Subgroups — C₇₃×#61415 #32970819

Order 18688.

1914 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₇₃×#3402	C₂	1	4	yes	maximal, complemented
5	C₇₃×#3400	C₂	1	4	yes	maximal, complemented
6	C₇₃×#3397	C₂	1	4	yes	maximal, complemented
7	C₇₃×#3154	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#3046	C₂	1	2	yes	maximal, complemented
10	C₇₃×#3045	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2951	C₂	1	2	yes	maximal, complemented
15	C₂×#440×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#137×C₇₃	C₂²	1	2	yes	—
17	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
18	C₂×#135×C₇₃	C₂²	1	2	yes	—
19	C₂×#135×C₇₃	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
21	#559×C₇₃	C₂²	1	4	yes	—
22	#559×C₇₃	C₂²	1	2	yes	complemented
23	#557×C₇₃	C₂²	1	2	yes	complemented
24	#556×C₇₃	—	2	1	no	—
25	#556×C₇₃	C₂²	1	2	yes	—
26	#556×C₇₃	C₂²	1	4	yes	complemented
27	#555×C₇₃	—	2	1	no	—
28	#554×C₇₃	—	2	1	no	—
29	#553×C₇₃	—	2	2	no	—
30	#552×C₇₃	—	2	2	no	—
31	#550×C₇₃	C₂²	1	2	yes	—
32	#547×C₇₃	—	2	1	no	—
33	#539×C₇₃	—	2	2	no	—
34	#538×C₇₃	—	2	2	no	—
35	#536×C₇₃	C₂²	1	2	yes	—
36	#535×C₇₃	C₂²	1	2	yes	—
37	#533×C₇₃	C₂²	1	1	yes	characteristic
38	#532×C₇₃	C₂²	1	1	yes	characteristic
39	#532×C₇₃	C₂²	1	1	yes	characteristic
40	#529×C₇₃	—	2	2	no	—
41	#525×C₇₃	—	2	2	no	—
42	#520×C₇₃	C₂²	1	2	yes	—
43	#520×C₇₃	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
46	#497×C₇₃	C₂²	1	4	yes	—
47	#497×C₇₃	C₂²	1	2	yes	complemented
48	#497×C₇₃	C₂²	1	2	yes	complemented
49	#496×C₇₃	C₂²	1	4	yes	—
50	#496×C₇₃	C₂²	1	2	yes	complemented
51	#496×C₇₃	C₂²	1	2	yes	complemented
52	#495×C₇₃	C₂²	1	4	yes	—
53	#492×C₇₃	C₂²	1	4	yes	—
54	#464×C₇₃	C₂²	1	4	yes	—
55	#464×C₇₃	C₂²	1	4	yes	complemented
56	#464×C₇₃	C₂²	1	4	yes	complemented
57	#463×C₇₃	C₂²	1	4	yes	—
58	#463×C₇₃	C₂²	1	4	yes	—
59	#463×C₇₃	C₂²	1	4	yes	complemented
60	#462×C₇₃	C₂²	1	2	yes	complemented
61	#462×C₇₃	C₂²	1	4	yes	complemented
62	#461×C₇₃	C₂²	1	2	yes	—
63	#461×C₇₃	C₂²	1	4	yes	complemented
64	#460×C₇₃	C₂²	1	4	yes	—
65	#460×C₇₃	C₂²	1	2	yes	complemented
66	#459×C₇₃	C₂²	1	2	yes	—
67	#459×C₇₃	C₂²	1	4	yes	—
68	#446×C₇₃	C₂²	1	4	yes	complemented
69	#446×C₇₃	C₂²	1	4	yes	complemented
70	#440×C₇₃	C₂²	1	4	yes	—
71	#440×C₇₃	C₂²	1	4	yes	—
72	#440×C₇₃	C₂²	1	4	yes	complemented
73	#440×C₇₃	C₂²	1	4	yes	complemented
74	C₄×Q₁₆×C₇₃	C₂²	1	4	yes	complemented
75	C₄×D₈×C₇₃	C₂²	1	4	yes	complemented
76	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
77	#424×C₇₃	C₂²	1	2	yes	—
78	#423×C₇₃	C₂²	1	1	yes	characteristic
79	#417×C₇₃	C₂²	1	2	yes	—
80	#417×C₇₃	C₂²	1	2	yes	—
81	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
82	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
83	#405×C₇₃	C₂²	1	2	yes	—
84	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
85	C₂×#41×C₇₃	—	2	2	no	—
86	C₂×#41×C₇₃	C₂³	1	2	yes	—
87	C₂×#41×C₇₃	C₂³	1	2	yes	—
88	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇₃	—	2	1	no	—
91	#137×C₇₃	—	4	4	no	—
92	AGL(1,ℤ/8)×C₇₃	—	4	4	no	—
93	#135×C₇₃	—	2	8	no	—
94	#135×C₇₃	—	4	4	no	—
95	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₇₃	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₇₃	—	2	4	no	—
99	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
101	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₇₃	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
106	C₂×D₈×C₇₃	C₂³	1	2	yes	—
107	C₂×D₈×C₇₃	C₂³	1	4	yes	—
108	C₂×D₈×C₇₃	C₂³	1	2	yes	—
109	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
110	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
113	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
114	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
115	C₄⋊Q₈×C₇₃	C₂³	1	4	yes	—
116	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
117	#127×C₇₃	C₂³	1	1	yes	characteristic
118	#127×C₇₃	C₂³	1	4	yes	—
119	#127×C₇₃	C₂³	1	1	yes	characteristic
120	#126×C₇₃	—	2	4	no	—
121	#126×C₇₃	—	2	4	no	—
122	#126×C₇₃	—	2	4	no	—
123	#125×C₇₃	—	2	2	no	—
124	#125×C₇₃	—	2	4	no	—
125	#125×C₇₃	D₄	1	2	yes	—
126	#124×C₇₃	—	2	2	no	—
127	#124×C₇₃	—	2	4	no	—
128	#124×C₇₃	C₂³	1	2	yes	—
129	#124×C₇₃	C₂³	1	4	yes	—
130	#124×C₇₃	C₂³	1	4	yes	—
131	#124×C₇₃	C₂³	1	2	yes	—
132	#123×C₇₃	—	2	4	no	—
133	#123×C₇₃	—	2	4	no	—
134	#123×C₇₃	—	2	4	no	—
135	#123×C₇₃	—	2	4	no	—
136	C₂²⋊Q₈×C₇₃	—	2	2	no	—
137	C₂²⋊Q₈×C₇₃	—	2	4	no	—
138	C₂²⋊Q₈×C₇₃	—	2	2	no	—
139	C₂²⋊Q₈×C₇₃	—	2	2	no	—
140	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
141	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
142	#121×C₇₃	—	2	1	no	—
143	#121×C₇₃	—	2	1	no	—
144	#121×C₇₃	—	2	1	no	—
145	#121×C₇₃	—	2	1	no	—
146	#121×C₇₃	—	2	2	no	—
147	#121×C₇₃	—	2	2	no	—
148	#121×C₇₃	—	2	2	no	—
149	#121×C₇₃	—	2	4	no	—
150	#120×C₇₃	—	2	4	no	—
151	C₄×Q₈×C₇₃	—	2	2	no	—
152	C₄×Q₈×C₇₃	—	2	1	no	—
153	C₄×Q₈×C₇₃	—	2	1	no	—
154	C₄×Q₈×C₇₃	C₂³	1	4	yes	—
155	C₄×Q₈×C₇₃	C₂³	1	4	yes	—
156	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
160	C₄×D₄×C₇₃	—	2	4	no	—
161	C₄×D₄×C₇₃	—	2	2	no	—
162	C₄×D₄×C₇₃	—	2	4	no	—
163	C₄×D₄×C₇₃	—	2	4	no	—
164	C₄×D₄×C₇₃	—	2	1	no	—
165	C₄×D₄×C₇₃	—	2	1	no	—
166	C₄×D₄×C₇₃	—	2	1	no	—
167	C₄×D₄×C₇₃	—	2	1	no	—
168	C₄×D₄×C₇₃	—	2	1	no	—
169	C₄×D₄×C₇₃	—	2	1	no	—
170	C₄×D₄×C₇₃	C₂³	1	4	yes	—
171	C₄×D₄×C₇₃	C₂³	1	4	yes	—
172	C₄×D₄×C₇₃	C₂³	1	2	yes	—
173	C₄×D₄×C₇₃	C₂³	1	2	yes	—
174	#117×C₇₃	—	2	2	no	—
175	#117×C₇₃	—	2	2	no	—
176	#117×C₇₃	—	2	2	no	—
177	#117×C₇₃	—	2	4	no	—
178	#117×C₇₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
180	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
181	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
182	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
185	C₂×C₄²×C₇₃	—	2	1	no	—
186	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
187	#107×C₇₃	C₂³	1	4	yes	—
188	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
189	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
190	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
191	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
192	#103×C₇₃	C₂³	1	4	yes	—
193	#103×C₇₃	C₂³	1	4	yes	—
194	#103×C₇₃	C₂³	1	4	yes	—
195	#102×C₇₃	C₂³	1	4	yes	—
196	#102×C₇₃	C₂³	1	4	yes	—
197	#102×C₇₃	C₂³	1	4	yes	—
198	#97×C₇₃	C₂³	1	2	yes	—
199	#97×C₇₃	C₂³	1	2	yes	—
200	#97×C₇₃	C₂³	1	4	yes	—
201	C₄×C₈×C₇₃	C₂³	1	4	yes	—
202	C₂⁴×C₇₃	—	2	1	no	—
203	#41×C₇₃	—	2	4	no	—
204	#41×C₇₃	—	2	4	no	—
205	#41×C₇₃	—	2	4	no	—
206	#41×C₇₃	—	2	4	no	—
207	#41×C₇₃	—	8	4	no	—
208	C₂×Q₈×C₇₃	—	2	1	no	—
209	C₂×Q₈×C₇₃	—	2	2	no	—
210	C₂×Q₈×C₇₃	—	2	2	no	—
211	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
212	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
214	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
216	C₂×D₄×C₇₃	—	2	2	no	—
217	C₂×D₄×C₇₃	—	2	2	no	—
218	C₂×D₄×C₇₃	—	2	1	no	—
219	C₂×D₄×C₇₃	—	2	1	no	—
220	C₂×D₄×C₇₃	—	2	1	no	—
221	C₂×D₄×C₇₃	—	2	4	no	—
222	C₂×D₄×C₇₃	—	2	1	no	—
223	C₂×D₄×C₇₃	—	2	1	no	—
224	C₂×D₄×C₇₃	—	2	4	no	—
225	C₂×D₄×C₇₃	—	2	2	no	—
226	C₂×D₄×C₇₃	—	2	2	no	—
227	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
228	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
229	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₇₃	—	2	1	no	—
231	C₂²×C₄×C₇₃	—	2	1	no	—
232	C₂²×C₄×C₇₃	—	2	1	no	—
233	C₂²×C₄×C₇₃	—	2	2	no	—
234	C₂²×C₄×C₇₃	—	2	2	no	—
235	C₂²×C₄×C₇₃	—	2	2	no	—
236	C₂²×C₄×C₇₃	—	2	4	no	—
237	C₂²×C₄×C₇₃	—	2	4	no	—
238	C₂²×C₄×C₇₃	—	2	2	no	—
239	C₂²×C₄×C₇₃	—	8	2	no	—
240	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
243	Q₁₆×C₇₃	—	2	4	no	—
244	Q₁₆×C₇₃	—	4	2	no	—
245	Q₁₆×C₇₃	—	4	4	no	—
246	SD₁₆×C₇₃	—	2	8	no	—
247	SD₁₆×C₇₃	—	2	4	no	—
248	SD₁₆×C₇₃	—	2	4	no	—
249	SD₁₆×C₇₃	—	4	2	no	—
250	SD₁₆×C₇₃	—	4	2	no	—
251	SD₁₆×C₇₃	—	4	4	no	—
252	SD₁₆×C₇₃	—	4	4	no	—
253	D₈×C₇₃	—	2	4	no	—
254	D₈×C₇₃	—	4	2	no	—
255	D₈×C₇₃	—	4	4	no	—
256	M₁₆×C₇₃	—	2	4	no	—
257	C₂×C₈×C₇₃	—	2	2	no	—
258	C₂×C₈×C₇₃	#41	1	4	yes	complemented
259	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
260	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₇₃	—	2	1	no	—
263	C₄⋊C₄×C₇₃	—	2	1	no	—
264	C₄⋊C₄×C₇₃	—	2	4	no	—
265	C₄⋊C₄×C₇₃	—	2	4	no	—
266	C₄⋊C₄×C₇₃	—	2	2	no	—
267	C₄⋊C₄×C₇₃	—	2	2	no	—
268	C₄⋊C₄×C₇₃	—	2	1	no	—
269	C₄⋊C₄×C₇₃	—	2	4	no	—
270	C₄⋊C₄×C₇₃	—	2	1	no	—
271	C₄⋊C₄×C₇₃	—	2	1	no	—
272	C₄⋊C₄×C₇₃	—	2	1	no	—
273	C₄⋊C₄×C₇₃	—	2	4	no	—
274	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
275	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
276	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
277	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
279	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
282	C₂²⋊C₄×C₇₃	—	2	2	no	—
283	C₂²⋊C₄×C₇₃	—	2	2	no	—
284	C₂²⋊C₄×C₇₃	—	2	2	no	—
285	C₂²⋊C₄×C₇₃	—	2	4	no	—
286	C₂²⋊C₄×C₇₃	—	2	4	no	—
287	C₂²⋊C₄×C₇₃	—	2	4	no	—
288	C₂²⋊C₄×C₇₃	—	2	4	no	—
289	C₂²⋊C₄×C₇₃	—	2	2	no	—
290	C₂²⋊C₄×C₇₃	—	2	4	no	—
291	C₂²⋊C₄×C₇₃	—	2	2	no	—
292	C₂²⋊C₄×C₇₃	—	2	2	no	—
293	C₂²⋊C₄×C₇₃	—	2	4	no	—
294	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
295	C₄²×C₇₃	—	2	2	no	—
296	C₄²×C₇₃	—	2	2	no	—
297	C₄²×C₇₃	—	2	4	no	—
298	C₄²×C₇₃	—	2	4	no	—
299	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₇₃	C₂⁴	1	4	yes	—
302	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
303	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
304	C₂³×C₇₃	—	2	2	no	—
305	C₂³×C₇₃	—	2	2	no	—
306	C₂³×C₇₃	—	2	2	no	—
307	C₂³×C₇₃	—	4	2	no	—
308	C₂³×C₇₃	—	8	1	no	—
309	C₂³×C₇₃	—	8	1	no	—
310	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
311	Q₈×C₇₃	—	2	2	no	—
312	Q₈×C₇₃	—	2	2	no	—
313	Q₈×C₇₃	—	2	2	no	—
314	Q₈×C₇₃	—	2	2	no	—
315	Q₈×C₇₃	—	2	2	no	—
316	Q₈×C₇₃	—	2	2	no	—
317	Q₈×C₇₃	—	4	2	no	—
318	Q₈×C₇₃	—	4	2	no	—
319	Q₈×C₇₃	—	4	2	no	—
320	D₄×C₇₃	—	2	2	no	—
321	D₄×C₇₃	—	2	2	no	—
322	D₄×C₇₃	—	2	2	no	—
323	D₄×C₇₃	—	2	2	no	—
324	D₄×C₇₃	—	2	2	no	—
325	D₄×C₇₃	—	2	2	no	—
326	D₄×C₇₃	—	4	2	no	—
327	D₄×C₇₃	—	4	2	no	—
328	D₄×C₇₃	—	4	4	no	—
329	D₄×C₇₃	—	4	4	no	—
330	D₄×C₇₃	—	4	2	no	—
331	D₄×C₇₃	—	8	1	no	—
332	D₄×C₇₃	—	8	1	no	—
333	D₄×C₇₃	—	8	4	no	—
334	D₄×C₇₃	—	8	4	no	—
335	C₂×C₄×C₇₃	—	2	2	no	—
336	C₂×C₄×C₇₃	—	2	2	no	—
337	C₂×C₄×C₇₃	—	2	2	no	—
338	C₂×C₄×C₇₃	—	2	2	no	—
339	C₂×C₄×C₇₃	—	2	2	no	—
340	C₂×C₄×C₇₃	—	4	1	no	—
341	C₂×C₄×C₇₃	—	4	1	no	—
342	C₂×C₄×C₇₃	—	4	4	no	—
343	C₂×C₄×C₇₃	—	4	2	no	—
344	C₂×C₄×C₇₃	—	4	4	no	—
345	C₂×C₄×C₇₃	—	4	4	no	—
346	C₂×C₄×C₇₃	—	8	4	no	—
347	C₂×C₄×C₇₃	—	8	2	no	—
348	C₂×C₄×C₇₃	—	8	4	no	—
349	C₂×C₄×C₇₃	—	8	1	no	—
350	C₂×C₄×C₇₃	—	8	1	no	—
351	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
354	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
359	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
360	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
361	C₈×C₇₃	—	2	2	no	—
362	C₈×C₇₃	—	2	4	no	—
363	C₈×C₇₃	C₂×#41	1	4	yes	—
364	C₂²×C₇₃	—	2	1	no	—
365	C₂²×C₇₃	—	2	1	no	—
366	C₂²×C₇₃	—	4	2	no	—
367	C₂²×C₇₃	—	4	2	no	—
368	C₂²×C₇₃	—	4	2	no	—
369	C₂²×C₇₃	—	4	2	no	—
370	C₂²×C₇₃	—	4	2	no	—
371	C₂²×C₇₃	—	4	2	no	—
372	C₂²×C₇₃	—	4	2	no	—
373	C₂²×C₇₃	—	4	2	no	—
374	C₂²×C₇₃	—	4	2	no	—
375	C₂²×C₇₃	—	8	4	no	—
376	C₂²×C₇₃	#550	1	2	yes	—
377	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
378	C₄×C₇₃	—	2	1	no	—
379	C₄×C₇₃	—	2	1	no	—
380	C₄×C₇₃	—	2	4	no	—
381	C₄×C₇₃	—	2	1	no	—
382	C₄×C₇₃	—	2	1	no	—
383	C₄×C₇₃	—	2	4	no	—
384	C₄×C₇₃	—	4	2	no	—
385	C₄×C₇₃	—	4	2	no	—
386	C₄×C₇₃	—	4	2	no	—
387	C₄×C₇₃	—	4	2	no	—
388	C₄×C₇₃	—	4	2	no	—
389	C₄×C₇₃	#550	1	2	yes	—
390	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
391	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	#61415	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
393	C₂×C₇₃	—	2	2	no	—
394	C₂×C₇₃	—	8	2	no	—
395	C₂×C₇₃	—	8	2	no	—
396	C₂×C₇₃	—	8	2	no	—
397	C₂×C₇₃	C₂×#550	1	1	yes	characteristic
398	C₂×C₇₃	#3585	1	1	yes	characteristic
399	C₂×C₇₃	#3586	1	1	yes	characteristic
400	#3507	C₂×C₇₃	1	1	yes	characteristic, complemented
401	#3506	C₂×C₇₃	1	1	yes	characteristic, complemented
402	#3403	C₂×C₇₃	1	4	yes	complemented
403	#3402	C₂×C₇₃	1	4	yes	complemented
404	#3400	C₂×C₇₃	1	4	yes	complemented
405	#3397	C₂×C₇₃	1	4	yes	complemented
406	#3154	C₂×C₇₃	1	2	yes	complemented
407	#3150	C₂×C₇₃	1	1	yes	characteristic, complemented
408	#3046	C₂×C₇₃	1	2	yes	complemented
409	#3045	C₂×C₇₃	1	2	yes	complemented
410	#3037	C₂×C₇₃	1	1	yes	characteristic, complemented
411	#3036	C₂×C₇₃	1	1	yes	characteristic, complemented
412	#2961	C₂×C₇₃	1	1	yes	characteristic, complemented
413	#2951	C₂×C₇₃	1	2	yes	complemented
414	C₂×#440	C₂×C₇₃	1	1	yes	characteristic, complemented
415	C₇₃	#61415	1	1	yes	characteristic, direct product factor, Sylow
416	C₂×#137	C₂²×C₇₃	1	2	yes	—
417	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
418	C₂×#135	C₂²×C₇₃	1	2	yes	—
419	C₂×#135	C₂²×C₇₃	1	2	yes	—
420	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
421	#559	C₂²×C₇₃	1	4	yes	—
422	#559	C₂²×C₇₃	1	2	yes	complemented
423	#557	C₂²×C₇₃	1	2	yes	complemented
424	#556	—	2	1	no	—
425	#556	C₂²×C₇₃	1	2	yes	—
426	#556	C₂²×C₇₃	1	4	yes	complemented
427	#555	—	2	1	no	—
428	#554	—	2	1	no	—
429	#553	—	2	2	no	—
430	#552	—	2	2	no	—
431	#550	C₂²×C₇₃	1	2	yes	—
432	#547	—	2	1	no	—
433	#539	—	2	2	no	—
434	#538	—	2	2	no	—
435	#536	C₂²×C₇₃	1	2	yes	—
436	#535	C₂²×C₇₃	1	2	yes	—
437	#533	C₂²×C₇₃	1	1	yes	characteristic
438	#532	C₂²×C₇₃	1	1	yes	characteristic
439	#532	C₂²×C₇₃	1	1	yes	characteristic
440	#529	—	2	2	no	—
441	#525	—	2	2	no	—
442	#520	C₂²×C₇₃	1	2	yes	—
443	#520	C₂²×C₇₃	1	2	yes	—
444	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
446	#497	C₂²×C₇₃	1	4	yes	—
447	#497	C₂²×C₇₃	1	2	yes	complemented
448	#497	C₂²×C₇₃	1	2	yes	complemented
449	#496	C₂²×C₇₃	1	4	yes	—
450	#496	C₂²×C₇₃	1	2	yes	complemented
451	#496	C₂²×C₇₃	1	2	yes	complemented
452	#495	C₂²×C₇₃	1	4	yes	—
453	#492	C₂²×C₇₃	1	4	yes	—
454	#464	C₂²×C₇₃	1	4	yes	—
455	#464	C₂²×C₇₃	1	4	yes	complemented
456	#464	C₂²×C₇₃	1	4	yes	complemented
457	#463	C₂²×C₇₃	1	4	yes	—
458	#463	C₂²×C₇₃	1	4	yes	—
459	#463	C₂²×C₇₃	1	4	yes	complemented
460	#462	C₂²×C₇₃	1	4	yes	complemented
461	#462	C₂²×C₇₃	1	2	yes	complemented
462	#461	C₂²×C₇₃	1	2	yes	—
463	#461	C₂²×C₇₃	1	4	yes	complemented
464	#460	C₂²×C₇₃	1	4	yes	—
465	#460	C₂²×C₇₃	1	2	yes	complemented
466	#459	C₂²×C₇₃	1	4	yes	—
467	#459	C₂²×C₇₃	1	2	yes	—
468	#446	C₂²×C₇₃	1	4	yes	complemented
469	#446	C₂²×C₇₃	1	4	yes	complemented
470	#440	C₂²×C₇₃	1	4	yes	—
471	#440	C₂²×C₇₃	1	4	yes	—
472	#440	C₂²×C₇₃	1	4	yes	complemented
473	#440	C₂²×C₇₃	1	4	yes	complemented
474	C₄×Q₁₆	C₂²×C₇₃	1	4	yes	complemented
475	C₄×D₈	C₂²×C₇₃	1	4	yes	complemented
476	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
477	#424	C₂²×C₇₃	1	2	yes	—
478	#423	C₂²×C₇₃	1	1	yes	characteristic
479	#417	C₂²×C₇₃	1	2	yes	—
480	#417	C₂²×C₇₃	1	2	yes	—
481	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
482	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
483	#405	C₂²×C₇₃	1	2	yes	—
484	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
485	C₂×#41	—	2	2	no	—
486	C₂×#41	C₂³×C₇₃	1	2	yes	—
487	C₂×#41	C₂³×C₇₃	1	2	yes	—
488	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
490	C₂³×C₄	—	2	1	no	—
491	#137	—	4	4	no	—
492	AGL(1,ℤ/8)	—	4	4	no	—
493	#135	—	2	8	no	—
494	#135	—	4	4	no	—
495	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
496	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
497	C₂×Q₁₆	C₂³×C₇₃	1	4	yes	—
498	C₂×SD₁₆	—	2	4	no	—
499	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
500	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
501	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
502	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
503	C₂×SD₁₆	C₂³×C₇₃	1	2	yes	—
504	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
505	C₂×SD₁₆	C₂³×C₇₃	1	4	yes	—
506	C₂×D₈	C₂³×C₇₃	1	2	yes	—
507	C₂×D₈	C₂³×C₇₃	1	2	yes	—
508	C₂×D₈	C₂³×C₇₃	1	4	yes	—
509	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
510	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
512	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
513	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₇₃	1	4	yes	—
517	#127	C₂³×C₇₃	1	1	yes	characteristic
518	#127	C₂³×C₇₃	1	1	yes	characteristic
519	#127	C₂³×C₇₃	1	4	yes	—
520	#126	—	2	4	no	—
521	#126	—	2	4	no	—
522	#126	—	2	4	no	—
523	#125	—	2	2	no	—
524	#125	—	2	4	no	—
525	#125	D₄×C₇₃	1	2	yes	—
526	#124	—	2	2	no	—
527	#124	—	2	4	no	—
528	#124	C₂³×C₇₃	1	2	yes	—
529	#124	C₂³×C₇₃	1	2	yes	—
530	#124	C₂³×C₇₃	1	4	yes	—
531	#124	C₂³×C₇₃	1	4	yes	—
532	#123	—	2	4	no	—
533	#123	—	2	4	no	—
534	#123	—	2	4	no	—
535	#123	—	2	4	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
541	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
542	#121	—	2	1	no	—
543	#121	—	2	1	no	—
544	#121	—	2	1	no	—
545	#121	—	2	1	no	—
546	#121	—	2	2	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	—	2	4	no	—
550	#120	—	2	4	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
555	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
556	C₄×Q₈	C₂³×C₇₃	1	4	yes	—
557	C₄×Q₈	C₂³×C₇₃	1	4	yes	—
558	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
559	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
560	C₄×D₄	—	2	4	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	4	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	C₂³×C₇₃	1	2	yes	—
571	C₄×D₄	C₂³×C₇₃	1	2	yes	—
572	C₄×D₄	C₂³×C₇₃	1	4	yes	—
573	C₄×D₄	C₂³×C₇₃	1	4	yes	—
574	#117	—	2	2	no	—
575	#117	—	2	2	no	—
576	#117	—	2	2	no	—
577	#117	—	2	4	no	—
578	#117	C₂³×C₇₃	1	2	yes	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	2	no	—
581	C₂×C₄⋊C₄	—	2	2	no	—
582	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₄²	—	2	1	no	—
586	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
587	#107	C₂³×C₇₃	1	4	yes	—
588	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
589	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
590	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
591	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
592	#103	C₂³×C₇₃	1	4	yes	—
593	#103	C₂³×C₇₃	1	4	yes	—
594	#103	C₂³×C₇₃	1	4	yes	—
595	#102	C₂³×C₇₃	1	4	yes	—
596	#102	C₂³×C₇₃	1	4	yes	—
597	#102	C₂³×C₇₃	1	4	yes	—
598	#97	C₂³×C₇₃	1	2	yes	—
599	#97	C₂³×C₇₃	1	2	yes	—
600	#97	C₂³×C₇₃	1	4	yes	—
601	C₄×C₈	C₂³×C₇₃	1	4	yes	—
602	C₂⁴	—	2	1	no	—
603	#41	—	2	4	no	—
604	#41	—	2	4	no	—
605	#41	—	2	4	no	—
606	#41	—	2	4	no	—
607	#41	—	8	4	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
612	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
613	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
614	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
615	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
628	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
629	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	8	2	no	—
640	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
643	Q₁₆	—	2	4	no	—
644	Q₁₆	—	4	2	no	—
645	Q₁₆	—	4	4	no	—
646	SD₁₆	—	2	8	no	—
647	SD₁₆	—	2	4	no	—
648	SD₁₆	—	2	4	no	—
649	SD₁₆	—	4	2	no	—
650	SD₁₆	—	4	2	no	—
651	SD₁₆	—	4	4	no	—
652	SD₁₆	—	4	4	no	—
653	D₈	—	2	4	no	—
654	D₈	—	4	2	no	—
655	D₈	—	4	4	no	—
656	M₁₆	—	2	4	no	—
657	C₂×C₈	—	2	2	no	—
658	C₂×C₈	#41×C₇₃	1	4	yes	complemented
659	C₂×C₈	C₂⁴×C₇₃	1	4	yes	—
660	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
661	C₂×C₈	C₂⁴×C₇₃	1	2	yes	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	4	no	—
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	2	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
675	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
676	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
677	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
678	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
679	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₇₃	1	2	yes	—
682	C₂²⋊C₄	—	2	2	no	—
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	2	no	—
697	C₄²	—	2	4	no	—
698	C₄²	—	2	4	no	—
699	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
700	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
701	C₄²	C₂⁴×C₇₃	1	4	yes	—
702	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
703	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	8	1	no	—
709	C₂³	—	8	1	no	—
710	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
711	Q₈	—	2	2	no	—
712	Q₈	—	2	2	no	—
713	Q₈	—	2	2	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	4	2	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	4	2	no	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	4	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	2	no	—
731	D₄	—	8	4	no	—
732	D₄	—	8	1	no	—
733	D₄	—	8	1	no	—
734	D₄	—	8	4	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	4	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	4	4	no	—
745	C₂×C₄	—	4	4	no	—
746	C₂×C₄	—	8	2	no	—
747	C₂×C₄	—	8	4	no	—
748	C₂×C₄	—	8	4	no	—
749	C₂×C₄	—	8	1	no	—
750	C₂×C₄	—	8	1	no	—
751	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
752	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
753	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
754	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
755	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
756	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
757	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
758	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
759	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
760	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
761	C₈	—	2	2	no	—
762	C₈	—	2	4	no	—
763	C₈	C₂×#41×C₇₃	1	4	yes	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	2	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	8	4	no	—
776	C₂²	#550×C₇₃	1	2	yes	—
777	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
778	C₄	—	2	1	no	—
779	C₄	—	2	1	no	—
780	C₄	—	2	4	no	—
781	C₄	—	2	1	no	—
782	C₄	—	2	1	no	—
783	C₄	—	2	4	no	—
784	C₄	—	4	2	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	4	2	no	—
788	C₄	—	4	2	no	—
789	C₄	#550×C₇₃	1	2	yes	—
790	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
791	C₄	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
792	C₂	—	2	2	no	—
793	C₂	—	8	2	no	—
794	C₂	—	8	2	no	—
795	C₂	—	8	2	no	—
796	C₂	C₂×#550×C₇₃	1	1	yes	characteristic
797	C₂	C₇₃×#3585	1	1	yes	characteristic
798	C₂	C₇₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ #533×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3507	C₂	semidirect
2. C₇₃×#3506	C₂	semidirect
3. C₇₃×#3403	C₂	semidirect
4. C₇₃×#3402	C₂	semidirect
5. C₇₃×#3400	C₂	semidirect
6. C₇₃×#3397	C₂	semidirect
7. C₇₃×#3154	C₂	semidirect
8. C₇₃×#3150	C₂	semidirect
9. C₇₃×#3046	C₂	semidirect
10. C₇₃×#3045	C₂	semidirect
11. C₇₃×#3037	C₂	semidirect
12. C₇₃×#3036	C₂	semidirect
13. C₇₃×#2961	C₂	semidirect
14. C₇₃×#2951	C₂	semidirect
15. C₂×#440×C₇₃	C₂	semidirect
22. #559×C₇₃	C₂²	semidirect
23. #557×C₇₃	C₂²	semidirect
26. #556×C₇₃	C₂²	semidirect
47. #497×C₇₃	C₂²	semidirect
48. #497×C₇₃	C₂²	semidirect
50. #496×C₇₃	C₂²	semidirect
51. #496×C₇₃	C₂²	semidirect
55. #464×C₇₃	C₂²	semidirect
56. #464×C₇₃	C₂²	semidirect
59. #463×C₇₃	C₂²	semidirect
60. #462×C₇₃	C₂²	semidirect
61. #462×C₇₃	C₂²	semidirect
63. #461×C₇₃	C₂²	semidirect
65. #460×C₇₃	C₂²	semidirect
68. #446×C₇₃	C₂²	semidirect
69. #446×C₇₃	C₂²	semidirect
72. #440×C₇₃	C₂²	semidirect
73. #440×C₇₃	C₂²	semidirect
74. C₄×Q₁₆×C₇₃	C₂²	semidirect
75. C₄×D₈×C₇₃	C₂²	semidirect
258. C₂×C₈×C₇₃	#41	semidirect
392. #61415	C₇₃	direct (N × H)
400. #3507	C₂×C₇₃	semidirect
401. #3506	C₂×C₇₃	semidirect
402. #3403	C₂×C₇₃	semidirect
403. #3402	C₂×C₇₃	semidirect
404. #3400	C₂×C₇₃	semidirect
405. #3397	C₂×C₇₃	semidirect
406. #3154	C₂×C₇₃	semidirect
407. #3150	C₂×C₇₃	semidirect
408. #3046	C₂×C₇₃	semidirect
409. #3045	C₂×C₇₃	semidirect
410. #3037	C₂×C₇₃	semidirect
411. #3036	C₂×C₇₃	semidirect
412. #2961	C₂×C₇₃	semidirect
413. #2951	C₂×C₇₃	semidirect
414. C₂×#440	C₂×C₇₃	semidirect
415. C₇₃	#61415	direct (N × H)
422. #559	C₂²×C₇₃	semidirect
423. #557	C₂²×C₇₃	semidirect
426. #556	C₂²×C₇₃	semidirect
447. #497	C₂²×C₇₃	semidirect
448. #497	C₂²×C₇₃	semidirect
450. #496	C₂²×C₇₃	semidirect
451. #496	C₂²×C₇₃	semidirect
455. #464	C₂²×C₇₃	semidirect
456. #464	C₂²×C₇₃	semidirect
459. #463	C₂²×C₇₃	semidirect
460. #462	C₂²×C₇₃	semidirect
461. #462	C₂²×C₇₃	semidirect
463. #461	C₂²×C₇₃	semidirect
465. #460	C₂²×C₇₃	semidirect
468. #446	C₂²×C₇₃	semidirect
469. #446	C₂²×C₇₃	semidirect
472. #440	C₂²×C₇₃	semidirect
473. #440	C₂²×C₇₃	semidirect
474. C₄×Q₁₆	C₂²×C₇₃	semidirect
475. C₄×D₈	C₂²×C₇₃	semidirect
658. C₂×C₈	#41×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3507	2
C₇₃×#3506	2
C₇₃×#3403	2
C₇₃×#3402	2
C₇₃×#3400	2
C₇₃×#3397	2
C₇₃×#3154	2
C₇₃×#3150	2
C₇₃×#3046	2
C₇₃×#3045	2
C₇₃×#3037	2
C₇₃×#3036	2
C₇₃×#2961	2
C₇₃×#2951	2
C₂×#440×C₇₃	2
#61415	73

Subgroups — C73×#61415 #32970819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#61415 #32970819