Subgroups — C₆₇×#61220 #30740471

Order 17152.

2082 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3321	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3320	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3309	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3308	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3098	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3062	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3010	C₂	1	2	yes	maximal, complemented
13	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2898	C₂	1	2	yes	maximal, complemented
16	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	—
17	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#131×C₆₇	C₂²	1	2	yes	—
20	#559×C₆₇	—	2	2	no	—
21	#556×C₆₇	—	2	1	no	—
22	#555×C₆₇	C₂²	1	2	yes	—
23	#553×C₆₇	C₂²	1	4	yes	—
24	#550×C₆₇	—	2	1	no	—
25	#550×C₆₇	—	2	1	no	—
26	#550×C₆₇	C₂²	1	2	yes	complemented
27	D₄×Q₈×C₆₇	—	2	1	no	—
28	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
29	#548×C₆₇	—	2	2	no	—
30	#548×C₆₇	C₂²	1	4	yes	complemented
31	#547×C₆₇	C₂²	1	2	yes	—
32	#538×C₆₇	—	2	2	no	—
33	#537×C₆₇	—	2	2	no	—
34	#537×C₆₇	C₂²	1	2	yes	—
35	#535×C₆₇	C₂²	1	2	yes	—
36	#533×C₆₇	C₂²	1	1	yes	characteristic
37	#532×C₆₇	—	2	2	no	—
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#525×C₆₇	—	2	2	no	—
41	#520×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	#491×C₆₇	C₂²	1	2	yes	complemented
45	#490×C₆₇	C₂²	1	2	yes	complemented
46	#489×C₆₇	C₂²	1	2	yes	complemented
47	#489×C₆₇	C₂²	1	2	yes	complemented
48	#485×C₆₇	C₂²	1	4	yes	complemented
49	#484×C₆₇	C₂²	1	4	yes	complemented
50	#482×C₆₇	C₂²	1	4	yes	complemented
51	#480×C₆₇	C₂²	1	4	yes	complemented
52	#479×C₆₇	C₂²	1	4	yes	complemented
53	#477×C₆₇	C₂²	1	2	yes	complemented
54	#475×C₆₇	C₂²	1	2	yes	complemented
55	#469×C₆₇	C₂²	1	4	yes	—
56	#468×C₆₇	C₂²	1	4	yes	—
57	#466×C₆₇	C₂²	1	4	yes	—
58	#465×C₆₇	C₂²	1	4	yes	—
59	#463×C₆₇	C₂²	1	4	yes	—
60	#461×C₆₇	C₂²	1	2	yes	—
61	#459×C₆₇	C₂²	1	2	yes	—
62	#449×C₆₇	C₂²	1	4	yes	—
63	#449×C₆₇	C₂²	1	4	yes	—
64	#448×C₆₇	C₂²	1	4	yes	—
65	#448×C₆₇	C₂²	1	4	yes	—
66	#440×C₆₇	C₂²	1	4	yes	—
67	#440×C₆₇	C₂²	1	4	yes	—
68	#435×C₆₇	C₂²	1	4	yes	complemented
69	#435×C₆₇	C₂²	1	4	yes	complemented
70	#428×C₆₇	C₂²	1	2	yes	—
71	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
72	#423×C₆₇	C₂²	1	1	yes	characteristic
73	#419×C₆₇	C₂²	1	2	yes	—
74	#419×C₆₇	C₂²	1	4	yes	complemented
75	#417×C₆₇	C₂²	1	2	yes	—
76	#417×C₆₇	C₂²	1	4	yes	complemented
77	#416×C₆₇	C₂²	1	2	yes	—
78	#416×C₆₇	C₂²	1	2	yes	—
79	#416×C₆₇	C₂²	1	4	yes	complemented
80	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
81	C₂×#103×C₆₇	C₂²	1	4	yes	complemented
82	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
83	#408×C₆₇	C₂²	1	2	yes	—
84	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
85	2₋¹⁺⁴×C₆₇	—	2	8	no	—
86	2₋¹⁺⁴×C₆₇	—	4	4	no	—
87	C₂×#41×C₆₇	—	2	4	no	—
88	C₂×#41×C₆₇	—	2	2	no	—
89	C₂×#41×C₆₇	—	2	2	no	—
90	C₂×#41×C₆₇	C₂³	1	2	yes	—
91	C₂×#41×C₆₇	C₂³	1	4	yes	—
92	C₂×#41×C₆₇	C₂³	1	2	yes	—
93	C₂²×Q₈×C₆₇	—	2	2	no	—
94	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
95	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	—	2	1	no	—
98	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
99	C₂×SD₁₆×C₆₇	—	2	4	no	—
100	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×D₈×C₆₇	C₂³	1	4	yes	—
103	#131×C₆₇	—	4	4	no	—
104	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
105	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
106	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₆₇	—	2	2	no	—
110	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	#127×C₆₇	—	2	2	no	—
115	#127×C₆₇	—	2	2	no	—
116	#127×C₆₇	D₄	1	1	yes	characteristic
117	#127×C₆₇	C₂³	1	1	yes	characteristic
118	#126×C₆₇	—	2	4	no	—
119	#125×C₆₇	C₂³	1	2	yes	—
120	#124×C₆₇	—	2	2	no	—
121	#124×C₆₇	—	2	4	no	—
122	#124×C₆₇	—	2	4	no	—
123	#124×C₆₇	D₄	1	2	yes	—
124	#124×C₆₇	C₂³	1	2	yes	—
125	#123×C₆₇	—	2	4	no	—
126	#123×C₆₇	—	2	4	no	—
127	C₂²⋊Q₈×C₆₇	—	2	2	no	—
128	C₂²⋊Q₈×C₆₇	—	2	1	no	—
129	C₂²⋊Q₈×C₆₇	—	2	1	no	—
130	C₂²⋊Q₈×C₆₇	—	2	2	no	—
131	C₂²⋊Q₈×C₆₇	—	2	4	no	—
132	C₂²⋊Q₈×C₆₇	—	2	4	no	—
133	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
134	#121×C₆₇	—	2	2	no	—
135	#121×C₆₇	—	2	4	no	—
136	#121×C₆₇	—	2	4	no	—
137	#121×C₆₇	—	2	2	no	—
138	#121×C₆₇	—	2	4	no	—
139	#121×C₆₇	—	2	1	no	—
140	#121×C₆₇	—	2	1	no	—
141	#121×C₆₇	—	2	4	no	—
142	#121×C₆₇	D₄	1	2	yes	—
143	#121×C₆₇	D₄	1	2	yes	—
144	#121×C₆₇	C₂³	1	4	yes	—
145	#121×C₆₇	C₂³	1	4	yes	—
146	#121×C₆₇	C₂³	1	4	yes	—
147	#120×C₆₇	—	2	4	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	1	no	—
150	C₄×Q₈×C₆₇	—	2	1	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	—	2	1	no	—
153	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
154	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
155	C₄×D₄×C₆₇	—	2	4	no	—
156	C₄×D₄×C₆₇	—	2	2	no	—
157	C₄×D₄×C₆₇	—	2	2	no	—
158	C₄×D₄×C₆₇	—	2	2	no	—
159	C₄×D₄×C₆₇	—	2	4	no	—
160	C₄×D₄×C₆₇	—	2	4	no	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	1	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	C₂³	1	2	yes	—
168	C₄×D₄×C₆₇	C₂³	1	2	yes	—
169	#117×C₆₇	—	2	2	no	—
170	#117×C₆₇	C₂³	1	4	yes	—
171	#117×C₆₇	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
177	C₂×C₄²×C₆₇	—	2	1	no	—
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	#107×C₆₇	C₂³	1	4	yes	—
180	#107×C₆₇	C₂³	1	4	yes	—
181	#106×C₆₇	C₂³	1	4	yes	—
182	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
183	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
184	#103×C₆₇	C₂³	1	2	yes	—
185	#103×C₆₇	C₂³	1	2	yes	—
186	#103×C₆₇	C₂³	1	4	yes	—
187	#103×C₆₇	C₂³	1	4	yes	—
188	#103×C₆₇	C₂³	1	4	yes	—
189	#103×C₆₇	C₂³	1	2	yes	—
190	#103×C₆₇	C₂³	1	2	yes	—
191	#103×C₆₇	C₂³	1	4	yes	—
192	#102×C₆₇	C₂³	1	2	yes	—
193	#102×C₆₇	C₂³	1	2	yes	—
194	#102×C₆₇	C₂³	1	4	yes	—
195	#102×C₆₇	C₂³	1	4	yes	—
196	#102×C₆₇	C₂³	1	2	yes	—
197	#102×C₆₇	C₂³	1	2	yes	—
198	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
199	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
200	#97×C₆₇	C₂³	1	2	yes	—
201	#97×C₆₇	C₂³	1	2	yes	—
202	C₂⁴×C₆₇	—	2	1	no	—
203	#41×C₆₇	—	2	4	no	—
204	#41×C₆₇	—	2	4	no	—
205	#41×C₆₇	—	2	8	no	—
206	#41×C₆₇	—	2	4	no	—
207	#41×C₆₇	—	2	4	no	—
208	#41×C₆₇	—	4	4	no	—
209	#41×C₆₇	—	4	16	no	—
210	#41×C₆₇	—	4	8	no	—
211	#41×C₆₇	—	8	4	no	—
212	C₂×Q₈×C₆₇	—	2	1	no	—
213	C₂×Q₈×C₆₇	—	2	1	no	—
214	C₂×Q₈×C₆₇	—	2	4	no	—
215	C₂×Q₈×C₆₇	—	2	1	no	—
216	C₂×Q₈×C₆₇	—	2	2	no	—
217	C₂×Q₈×C₆₇	—	2	8	no	—
218	C₂×Q₈×C₆₇	—	4	4	no	—
219	C₂×Q₈×C₆₇	—	4	8	no	—
220	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
221	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
222	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
223	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
224	C₂×D₄×C₆₇	—	2	2	no	—
225	C₂×D₄×C₆₇	—	2	4	no	—
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	4	no	—
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	2	1	no	—
231	C₂×D₄×C₆₇	—	2	1	no	—
232	C₂×D₄×C₆₇	—	2	2	no	—
233	C₂×D₄×C₆₇	—	2	2	no	—
234	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
235	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
237	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	—	2	4	no	—
242	C₂²×C₄×C₆₇	—	2	1	no	—
243	C₂²×C₄×C₆₇	—	2	1	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	2	4	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	8	2	no	—
250	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	SD₁₆×C₆₇	—	2	8	no	—
255	SD₁₆×C₆₇	—	4	4	no	—
256	D₈×C₆₇	—	4	4	no	—
257	M₁₆×C₆₇	—	2	4	no	—
258	M₁₆×C₆₇	—	4	4	no	—
259	C₂×C₈×C₆₇	—	2	2	no	—
260	C₂×C₈×C₆₇	—	2	2	no	—
261	C₂×C₈×C₆₇	—	4	4	no	—
262	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
263	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
264	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
265	C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₄⋊C₄×C₆₇	—	2	2	no	—
267	C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	1	no	—
270	C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₄⋊C₄×C₆₇	—	2	1	no	—
272	C₄⋊C₄×C₆₇	—	2	2	no	—
273	C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₄⋊C₄×C₆₇	—	2	4	no	—
275	C₄⋊C₄×C₆₇	—	2	2	no	—
276	C₄⋊C₄×C₆₇	—	2	1	no	—
277	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₆₇	—	2	2	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	2	no	—
287	C₂²⋊C₄×C₆₇	—	2	2	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	2	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	no	—
293	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
294	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
295	C₄²×C₆₇	—	2	2	no	—
296	C₄²×C₆₇	—	2	2	no	—
297	C₄²×C₆₇	—	2	4	no	—
298	C₄²×C₆₇	—	2	2	no	—
299	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	2	no	—
305	C₂³×C₆₇	—	4	2	no	—
306	C₂³×C₆₇	—	8	1	no	—
307	C₂³×C₆₇	—	8	1	no	—
308	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
309	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
310	Q₈×C₆₇	—	2	4	no	—
311	Q₈×C₆₇	—	2	4	no	—
312	Q₈×C₆₇	—	2	2	no	—
313	Q₈×C₆₇	—	2	2	no	—
314	Q₈×C₆₇	—	2	2	no	—
315	Q₈×C₆₇	—	4	8	no	—
316	Q₈×C₆₇	—	4	2	no	—
317	Q₈×C₆₇	—	8	1	no	—
318	Q₈×C₆₇	C₂×#41	1	4	yes	—
319	D₄×C₆₇	—	2	8	no	—
320	D₄×C₆₇	—	2	4	no	—
321	D₄×C₆₇	—	2	2	no	—
322	D₄×C₆₇	—	2	2	no	—
323	D₄×C₆₇	—	2	2	no	—
324	D₄×C₆₇	—	2	2	no	—
325	D₄×C₆₇	—	4	2	no	—
326	D₄×C₆₇	—	4	2	no	—
327	D₄×C₆₇	—	4	8	no	—
328	D₄×C₆₇	—	4	2	no	—
329	D₄×C₆₇	—	4	4	no	—
330	D₄×C₆₇	—	4	2	no	—
331	D₄×C₆₇	—	8	1	no	—
332	D₄×C₆₇	—	8	4	no	—
333	D₄×C₆₇	—	8	4	no	—
334	D₄×C₆₇	—	8	4	no	—
335	C₂×C₄×C₆₇	—	2	4	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	4	no	—
338	C₂×C₄×C₆₇	—	2	4	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	4	1	no	—
345	C₂×C₄×C₆₇	—	4	1	no	—
346	C₂×C₄×C₆₇	—	4	8	no	—
347	C₂×C₄×C₆₇	—	4	8	no	—
348	C₂×C₄×C₆₇	—	4	4	no	—
349	C₂×C₄×C₆₇	—	4	4	no	—
350	C₂×C₄×C₆₇	—	8	2	no	—
351	C₂×C₄×C₆₇	—	8	1	no	—
352	C₂×C₄×C₆₇	—	8	1	no	—
353	C₂×C₄×C₆₇	—	8	4	no	—
354	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
361	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
363	C₈×C₆₇	—	2	2	no	—
364	C₈×C₆₇	—	2	2	no	—
365	C₈×C₆₇	—	2	4	no	—
366	C₂²×C₆₇	—	2	1	no	—
367	C₂²×C₆₇	—	2	1	no	—
368	C₂²×C₆₇	—	2	4	no	—
369	C₂²×C₆₇	—	2	4	no	—
370	C₂²×C₆₇	—	2	4	no	—
371	C₂²×C₆₇	—	4	2	no	—
372	C₂²×C₆₇	—	4	2	no	—
373	C₂²×C₆₇	—	4	2	no	—
374	C₂²×C₆₇	—	4	2	no	—
375	C₂²×C₆₇	—	4	2	no	—
376	C₂²×C₆₇	—	4	2	no	—
377	C₂²×C₆₇	—	8	4	no	—
378	C₂²×C₆₇	#546	1	2	yes	—
379	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
380	C₄×C₆₇	—	2	1	no	—
381	C₄×C₆₇	—	2	1	no	—
382	C₄×C₆₇	—	2	1	no	—
383	C₄×C₆₇	—	2	1	no	—
384	C₄×C₆₇	—	2	4	no	—
385	C₄×C₆₇	—	2	4	no	—
386	C₄×C₆₇	—	4	2	no	—
387	C₄×C₆₇	—	4	2	no	—
388	C₄×C₆₇	—	4	2	no	—
389	C₄×C₆₇	—	4	2	no	—
390	C₄×C₆₇	—	4	2	no	—
391	C₄×C₆₇	#546	1	2	yes	—
392	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
393	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
394	#61220	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
395	C₂×C₆₇	—	2	2	no	—
396	C₂×C₆₇	—	4	4	no	—
397	C₂×C₆₇	—	8	2	no	—
398	C₂×C₆₇	—	8	2	no	—
399	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
400	C₂×C₆₇	#3585	1	1	yes	characteristic
401	C₂×C₆₇	#3586	1	1	yes	characteristic
402	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
403	#3497	C₂×C₆₇	1	1	yes	characteristic, complemented
404	#3321	C₂×C₆₇	1	4	yes	complemented
405	#3320	C₂×C₆₇	1	4	yes	complemented
406	#3309	C₂×C₆₇	1	4	yes	complemented
407	#3308	C₂×C₆₇	1	4	yes	complemented
408	#3135	C₂×C₆₇	1	1	yes	characteristic, complemented
409	#3098	C₂×C₆₇	1	2	yes	complemented
410	#3078	C₂×C₆₇	1	1	yes	characteristic, complemented
411	#3062	C₂×C₆₇	1	2	yes	complemented
412	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
413	#3010	C₂×C₆₇	1	2	yes	complemented
414	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
415	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
416	#2898	C₂×C₆₇	1	2	yes	complemented
417	C₆₇	#61220	1	1	yes	characteristic, direct product factor, Sylow
418	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	—
419	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
420	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
421	C₂×#131	C₂²×C₆₇	1	2	yes	—
422	#559	—	2	2	no	—
423	#556	—	2	1	no	—
424	#555	C₂²×C₆₇	1	2	yes	—
425	#553	C₂²×C₆₇	1	4	yes	—
426	#550	—	2	1	no	—
427	#550	—	2	1	no	—
428	#550	C₂²×C₆₇	1	2	yes	complemented
429	D₄×Q₈	—	2	1	no	—
430	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
431	#548	—	2	2	no	—
432	#548	C₂²×C₆₇	1	4	yes	complemented
433	#547	C₂²×C₆₇	1	2	yes	—
434	#538	—	2	2	no	—
435	#537	—	2	2	no	—
436	#537	C₂²×C₆₇	1	2	yes	—
437	#535	C₂²×C₆₇	1	2	yes	—
438	#533	C₂²×C₆₇	1	1	yes	characteristic
439	#532	—	2	2	no	—
440	#532	C₂²×C₆₇	1	1	yes	characteristic
441	#532	C₂²×C₆₇	1	1	yes	characteristic
442	#525	—	2	2	no	—
443	#520	C₂²×C₆₇	1	2	yes	—
444	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
445	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
446	#491	C₂²×C₆₇	1	2	yes	complemented
447	#490	C₂²×C₆₇	1	2	yes	complemented
448	#489	C₂²×C₆₇	1	2	yes	complemented
449	#489	C₂²×C₆₇	1	2	yes	complemented
450	#485	C₂²×C₆₇	1	4	yes	complemented
451	#484	C₂²×C₆₇	1	4	yes	complemented
452	#482	C₂²×C₆₇	1	4	yes	complemented
453	#480	C₂²×C₆₇	1	4	yes	complemented
454	#479	C₂²×C₆₇	1	4	yes	complemented
455	#477	C₂²×C₆₇	1	2	yes	complemented
456	#475	C₂²×C₆₇	1	2	yes	complemented
457	#469	C₂²×C₆₇	1	4	yes	—
458	#468	C₂²×C₆₇	1	4	yes	—
459	#466	C₂²×C₆₇	1	4	yes	—
460	#465	C₂²×C₆₇	1	4	yes	—
461	#463	C₂²×C₆₇	1	4	yes	—
462	#461	C₂²×C₆₇	1	2	yes	—
463	#459	C₂²×C₆₇	1	2	yes	—
464	#449	C₂²×C₆₇	1	4	yes	—
465	#449	C₂²×C₆₇	1	4	yes	—
466	#448	C₂²×C₆₇	1	4	yes	—
467	#448	C₂²×C₆₇	1	4	yes	—
468	#440	C₂²×C₆₇	1	4	yes	—
469	#440	C₂²×C₆₇	1	4	yes	—
470	#435	C₂²×C₆₇	1	4	yes	complemented
471	#435	C₂²×C₆₇	1	4	yes	complemented
472	#428	C₂²×C₆₇	1	2	yes	—
473	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
474	#423	C₂²×C₆₇	1	1	yes	characteristic
475	#419	C₂²×C₆₇	1	2	yes	—
476	#419	C₂²×C₆₇	1	4	yes	complemented
477	#417	C₂²×C₆₇	1	2	yes	—
478	#417	C₂²×C₆₇	1	4	yes	complemented
479	#416	C₂²×C₆₇	1	2	yes	—
480	#416	C₂²×C₆₇	1	2	yes	—
481	#416	C₂²×C₆₇	1	4	yes	complemented
482	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
483	C₂×#103	C₂²×C₆₇	1	4	yes	complemented
484	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
485	#408	C₂²×C₆₇	1	2	yes	—
486	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
487	2₋¹⁺⁴	—	2	8	no	—
488	2₋¹⁺⁴	—	4	4	no	—
489	C₂×#41	—	2	4	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	C₂³×C₆₇	1	2	yes	—
493	C₂×#41	C₂³×C₆₇	1	4	yes	—
494	C₂×#41	C₂³×C₆₇	1	2	yes	—
495	C₂²×Q₈	—	2	2	no	—
496	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
497	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
499	C₂³×C₄	—	2	1	no	—
500	AGL(1,ℤ/8)	—	4	4	no	—
501	C₂×SD₁₆	—	2	4	no	—
502	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
503	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
504	C₂×D₈	C₂³×C₆₇	1	4	yes	—
505	#131	—	4	4	no	—
506	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
507	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
508	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
509	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
516	#127	—	2	2	no	—
517	#127	—	2	2	no	—
518	#127	D₄×C₆₇	1	1	yes	characteristic
519	#127	C₂³×C₆₇	1	1	yes	characteristic
520	#126	—	2	4	no	—
521	#125	C₂³×C₆₇	1	2	yes	—
522	#124	—	2	2	no	—
523	#124	—	2	4	no	—
524	#124	—	2	4	no	—
525	#124	D₄×C₆₇	1	2	yes	—
526	#124	C₂³×C₆₇	1	2	yes	—
527	#123	—	2	4	no	—
528	#123	—	2	4	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	—	2	1	no	—
531	C₂²⋊Q₈	—	2	1	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
536	#121	—	2	2	no	—
537	#121	—	2	4	no	—
538	#121	—	2	4	no	—
539	#121	—	2	2	no	—
540	#121	—	2	4	no	—
541	#121	—	2	1	no	—
542	#121	—	2	1	no	—
543	#121	—	2	4	no	—
544	#121	D₄×C₆₇	1	2	yes	—
545	#121	D₄×C₆₇	1	2	yes	—
546	#121	C₂³×C₆₇	1	4	yes	—
547	#121	C₂³×C₆₇	1	4	yes	—
548	#121	C₂³×C₆₇	1	4	yes	—
549	#120	—	2	4	no	—
550	C₄×Q₈	—	2	2	no	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
556	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
557	C₄×D₄	—	2	4	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	4	no	—
562	C₄×D₄	—	2	4	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	C₂³×C₆₇	1	2	yes	—
568	C₄×D₄	C₂³×C₆₇	1	2	yes	—
569	C₄×D₄	C₂³×C₆₇	1	2	yes	—
570	C₄×D₄	C₂³×C₆₇	1	2	yes	—
571	#117	—	2	2	no	—
572	#117	C₂³×C₆₇	1	2	yes	—
573	#117	C₂³×C₆₇	1	4	yes	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₄²	—	2	1	no	—
580	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
581	#107	C₂³×C₆₇	1	4	yes	—
582	#107	C₂³×C₆₇	1	4	yes	—
583	#106	C₂³×C₆₇	1	4	yes	—
584	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
585	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
586	#103	C₂³×C₆₇	1	4	yes	—
587	#103	C₂³×C₆₇	1	2	yes	—
588	#103	C₂³×C₆₇	1	4	yes	—
589	#103	C₂³×C₆₇	1	4	yes	—
590	#103	C₂³×C₆₇	1	2	yes	—
591	#103	C₂³×C₆₇	1	2	yes	—
592	#103	C₂³×C₆₇	1	2	yes	—
593	#103	C₂³×C₆₇	1	4	yes	—
594	#102	C₂³×C₆₇	1	4	yes	—
595	#102	C₂³×C₆₇	1	2	yes	—
596	#102	C₂³×C₆₇	1	2	yes	—
597	#102	C₂³×C₆₇	1	2	yes	—
598	#102	C₂³×C₆₇	1	2	yes	—
599	#102	C₂³×C₆₇	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
602	#97	C₂³×C₆₇	1	2	yes	—
603	#97	C₂³×C₆₇	1	2	yes	—
604	C₂⁴	—	2	1	no	—
605	#41	—	2	4	no	—
606	#41	—	2	4	no	—
607	#41	—	2	8	no	—
608	#41	—	2	4	no	—
609	#41	—	2	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	16	no	—
612	#41	—	4	8	no	—
613	#41	—	8	4	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	—	2	8	no	—
620	C₂×Q₈	—	4	4	no	—
621	C₂×Q₈	—	4	8	no	—
622	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
623	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
624	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
625	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	4	no	—
630	C₂×D₄	—	2	4	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
637	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
638	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
639	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
640	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
641	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	8	2	no	—
652	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
655	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
656	SD₁₆	—	2	8	no	—
657	SD₁₆	—	4	4	no	—
658	D₈	—	4	4	no	—
659	M₁₆	—	2	4	no	—
660	M₁₆	—	4	4	no	—
661	C₂×C₈	—	2	2	no	—
662	C₂×C₈	—	2	2	no	—
663	C₂×C₈	—	4	4	no	—
664	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
665	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
666	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
680	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
681	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
696	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
697	C₄²	—	2	2	no	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	2	no	—
701	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
702	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
703	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
704	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
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×C₆₇	1	4	yes	—
711	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
712	Q₈	—	2	4	no	—
713	Q₈	—	2	4	no	—
714	Q₈	—	2	2	no	—
715	Q₈	—	2	2	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	4	8	no	—
718	Q₈	—	4	2	no	—
719	Q₈	—	8	1	no	—
720	Q₈	C₂×#41×C₆₇	1	4	yes	—
721	D₄	—	2	8	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	2	no	—
733	D₄	—	8	1	no	—
734	D₄	—	8	4	no	—
735	D₄	—	8	4	no	—
736	D₄	—	8	4	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	8	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	8	2	no	—
753	C₂×C₄	—	8	1	no	—
754	C₂×C₄	—	8	4	no	—
755	C₂×C₄	—	8	1	no	—
756	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
757	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
759	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
760	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
762	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
763	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
764	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
765	C₈	—	2	2	no	—
766	C₈	—	2	2	no	—
767	C₈	—	2	4	no	—
768	C₂²	—	2	1	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	8	4	no	—
780	C₂²	#546×C₆₇	1	2	yes	—
781	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
782	C₄	—	2	1	no	—
783	C₄	—	2	1	no	—
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	4	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	#546×C₆₇	1	2	yes	—
794	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
795	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
796	C₂	—	2	2	no	—
797	C₂	—	4	4	no	—
798	C₂	—	8	2	no	—
799	C₂	—	8	2	no	—
800	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
801	C₂	C₆₇×#3585	1	1	yes	characteristic
802	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3506	C₂	semidirect
2. C₆₇×#3497	C₂	semidirect
3. C₆₇×#3321	C₂	semidirect
4. C₆₇×#3320	C₂	semidirect
5. C₆₇×#3309	C₂	semidirect
6. C₆₇×#3308	C₂	semidirect
7. C₆₇×#3135	C₂	semidirect
8. C₆₇×#3098	C₂	semidirect
9. C₆₇×#3078	C₂	semidirect
10. C₆₇×#3062	C₂	semidirect
11. C₆₇×#3036	C₂	semidirect
12. C₆₇×#3010	C₂	semidirect
13. C₂×#440×C₆₇	C₂	semidirect
14. C₆₇×#2932	C₂	semidirect
15. C₆₇×#2898	C₂	semidirect
26. #550×C₆₇	C₂²	semidirect
28. D₄×Q₈×C₆₇	C₂²	semidirect
30. #548×C₆₇	C₂²	semidirect
44. #491×C₆₇	C₂²	semidirect
45. #490×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #489×C₆₇	C₂²	semidirect
48. #485×C₆₇	C₂²	semidirect
49. #484×C₆₇	C₂²	semidirect
50. #482×C₆₇	C₂²	semidirect
51. #480×C₆₇	C₂²	semidirect
52. #479×C₆₇	C₂²	semidirect
53. #477×C₆₇	C₂²	semidirect
54. #475×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #435×C₆₇	C₂²	semidirect
74. #419×C₆₇	C₂²	semidirect
76. #417×C₆₇	C₂²	semidirect
79. #416×C₆₇	C₂²	semidirect
81. C₂×#103×C₆₇	C₂²	semidirect
221. C₂×Q₈×C₆₇	#41	semidirect
394. #61220	C₆₇	direct (N × H)
402. #3506	C₂×C₆₇	semidirect
403. #3497	C₂×C₆₇	semidirect
404. #3321	C₂×C₆₇	semidirect
405. #3320	C₂×C₆₇	semidirect
406. #3309	C₂×C₆₇	semidirect
407. #3308	C₂×C₆₇	semidirect
408. #3135	C₂×C₆₇	semidirect
409. #3098	C₂×C₆₇	semidirect
410. #3078	C₂×C₆₇	semidirect
411. #3062	C₂×C₆₇	semidirect
412. #3036	C₂×C₆₇	semidirect
413. #3010	C₂×C₆₇	semidirect
414. C₂×#440	C₂×C₆₇	semidirect
415. #2932	C₂×C₆₇	semidirect
416. #2898	C₂×C₆₇	semidirect
417. C₆₇	#61220	direct (N × H)
428. #550	C₂²×C₆₇	semidirect
430. D₄×Q₈	C₂²×C₆₇	semidirect
432. #548	C₂²×C₆₇	semidirect
446. #491	C₂²×C₆₇	semidirect
447. #490	C₂²×C₆₇	semidirect
448. #489	C₂²×C₆₇	semidirect
449. #489	C₂²×C₆₇	semidirect
450. #485	C₂²×C₆₇	semidirect
451. #484	C₂²×C₆₇	semidirect
452. #482	C₂²×C₆₇	semidirect
453. #480	C₂²×C₆₇	semidirect
454. #479	C₂²×C₆₇	semidirect
455. #477	C₂²×C₆₇	semidirect
456. #475	C₂²×C₆₇	semidirect
470. #435	C₂²×C₆₇	semidirect
471. #435	C₂²×C₆₇	semidirect
476. #419	C₂²×C₆₇	semidirect
478. #417	C₂²×C₆₇	semidirect
481. #416	C₂²×C₆₇	semidirect
483. C₂×#103	C₂²×C₆₇	semidirect
623. C₂×Q₈	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3506	2
C₆₇×#3497	2
C₆₇×#3321	2
C₆₇×#3320	2
C₆₇×#3309	2
C₆₇×#3308	2
C₆₇×#3135	2
C₆₇×#3098	2
C₆₇×#3078	2
C₆₇×#3062	2
C₆₇×#3036	2
C₆₇×#3010	2
C₂×#440×C₆₇	2
C₆₇×#2932	2
C₆₇×#2898	2
#61220	67

Subgroups — C67×#61220 #30740471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61220 #30740471