Subgroups — C₆₇×#61213 #30740464

Order 17152.

2090 conjugacy classes of subgroups.

The subgroup lattice has 842 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×#3332	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3329	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3326	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3305	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3301	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3298	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3099	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3062	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3010	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2898	C₂	1	2	yes	maximal, complemented
18	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	—
19	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#131×C₆₇	C₂²	1	2	yes	—
22	#559×C₆₇	—	2	2	no	—
23	#556×C₆₇	—	2	1	no	—
24	#555×C₆₇	C₂²	1	2	yes	—
25	#553×C₆₇	C₂²	1	4	yes	—
26	#550×C₆₇	—	2	1	no	—
27	#550×C₆₇	—	2	1	no	—
28	#550×C₆₇	C₂²	1	2	yes	complemented
29	D₄×Q₈×C₆₇	—	2	1	no	—
30	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
31	#548×C₆₇	—	2	2	no	—
32	#548×C₆₇	C₂²	1	4	yes	complemented
33	#547×C₆₇	C₂²	1	2	yes	—
34	#538×C₆₇	—	2	2	no	—
35	#537×C₆₇	—	2	2	no	—
36	#537×C₆₇	C₂²	1	2	yes	—
37	#535×C₆₇	C₂²	1	2	yes	—
38	#533×C₆₇	C₂²	1	1	yes	characteristic
39	#532×C₆₇	—	2	2	no	—
40	#532×C₆₇	C₂²	1	1	yes	characteristic
41	#532×C₆₇	C₂²	1	1	yes	characteristic
42	#525×C₆₇	—	2	2	no	—
43	#520×C₆₇	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
46	#488×C₆₇	C₂²	1	2	yes	complemented
47	#488×C₆₇	C₂²	1	2	yes	complemented
48	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#485×C₆₇	C₂²	1	4	yes	complemented
53	#483×C₆₇	C₂²	1	4	yes	complemented
54	#482×C₆₇	C₂²	1	4	yes	complemented
55	#481×C₆₇	C₂²	1	4	yes	complemented
56	#479×C₆₇	C₂²	1	4	yes	complemented
57	#477×C₆₇	C₂²	1	2	yes	complemented
58	#475×C₆₇	C₂²	1	2	yes	complemented
59	#469×C₆₇	C₂²	1	4	yes	—
60	#468×C₆₇	C₂²	1	4	yes	—
61	#466×C₆₇	C₂²	1	4	yes	—
62	#465×C₆₇	C₂²	1	4	yes	—
63	#463×C₆₇	C₂²	1	4	yes	—
64	#461×C₆₇	C₂²	1	2	yes	—
65	#459×C₆₇	C₂²	1	2	yes	—
66	#449×C₆₇	C₂²	1	4	yes	—
67	#449×C₆₇	C₂²	1	4	yes	—
68	#448×C₆₇	C₂²	1	4	yes	—
69	#448×C₆₇	C₂²	1	4	yes	—
70	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
71	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
72	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
73	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
74	#436×C₆₇	C₂²	1	2	yes	complemented
75	#436×C₆₇	C₂²	1	2	yes	complemented
76	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
77	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
78	#428×C₆₇	C₂²	1	2	yes	—
79	C₂×#106×C₆₇	C₂²	1	1	yes	characteristic
80	#423×C₆₇	C₂²	1	1	yes	characteristic
81	#419×C₆₇	C₂²	1	2	yes	—
82	#419×C₆₇	C₂²	1	4	yes	complemented
83	#417×C₆₇	C₂²	1	2	yes	—
84	#417×C₆₇	C₂²	1	4	yes	complemented
85	#416×C₆₇	C₂²	1	2	yes	—
86	#416×C₆₇	C₂²	1	2	yes	—
87	#416×C₆₇	C₂²	1	4	yes	complemented
88	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
89	C₂×#103×C₆₇	C₂²	1	4	yes	complemented
90	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
91	#408×C₆₇	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
93	2₋¹⁺⁴×C₆₇	—	2	8	no	—
94	2₋¹⁺⁴×C₆₇	—	4	4	no	—
95	C₂×#41×C₆₇	—	2	4	no	—
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	2	no	—
98	C₂×#41×C₆₇	C₂³	1	2	yes	—
99	C₂×#41×C₆₇	C₂³	1	4	yes	—
100	C₂×#41×C₆₇	C₂³	1	2	yes	—
101	C₂²×Q₈×C₆₇	—	2	2	no	—
102	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
103	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₆₇	—	2	1	no	—
106	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
107	C₂×SD₁₆×C₆₇	—	2	4	no	—
108	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
111	C₂×D₈×C₆₇	C₂³	1	4	yes	—
112	#131×C₆₇	—	4	4	no	—
113	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
114	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
115	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
118	C₄⋊Q₈×C₆₇	—	2	2	no	—
119	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
120	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
123	#127×C₆₇	—	2	2	no	—
124	#127×C₆₇	—	2	2	no	—
125	#127×C₆₇	D₄	1	1	yes	characteristic
126	#127×C₆₇	C₂³	1	1	yes	characteristic
127	#126×C₆₇	—	2	4	no	—
128	#125×C₆₇	C₂³	1	2	yes	—
129	#124×C₆₇	—	2	2	no	—
130	#124×C₆₇	—	2	4	no	—
131	#124×C₆₇	—	2	4	no	—
132	#124×C₆₇	D₄	1	2	yes	—
133	#124×C₆₇	C₂³	1	2	yes	—
134	#123×C₆₇	—	2	4	no	—
135	#123×C₆₇	—	2	4	no	—
136	C₂²⋊Q₈×C₆₇	—	2	2	no	—
137	C₂²⋊Q₈×C₆₇	—	2	1	no	—
138	C₂²⋊Q₈×C₆₇	—	2	1	no	—
139	C₂²⋊Q₈×C₆₇	—	2	2	no	—
140	C₂²⋊Q₈×C₆₇	—	2	4	no	—
141	C₂²⋊Q₈×C₆₇	—	2	4	no	—
142	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
143	#121×C₆₇	—	2	2	no	—
144	#121×C₆₇	—	2	4	no	—
145	#121×C₆₇	—	2	4	no	—
146	#121×C₆₇	—	2	2	no	—
147	#121×C₆₇	—	2	4	no	—
148	#121×C₆₇	—	2	1	no	—
149	#121×C₆₇	—	2	1	no	—
150	#121×C₆₇	—	2	4	no	—
151	#121×C₆₇	D₄	1	2	yes	—
152	#121×C₆₇	D₄	1	2	yes	—
153	#121×C₆₇	C₂³	1	4	yes	—
154	#121×C₆₇	C₂³	1	4	yes	—
155	#121×C₆₇	C₂³	1	4	yes	—
156	#120×C₆₇	—	2	4	no	—
157	C₄×Q₈×C₆₇	—	2	2	no	—
158	C₄×Q₈×C₆₇	—	2	1	no	—
159	C₄×Q₈×C₆₇	—	2	1	no	—
160	C₄×Q₈×C₆₇	—	2	1	no	—
161	C₄×Q₈×C₆₇	—	2	1	no	—
162	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
163	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
164	C₄×D₄×C₆₇	—	2	4	no	—
165	C₄×D₄×C₆₇	—	2	2	no	—
166	C₄×D₄×C₆₇	—	2	2	no	—
167	C₄×D₄×C₆₇	—	2	2	no	—
168	C₄×D₄×C₆₇	—	2	4	no	—
169	C₄×D₄×C₆₇	—	2	4	no	—
170	C₄×D₄×C₆₇	—	2	1	no	—
171	C₄×D₄×C₆₇	—	2	1	no	—
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	—	2	1	no	—
174	C₄×D₄×C₆₇	C₂³	1	2	yes	—
175	C₄×D₄×C₆₇	C₂³	1	2	yes	—
176	C₄×D₄×C₆₇	C₂³	1	2	yes	—
177	C₄×D₄×C₆₇	C₂³	1	2	yes	—
178	#117×C₆₇	—	2	2	no	—
179	#117×C₆₇	C₂³	1	4	yes	—
180	#117×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
186	C₂×C₄²×C₆₇	—	2	1	no	—
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	#107×C₆₇	C₂³	1	4	yes	—
189	#106×C₆₇	C₂³	1	4	yes	—
190	#106×C₆₇	C₂³	1	2	yes	—
191	#106×C₆₇	C₂³	1	2	yes	—
192	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
193	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
194	#103×C₆₇	C₂³	1	2	yes	—
195	#103×C₆₇	C₂³	1	2	yes	—
196	#103×C₆₇	C₂³	1	4	yes	—
197	#103×C₆₇	C₂³	1	4	yes	—
198	#103×C₆₇	C₂³	1	4	yes	—
199	#103×C₆₇	C₂³	1	2	yes	—
200	#103×C₆₇	C₂³	1	2	yes	—
201	#103×C₆₇	C₂³	1	2	yes	—
202	#103×C₆₇	C₂³	1	2	yes	—
203	#102×C₆₇	C₂³	1	2	yes	—
204	#102×C₆₇	C₂³	1	2	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	#102×C₆₇	C₂³	1	2	yes	—
207	#102×C₆₇	C₂³	1	2	yes	—
208	#102×C₆₇	C₂³	1	2	yes	—
209	#102×C₆₇	C₂³	1	2	yes	—
210	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
211	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
212	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
214	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
215	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₂⁴×C₆₇	—	2	1	no	—
217	#41×C₆₇	—	2	4	no	—
218	#41×C₆₇	—	2	4	no	—
219	#41×C₆₇	—	2	8	no	—
220	#41×C₆₇	—	2	4	no	—
221	#41×C₆₇	—	2	4	no	—
222	#41×C₆₇	—	4	4	no	—
223	#41×C₆₇	—	4	16	no	—
224	#41×C₆₇	—	4	8	no	—
225	#41×C₆₇	—	8	4	no	—
226	C₂×Q₈×C₆₇	—	2	1	no	—
227	C₂×Q₈×C₆₇	—	2	1	no	—
228	C₂×Q₈×C₆₇	—	2	4	no	—
229	C₂×Q₈×C₆₇	—	2	1	no	—
230	C₂×Q₈×C₆₇	—	2	2	no	—
231	C₂×Q₈×C₆₇	—	2	8	no	—
232	C₂×Q₈×C₆₇	—	4	4	no	—
233	C₂×Q₈×C₆₇	—	4	8	no	—
234	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
235	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
236	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
238	C₂×D₄×C₆₇	—	2	2	no	—
239	C₂×D₄×C₆₇	—	2	4	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	2	4	no	—
242	C₂×D₄×C₆₇	—	2	4	no	—
243	C₂×D₄×C₆₇	—	2	1	no	—
244	C₂×D₄×C₆₇	—	2	1	no	—
245	C₂×D₄×C₆₇	—	2	1	no	—
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
249	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
250	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
251	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₆₇	—	2	1	no	—
255	C₂²×C₄×C₆₇	—	2	4	no	—
256	C₂²×C₄×C₆₇	—	2	1	no	—
257	C₂²×C₄×C₆₇	—	2	1	no	—
258	C₂²×C₄×C₆₇	—	2	4	no	—
259	C₂²×C₄×C₆₇	—	2	2	no	—
260	C₂²×C₄×C₆₇	—	2	4	no	—
261	C₂²×C₄×C₆₇	—	2	2	no	—
262	C₂²×C₄×C₆₇	—	2	2	no	—
263	C₂²×C₄×C₆₇	—	8	2	no	—
264	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	SD₁₆×C₆₇	—	2	4	no	—
269	SD₁₆×C₆₇	—	2	4	no	—
270	SD₁₆×C₆₇	—	4	4	no	—
271	D₈×C₆₇	—	4	4	no	—
272	M₁₆×C₆₇	—	2	4	no	—
273	M₁₆×C₆₇	—	4	4	no	—
274	C₂×C₈×C₆₇	—	2	2	no	—
275	C₂×C₈×C₆₇	—	2	2	no	—
276	C₂×C₈×C₆₇	—	4	4	no	—
277	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
278	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
279	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
280	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
282	C₄⋊C₄×C₆₇	—	2	2	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	1	no	—
285	C₄⋊C₄×C₆₇	—	2	4	no	—
286	C₄⋊C₄×C₆₇	—	2	1	no	—
287	C₄⋊C₄×C₆₇	—	2	1	no	—
288	C₄⋊C₄×C₆₇	—	2	1	no	—
289	C₄⋊C₄×C₆₇	—	2	2	no	—
290	C₄⋊C₄×C₆₇	—	2	1	no	—
291	C₄⋊C₄×C₆₇	—	2	4	no	—
292	C₄⋊C₄×C₆₇	—	2	2	no	—
293	C₄⋊C₄×C₆₇	—	2	1	no	—
294	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²⋊C₄×C₆₇	—	2	2	no	—
301	C₂²⋊C₄×C₆₇	—	2	4	no	—
302	C₂²⋊C₄×C₆₇	—	2	4	no	—
303	C₂²⋊C₄×C₆₇	—	2	2	no	—
304	C₂²⋊C₄×C₆₇	—	2	2	no	—
305	C₂²⋊C₄×C₆₇	—	2	4	no	—
306	C₂²⋊C₄×C₆₇	—	2	2	no	—
307	C₂²⋊C₄×C₆₇	—	2	4	no	—
308	C₂²⋊C₄×C₆₇	—	2	2	no	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
311	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
312	C₄²×C₆₇	—	2	2	no	—
313	C₄²×C₆₇	—	2	2	no	—
314	C₄²×C₆₇	—	2	4	no	—
315	C₄²×C₆₇	—	2	2	no	—
316	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
317	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
318	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	4	2	no	—
323	C₂³×C₆₇	—	8	1	no	—
324	C₂³×C₆₇	—	8	1	no	—
325	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
326	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
327	Q₈×C₆₇	—	2	4	no	—
328	Q₈×C₆₇	—	2	4	no	—
329	Q₈×C₆₇	—	2	2	no	—
330	Q₈×C₆₇	—	2	2	no	—
331	Q₈×C₆₇	—	2	2	no	—
332	Q₈×C₆₇	—	4	8	no	—
333	Q₈×C₆₇	—	4	2	no	—
334	Q₈×C₆₇	—	8	1	no	—
335	Q₈×C₆₇	C₂×#41	1	4	yes	—
336	D₄×C₆₇	—	2	8	no	—
337	D₄×C₆₇	—	2	4	no	—
338	D₄×C₆₇	—	2	4	no	—
339	D₄×C₆₇	—	2	2	no	—
340	D₄×C₆₇	—	2	2	no	—
341	D₄×C₆₇	—	2	2	no	—
342	D₄×C₆₇	—	2	2	no	—
343	D₄×C₆₇	—	4	2	no	—
344	D₄×C₆₇	—	4	8	no	—
345	D₄×C₆₇	—	4	4	no	—
346	D₄×C₆₇	—	4	2	no	—
347	D₄×C₆₇	—	4	2	no	—
348	D₄×C₆₇	—	8	1	no	—
349	D₄×C₆₇	—	8	4	no	—
350	D₄×C₆₇	—	8	4	no	—
351	D₄×C₆₇	—	8	4	no	—
352	C₂×C₄×C₆₇	—	2	4	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	4	no	—
356	C₂×C₄×C₆₇	—	2	4	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	4	1	no	—
363	C₂×C₄×C₆₇	—	4	8	no	—
364	C₂×C₄×C₆₇	—	4	8	no	—
365	C₂×C₄×C₆₇	—	4	4	no	—
366	C₂×C₄×C₆₇	—	4	4	no	—
367	C₂×C₄×C₆₇	—	8	2	no	—
368	C₂×C₄×C₆₇	—	8	1	no	—
369	C₂×C₄×C₆₇	—	8	1	no	—
370	C₂×C₄×C₆₇	—	8	4	no	—
371	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
373	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
378	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
379	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
380	C₈×C₆₇	—	2	1	no	—
381	C₈×C₆₇	—	2	1	no	—
382	C₈×C₆₇	—	2	1	no	—
383	C₈×C₆₇	—	2	1	no	—
384	C₈×C₆₇	—	2	4	no	—
385	C₂²×C₆₇	—	2	1	no	—
386	C₂²×C₆₇	—	2	1	no	—
387	C₂²×C₆₇	—	2	4	no	—
388	C₂²×C₆₇	—	2	4	no	—
389	C₂²×C₆₇	—	2	4	no	—
390	C₂²×C₆₇	—	4	2	no	—
391	C₂²×C₆₇	—	4	2	no	—
392	C₂²×C₆₇	—	4	2	no	—
393	C₂²×C₆₇	—	4	2	no	—
394	C₂²×C₆₇	—	4	2	no	—
395	C₂²×C₆₇	—	4	2	no	—
396	C₂²×C₆₇	—	8	4	no	—
397	C₂²×C₆₇	#546	1	2	yes	—
398	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
399	C₄×C₆₇	—	2	1	no	—
400	C₄×C₆₇	—	2	1	no	—
401	C₄×C₆₇	—	2	4	no	—
402	C₄×C₆₇	—	2	4	no	—
403	C₄×C₆₇	—	2	1	no	—
404	C₄×C₆₇	—	4	2	no	—
405	C₄×C₆₇	—	4	2	no	—
406	C₄×C₆₇	—	4	2	no	—
407	C₄×C₆₇	—	4	2	no	—
408	C₄×C₆₇	—	4	2	no	—
409	C₄×C₆₇	#546	1	2	yes	—
410	C₄×C₆₇	#577	1	2	yes	—
411	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
412	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
413	#61213	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₂×C₆₇	—	2	2	no	—
415	C₂×C₆₇	—	4	4	no	—
416	C₂×C₆₇	—	8	2	no	—
417	C₂×C₆₇	—	8	2	no	—
418	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
419	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
420	C₂×C₆₇	#3584	1	1	yes	characteristic
421	#3506	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#3497	C₂×C₆₇	1	1	yes	characteristic, complemented
423	#3332	C₂×C₆₇	1	2	yes	complemented
424	#3329	C₂×C₆₇	1	2	yes	complemented
425	#3326	C₂×C₆₇	1	4	yes	complemented
426	#3305	C₂×C₆₇	1	2	yes	complemented
427	#3301	C₂×C₆₇	1	4	yes	complemented
428	#3298	C₂×C₆₇	1	2	yes	complemented
429	#3131	C₂×C₆₇	1	1	yes	characteristic, complemented
430	#3099	C₂×C₆₇	1	2	yes	complemented
431	#3078	C₂×C₆₇	1	1	yes	characteristic, complemented
432	#3062	C₂×C₆₇	1	2	yes	complemented
433	#3036	C₂×C₆₇	1	1	yes	characteristic, complemented
434	#3010	C₂×C₆₇	1	2	yes	complemented
435	C₂×C₄×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
436	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
437	#2898	C₂×C₆₇	1	2	yes	complemented
438	C₆₇	#61213	1	1	yes	characteristic, direct product factor, Sylow
439	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	—
440	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
441	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
442	C₂×#131	C₂²×C₆₇	1	2	yes	—
443	#559	—	2	2	no	—
444	#556	—	2	1	no	—
445	#555	C₂²×C₆₇	1	2	yes	—
446	#553	C₂²×C₆₇	1	4	yes	—
447	#550	—	2	1	no	—
448	#550	—	2	1	no	—
449	#550	C₂²×C₆₇	1	2	yes	complemented
450	D₄×Q₈	—	2	1	no	—
451	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
452	#548	—	2	2	no	—
453	#548	C₂²×C₆₇	1	4	yes	complemented
454	#547	C₂²×C₆₇	1	2	yes	—
455	#538	—	2	2	no	—
456	#537	—	2	2	no	—
457	#537	C₂²×C₆₇	1	2	yes	—
458	#535	C₂²×C₆₇	1	2	yes	—
459	#533	C₂²×C₆₇	1	1	yes	characteristic
460	#532	—	2	2	no	—
461	#532	C₂²×C₆₇	1	1	yes	characteristic
462	#532	C₂²×C₆₇	1	1	yes	characteristic
463	#525	—	2	2	no	—
464	#520	C₂²×C₆₇	1	2	yes	—
465	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
467	#488	C₂²×C₆₇	1	2	yes	complemented
468	#488	C₂²×C₆₇	1	2	yes	complemented
469	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
470	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
471	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
472	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
473	#485	C₂²×C₆₇	1	4	yes	complemented
474	#483	C₂²×C₆₇	1	4	yes	complemented
475	#482	C₂²×C₆₇	1	4	yes	complemented
476	#481	C₂²×C₆₇	1	4	yes	complemented
477	#479	C₂²×C₆₇	1	4	yes	complemented
478	#477	C₂²×C₆₇	1	2	yes	complemented
479	#475	C₂²×C₆₇	1	2	yes	complemented
480	#469	C₂²×C₆₇	1	4	yes	—
481	#468	C₂²×C₆₇	1	4	yes	—
482	#466	C₂²×C₆₇	1	4	yes	—
483	#465	C₂²×C₆₇	1	4	yes	—
484	#463	C₂²×C₆₇	1	4	yes	—
485	#461	C₂²×C₆₇	1	2	yes	—
486	#459	C₂²×C₆₇	1	2	yes	—
487	#449	C₂²×C₆₇	1	4	yes	—
488	#449	C₂²×C₆₇	1	4	yes	—
489	#448	C₂²×C₆₇	1	4	yes	—
490	#448	C₂²×C₆₇	1	4	yes	—
491	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
492	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
493	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
494	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
495	#436	C₂²×C₆₇	1	2	yes	complemented
496	#436	C₂²×C₆₇	1	2	yes	complemented
497	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
498	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
499	#428	C₂²×C₆₇	1	2	yes	—
500	C₂×#106	C₂²×C₆₇	1	1	yes	characteristic
501	#423	C₂²×C₆₇	1	1	yes	characteristic
502	#419	C₂²×C₆₇	1	2	yes	—
503	#419	C₂²×C₆₇	1	4	yes	complemented
504	#417	C₂²×C₆₇	1	2	yes	—
505	#417	C₂²×C₆₇	1	4	yes	complemented
506	#416	C₂²×C₆₇	1	2	yes	—
507	#416	C₂²×C₆₇	1	2	yes	—
508	#416	C₂²×C₆₇	1	4	yes	complemented
509	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
510	C₂×#103	C₂²×C₆₇	1	4	yes	complemented
511	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
512	#408	C₂²×C₆₇	1	2	yes	—
513	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
514	2₋¹⁺⁴	—	2	8	no	—
515	2₋¹⁺⁴	—	4	4	no	—
516	C₂×#41	—	2	4	no	—
517	C₂×#41	—	2	2	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	C₂³×C₆₇	1	2	yes	—
520	C₂×#41	C₂³×C₆₇	1	4	yes	—
521	C₂×#41	C₂³×C₆₇	1	2	yes	—
522	C₂²×Q₈	—	2	2	no	—
523	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
524	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
525	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
526	C₂³×C₄	—	2	1	no	—
527	AGL(1,ℤ/8)	—	4	4	no	—
528	C₂×SD₁₆	—	2	4	no	—
529	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
530	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
531	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
532	C₂×D₈	C₂³×C₆₇	1	4	yes	—
533	#131	—	4	4	no	—
534	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
535	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
536	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
537	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
538	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
539	C₄⋊Q₈	—	2	2	no	—
540	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
541	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
543	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
544	#127	—	2	2	no	—
545	#127	—	2	2	no	—
546	#127	D₄×C₆₇	1	1	yes	characteristic
547	#127	C₂³×C₆₇	1	1	yes	characteristic
548	#126	—	2	4	no	—
549	#125	C₂³×C₆₇	1	2	yes	—
550	#124	—	2	2	no	—
551	#124	—	2	4	no	—
552	#124	—	2	4	no	—
553	#124	D₄×C₆₇	1	2	yes	—
554	#124	C₂³×C₆₇	1	2	yes	—
555	#123	—	2	4	no	—
556	#123	—	2	4	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	1	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	2	no	—
561	C₂²⋊Q₈	—	2	4	no	—
562	C₂²⋊Q₈	—	2	4	no	—
563	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
564	#121	—	2	2	no	—
565	#121	—	2	4	no	—
566	#121	—	2	4	no	—
567	#121	—	2	2	no	—
568	#121	—	2	4	no	—
569	#121	—	2	1	no	—
570	#121	—	2	1	no	—
571	#121	—	2	4	no	—
572	#121	D₄×C₆₇	1	2	yes	—
573	#121	D₄×C₆₇	1	2	yes	—
574	#121	C₂³×C₆₇	1	4	yes	—
575	#121	C₂³×C₆₇	1	4	yes	—
576	#121	C₂³×C₆₇	1	4	yes	—
577	#120	—	2	4	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	—	2	1	no	—
583	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
584	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
585	C₄×D₄	—	2	4	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	4	no	—
590	C₄×D₄	—	2	4	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	C₂³×C₆₇	1	2	yes	—
596	C₄×D₄	C₂³×C₆₇	1	2	yes	—
597	C₄×D₄	C₂³×C₆₇	1	2	yes	—
598	C₄×D₄	C₂³×C₆₇	1	2	yes	—
599	#117	—	2	2	no	—
600	#117	C₂³×C₆₇	1	2	yes	—
601	#117	C₂³×C₆₇	1	4	yes	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₄²	—	2	1	no	—
608	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
609	#107	C₂³×C₆₇	1	4	yes	—
610	#106	C₂³×C₆₇	1	2	yes	—
611	#106	C₂³×C₆₇	1	2	yes	—
612	#106	C₂³×C₆₇	1	4	yes	—
613	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
614	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
615	#103	C₂³×C₆₇	1	2	yes	—
616	#103	C₂³×C₆₇	1	2	yes	—
617	#103	C₂³×C₆₇	1	2	yes	—
618	#103	C₂³×C₆₇	1	4	yes	—
619	#103	C₂³×C₆₇	1	4	yes	—
620	#103	C₂³×C₆₇	1	2	yes	—
621	#103	C₂³×C₆₇	1	2	yes	—
622	#103	C₂³×C₆₇	1	2	yes	—
623	#103	C₂³×C₆₇	1	4	yes	—
624	#102	C₂³×C₆₇	1	2	yes	—
625	#102	C₂³×C₆₇	1	2	yes	—
626	#102	C₂³×C₆₇	1	2	yes	—
627	#102	C₂³×C₆₇	1	2	yes	—
628	#102	C₂³×C₆₇	1	2	yes	—
629	#102	C₂³×C₆₇	1	2	yes	—
630	#102	C₂³×C₆₇	1	4	yes	—
631	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
632	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
633	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
634	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
635	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
636	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
637	C₂⁴	—	2	1	no	—
638	#41	—	2	4	no	—
639	#41	—	2	4	no	—
640	#41	—	2	8	no	—
641	#41	—	2	4	no	—
642	#41	—	2	4	no	—
643	#41	—	4	4	no	—
644	#41	—	4	16	no	—
645	#41	—	4	8	no	—
646	#41	—	8	4	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	4	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	8	no	—
653	C₂×Q₈	—	4	4	no	—
654	C₂×Q₈	—	4	8	no	—
655	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
656	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
657	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
658	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
659	C₂×D₄	—	2	2	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	1	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	2	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
670	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
671	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
672	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
673	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
674	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	2	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	8	2	no	—
685	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
688	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
689	SD₁₆	—	2	4	no	—
690	SD₁₆	—	2	4	no	—
691	SD₁₆	—	4	4	no	—
692	D₈	—	4	4	no	—
693	M₁₆	—	2	4	no	—
694	M₁₆	—	4	4	no	—
695	C₂×C₈	—	2	2	no	—
696	C₂×C₈	—	2	2	no	—
697	C₂×C₈	—	4	4	no	—
698	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
699	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
700	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
701	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
702	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	4	no	—
707	C₄⋊C₄	—	2	1	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
720	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	4	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	2	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
732	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	4	no	—
736	C₄²	—	2	2	no	—
737	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
738	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
739	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
740	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	4	2	no	—
744	C₂³	—	8	1	no	—
745	C₂³	—	8	1	no	—
746	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
747	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
748	Q₈	—	2	4	no	—
749	Q₈	—	2	4	no	—
750	Q₈	—	2	2	no	—
751	Q₈	—	2	2	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	4	8	no	—
754	Q₈	—	4	2	no	—
755	Q₈	—	8	1	no	—
756	Q₈	C₂×#41×C₆₇	1	4	yes	—
757	D₄	—	2	8	no	—
758	D₄	—	2	4	no	—
759	D₄	—	2	4	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	2	2	no	—
764	D₄	—	4	2	no	—
765	D₄	—	4	8	no	—
766	D₄	—	4	4	no	—
767	D₄	—	4	2	no	—
768	D₄	—	4	2	no	—
769	D₄	—	8	1	no	—
770	D₄	—	8	4	no	—
771	D₄	—	8	4	no	—
772	D₄	—	8	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	4	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	8	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	8	2	no	—
789	C₂×C₄	—	8	1	no	—
790	C₂×C₄	—	8	4	no	—
791	C₂×C₄	—	8	1	no	—
792	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
793	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
794	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
798	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
799	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
800	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
801	C₈	—	2	1	no	—
802	C₈	—	2	1	no	—
803	C₈	—	2	1	no	—
804	C₈	—	2	1	no	—
805	C₈	—	2	4	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	2	1	no	—
808	C₂²	—	2	4	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	4	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	8	4	no	—
818	C₂²	#546×C₆₇	1	2	yes	—
819	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
820	C₄	—	2	1	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	4	no	—
824	C₄	—	2	4	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	#546×C₆₇	1	2	yes	—
831	C₄	#577×C₆₇	1	2	yes	—
832	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
833	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
834	C₂	—	2	2	no	—
835	C₂	—	4	4	no	—
836	C₂	—	8	2	no	—
837	C₂	—	8	2	no	—
838	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
839	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
840	C₂	C₆₇×#3584	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×#3332	C₂	semidirect
4. C₆₇×#3329	C₂	semidirect
5. C₆₇×#3326	C₂	semidirect
6. C₆₇×#3305	C₂	semidirect
7. C₆₇×#3301	C₂	semidirect
8. C₆₇×#3298	C₂	semidirect
9. C₆₇×#3131	C₂	semidirect
10. C₆₇×#3099	C₂	semidirect
11. C₆₇×#3078	C₂	semidirect
12. C₆₇×#3062	C₂	semidirect
13. C₆₇×#3036	C₂	semidirect
14. C₆₇×#3010	C₂	semidirect
15. C₂×C₄×SD₁₆×C₆₇	C₂	semidirect
16. C₆₇×#2931	C₂	semidirect
17. C₆₇×#2898	C₂	semidirect
28. #550×C₆₇	C₂²	semidirect
30. D₄×Q₈×C₆₇	C₂²	semidirect
32. #548×C₆₇	C₂²	semidirect
46. #488×C₆₇	C₂²	semidirect
47. #488×C₆₇	C₂²	semidirect
48. #487×C₆₇	C₂²	semidirect
49. #487×C₆₇	C₂²	semidirect
50. #486×C₆₇	C₂²	semidirect
51. #486×C₆₇	C₂²	semidirect
52. #485×C₆₇	C₂²	semidirect
53. #483×C₆₇	C₂²	semidirect
54. #482×C₆₇	C₂²	semidirect
55. #481×C₆₇	C₂²	semidirect
56. #479×C₆₇	C₂²	semidirect
57. #477×C₆₇	C₂²	semidirect
58. #475×C₆₇	C₂²	semidirect
74. #436×C₆₇	C₂²	semidirect
75. #436×C₆₇	C₂²	semidirect
76. C₈×D₄×C₆₇	C₂²	semidirect
77. C₈×D₄×C₆₇	C₂²	semidirect
82. #419×C₆₇	C₂²	semidirect
84. #417×C₆₇	C₂²	semidirect
87. #416×C₆₇	C₂²	semidirect
89. C₂×#103×C₆₇	C₂²	semidirect
235. C₂×Q₈×C₆₇	#41	semidirect
413. #61213	C₆₇	direct (N × H)
421. #3506	C₂×C₆₇	semidirect
422. #3497	C₂×C₆₇	semidirect
423. #3332	C₂×C₆₇	semidirect
424. #3329	C₂×C₆₇	semidirect
425. #3326	C₂×C₆₇	semidirect
426. #3305	C₂×C₆₇	semidirect
427. #3301	C₂×C₆₇	semidirect
428. #3298	C₂×C₆₇	semidirect
429. #3131	C₂×C₆₇	semidirect
430. #3099	C₂×C₆₇	semidirect
431. #3078	C₂×C₆₇	semidirect
432. #3062	C₂×C₆₇	semidirect
433. #3036	C₂×C₆₇	semidirect
434. #3010	C₂×C₆₇	semidirect
435. C₂×C₄×SD₁₆	C₂×C₆₇	semidirect
436. #2931	C₂×C₆₇	semidirect
437. #2898	C₂×C₆₇	semidirect
438. C₆₇	#61213	direct (N × H)
449. #550	C₂²×C₆₇	semidirect
451. D₄×Q₈	C₂²×C₆₇	semidirect
453. #548	C₂²×C₆₇	semidirect
467. #488	C₂²×C₆₇	semidirect
468. #488	C₂²×C₆₇	semidirect
469. #487	C₂²×C₆₇	semidirect
470. #487	C₂²×C₆₇	semidirect
471. #486	C₂²×C₆₇	semidirect
472. #486	C₂²×C₆₇	semidirect
473. #485	C₂²×C₆₇	semidirect
474. #483	C₂²×C₆₇	semidirect
475. #482	C₂²×C₆₇	semidirect
476. #481	C₂²×C₆₇	semidirect
477. #479	C₂²×C₆₇	semidirect
478. #477	C₂²×C₆₇	semidirect
479. #475	C₂²×C₆₇	semidirect
495. #436	C₂²×C₆₇	semidirect
496. #436	C₂²×C₆₇	semidirect
497. C₈×D₄	C₂²×C₆₇	semidirect
498. C₈×D₄	C₂²×C₆₇	semidirect
503. #419	C₂²×C₆₇	semidirect
505. #417	C₂²×C₆₇	semidirect
508. #416	C₂²×C₆₇	semidirect
510. C₂×#103	C₂²×C₆₇	semidirect
656. 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×#3332	2
C₆₇×#3329	2
C₆₇×#3326	2
C₆₇×#3305	2
C₆₇×#3301	2
C₆₇×#3298	2
C₆₇×#3131	2
C₆₇×#3099	2
C₆₇×#3078	2
C₆₇×#3062	2
C₆₇×#3036	2
C₆₇×#3010	2
C₂×C₄×SD₁₆×C₆₇	2
C₆₇×#2931	2
C₆₇×#2898	2
#61213	67

Subgroups — C67×#61213 #30740464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61213 #30740464