₂²×C₇₃	1	1	yes	characteristic
331	#459	C₂²×C₇₃	1	2	yes	—
332	#449	—	2	1	no	—
333	#449	—	2	2	no	—
334	#448	—	2	2	no	—
335	#442	—	2	1	no	—
336	#440	—	2	1	no	—
337	#432	C₂²×C₇₃	1	1	yes	characteristic
338	#432	C₂²×C₇₃	1	1	yes	characteristic
339	#431	C₂²×C₇₃	1	1	yes	characteristic
340	#333	C₂²×C₇₃	1	2	yes	—
341	#333	C₂²×C₇₃	1	2	yes	—
342	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	—
343	D₄⋊C₈	C₂²×C₇₃	1	2	yes	—
344	D₄⋊C₈	C₂²×C₇₃	1	2	yes	—
345	D₄⋊C₈	C₂²×C₇₃	1	2	yes	—
346	C₂×#41	—	2	2	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
350	C₂²×Q₈	D₄×C₇₃	1	2	yes	—
351	C₂×SD₁₆	—	2	1	no	—
352	C₂×SD₁₆	—	2	4	no	—
353	C₂×SD₁₆	—	2	2	no	—
354	C₂×D₈	—	2	1	no	—
355	C₂×D₈	—	2	2	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
359	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
361	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
362	#127	D₄×C₇₃	1	1	yes	characteristic
363	#127	C₂³×C₇₃	1	1	yes	characteristic
364	#126	—	2	4	no	—
365	#125	—	2	2	no	—
366	#124	—	2	2	no	—
367	#124	—	2	4	no	—
368	#124	—	2	1	no	—
369	#124	—	2	1	no	—
370	#123	—	2	4	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	4	no	—
375	#121	—	2	2	no	—
376	#121	—	2	4	no	—
377	#121	—	2	2	no	—
378	#121	—	2	2	no	—
379	#121	—	2	1	no	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	#121	D₄×C₇₃	1	2	yes	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
386	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
396	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
397	C₄×D₄	C₂³×C₇₃	1	2	yes	—
398	#117	—	2	2	no	—
399	#117	—	2	2	no	—
400	#117	—	2	1	no	—
401	#117	D₄×C₇₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
407	#107	—	2	1	no	—
408	#106	—	2	1	no	—
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
413	#103	—	2	1	no	—
414	#103	—	2	4	no	—
415	#103	—	2	2	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	2	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	#97	—	2	1	no	—
424	#97	—	2	1	no	—
425	C₄×C₈	C₂³×C₇₃	1	2	yes	—
426	#41	—	4	1	no	—
427	#41	—	4	1	no	—
428	#41	—	4	2	no	—
429	#41	—	4	2	no	—
430	#41	—	8	2	no	—
431	#41	—	8	4	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	8	2	no	—
436	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
437	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
448	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
459	SD₁₆	—	4	2	no	—
460	SD₁₆	—	8	2	no	—
461	SD₁₆	—	8	4	no	—
462	D₈	—	4	2	no	—
463	D₈	—	8	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	2	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
480	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
499	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	4	1	no	—
503	C₂³	#120×C₇₃	1	1	yes	characteristic
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	4	4	no	—
507	Q₈	—	4	4	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	2	no	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	4	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	2	no	—
522	D₄	—	8	4	no	—
523	D₄	—	8	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	8	4	no	—
542	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
543	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
544	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
548	C₈	—	4	2	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	4	no	—
574	C₄	—	8	1	no	—
575	C₄	#575×C₇₃	1	1	yes	characteristic
576	C₄	#575×C₇₃	1	1	yes	characteristic
577	C₄	#577×C₇₃	1	2	yes	—
578	C₂	—	4	1	no	—
579	C₂	—	8	1	no	—
580	C₂	—	8	2	no	—
581	C₂	—	16	1	no	—
582	C₂	C₇₃×#3005	1	1	yes	characteristic
583	C₂	C₇₃×#3010	1	1	yes	characteristic
584	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×#3511	C₂	semidirect
2. C₇₃×#3214	C₂	semidirect
3. C₇₃×#3206	C₂	semidirect
4. C₇₃×#3115	C₂	semidirect
5. C₇₃×#1646	C₂	semidirect
6. C₇₃×#1643	C₂	semidirect
7. C₇₃×#1624	C₂	semidirect
8. C₇₃×#1622	C₂	semidirect
9. C₇₃×#1558	C₂	semidirect
10. C₇₃×#1496	C₂	semidirect
11. C₇₃×#1488	C₂	semidirect
285. #18820	C₇₃	direct (N × H)
293. #3511	C₂×C₇₃	semidirect
294. #3214	C₂×C₇₃	semidirect
295. #3206	C₂×C₇₃	semidirect
296. #3115	C₂×C₇₃	semidirect
297. #1646	C₂×C₇₃	semidirect
298. #1643	C₂×C₇₃	semidirect
299. #1624	C₂×C₇₃	semidirect
300. #1622	C₂×C₇₃	semidirect
301. #1558	C₂×C₇₃	semidirect
302. #1496	C₂×C₇₃	semidirect
303. #1488	C₂×C₇₃	semidirect
304. C₇₃	#18820	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×#3511	2
C₇₃×#3214	2
C₇₃×#3206	2
C₇₃×#3115	2
C₇₃×#1646	2
C₇₃×#1643	2
C₇₃×#1624	2
C₇₃×#1622	2
C₇₃×#1558	2
C₇₃×#1496	2
C₇₃×#1488	2
#18820	73

Subgroups — C73×#18820 #32928224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18820 #32928224